Microstructure Design
of Mechanically Alloyed Materials
ARCHIVES
by
Zachary C. Cordero
B.S. Physics
Massachusetts Institute of Technology, 2010
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY-
OCT 28 2015
LIBRARIES
SUBMITTED TO THE DEPARTMENT OF MATERIALS SCIENCE & ENGINEERING IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY IN MATERIALS SCIENCE & ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
SEPTEMBER 2015
0 2015 Massachusetts Institute of Technology
Signature redacted
Signature of Author:
C
Defartment of Materials Science & Engineering
August 14, 2015
Signature redacted
Certified by:
D
Accepted by:
,
en
Christopher A. Schuh
d Danae and Vasilis Sal apatas Professor of Metallurgy
Thesis Supervisor
Signature redacted
\Z
w
Donald Sadoway
John F. Elliott Professor of Materials Chemistry
hair, Departmental Committee on Graduate Students
77 Massachusetts Avenue
Cambridge, MA 02139
MITLibranes
h-tp://'ibraries.mit.edu/ask
DISCLAIMER NOTICE
Due to the condition of the original material, there are unavoidable
flaws in this reproduction. We have made every effort possible to
provide you with the best copy available.
Thank you.
The first 61 pages are un-numbered. The remaining
pages (62-120) have pagination numbers.
Microstructure Design of Mechanically Alloyed Materials
by
Zachary C. Cordero
Submitted to the Department of Materials Science and Engineering
on August 14, 2015 in Partial Fulfillment of the Requirements
for the Degree of the Doctor of Philosophy in
Materials Science and Engineering
ABSTRACT
Nanocrystalline metals have exceptional mechanical properties that make them attractive for
structural applications. However, these materials' properties tend to degrade due to grain growth
when they are exposed to high temperatures; this makes producing bulk, nanocrystalline
components particularly difficult as the most promising synthesis methods involve high
temperature densification of powders or foils. Several alloy design strategies have been
developed to overcome these thermal stability issues, but their efficacy depends on the spatial
distribution of the stabilizing element in the feedstock materials, which are typically prepared
using extensive plastic deformation or mechanical alloying. There is thus a need to predict the
chemical mixity of mechanically alloyed materials, and this thesis seeks to address this need. To
this end, phase strength effects are incorporated into a kinetic Monte Carlo simulation of a
mechanically-driven, binary alloy, which can provide quantitative insight into the combination of
processing and material parameters that dictate the steady state chemical mixity. Using such
simulations, dynamical phase diagrams are generated that predict temperatures and compositions
at which a couple with a given phase strength mismatch should chemically homogenize during
mechanical alloying. Several of these dynamical phase diagrams are validated using mechanical
alloying experiments, in which tungsten-transition metal couples with various phase strength
mismatches are mechanically alloyed in a high energy ball mill. This thesis also describes an
alloy design case study in which the insights from these simulations and experiments are used to
develop a nanocrystalline W-based (W-7Cr-9Fe, at%) alloy powder that can be rapidly
compacted to high relative densities while maintaining ultrafine grain sizes. Two-phase compacts
made from the alloy exhibit microhardnesses of 13 GPa and dynamic compressive strengths in
excess of 4 GPa. Furthermore, postmortem images of compressed micropillars machined out of
these compacts suggest that this alloy deforms by shear localization.
The penetration
performance of this alloy is explored in sub-scale ballistic tests into concrete targets, and is found
to be at least as good as current state-of-the-art penetrator materials.
Thesis Supervisor: Christopher A. Schuh
Title: Department Head and Danae and Vasilis Salapatas Professor of Metallurgy
Acknowledgments
First and foremost, I owe a big thank you to my adviser, Prof. Chris Schuh, for showing me how
to do cutting-edge scientific research, how to communicate my results through presentations and
manuscripts, how to develop and pursue research ideas, how to manage collaborations, and how
to lead a research group. I feel very fortunate to have had the opportunity to work with him these
past four years.
I also want to acknowledge the support and guidance of my committee members, Profs. Tom
Eagar and Michael Demkowicz. I especially want to thank Prof. Demkowicz for allowing me to
TA Mechanics of Materials for him. This was one of the most rewarding experiences that I had
in my time at MIT.
This thesis would not have possible without the guidance of my unofficial, fourth committee
member, Dr. Brian Schuster of the Army Research Laboratory. I enjoyed collaborating with him
very much and hope to continue this collaboration in the future. His semi-serious taunt that I
would end up a metallographer at NIST gave me nightmares that motivated me to work harder.
In addition to developing a novel penetrator material together, I'm pretty sure that we also
invented the shelfie, i.e., a selfie with a shellfish. Only time will tell which of these two
innovations is the more lasting.
Thanks also go to the other members of the DMSE faculty who have mentored me along the
way. In particular, I am indebted to Prof. Jeff Grossman for introducing me to materials science
when I was an undergrad. When he hired me as a UROP, he set off a chain reaction that
ultimately led to me pursuing a doctorate.
One step in this chain reaction was the year that I spent at Berkeley, where early on I stumbled
into James Wu's powder processing lab. When I was a clueless physicist, James took me under
his wing and showed me how to press, sinter, heat-treat, arc melt, machine, and roll. He molded
me into the card-carrying metallurgist that I am today, and for that, I am eternally grateful.
Back at MIT, the past four years were made exponentially more fun by the people I interacted
with every day. The other Schuh groupers are a great bunch who inspired me to work harder, be
smarter, present better, and be a better person. Some of my best memories from the past four
years are from board game nights with the Schuh groupers who helped me get started in my
graduate studies: Samwell Humpfree Baker, Alan The Lai Guy, and Lil' Stian Ueland. Matt
Humbert and Mike Tarkanian are two more MIT people who had a tremendous positive impact
on my graduate studies and my engineering abilities; when I'm asked what makes MIT special, I
say the people and give those two as examples. Finally, there are my training buddies on the
MIT masters swim team: Bill Paine, Wishy Washy Joshy, Sebby Binx, Derrick Cow, and Johnny
McKelleher. Swimming with all of them helped keep me focused.
My parents, Ella and Pedro, put me on this planet and have always given me with their love and
unwavering support. They passed their crazy on to me, and instilled in me the drive to work hard
on meaningful things. Both of these were essential to me starting and then finishing this
dissertation. My brother Ben is a big ball of joy who kept me in check when I needed it most
these past couple of years. Finally, there's the newest member of the Cordero clan, Margaret.
Meeting her was the best thing to happen to me during my PhD. I feel blessed to have you all as
my family.
And last but not least, I want to express my gratitude to the US for paying for my graduate
studies through the NDSEG fellowship. I think the US made a good investment, but again, only
time will tell.
Table of Contents
Acknow ledgm ents ..........................................................................................................................
3
Table of Contents ...........................................................................................................................
5
List of Figures ................................................................................................................................
7
List of Tables ...............................................................................................................................
12
1.
Introduction ..........................................................................................................................
13
2.
Phase Strength Effects on Chemical Mixing in Extensively Deformed Alloys...............26
2.1.
M aterials and M ethods ..........................................................................................
27
2.1.1.
Powder Processing .............................................................................................
27
2.1.2.
M icro structural and Chem ical Characterization ...............................................
28
2.1.3.
Mechanical Testing.............................................................................................31
2.2.
M icrostructure and Hardness Evolution...............................................................
31
2.3.
Factors A ffecting Deform ation-Induced M ixing..................................................
44
2.4.
Generalized Phase Strength Effects......................................................................
45
2.4.1.
Bi-stability and History-Dependent Steady States.............................................
48
2.4.2.
M icrostructure and M ixing Kinetics.................................................................
50
2.4.3.
Tem perature and Com position Effects ...............................................................
52
2.5.
Concluding Rem arks ............................................................................................
57
3.
Guidelines for the Microstructure Design of Mechanically Alloyed Materials................59
4.
Powder-Route Synthesis and Mechanical Testing of Ultrafine Grain Tungsten Alloys......68
4.1.
M aterials and M ethods ..........................................................................................
69
4.1.1.
Powder Processing and Consolidation...............................................................
69
4.1.2.
M icrostructural Characterization ........................................................................
70
4.1.3.
M echanical Testing.............................................................................................
71
4.2.
Powder Characterization.........................................................................................
72
4.3.
Com paction and Com pact M icrostructure.............................................................
75
4.4.
M echanical Properties ............................................................................................
82
4.4.1.
Strengthening Contributions ...............................................................................
82
4.4.2.
M icropillar Com pression ...................................................................................
85
4.4.3.
High Strain Rate Deforn ation ..........................................................................
87
4.5.
5.
6.
Concluding Remarks ..............................................................................................
Sub-Scale Ballistic Testing of an Ultrafine Grained Tungsten Alloy ..............................
88
90
5.1.
Experimental M ethods...........................................................................................
90
5.2.
Sub-Scale Ballistic Testing into Concrete .............................................................
93
5.3.
Concluding Remarks ............................................................................................
98
C o n c lu sio n s ..........................................................................................................................
99
Appendix A: Aggregated Hall-Petch Data ................................................................................
102
References............................................................................................
107
List of Figures
Figure 1.1 - Engineering stress-strain curves from microcompression tests on micropillars
machined out of W powder particles with a grain size of ~10 nm. ..............................................
13
Figure 1.2 - Ashby map comparing the predicted performance of different kinetic penetrator
materials. The grey lines are isocontours of constant kinetic energy density, which indicate
similar ballistic performance for a given penetrator geometry. Nanocrystalline tungsten's
exceptionally high strength and density make it ideal for penetration applications.................
14
Figure 1.3 - Effective temperature as a function of ambient temperature under a constant
intensity driving force. At high temperatures, Teii and T are similar because thermally activated
processes outpace processes related to the driving force, while at low temperatures, Terr and T
diverge because the thermally activated processes are suppressed. .........................................
18
Figure 1.4 - Cross-section of a 3-dimensional phase diagram [45]. The axes indicate the
concentration on each of the four, interpenetrating simple cubic sublattices of a face-centered
cubic metal. To identify the steady-state order parameter of an irradiated material with this
diagram, follow the arrows from a starting order parameter to one of the steady state order
21
parameters indicated by the triangle, diamond, or square. ......................................................
Figure 1.5 - Cross-sections from kinetic Monte Carlo simulations of mechanical alloying [70].
Above each of the cross-sections is the shearing rate and temperature used in the simulation.
The black dots indicate atoms of one of the alloying elements. The cross-sections show that with
decreasing shearing frequency, the alloy is able to phase separate. .........................................
23
Figure 1.6 -MD simulations of shear-induced mixing in a (a) Cu-Ag and a (b) Cu-V
nanocomposite [77]. Both of the simulations began with all of the solute in a single precipitate,
and both volume elements have accumulated plastic strains of 60. The solute atoms are colored
to indicate their local chemical environment, with green atoms indicating solute surrounded by
solute nearest neighbors. The simulations reveal that the V precipitate is still relatively in-tact,
while the Ag precipitate is nearly completely dissolved. .........................................................
24
Figure 2.1 - Fe contamination as measured using EDS in the initially pure W and W-transition
metal powders as a function of milling time. The W, W 5 oCr5 o, and W5 oNb50 powders are harder
than the W5 oNi5 o, W 50 Hf50 , and W50 Zr5 Opowders, and abrade more Fe as a result. ................ 28
Figure 2.2 - XRD patterns from the a) W 5oCr5o and b) W5 oZr5o powders with increasing milling
time. The region around the W (110) Bragg peaks is highlighted to emphasize how, in the
W5 oCr 50 patterns, the W and Cr peaks gradually merge with increasing milling time, whereas in
the W5 oZr5 o patterns, the W peak essentially remains unmoved...................................................
33
Figure 2.3 - a) The BCC W phase's lattice parameter measured using Rietveld refinement for the
various W5 oTM50 couples with increasing milling time. b) Solute concentration in the BCC W
phase normalized by the total solute concentration as function of milling time for the same
couples. These values were calculated from the BCC W phase's lattice parameter and the data in
Fig. 2.1 using a modified Vegard's law as described in the text. c) Average integrated intensities
of the W Bragg peaks in the W-Ni/Zr/Hf couples' XRD patterns, I, normalized by their
integrated intensities after m illing for one hour, 10 ...................................................................
34
Figure 2.4 - Grain size of the initially pure W phase as a function of milling time measured using
the Williamson-Hall technique. Fits to the raw data using Eqn 2.3 are shown as well. The
similar rate of grain refinement among the three powders suggests that, at least for short milling
times, the W domains are being plastically strained similarly in all three powders.......... 35
Figure 2.5 - SEM micrographs of the a-d) W 5oCr5o and e-h) W5 oZr50 powders milled for the
times indicated; scale bars are all 200 nm. The light regions contain W and the dark regions
contain either Cr or Zr. Note the lamellar and particulate morphologies of the W5 oCrso and
W5 oZr50 couples' microstructures, respectively. Additionally, the lack of contrast in the
micrograph of the W 5oCr5s powder milled for 15 hours suggests that this powder is chemically
homogeneous, in agreement with the XRD results. i) Mean spacing measured using Eqn. 2.2 of
the W5 oCr5 o and W5 oZr5o powders milled for 1, 3 and 5 hours; the data points at 0 hours
correspond to the mean particle diameters of the starting powder. Also shown are fits to the
mean spacing versus time data using Eqn. 5 in Reference [26].................................................
37
Figure 2.6 - a) Dark field STEM micrograph of a W 5oZr5o powder particle milled for 45 hours.
The white regions are residual W particles in a dark, Zr matrix. b) Cumulative distribution of the
W particles' circular equivalent diameters along with an integrated log-normal fit to the diameter
data. The mean diameter of the fit is 8 nm, in agreement with the W grain size measured using
X R D ..............................................................................................................................................
39
Figure 2.7 - a) Hall-Petch plots for the initially pure W, Cr, and Zr powders. All of the initially
pure powders' hardnesses increase, to varying degrees, with milling time, mainly due to grain
refinement. Also shown are Hall-Petch trendlines for Ni [ l ], Hf [110], and Nb [1 12] taken
from the literature. b) Hardness as a function of milling time for the W 5 oCr5 o and W5 oZr5 O
powders along with spline fits to the W, Cr, and Zr powders' hardnesses. The W50Cr50 powder's
hardness increased until it was nearly the same as the initially pure W powder, whereas the
hardness of the W5 oZr50 powder actually decreased until it is was the same as that of the initially
p u re Zr p o w d er..............................................................................................................................
41
Figure 2.8 - Micrographs of nanoindentations using a cube corner tip into a,b) W50 Cr5 Oand c,d)
W 5oZr50 powder particles that were milled for 15 hours. Both powders' pile-up patterns exhibit
non-homogeneous plastic deformation (i.e., shear localization). In the W 5oZr5o powder's pile-up,
the shear offsets appear to be skirting around the larger W particles in the regions indicated by
th e arro w s......................................................................................................................................
43
Figure 2.9 - a) Evolution in the order parameter a for kinetic Monte Carlo simulations using two
different temperatures in a couple with no difference in strength. The two lines that converge for
each temperature correspond to two different starting configurations. b) The same set of
simulations but using a couple having a large difference in strength between the phases. Note
that in the low temperature simulations, the initially segregated and chemically mixed curves do
not converge. The insets are two-dimensional slices across the low temperature simulation cells
with the A atoms colored grey and the B atoms invisible. ......................................................
49
Figure 2.10 - Steady state unit cells of A5 oB50 simulations with a-c) no difference in strength and
d-f) a large difference in strength. The simulations were performed using the temperatures
indicated, and the color scheme is the same as in Figure 2.9. All of the simulations were
initialized w ith a segregated m icrostructure. ...........................................................................
52
Figure 2.11 - Evolution in order parameter a during simulations following a cooling trajectory
while shearing, using the A's and c's indicated. Note that with increasing c, a large difference in
strength is no longer sufficient for preventing mixing: when c equals 0.8, all of the simulations
hom ogen ize b y 2 30 K . ..................................................................................................................
53
Figure 2.12 - Dynamical phase diagrams for systems studied as a function of temperature and
composition. The regions below the lines correspond to the temperatures at which the various
simulations homogenized during the simulated anneals. With increasing phase strength
mismatch A, a two-phase region opens up where certain couples remain segregated if they start
as such. The open circles on the x-axis indicate compositions that remained dual phase over the
range of temperatures studied. Experimental compositions are placed on these diagrams at their
expected locations based on the strength differential in a fine nanocrystalline structure from
F ig u re 2 .7 ......................................................................................................................................
55
Figure 3.1 - E1/(D/b2) of binary alloys processed by high-energy ball milling. All of the
couples are expected to form single phase solid solutions. While experiments show that the
couples colored red do in fact form solid solutions, the couples colored blue form simple
m ech an ical m ix tu res. ....................................................................................................................
62
Figure 3.2 - Aggregated Hall-Petch data for pure Cu and Ag. The solid dots indicate the
maxim um strength of pure, as-milled Cu and Ag......................................................................
63
Figure 3.3 - A values for various metal-metal couples whose mixing behaviors have been studied
in d eta il..........................................................................................................................................
65
Figure 3.4 - A values for all metals whose grain size strengthening behavior has been studied.
The red and blue squares indicate couples expected to be either mechanically miscible or
immiscible, respectively. The grey squares indicate couples that could exhibit either behavior. 66
Figure 4.1 - a) Set of XRD scans taken from the feedstock and W-7Cr-9Fe powder milled for 10
and 20 hrs. Note the disappearance of the Cr (110) Bragg peak in the highlighted region after 10
hrs of milling. This, along with the change in W lattice parameter, suggests the formation of a
solid solution. b) Williamson-Hall and Rietveld analysis give the W-rich BCC phase's grain size
and lattice parameter as a function of milling time for both alloys. .........................................
73
Figure 4.2 - Representative TEM micrographs of the as-milled a) W-7Cr-9Fe and b) W-9Fe
powders illustrating the powders' nanocrystalline grain structure. The inset electron diffraction
patterns feature the uniform rings characteristic of nanocrystalline materials. ........................ 74
Figure 4.3 - Punch displacement curves measured during the heating ramp-up phase for the two
alloys, under an applied stress of 100 M Pa...............................................................................
75
Figure 4.4 - Stereological porosity after compaction experiments at a variety of soak
temperatures and two soak times, I and 20 minutes.................................................................
76
Figure 4.5 - Backscatter electron micrographs of a) W-7Cr-9Fe and b) W-9Fe compacts
consolidated at 1673 K (1400 'C) for 20 minutes. These samples had the coarsest
microstructures of all the compacts. The p-phase precipitates in both samples are generally
darker than the BCC solid solution due to the lower W content. The precipitates are also
distributed randomly throughout the BCC solid solution, which itself is composed of many
individual grains. The black dots in both micrographs are residual pores...............................
78
Figure 4.6 - Volume fraction intermetallic predicted by THERMOCALC and measured using
stereology for compacts consolidated at temperatures greater than 1373 K. All of the predicted
and experimental volume fractions are within 3 vol% of each other, which is reasonable given
uncertainties in the global stoichiometry of the powder and the stereology measurements......... 80
Figure 4.7 - Grain sizes of compacts made from both alloys and consolidated at various soak
temperatures and two soak times, 1 and 20 minutes. Also shown for comparison is the grain size
81
of th e as-m illed p ow d er. ...............................................................................................................
Figure 4.8 - a) Low- and b) high-magnification secondary electron micrographs of the optimized
W-7Cr-9Fe compact consolidated using the 20 mm die at 1473 K for 1 min. The lowmagnification micrograph illustrates the distribution of porosity (black regions) and the p-phase
intermetallic (darker grey contrast). The high-magnification micrograph illustrates this sample's
ultrafine grain structure (D - 130 nm )........................................................................................
82
Figure 4.9 - Hall-Petch plot for compacts made with both alloys, from samples compacted at
various times and temperatures to densities in excess of 98%. Microhardness values from Vashi
et al. on nominally pure W compacted to 95% relative density are also presented for comparison
[222]. According to Vashi et al., the hardness of their W specimens was independent of load
between loads of 0.2 and 2 kgf, and the data shown is the average of the hardnesses measured
using loads of 0.2, 0.3 and 2 kgf. The data point labeled with a star is the hardness of the W-7Cr9Fe sam ple consolidated with the 20 m m die..........................................................................
83
Figure 4.10 - Some typical engineering stress-strain curves from micropillar compression tests
on pillars preferentially milled from the BCC solid solution phase. Inset shows a shear offset in
a m icropillar loaded to 6.3 G Pa. ...............................................................................................
86
Figure 4.11 - An engineering stress-time curve collected during a Kolsky bar test conducted at a
strain rate of 600 s-. The test specimen was cut from the W-7Cr-9Fe compact consolidated at
1473 K using the 20 mm die. The accompanying high speed photographs were taken at the times
indicated by the lines. The arrows next to the first frame indicate the loading direction, and the
test specimen's orientation is the same in all of the photographs.............................................
87
Figure 5.1 - Schematics of the a) cemented carbide and b) W-8Cr-4Fe penetrators............... 91
Figure 5.2 - a) Radiographs of cemented carbide rounds that struck the targets at the velocities
indicated. The crater region is highlighted in the radiograph of the penetrator that had an
incident velocity of 720 m/s. b) Cemented carbide rounds' depths of penetration as a function of
incident velocity. The dashed line is the best fit to the data using Eqn 5.4, and the grey shaded
region indicates the 95% confidence intervals..........................................................................
95
Figure 5.3 - a) Radiographs of W-8Cr-4Fe rounds embedded in the concrete targets. b) Depth of
penetration of the W-8Cr-4Fe penetrators as a function of incident velocity. The rigid body
depth of penetration predicted using Eqn 5.4 is shown as well.................................................
96
Figure 5.4 - a) Radiographs of cemented carbide penetrators that shattered on impact. b) Incident
velocity versus angle of incidence, y, of the W alloy and cemented carbide shots with the
cemented carbide shots that fractured indicated by crosses......................................................
97
Figure A.1 - Hall-Petch data for the FCC metals. The horizontal grey line indicates the metal's
theoretical strength and the vertical gray line indicates the grain size that the pure as-milled
po wders w ill d ev elo p ..................................................................................................................
102
Figure A.2 - Hall-Petch data for the BCC metals. .....................................................................
104
Figure A.3 - Hall-Petch data for the HCP metals.......................................................................
106
List of Tables
Table 2.1 - aFe and asolue values used in Eqn 2. 1. The Zr lattice parameter was estimated by
extrapolating the P-phase's lattice parameter at 862 'C (3.609 A) to room temperature using the
P-phase's coefficient of thermal expansion reported in Reference [104]. The Hf lattice parameter
was estimated from P-stabilized alloys [105]. The Ni lattice parameter was estimated from its
FCC lattice parameter using the procedure outlined in Reference [106]................................... 30
Table 3.1 - Mechanical alloying behaviors reported for positive heat of mixing metal-metal
c o u p le s . .........................................................................................................................................
60
Table 3.2 - Steady state grain sizes of pure metals during high energy ball milling at room
temperature and estimated strength of the pure, as-milled powders from their grain size
strengthening data. Grain sizes were either taken from [82-84] or estimated using the trends
reported in those References.....................................................................................................
64
Table 4.1 - Compact properties after densification, including specific gravity, p (relative
uncertainty: 0.5%), porosity measured using stereology (relative uncertainty: 50%), and porosity
calculated from the relative density (relative uncertainty: 20%) for each compact. ................ 77
Table 5.1 - Properties of the cemented carbide and tungsten alloy penetrators....................... 94
1. Introduction
The strength of a metal, a, is related to its grain size, D, through the Hall-Petch equation:
O
(1.1)
where o-o and k are material-dependent constants [1].
In Eqn 1, the reciprocal square root
dependence on grain size suggests that there should be a dramatic increase in strength as the
grain size is refined to the nanoscale. This expectation has been validated in mechanical tests on
nanocrystalline materials, where strengths approaching theoretical values have been observed
[2]. Figure 1, for example, shows engineering stress-strain curves from microcompression tests
on micron-scale pillars ion-milled out of nanocrystalline W powder particles. These stress-strain
curves give an average 0.2% offset yield stress of 6.5 GPa, which is ~70% of W's theoretical
yield strength [3,4].
8
6
~144
2
0
i
I
strain
I
i
4%
Figure 1. 1 - Engineering stress-strain curves from microcompression tests on micropillars
machined out of W powder particles with a grain size of~-10 nm.
Because of their high strengths, nanocrystalline materials are very attractive for use in structural
applications, and nanocrystalline tungsten in particular would make an ideal penetrator material
because it also has a high density. We can illustrate the full potential of nanocrystalline tungsten
penetrators by plotting them alongside other penetrator materials in an Ashby map like that
shown in Fig. 1.2. Here the x-axis is the density of the penetrator material and the y-axis is the
striking velocity at which the penetrator material should transition from rigid body to eroding
during penetration into concrete. For a given penetrator geometry, materials that are closer to the
upper-right corner of Figure 1.2 can deliver a larger kinetic energy to the target and achieve a
greater depth of penetration as a result. Figure 1.2 therefore shows that nanocrystalline tungsten
could far outperform currently available penetrator materials such as cemented carbides and high
strength steels.
2.0
nanocrystalline_...*
tungsten
1.5Limit
Velocity
(km/s) 1.0-
38 GJ/m
cemented
carbides
3
15 GJ/m 3
high-strength
steels
0.55
3
KE Density = 3 GJ/m
10
15
20
)
Density (103 kg/m 3
Figure 1.2 - Ashby map comparing the predicted performance of different kinetic
penetrator materials. The grey lines are isocontours of constant kinetic energy density,
which indicate similar ballistic performance for a given penetrator geometry.
Nanocrystalline tungsten's exceptionally high strength and density make it ideal for
penetration applications.
Despite their promise, nanocrystalline materials' commercial applications at the time of this
writing tend to be mostly as hard, wear-resistant coatings. This is because their microstructures
tend to degrade when exposed to high temperatures due to grain growth [5], which makes
producing bulk nanostructured materials particularly difficult as the most promising synthesis
method is high temperature densification of powders or foils.
To overcome these thermal stability issues, two groups of alloying strategies have been
developed. The first group of alloying strategies reduce the soak time and temperature required
to sinter a green compact by accelerating low-temperature densification processes [6-8]. The
second group of alloying strategies slow or altogether prevent grain growth at elevated
temperatures. This is accomplished through the addition of inert second phases that pin the grain
boundaries (i.e., Zener pinning) or grain boundary segregating solute elements that reduce either
the driving force for grain growth or the grain boundary mobility [9-13].
Since alloying is critical to retaining a fine grain size, high energy ball milling is an important
processing step in the powder-route synthesis of bulk nanocrystalline materials because it can
simultaneously refine a metal's grain size and introduce a solute element [14-17].
In this
process, metal powders and grinding media are sealed in a vial that is then agitated vigorously.
Powder particles that get trapped between the grinding media during milling are subjected to
plastic strains on the order of 100%, and with an increasing number of such collision events, the
powder particles can accumulate very large plastic strains [18-20].
The microstructures that develop as a result of these large plastic strains depend on the milling
parameters and the properties of the powders being milled, but in general, they are determined by
a competition between plastic deformation and recovery processes.
This competition is
illustrated most simply with pure metal powders, which all exhibit the same monotonic decrease
in grain size to a steady state value during milling [21,22]. In this case, the competition that
determines the steady state grain size is between grain refinement, which depends on the milling
intensity, and recrystallization, which depends on material properties and the ambient milling
temperature. Increasing the ambient milling temperature accelerates recrystallization processes,
which in turn leads to higher steady state grain sizes. This was demonstrated by Atzmon et al. in
experiments on iron, in which as-milled iron powder's steady state grain size increased by a
factor of -2 when the milling temperature was increased from 25 to 160 'C [23]. Because these
mechanically alloyed powders possess non-equilibrium steady-state microstructures that result
from a dynamic competition between deformation and recovery processes, they are considered
driven materials.
This same basic competition between plastic deformation and recovery processes also
determines the steady state microstructure of alloy powders processed by high energy ball
milling, but in an alloy, there can be an additional competition between shear-induced chemical
mixing and thermally activated chemical diffusion.
As a result, and in contrast with the
relatively simple behavior of pure metals, there is a diversity of possible microstructures that can
emerge when two or more metals are mechanically alloyed.
Some mechanically alloyed
powders will mix and form single phase solid solutions, while others will forn dual-phase
mechanical mixtures [24]. What is more, even if two metals do not mix completely, they might
still dissolve in one another such that they form supersaturated solid solutions [25]. Further,
negative heat of mixing couples can form intermetallics [26] or even undergo solid state
amorphization reactions [27].
Predicting which of these microstructures will result is critical
when designing nanocrystalline alloy powders for consolidation, since the efficacy of the
alloying strategies mentioned earlier depend not just on the specific alloying elements, but also
on the alloying element's spatial distribution in the base metal.
There are three main challenges in predicting the microstructural evolution of a mechanically
alloyed powder that are common to all driven materials:
1) Driven materials can develop multiple, distinct steady-state microstructures under a given
set of processing conditions [28].
2) Identifying the steady-state microstructure that a driven material will settle into requires
solving an initial value problem in which the initial microstructure evolves with time
according to some master equation that is often challenging to develop [28,29].
3) This master equation is typically noisy, making it difficult to predict which steady state
microstructure a driven alloy will settle into when the microstructure starts near a
manifold that separates basins containing distinct steady states. What is more, because
the magnitude of the noise varies with the instantaneous microstructure, linear stability
analyses of steady states cannot be trusted [30-33].
Much of the work addressing these challenges has focused on irradiated materials, which are
another type of driven material.
So we now turn our attention to the tools that have been
developed to describe irradiated materials and mention how these tools have been adapted to
mechanical alloying.
The earliest attempts at describing the microstructural evolution of irradiated materials mainly
focused on solving mass transport equations at hetero-phase interfaces [34,35].
A notable
example of this approach is Ref [35], in which Frost and Russell modeled how a precipitate's
size evolves under radiation. These investigators developed a mass conservation equation, with
a source term that accounted for radiation-induced ballistic mixing, which they then solved in the
matrix region adjacent to the precipitate using a mean field approximation. In this way, Frost
and Russell were able to predict radiation conditions under which the precipitates would
dissolve, coarsen, or even pattern, i.e., shrink or grow to some uniform size.
Though this
approach could explain several behaviors seen in irradiated materials containing precipitates, it
suffered from several deficiencies, including the fact that the solute concentration was not
conserved. Adapting this approach to mechanically alloyed materials has also proven difficult
because it is unclear how to account for shear-induced chemical mixing in a conservation
equation.
A more general framework for describing irradiated materials was proposed by Martin, who
added a ballistic mixing term to Cahn's free energy functional and then studied what this new
functional predicted for the steady-state microstructure under irradiation [36-38].
Using this
modified functional, Martin showed how the phases present in a driven material are the same
ones present at some elevated, effective temperature, Ter, given by
Teff = T(1 + 0)
(1.2)
where T is the actual temperature of the irradiated material, and 0 reflects the competition
between ballistic mixing and thermally activated recovery and is always positive.
For an
irradiated material, Martin demonstrated that
0 = Db,rad/Dt
(1.3)
where Dt is the classic interdiffusivity that follows an Arrehnius-law temperature dependence,
and Db,rad is a ballistic diffusivity that accounts for chemical homogenization due to irradiation.
Figure 1.3 shows the effective temperature as a function of temperature for a material subjected
to a constant intensity driving force. Here T and Tef are nearly equal above ~500 K because Dt
is much larger than Db,rad so that 6 is approximately 0. T and Terr diverge at lower temperatures,
since Dt's exponential dependence on temperature causes it to decrease dramatically with
decreasing temperature, thereby causing 0 to blow up. At temperatures below the minimum in
the Tetf curve, decreasing the temperature or increasing the driving force's intensity result in
higher effective temperatures, which in turn correspond to non-equilibrium microstructures with
higher free energies.
To help explain his "rule of corresponding states," Martin suggested that
radiation, or any other driving force, contributes an additional entropy-like term to the free
energy, which stabilizes high temperature phases at low ambient temperatures. With this rule-ofthumb, Martin successfully explained a number of phenomena observed during the irradiation of
alloys, such as the disordering of ordered compounds, the formation of supersaturated solid
solutions, and the amorphization of certain alloys [39].
1200
800
TO (K)
Te = T(1 + 0)
400
400
800
T (K)
1200
Figure 1.3 - Effective temperature as a function of ambient temperature under a constant
intensity driving force. At high temperatures, Teti and T are similar because thermally
activated processes outpace processes related to the driving force, while at low
temperatures, Tety and T diverge because the thermally activated processes are suppressed.
Two mechanical alloying studies have demonstrated that Martin's rule of corresponding states
can also be extended to certain materials subjected to extensive plastic deformation. In the first
of these studies, Pochet et al. mechanically milled an FeAl intermetallic at various temperatures
and intensities and then measured the as-milled powder's long range order parameter (LRO)
[40]. These investigators found that they could decrease the LRO, in other words drive the
intenmetallic from its equilibrium state, by either increasing the milling intensity at constant
temperature or by lowering the temperature at constant milling intensity. They rationalized the
effects that these processing changes had on the LRO with Martin's effective temperature
concept by replacing
Dbrad
in Eqn 1.2 with a new ballistic diffusivity,
Db,MA,
that accounts for
shear-induced chemical mixing. In this case, increases in the milling intensity, which increase
DbMA,
or decreases in temperature, which decrease Dt, both translate to higher effective
temperatures that correspond to non-equilibrium microstructures with a smaller LRO.
In another mechanical alloying study whose results support the rule of corresponding states,
Klassen et al. investigated the effect of ambient milling temperature on the chemical mixity of
Ag 5oCu 5o alloy powders [41].
In these experiments, Klassen et al. mechanically alloyed the
powders at temperatures between 85 and 473 K and found that the solubility in the terminal solid
solutions increased with decreasing temperature, until at low enough temperatures, the alloy
homogenized.
Since this alloy is dual-phase with negligible solid solubility in either phase at
equilibrium at room temperature, by lowering the milling temperature, Klassen and coworkers
were driving the alloy into a non-equilibrium, high-temperature configuration. Their explanation
of this behavior followed that of Pochet et al.: by decreasing the milling temperature, they were
decreasing Dt, which in turn raised the effective temperature, thereby stabilizing the phases'
high-temperature solid solubilities.
The results from both of these mechanical alloying studies are well described by the effective
temperature framework because the systems studied obey one of Martin's core assumptions: the
driving force affects both components of the alloy equally. This assumption, however, is invalid
for many mechanically driven materials, particularly those with initial microstructures that
contain two phases, since there can be strain localization in one of the phases.
Such strain
localization does not affect the FeAl intermetallic studied by Pochet et al. because it is already
chemically homogeneous, nor does it affect the Cu-Ag couple studied by Klassen and coworkers
because these alloying elements have similar strengths when nanocrystalline and so co-deform;
however, one must account for the fact that the driving force can have a stronger effect on one of
the components in order to generalize the effective temperature concept to all mechanically
alloyed systems.
Besides the rule of corresponding states, which serves well as a qualitative rule-of-thumb, other
theoretical tools have been developed that provide more quantitative descriptions of driven
materials.
Of these tools, many of which are adapted from the physical chemistry field of
dissipative systems, the master equation initially found the most use [42]. The master equation is
a differential equation that describes the time evolution of the microstructure, and its steady state
solutions correspond to the steady state microstructures. The first master equation describing an
irradiated material was developed by Bellon and Martin in their work on electron-irradiated
Ni 4 Mo [29]. This particular system was of interest because it had been experimentally studied in
detail by Urban and coworkers and was known to exhibit several interesting behaviors, including
bi-stability and path-dependent steady state order parameters [43,44].
To describe these
behaviors, Bellon and Martin first developed equations that gave the probability of transitions
between different states of ordering. They then incorporated these transition probabilities into a
master equation, with which they developed a dynamical potential whose maximum indicated
the order parameter most likely to be observed.
Following Bellon and Martin, Haider et al.
developed another master equation that described a different ordered compound [45-47]. These
investigators used their master equation to generate maps like that shown in Figure 1.4. With
one of these maps, one can identify the microstructures that an irradiated alloy will eventually
settle into by tracing the arrows from a starting point, which corresponds to the initial order
parameter, to a steady state order parameter. In their study on the mechanical milling of FeAl,
Pochet et al. developed a master equation for mechanically alloyed materials [40]. With this
master equation, these investigators calculated dynamical phase diagrams that indicated milling
conditions under which the alloy should disorder.
00
%% %-%
%
.0.0%
//ef%%* a
.&o tI
-
%
I'.
'tV
OX3
Figure 1.4 - Cross-section of a 3-dimensional phase diagram [451. The axes indicate the
concentration on each of the four, interpenetrating simple cubic sublattices of a facecentered cubic metal. To identify the steady-state order parameter of an irradiated
material with this diagram, follow the arrows from a starting order parameter to one of the
steady state order parameters indicated by the triangle, diamond, or square.
In addition to the master equation, fixed-lattice, kinetic Monte Carlo simulations have been
borrowed from the dissipative systems community and adapted to describe driven materials [4851].
The advantage of kinetic Monte Carlo simulations over the master equation is that the
simulations better capture the stochastic nature of the driving process [52-55].
The kinetic
Monte Carlo simulations of driven materials that Bellon and colleagues have developed all
feature the same two competing dynamics: a temperature-dependent vacancy migration
mechanism and an athermal mixing mechanism. The specific mixing mechanism depends on the
system being studied, but in kinetic Monte Carlo simulations of irradiated materials, it involves
random exchanges of atoms [55-58].
With these kinetic Monte Carlo simulations, Bellon and
colleagues have studied how the order parameter of compounds as well as the chemical mixity of
positive heat of mixing, immiscible alloys evolve under irradiation [59-61].
In general, the
simulation results have aligned well with Martin's rule of corresponding states: higher effective
temperatures achieved by lowering the temperature or increasing the rate of ballistic exchanges
correspond to microstructures with higher excess free energies. However, the simulations have
also revealed behaviors that could not have been predicted by the effective temperature concept
such as patterning [62-67], which have recently been demonstrated in experiments [68].
The kinetic Monte Carlo simulations use a different mixing mechanism to model mechanically
alloyed materials: instead of exchanging randomly selected atoms, the simulation cell is sheared
along two randomly selected glide planes in the same slip system [69,70].
From a historic
perspective, it is interesting to note the similarity between this shearing mechanism and that from
simulations used by the fatigue community in the 70's and 80's to model precipitate dissolution
during the low-cycle fatigue of age-hardened materials [71,72].
In one of these earlier fatigue
studies, Lee et al. even went so far as to build a two-dimensional physical model of the BellonAverback kinetic Monte Carlo simulations [72]!
Historical notes aside, these kinetic Monte Carlo simulations of mechanical alloying have been
used to study the evolution in chemical mixity of binary, phase-separating alloys. In line with
expectations, the simulations demonstrate that the steady-state chemical mixity is determined by
a competition between shear-induced mixing and thermally activated phase separation and that it
is possible to tune the chemical mixity of the simulation cell by independently changing the rate
of either process.
Figure 1.5, for example, shows cross-sections of simulation cells that had
reached their steady state chemical mixity.
Each of these simulations were conducted at the
same temperature but with different shearing frequencies, as indicated. The black dots in the
cross-sections correspond to one of the alloying elements, and they are clearly more
homogeneously distributed in the solvent in the simulations with higher shearing frequencies.
Another behavior seen in these Bellon-Averback simulations was that domains of the two phases
developed a characteristic length scale that depended on the effective temperature.
Such
patterning behavior was subsequently demonstrated in Cu-Ag alloys mechanically alloyed at
elevated temperatures [73,74].
In general, the mixing phenomenology seen in the simulations matches closely that seen in CuAg alloys, but not most other couples. This is because the classical Bellon-Averback simulations
share the same deficiency as Martin's law of corresponding states: they do not account for strain
localization.
In fact, these kinetic Monte Carlo simulations ignore essentially all of the
mechanisms of plastic deformation in a nanocomposite. In a real nanocomposite prepared by
high energy ball milling, there are line defects, incoherent heterophase interfaces, and high angle
grain boundaries separating misoriented grains, and all of these features influence the plastic
deforiation behavior and as a result the rate of shear-induced chemical mixing. By contrast, in
these kinetic Monte Carlo simulations, there are no defects and only one deformation mode,
shearing of one plane of atoms over another.
y = 10, ST = 400 K
y = 10 3 sO
T = 400 K
y = 1 s1
T = 400 K
Figure 1.5 - Cross-sections from kinetic Monte Carlo simulations of mechanical alloying
[70]. Above each of the cross-sections is the shearing rate and temperature used in the
simulation. The black dots indicate atoms of one of the alloying elements. The crosssections show that with decreasing shearing frequency, the alloy is able to phase separate.
To develop a better understanding of how mixing proceeds in reality, researchers have studied
the deformation of dual-phase nanocomposites in molecular dynamics (MD) simulations [7579]. In these simulations, the atoms are not constrained to a lattice so the mixing processes more
closely reflect reality, revealing behaviors that could not have manifested in the kinetic Monte
Carlo simulations.
For example, the MD simulations have revealed that the character of a
heterophase interface influences the rate of shear induced mixing across that interface [79], an
effect that is absent from the kinetic Monte Carlo simulations since there are no interfaces per se.
The simulations have also highlighted the dramatic effect that differences in the constituent
phases' strengths can have on their mixing behaviors. This is illustrated by Figure 1.6, taken
from Ref [77], which shows results from MD simulations in which precipitates of Ag and V are
being dissolved in a Cu matrix through cyclic plastic straining. In Figure 1.6, the atoms' colors
indicate their local chemical environment, with atoms colored green representing solute atoms
whose nearest neighbors are also all solute atoms.
Since the initial volume fraction of the
precipitate was the same in both simulations and both simulations received the same total plastic
strain, the much larger fraction of green atoms in Fig 1.6b relative to Fig 1.6a demonstrates that
shear-induced mixing proceeds faster in the Cu-Ag couple than in the Cu-V couple. This can be
explained by the much smaller fractional difference in strength between Cu and Ag than between
Cu and V when nanocrystalline. This results in less strain localization in the matrix in the Cu-Ag
couple and faster shear-induced mixing as a result. Hence, these MD simulations reproduce the
strain localization behaviors that are absent from the kinetic Monte Carlo simulations and
Martin's law of corresponding states, but that are expected intuitively and that play a very
important role in the microstructural evolution of mechanically alloyed materials.
Cu-Ag
Cu-V
Figure 1.6 -MD simulations of shear-induced mixing in a (a) Cu-Ag and a (b) Cu-V
nanocomposite [771. Both of the simulations began with all of the solute in a single
precipitate, and both volume elements have accumulated plastic strains of 60. The solute
atoms are colored to indicate their local chemical environment, with green atoms
indicating solute surrounded by solute nearest neighbors. The simulations reveal that the
V precipitate is still relatively in-tact, while the Ag precipitate is nearly completely
dissolved.
Although these MD simulations are very useful for studying the mechanisms of mixing, they are
not without drawbacks: they simulate timescales on the order of nanoseconds; do not include
thermally-activated recovery phenomena; and are therefore incapable of predicting the steadystate microstructure of a mechanically alloyed powder.
The preceding discussion has highlighted the important role that mechanical alloying plays in the
powder-route synthesis of bulk nanostructured materials, and the need to predict the as-milled
powders' chemical mixity in order to design powders that can be consolidated. As the preceding
discussion also makes clear, all of the current tools and frameworks that predict the chemical
mixity of mechanically alloyed materials have drawbacks that limit their usefulness:
-
the core assumption of the rule of corresponding states does not apply to materials that
exhibit strain localization;
-
the master equation is often difficult to develop and is deterministic, while the actual
mechanical alloying processes are stochastic;
-
the MD simulations do not incorporate important thermally activated recovery processes;
-
and the kinetic Monte Carlo simulations treat plastic deformation too simplistically.
This thesis aims to enable the microstructure design of mechanically alloyed materials by
addressing the deficiencies of the classical Bellon-Averback Monte Carlo simulations with
insights provided by mechanical alloying experiments as well as the MD simulations in the open
literature. This thesis then seeks to apply the lessons learned from these improved simulations in
an engineering application: the synthesis of a nanocrystalline alloy powder with a specific
microstructure that enables its rapid consolidation into bulk, ultrafine grained articles.
These two, complementary goals are addressed in the following chapters which are organized as
follows:
*
Mechanical alloying experiments on tungsten-transition metal couples with various
fractional differences in strength are described in Chapter 2. Learning from these
experiments, we then modify the classical Bellon-Averback kinetic Monte Carlo
simulations to account for phase strength effects, thereby making them better predictors
of an extensively deformed material's chemical mixity.
"
In Chapter 3, maps are generated that are based on insights from our improved
simulations and that indicate couples expected to mix to a chemically homogeneous state
under different processing conditions.
" A specific nanocrystalline W-Cr-Fe alloy powder is introduced and its consolidation
behavior explored in detail in Chapter 4.
Because of this powder's highly non-
equilibrium, as-milled microstructure, it can be compacted into fully dense parts with a
high strength and specific gravity that are ideal for penetration applications.
0
Results from preliminary ballistic tests on rounds made from this alloy are described in
Chapter 5.
2. Phase Strength Effects on Chemical Mixing in Extensively Deformed
Alloys
Although there are examples of immiscible couples (e.g., Cu-Co [80] and Ag-Cu [81]) that form
solid solutions during mechanical alloying, others remain phase separated over a range of
compositions despite being milled at low homologous temperatures (e.g., Cu-W [82] and Cu-Ta
[83]). One reason that some couples remain dual phase, which was described in detail in the
Introduction, is that plastic deformation occurs preferentially in the softer phase, and as a result,
atoms are not sheared across the interphase interface [75,77]. Thus, alloying elements must codeform for deformation-induced mixing to occur, and one way to encourage co-deformation is to
mechanically alloy elements with "similar" mechanical properties [24]. For dual phase metallic
systems with coarse microstructures, it is also well established that the amount of co-deformation
depends not just on the individual phases' mechanical properties but also on microstructure, and
specifically the two phases' volume fractions and geometries [84-87].
For example, in alloys
with a small volume fraction of a hard element, the softer element can flow around the hard
element without the hard element deforming; however, this becomes more difficult as the
volume fraction of the hard element increases [88].
Hong and Fultz [25] and others [89,90] have suggested that microstructure and mechanical
properties can influence the amount of deformation-induced mixing during mechanical alloying.
There have also been several recent molecular dynamics studies investigating the effect of the
alloying elements' mechanical properties on the mechanisms of deformation-induced mixing
[76-79].
But while there are many isolated data points, some empirical rules-of-thumb, and
qualitative discussion about the roles of the constituent phases' mechanical properties and the
couple's microstructure in mechanical alloying, we are not aware of a general quantitative
heuristic by which mixable couples (or conditions under which couples can become mixable) can
be predicted. Our purpose in this Chapter is to provide a step towards such a view through
systematic study by both experiment and simulation.
Experimentally,
we track the
microstructure, mechanical properties, and amount of co-defornation and mixing in several Wtransition metal couples subjected to mechanical alloying. Computationally, we adapt a classical
Bellon-Averback kinetic Monte Carlo simulation of mechanical alloying [69,70,91] to
demonstrate how a difference in phase strength leads to multiply stable steady states. The results
together point to the possibility of understanding preferred conditions for forced mechanical
mixing.
2.1. Materials and Methods
2. 1.1.
Powder Processing
Elemental W, Cr, and Zr as well as several equiatomic W50 TM50 alloys (TM = Cr, Nb, Ni, Hf, or
Zr) were milled in a SPEX 8000 high-energy ball mill. The powders were acquired from Alfa
Aesar, and had the following purity and sizing: W, 99.95%, -200+325 mesh; Cr, 99+%, -325
mesh; Zr, 99.6%, -325 mesh; Nb, -325 mesh, 99.8%; Ni, 99.996%, -120 mesh; Hf, 99.6%, -325
mesh.
We selected W as the base alloying element because the maximum temperature
encountered in a SPEX ball mill (~100 'C [92]) is just 10% of its melting temperature. As a
result, interdiffusion in the W9 oTM 5 o couples is, to a good approximation, kinetically suppressed,
and structural evolution only proceeds through plastic deformation. The alloying elements were
selected because their maximum hardnesses (once refined into a nanocrystalline state) ranged
from a low of 6 GPa (Zr [93]), to a high of 16 GPa (Cr), as compared to 22 GPa for W.
M
25-
WwNbw
+.4 WsoCrso
20V
U_
Z150-
y4WwNiw
5
V*
V
*
+
W
5 Hf
25
30
01,
0
5
10
15
20
Time (hrs)
Figure 2.1 - Fe contamination as measured using EDS in the initially pure W and Wtransition metal powders as a function of milling time. The W, W5oCr5 o, and W 50Nb5 O
powders are harder than the W 5oNi5 o, W5oHf5o, and W50Zr5 o powders, and abrade more Fe
as a result.
The W 50 TM 50 alloys were prepared by mechanically alloying elemental feedstock powders. All
of the milling runs were conducted using a steel vial and grinding media with a ball-to-powder
ratio of 5:1 (10 g powder). To prevent oxidation, the milling was performed in a glovebox
maintained under an ultra-high purity Ar atmosphere. To monitor the structural evolution of the
powder particles, -0.2
g of the powder were removed periodically for subsequent
characterization.
2.1.2. Microstructuraland Chemical Characterization
The grain size and lattice parameter of the W-rich, BCC phase was tracked with milling time
using X-ray diffraction (XRD). XRD patterns were collected using a Cu-Ka source Panalytical
X'Pert Pro operated at 45 kV and 40 mA. The lattice parameter, which can be used to infer the
amount of solute dissolved in the W and therefore the degree of mixing, was measured using
Rietveld refinement. The grain size was calculated from the peak broadening using a
Williamson-Hall analysis after correcting out the contribution from instrumental broadening
using a NIST LaB6 standard.
Following XRD, the powders were cold-mounted in epoxy, rough ground, and polished;
polishing concluded with a colloidal silica suspension. Energy dispersive spectroscopy (EDS)
was performed on these mounted samples using a JEOL 6610-LV scanning electron microscope
(SEM) operated at 20kV, to measure the amount of Fe contamination due to abrasion of the steel
vial and media.
The total amount of Fe contamination as a function of milling time for the
various couples and pure W is shown in Figure 2.1. We highlight the W, W 5 oCr5 o, and W5 oNb5 O
data in red to emphasize that these powders had a similar amount of Fe contamination, which
was greater than that of the W 5oZrso, W5oHf5O, and W50 Ni50 powders, highlighted blue.
The concentration of solute, x, dissolved in the BCC W phase was calculated from the measured
lattice parameter using Vegard's law:
=
(a, -- a.,)
(a.,. -a,)
(2.1)
xFB(ae-ar)
(a,.
-a,)
where xFe is the concentration of Fe dissolved in the W and aw,
aFe,
asolite, and aBcc are the pure
W, pure Fe, pure solute, and measured lattice parameters, respectively.
The first term in this
expression is the standard form of Vegard's law for a binary couple, and the second term is
added as a correction to account for the pickup of iron from the milling media and vial. The
alloying elements' lattice parameters are given in Table 1; note that estimated BCC lattice
parameters were used for the non-BCC alloying elements: Zr, Hf, and Ni. We estimated xFe by
multiplying the global concentration of Fe in the as-milled powder (Figure 2.1) by the fraction of
Fe dissolved in the W phase. The fraction of Fe dissolved in the W phase was calculated from a
control experiment in which we milled initially pure W, and measured the global concentration
of Fe using EDS and the concentration of Fe in the W lattice using Vegard's law with milling
time. The ratio of these quantities gave the fraction of Fe dissolved in the W, which we assumed
to be the same for pure W and the W 50 TM50 couples for a given milling time.
The W5 oCr5o and W5 oZr5 Ocouples were down-selected for a more in-depth investigation of their
microstructure using SEM and dark field STEM. These couples were selected for two reasons.
First, the W5 oCr5 o and W5 oZr5 o couples' behaviors are representative of systems that either do or
do not mix, respectively, after long milling times, as will be seen shortly. Second, the difference
in atomic number between W and either Cr or Zr is such that, prior to atomic mixing, there is
sufficient contrast in either SEM or dark field STEM to qualitatively gauge chemical
inhomogeneity.
For milling times up to ~5 hours, the chemical inhomogeneity of the W 5oCr5 o and W5 oZr5 O
couples could be monitored using back scatter imaging in a FEI Helios Nanolab 600 SEM
operated at 5 kV. The mean spacing, X, between nominally pure W regions inside the powder
particles was measured using
I =
(2.2)
NL
where Vw is the volume fraction of W and NI is the number of interceptions of W per unit test
line [94]. We found that negligible atomic mixing occurs up to 5 hours (as will be seen in the
next section), so Vtw could be assumed constant and equal to that for the elemental powder
mixture of W 50 TM50 (Vw = 0.57 for W5 0 Cr5O; Vw= 0.41 for W5 oZro). The mean W spacing, k, is
also proportional to the mean intercept length of the W regions [94], with a proportionality
constant of 0.8 and 1.4 identified for W-Cr and W-Zr couples respectively.
Table 2.1 - ape and aSolte values used in Eqn 2.1. The Zr lattice parameter was estimated
by extrapolating the P-phase's lattice parameter at 862 'C (3.609 A) to room temperature
using the p-phase's coefficient of thermal expansion reported in Reference 1951. The Hf
lattice parameter was estimated from P-stabilized alloys [961. The Ni lattice parameter
was estimated from its FCC lattice parameter using the procedure outlined in Reference
1971.
Element
aVelaIe
(A) Ref.
Fe
2.866
[97]
Cr
2.885
[97]
Nb
3.301
[97]
Zr
3.57
[95]
Ni
2.793
[97]
Hf
3.50
[96]
Beyond 5 hours of milling, it became difficult to resolve the individual phases using the SEM.
Therefore, samples milled for 45 hours were inspected using dark field STEM in a JEOL 2010F
operated at 200 kV. TEM specimens were prepared from individual powder particles using the
FIB liftout technique [98] so as not to distort the as-milled microstructure.
2.1.3.
Mechanical Testing
Nanoindentation was also performed on as-milled W, Cr, Zr, W5oCr5 o and W 5 oZr5 O powders to
correlate the evolution in microstructure with that in mechanical properties.
The Zr, Cr, and
WSoZr5 o nanoindentation test specimens were prepared in the same manner as that used for the
SEM specimens. A different mounting material (solder glass EG2934 VWG from Ferro Corp.)
was used for the W and W 50Cr5 0 powders to minimize substrate compliance effects in
mechanical testing. The molten glass (~700 'C) was poured onto powder in a steel retaining
ring, which was then quenched in brine. The maximum temperature during this process was well
below the temperatures at which thermally activated relaxation processes become noticeable in
pure W [99], and the time of thermal exposure was only a few seconds. XRD and TEM were
used to confirm that there was no grain growth, segregation, or substantial oxidation during
mounting.
Nanoindentation tests were performed using a Hysitron Triboindenter 950 with a diamond
Berkovich tip. The tip's area function and the frame compliance were calibrated using a fused
silica standard.
The Oliver-Pharr method [100] was used to extract hardness and reduced
modulus from the load-displacement curves. Additional nanoindentation tests were performed
using a cube corner tip to augment the pile-up patterns, and these nanoindentations were
inspected by SEM.
2.2. Microstructure and Hardness Evolution
Inspection of the five W 50 TM50 couples' XRD patterns suggests that these couples exhibit one of
two main alloying behaviors, either forming a solid solution or remaining phase separated after
long milling times. These two behaviors are typified by W-Cr and W-Zr in Figure 2.2a and 2.2b,
respectively.
In the W5 0 Cr50 and W 50Nb5 Ocouples' XRD patterns, the W and Cr/Nb Bragg peaks broadened
and gradually merged with milling time (Figure 2.2a).
The merging Bragg peaks reflect a
homogenization of the two BCC phases' lattice parameters as the W and Cr/Nb dissolved in each
other to form a single BCC solid solution. In the other couples' (W5 oZr5o, W 50 Hf5 0 , and W 5oNi 5o)
XRD patterns, the W Bragg peaks broadened as well, but their integrated intensities decreased
and their positions did not change appreciably with milling time. Simultaneously, the low angle
Zr/Hf/Ni Bragg peaks broadened and merged into a single broad hump (Figure 2.2b),
characteristic of an amorphous solute-rich phase [101]. These latter couples were clearly still
dual phase after milling, and the stationary W Bragg peaks suggest that a limited amount of
solute dissolved in the W phase.
Applying our modified Vegard's law (Eqn 2. 1) to the W lattice parameter data shown in Figure
2.3a gives the amount of solute dissolved in the BCC W phase.
Figure 2.3b contains these
calculated solute contents normalized by the global non-ferrous solute content, xO. The values in
Figure 2.3b provide an indication of the powder's chemical homogeneity: the limiting values of
zero and one correspond to phase-separated and chemically homogeneous alloys, respectively.
Thus the results in Figure 2.3b support the interpretation that the W 50 Cr5 o and W5 oNb5 o couples
formed a solid solution when milled in excess of 15 hours, whereas in the W 5 oNi5 o, W 5 oHfO, and
W5 oZr5 o couples, there was negligible solute in the W phase even after 25 hours of milling.
a. .OW
e Cr
1 hr
3
C
25
01
-15
25
b Wr
1 hr
Zr
C
C5
015
50
75
100
Position (020)
Figure 2.2 - XRD patterns from the a) W5 oCr5 o and b) W5oZr5o powders with increasing
milling time. The region around the W (110) Bragg peaks is highlighted to emphasize
how, in the W 5oCr5 o patterns, the W and Cr peaks gradually merge with increasing
milling time, whereas in the W5oZrso patterns, the W peak essentially remains unmoved.
To a good approximation, changes in integrated intensity are proportional to changes in the
volume fraction of a phase during mechanical alloying [101].
Therefore, normalizing the
integrated intensities of the W Bragg peaks at later milling times by their integrated intensities
after milling for one hour as done in Figure 2.3c, gives a rough measure of relative changes in
the BCC W phase fraction. According to Figure 2.3c, the decreasing integrated intensity of the
W Bragg peaks in the W5 oZr5o, W 5oHf5 o, and W50Ni50 XRD patterns suggest that some W was
lost from the BCC W phase and thus dissolved into the second phase (rich in the alloying
M-
element) in each of these couples. Additionally, the volume fraction of W in the W5oZr5o and
W50Hf5 O couples started to plateau value after -15 hours of milling. As for the W 5oNi 5o couple,
the W volume fraction appears to continue decreasing even after 15 hours of milling but this is
most likely due to the comparatively larger Fe contamination in this system that continues to
alter the global powder composition.
a3.2 0
S--
I-
*el-
4) 3.1 5
E
,q~---~
W5 Hf50
-
--
W,0Nb 0
==-I
WeZr5O
WVNi5
------
W5Ni50
qW
3.1 0
- 3.0 5
-qW
b.
1. U
50rs
mixed
LI
0. 8-
X
0. 6-
X* 0. 40. 2
-0
C.
0.8
0.6
unmixed
+
0
0. 0
1. 0
0
t
1
10
V
0.4.
0.2-I
A'
. 0I
0
10
a
20
Time (hrs)
I
30
Figure 2.3 - a) The BCC W phase's lattice parameter measured using Rietveld
refinement for the various W5 oTM5 o couples with increasing milling time. b) Solute
concentration in the BCC W phase normalized by the total solute concentration as
function of milling time for the same couples. These values were calculated from the
BCC W phase's lattice parameter and the data in Fig. 2.1 using a modified Vegard's law
as described in the text. c) Average integrated intensities of the W Bragg peaks in the WNi/Zr/Hf couples' XRD patterns, I, normalized by their integrated intensities after milling
for one hour, 10.
It is significant that in the above systems, W appears to dissolve into the second element, while
the evidence suggests little dissolution of the second element in the BCC W. Similar asymmetric
mixing kinetics have been observed in other mechanically alloyed couples (Mo-Ni [102,103] and
W-Ni [101]), and Ashkenazy et al. [77] demonstrated using molecular dynamics simulations that
asymmetric mixing is likely a general feature of mechanical alloying in couples with a large
difference in strength.
80
V W
* W50Cr50
*
E
W 50Zr5
60 1
N
(n,
C
-
40 I
20 1
0
5
10
Time (hrs)
15
Figure 2.4 - Grain size of the initially pure W phase as a function of milling time
measured using the Williamson-Hall technique. Fits to the raw data using Eqn 2.3 are
shown as well. The similar rate of grain refinement among the three powders suggests
that, at least for short milling times, the W domains are being plastically strained
similarly in all three powders.
The peak broadening in all of the couples' XRD patterns was due predominantly to grain
refinement and microstrain with some contribution from chemical heterogeneity as evidenced by
the W Bragg peaks' asymmetric shapes. The grain size of the BCC W phase measured using the
Williamson Hall technique for the pure W, W5 oCrjo, and W5 oZr50 powders are shown in Figure
2.4 as a function of milling time. Note that the Williamson-Hall technique does not account for
chemical heterogeneity's contribution to peak broadening, so the grain size at later milling times
in Figure 2.4 may be artificially small.
All of the grain sizes exhibit a typical exponential
refinement trend given by [104]
(2.3)
D=DF+(DO -DF)e-"
where Do is the starting grain size, DF is the final grain size, t is the total time milled, and k1 is a
rate constant that depends on both the milling parameters and material properties; fits to the data
using Eqn. 2.3 are included in Figure 2.4. The three sets of data indicate that the W grain size
refines at a similar rate, but to a slightly different steady state grain size depending on the
presence and type of alloying element.
Because grain size is inversely proportional to the
accumulated plastic strain during the early stages of mechanical alloying [104,105], the data in
Figure 2.4 also reveal that, at least for short milling times, the W is co-deforming along with the
Zr. The grain size of the second phases could not be accurately tracked in any of these systems
because of their small diffraction signatures.
1 hr
3 hrs
5 hrs
15 hrs
L
4
10
0
W50Zr.
+
Cr
10 3
) 102
C
101 1
0
1
2
Time (hrs)
4
6
Figure 2.5 - SEM micrographs of the a-d) W 5 oCr5 o and e-h) W 5oZr5o powders milled for
the times indicated; scale bars are all 200 nm. The light regions contain W and the dark
regions contain either Cr or Zr. Note the lamellar and particulate morphologies of the
W5 oCr5 o and W 50 Zr5 O couples' microstructures, respectively. Additionally, the lack of
contrast in the micrograph of the W5 0 Cr5 0 powder milled for 15 hours suggests that this
powder is chemically homogeneous, in agreement with the XRD results. i) Mean spacing
measured using Eqn. 2.2 of the W5 oCr5 o and W 50 Zr50 powders milled for 1, 3 and 5 hours;
the data points at 0 hours correspond to the mean particle diameters of the starting
powder. Also shown are fits to the mean spacing versus time data using Eqn. 5 in
Reference [26].
For the WsoCrso and W5 oNb5 O couples, the amount of solute dissolved in the W phase exhibited a
typical sigmoidal time-dependence (cf. Figure 2.3b), with an incubation period prior to the onset
of substantial shear-induced mixing [106,107].
During the incubation period, the individual
powder particles consisted of nominally pure solute and W regions. The evolution in the W
regions' shape, mean spacing, and size provides insight into the degree of co-deformation, and is
explored in the series of SEM micrographs in Figure 2.5. For example, the W regions in the
W5 oCr5 o couple maintained a lamellar structure for milling times up to 5 hours, indicating that
the W and Cr were deforming compatibly (Figures 2.5a-c). Over this same period, the W
regions in the W5 oZr5 o couple were comminuted into smaller particles suggesting that the much
softer Zr was undergoing large plastic straining and that the W, unable to deform compatibly,
fractured instead (Figures 2.5e-g). Aning et al. observed a similar break-up of the W regions in
their study of mechanically alloyed W-Ni [101].
b. 1.0
afit
data
U-
0.5 L-I
0.5
:-XRD
0.0
0
j-------_A
10
Particle Diameter (nm)
-
"
20
Figure 2.6 - a) Dark field STEM micrograph of a W5oZr5 o powder particle milled for 45
hours. The white regions are residual W particles in a dark, Zr matrix. b) Cumulative
distribution of the W particles' circular equivalent diameters along with an integrated lognormal fit to the diameter data. The mean diameter of the fit is 8 nm, in agreement with
the W grain size measured using XRD.
Despite the couples' different morphologies, their mean spacings and domain sizes initially
refined at similar rates as shown in Figure 2.5i, only diverging after the onset of mixing in the
W 5oCr5o couple at -5 hours of milling. The onset of mixing in the W5oCr5o couple occurred
because refinement in the mean thickness of the W lamellae in the W 5oCr5o couple led to a
concomitant increase in the amount of interface between the W and Cr domains. This in turn led
to an increase in the rate of mixing because there was more material that could be carried across
the interface between the two phases by plastic deformation.
In contrast to the gradual dissolution of the W regions in the W5 oCr5o powder, the mean diameter
of the W regions in the W5oZr5 O powder was refined until it reached a lower limit, namely the W
grain size.
This is illustrated by the dark field STEM micrograph shown in Figure 2.6a of a
W 5 0Zr5 O
powder particle after milling for 45 hours.
residual W particles dispersed in a dark Zr matrix.
In this micrograph, the light regions are
The cumulative distribution of the W
particles' circular equivalent diameters is given in Figure 2.6b along with an integrated lognormal fit with a mean particle diameter of 8 nm, consistent with the W grain size measured
using XRD (9 nm).
Similar microstructures have been observed during severe plastic
deformation studies of Cu-Nb alloys [108,109]. Although the sample in Figure 2.6a was milled
for 45 hours, we estimate that the particle diameter and grain size reach similar values between 5
and 10 hours of milling based on the time dependencies measured in Figures 2.4 and 2.5i.
The elemental W, Cr, and Zr powders' hardnesses increased rapidly during milling, before
plateauing after roughly 5 hours. These elemental powders are predominantly grain size
strengthened, so this trend in hardness can be attributed to their grain refinement.
We
demonstrate this by plotting the powders' hardness against their reciprocal square root grain size
in Figure 2.7a; the Cr and Zr data both conform to a Hall-Petch scaling. As for the W data, there
is a slight, negative deviation from the expected linear dependence on reciprocal square root
grain size at the smallest grain sizes, which we ascribe to the presence of Fe that softens the W
powder. For comparison purposes, Figure 2.7a also contains Hall-Petch trendlines for Hf [110],
Ni [111], and Nb [112] taken from the literature.
Figure 2.7b shows the behavior of the mixed elemental powders, which contrast with the uniform
behavior of the elemental powders. The WsoCr5o powder's hardness increased with milling time
until it was similar to that of the W powder, whereas the W5 oZr5 Opowder's hardness actually
decreased until it was similar to that of the Zr powder. From the microstructure of the W5 oCr5 o
powder, these powders are both grain size and solid solution strengthened. Thus, the W5 0 Cr5 O
particles are an additional ~4 GPa harder than the as-milled Cr particles [113].
The W5oZr5 o
powder's decreasing hardness with milling time reflects a decreasing amount of co-deformation.
The convergence of the W5 oZr5 o and Zr hardnesses after 15 hours of milling suggests that, by this
point, plastic deformation was accommodated solely in the softer Zr phase and that this Zr phase
has a similar hardness to that of pure Zr (in a milled, refined state).
Grain Size (nm)
a.
100
25
11
-OW
-o Cr
20
09
[50]
.Nb,
-
15 -
-2 10-
-Hf,
CO
[48]
V
de
AZr
Ni, [49]
-
5
5
0.2
0.1
b.
2 (nm)-1 2
D 1/
*W
0.3
5Cr0
W50Zr50
- -
20-
1---
15
/C'
W
--
-,
Cr
(D
C
.
-
~20
Zr
50
5
10
Time (hrs)
15
Figure 2.7 - a) Hall-Petch plots for the initially pure W, Cr, and Zr powders. All of the
initially pure powders' hardnesses increase, to varying degrees, with milling time, mainly
due to grain refinement. Also shown are Hall-Petch trendlines for Ni [1111, Hf [110],
and Nb [112] taken from the literature. b) Hardness as a function of milling time for the
W 5 oCr5 O and W5 oZr5 o powders along with spline fits to the W, Cr, and Zr powders'
hardnesses. The W 5oCr5o powder's hardness increased until it was nearly the same as the
initially pure W powder, whereas the hardness of the W5 OZr5 O powder actually decreased
until it is was the same as that of the initially pure Zr powder.
We examined the pile-up around nanoindentations in the WsoCr5 o and W5oZr5o powders milled
for 15 hours, in order to better appreciate the nature of the deformation in these systems when
they are structurally quite refined. The lower magnification SEM micrographs shown in Figures
2.8a and 2.8b indicate that both alloys deform by shear localization after long milling times. The
higher magnification SEM micrograph of the pileup around the nanoindentation into WSOCrO
shown in Figure 2.8c lacks phase contrast, suggesting a chemically homogeneous powder. In
contrast, closer inspection of the edge of the indentation in the pile-up region in Figure 2.8d
reveals clear phase contrast, with the W-rich regions appearing lightly colored, and the Zr-rich
second phase dark. Additionally, the shear bands in this sample show highly serrated faulting
that seems to skirt around the W regions; places where this deflection behavior is particularly
evident are marked with arrows.
Figure 2.8 - Micrographs of nanoindentations using a cube corner tip into a,b) W5oCr5o
and c,d) W5 oZr5 o powder particles that were milled for 15 hours. Both powders' pile-up
patterns exhibit non-homogeneous plastic deformation (i.e., shear localization). In the
W5 oZr5o powder's pile-up, the shear offsets appear to be skirting around the larger W
particles in the regions indicated by the arrows.
Courtney et al. [114] observed that Fe contamination during mechanical alloying provides an
indirect measure of a powder's hardness: harder particles are more abrasive resulting in more Fe
contamination.
This observation is consistent with the present work in which we measured
substantially more Fe contamination in the harder W and W 50 Cr5 O powders than in the
comparatively soft W5 oZr5 O powder (Figure 2.1).
W5 0TM50
Inspection of Figure 2.1 suggests that the
couples' hardnesses divide roughly into two groups: the couples that homogenize (i.e.,
W 5 0Nb50 and WsoCr5 o) are similarly hard, whereas the couples that remain dual phase (i.e.,
W5 oNi50 , W 5 oZr5 o, and W5 oHf5 o) are similarly soft.
2.3. Factors Affecting Deformation-Induced Mixing
Considering all of the characterizations in the previous section together, we conclude that in
these W 5 oTM5 0 couples, differences in the strength of the two alloying elements, and the
subsequent two phases that they evolve into, clearly affect the mode and amount of codeformation and atomic mixing.
In the W-Cr couple, for example, nanocrystalline W and Cr
phases would differ in strength by about 30% (cf. Figure 2.7b). This difference is small enough
that when W and Cr are mechanically alloyed, plastic strain is partitioned between the W and Cr
domains even at longer milling times, as evidenced by the lamnellar microstructure in Figures
2.5a-c.
This in turn promotes deformation-induced mixing and the eventual formation of a
homogeneous BCC solid solution, with W and Cr phases shearing into each other.
Similarly,
milled phases of W and Nb have a strength mismatch of about 40% (cf. Figure 2.7a), which we
infer is not enough to prevent co-deformation and subsequent atomic mixing to a solid solution.
In contrast is the W-Zr couple, for which the milled phases differ in strength by 70%. This large
strength mismatch contributes to plastic strain localization in the softer Zr phase.
This in turn
leads to minimal mixing that is also more acutely asymmetric (practically no Zr dissolves in W,
while some W dissolves in Zr). Similar conclusions are reached for W-Ni. That a difference in
strength can play an important role in the amount of deformation-induced mixing is intuitive and
has been noted by many others [25,89,90,115,116], but the W-transition metal couples studied
here demonstrate this effect vividly.
Although in this study the only alloying elements that completely mix with BCC W have BCC
crystal structures themselves, in general, both elements do not need to have the same crystal
structure for there to be complete homogenization during mechanical alloying.
Of the many
examples supporting this statement, two specific ones are Cu5 oFe5 o, a positive heat of mixing
FCC-BCC couple that forms an FCC solid solution when mechanically alloyed [117-119], and
Ni 5 oNb50 , a negative heat of mixing FCC-BCC couple that forms a homogeneous amorphous
alloy when mechanically alloyed [120]. There are also examples of couples where both elements
have the same crystal structure but do not homogenize even when milled at low homologous
temperatures (e.g., Ni-Ag) [121]. These results suggest that nuanced effects like local interface
structure might be less relevant given the random and repeated nature of deformation in
mechanical alloying. For example, Vo et al. used molecular dynamics simulations of the Nb-Cu
couple to demonstrate that certain interphase interfaces with special crystallographic orientations
have enhanced resistance to deformation-induced mixing [78,79,122], but averaging over time
during milling, many weak interfaces might be expected to be sampled as well. We speculate
that crystal structure mismatch may correlate with the mixing behavior for a different reason,
namely, because the Hall-Petch coefficient of FCC or HCP metals tends to be smaller than that
of BCC metals [123]. Consequently, an initial difference in the coarse-grained metals' strengths
in a BCC-HCP/FCC couple typically increases to a greater extent than the same initial difference
in a BCC-BCC couple as the two alloying elements' grain sizes are refined. At least for the
present W-TM couples studied here, crystal structure correlates with mixing behavior primarily
because it affects the difference in phase strength at later milling times.
A parameter that apparently did not influence the amount of deformation-induced mixing in
these W-transition metal couples was the heat of mixing: W-Zr/Hf/Ni are all systems with mildly
negative heats of mixing (AH
= -8 kJ/mol; AH
= -6 kJ/mol; AH'
= -2 kJ/mol [124]),
but their as-milled powders remain dual phase because interdiffusion is kinetically suppressed
and their differences in strengths preclude much deformation-induced mixing. In contrast, W-Cr
has a modest positive heat of mixing (AHi = +8 kJ/mol [125]) and thus prefers to segregate
but forms a homogeneous solid solution instead.
2.4. Generalized Phase Strength Effects
Our experimental results demonstrate that a difference in strength strongly influences the amount
of chemical mixing attained during mechanical alloying, but they are limited in that only one
combination of composition and ambient milling temperature was studied for each couple, and
the gradual pickup of Fe during milling works against the study of steady-state structural
conditions in these experiments. Furthermore, as noted in the Introduction, although there are
theoretical constructs from driven alloy theory to rationalize mechanical mixing in systems that
intrinsically mix to the atomic level, these do not generally include the role of mechanical
strength on mixing.
For these reasons, we adapt a kinetic Monte Carlo simulation of forced
atomic mixing during mechanical milling.
This Bellon-Averback type model captures the
competition between deformation-induced mixing and thermally activated diffusion during
mechanical alloying [69,70,91].
Following Refs. [69,70,91], we simulate a system containing a single vacancy and two types of
atoms (given labels A and B for the stronger and weaker phases, respectively). The atoms have
an FCC crystal structure, and the simulation unit cell is a rhombohedron with the faces parallel to
FCC { 11
planes, 30 atoms along each of its edges, and periodic boundary conditions. To be
consistent with previous simulations [70], the atoms' interaction energy,
that
CAA + EBB -
2&B =
I-=
-0.05533 eV, where
EA
CAB,
was selected such
and BB are the atoms' respective cohesive
energies and were assumed to be equal. This interaction energy results in the system having a
symmetric miscibility gap with a critical temperature at 1573 K.
At each Monte Carlo step, either the vacancy exchanges positions with one of its nearest
neighbors or the simulation cell is sheared, according to a residence time algorithm. The vacancy
exchange frequency was configuration- and temperature-dependent,
whereas the shearing
frequency, 0, was held constant at 103 s- . The vacancy exchange frequency was calculated using
w = vexp{-(E +Ea)IkBT}
(2.4)
where kB is the Boltzmann constant, T is the temperature in Kelvin, v is an attempt frequency
(1015 s-'), EO is a configuration-independent energy set equal to 0.8 eV, andEN =En/2is an
energy that reflects the local environment of each of the vacancy's nearest neighbor atoms,
which we label exchange atoms [126]. The variable n is the number of each exchange atoms'
nearest neighbors that are of the opposite species.
After a number of Monte Carlo steps, the deformation-induced mixing and vacancy-mediated
segregation processes typically reach a dynamic equilibrium. The resulting simulation cell's
microstructure has a characteristic amount of chemical mixing, which we measured using the
first Warren-Cowley short-range order parameter, a [127], normalized such that the limiting
values of 0 and I correspond to a homogeneous solid solution and a completely segregated, dual
phase alloy, respectively. Values of a intermediate to 0 and I reflect an increased number of
dissimilar nearest neighbors, and can be attributed to either roughening of the interphase
interface or dissolution of one element into the other [55]. We can estimate the temperature at
which simulations with no difference in strength should be completely homogenized, TH, by
setting the shearing and maximum diffusion frequencies equal and solving for T to give:
T
(E0 +3e)
in
kB
12v
(2.5)
where the factor of 12 comes from the coordination number. For our simulations, TH is 244 K.
During a shearing event, two glide planes in the same slip system were selected, and the material
between the planes was displaced by a Burgers vector in a random slip direction.
The slip
system and two glide planes were selected as follows: first, the slip system (i.e., family of glide
planes and direction) was selected from one of the 12 possibilities using a uniform probability
distribution, such as might be expected for randomly applied shears that would occur in ball
milling. Next, two glide planes in this slip system were selected using a probability distribution
function that accounts for each of the planes' strengths. The probability of selecting a given
glide plane P(/) was calculated using
Pj)=N
(2.6)
i-4
where the summation in the denominator is over all of the glide planes in a given slip system and
Rj is defined as:
R
v=exp{-[N
+N B(1-A)+Naj(1-A/2)]/kBT1
(2.7)
where Ni, NB, and NB are the respective number of A-A, B-B, and A-B bonds across the
slip plane j; A is the fractional difference between the pure A and B phases' strength; and X is a
constant (2.4 x 1022 J) that gives the work required to move a dislocation across the plane j
when multiplied by the other terms in the exponent's numerator. After the first glide plane was
selected, the probability distribution was recalculated, omitting the plane that was already
selected.
According to Eqns. 2.6 and 2.7, setting A closer to unity makes selecting planes containing a
larger number of B-B bonds more likely, so by adjusting A, we influence the strain partitioning
(i.e., the A and B phases' difference in strength). For comparison with experimental results, we
can interpret A as the fractional difference between the A and B atoms' shear moduli when
information on the alloying elements' strengths is unavailable, because for nanocrystalline
metals, the maximum strength is roughly proportional to shear modulus [113]. Moreover, by
using an exponential in Eqn. 2.7, the probability distribution function is sufficiently steep that in
a couple with A
-
1, a small cluster of A atoms is unlikely to be sheared. In addition to varying
the temperature and A, we also controlled the concentration, c, of A. Note that increasing the
temperature tends to distribute the shearing events among the planes more uniformly by making
the shearing of harder planes more probable. This effect is most significant among planes with
similar strengths.
2.4. 1. Bi-stability and History-DependentSteady States
When there is no difference in strength (i.e., A = 0), the present model devolves to become
identical with that of Bellon and Averback [70], and the results match theirs in detail.
Specifically, the steady state chemical mixity is path-independent and determined solely by the
shearing rate and the vacancy exchange rate, which is in turn a function of the temperature. This
is demonstrated in Figure 2.9a where, for a given temperature, a converges to the same value
regardless of the starting configuration for an A 50B 50 alloy. This path-independence in couples
with little to no difference in strength aligns with experimental results such as those of Klassen et
al. [41] (for Cu-Ag), and is consistent with Martin's "rule of corresponding configurations" for
driven alloys, which states that an alloy should attain a unique steady state chemical mixity for a
given intensity of the driving force and ambient temperature [36].
In contrast, our simulations suggest that when there is a large difference in strength (i.e., A = 1),
the steady state chemical mixity becomes path dependent, at least if the temperature is
sufficiently low. Figure 2.9b, for example, depicts the evolution in chemical mixing for two
different starting configurations, completely segregated and chemically mixed, at two different
temperatures in a couple with a large difference in strength. In the high temperature simulation,
the a's converge as before, but interestingly, in the low temperature simulation, the initially
segregated and chemically mixed configurations remain as such. The insets in Figure 2.9b are
two-dimensional slices across the initially segregated and chemically mixed simulation cells that
illustrate their disparate initial and steady state amounts of chemical mixing.
a. 1.0
0.8
350 K
A
-
0.6
a
0.4
300 K
0.2
0.0
b. 1.0
a
300 K
0.4
0.2
0.C
0
1
2
3
MCS (107)
Figure 2.9 - a) Evolution in the order parameter a for kinetic Monte Carlo simulations
using two different temperatures in a couple with no difference in strength. The two lines
that converge for each temperature correspond to two different starting configurations. b)
The same set of simulations but using a couple having a large difference in strength
between the phases. Note that in the low temperature simulations, the initially segregated
and chemically mixed curves do not converge. The insets are two-dimensional slices
across the low temperature simulation cells with the A atoms colored grey and the B
atoms invisible.
In Figure 2.9b, both the low temperature segregated and chemically mixed states appear to be
stable steady states. The segregated state is stable because shearing occurs preferentially in the
softer phase and will not lead to mixing so long as there are two glide planes containing only B
atoms parallel to each plane in the { IlI} set. One set of these planes was missing from the
starting configuration, but it formed during the first 107 Monte Carlo steps as evidenced by the
dip in a. The disordered state is also stable because all planes in the simulation cell are equally
likely to be sheared so shearing does lead to mixing, and the vacancy exchanges are sufficiently
infrequent relative to shearing events that the A atoms cannot segregate into larger, unshearable
precipitates. At higher temperatures, however, the vacancy exchange frequency increases so the
A atoms can segregate into particles that subsequently coarsen. This is why both the initially
segregated and chemically mixed simulations arrive at the same steady state a value in the 350 K
simulation. Though the simulations are of positive heat of mixing couples, the negative heat of
mixing (W-Zr/Hf/Ni) couples that we studied experimentally also appear to be bi-stable. In the
case of W 5oZr5 o, for example, the steady state microstructure is dual phase when elemental W
and Zr powders are mechanically alloyed. If, however, the W and Zr were first reacted to form
an intermetallic and then this intermetallic was mechanically milled, the steady state
microstructure would in all likelihood be single phase.
There are many examples of multi-stability and path-dependent steady states in the literature on
driven systems [31,39,42]. In irradiated alloys, for example, Banerjee et al. irradiated Ni 4Mo
with high-energy electrons at various temperatures and found that the alloy either developed
short-range order (SRO) or long-range order (LRO) depending on its state prior to irradiation
[44]. Bellon and Martin subsequently explained this phenomenon by modeling the competition
between irradiation-induced disordering and thermally activated reordering [29].
The authors
concluded that bi-stability emerges because the SRO and LRO structures have different
sensitivities to radiation damage: the SRO structure is less sensitive to irradiation-induced
disordering than the LRO structure but the alloy's thermodynamic ground state has LRO. Both
this example and our simulations demonstrate that bi-stability emerges when the driving force
affects one phase disproportionately. That Martin's rule of corresponding configurations breaks
down for these systems is reasonable; its assumption that the driving force affects both phases
equally is not met.
2.4.2. Microstructureand Mixing Kinetics
In the initially segregated simulations, the microstructure that emerged after holding a simulation
for many MCS at a constant temperature was also affected by a difference in strength.
In
simulations where there is no difference in strength, Bellon and Averback [70] and others [69,9 1]
observed interfacial roughening and compositional patterning as the temperature was decreased
and vacancy exchanges suppressed.
A 5 0B 50
We observed similar behavior in our simulations of an
alloy equilibrated at various temperatures.
As shown in Figures 2.10a-c, the
characteristic length scales of the A and B regions decreased in step with the temperature. An
analogous dependence of microstructural length scales on the ambient milling temperature has
been confirmed experimentally in the Cu 5 oAg5o system using atom probe [74,128]
and
TEM/STEM [73,129].
When we introduced a difference in strength, the microstructures no longer featured interfacial
roughening. Instead, the A regions organized into smaller aggregates with flat faces along the
{1 11 } planes. Atoms that jutted out from these faces tended to be sheared off the surface into
the B matrix, and once inside the B matrix, were shuttled about, sometimes rejoining the A
cluster in a more stable position. Figures 2.10d-f demonstrate the development of these flat faces
as the simulation cell temperature was dropped from 400 to 300 K. This lack of roughening,
"chipping away" of A atoms at the interphase interface, and resultant asymmetric mixing kinetics
are all broadly consistent with molecular dynamics simulations of deformation-induced mixing
of hard, BCC precipitates in softer FCC matrices [77].
They are also consistent with the
microstructure and mode of mixing exhibited by our W50 Zr5 O couple; in that couple the steady
state microstructure featured nanoscale, equiaxed W particles in a Zr matrix and the W atoms
were sheared into the Zr matrix without an equal but opposite flux of Zr atoms into the W
particles.
A=0
a.
A
1
=
400 K
350 K
C.
300 K
Figure 2.10 - Steady state unit cells of A 50 B50 simulations with a-c) no difference in
strength and d-f) a large difference in strength. The simulations were performed using
the temperatures indicated, and the color scheme is the same as in Figure 2.9. All of the
simulations were initialized with a segregated microstructure.
2.4.3.
Temperature and Composition Effects
Knowing that the steady state chemical mixity is path dependent for some combinations of
temperature, A, and c, it is of particular interest to know at what temperatures a system with
given A and c will homogenize if the starting microstructure is initially segregated, as is
generally the case in high energy milling.
The temperature at which this occurs provides an
upper bound, below which the most likely stable state is the completely homogenized one. To
identify this temperature, we performed simulations in which an initially phase-separated cell
containing a single particle of the minority phase was cooled from 430 to 220 K by decrementing
the temperature by 0.05 K every 104 steps. We selected this temperature range because over it, a
couple with no strength mismatch (i.e., A = 0) transitions from phase-separated to chemically
homogeneous.
parameter space.
The composition and A were systematically varied to explore the entire c-A
Temperature (K)
380
330
280
230
1.0
0.6
-
0.8
a
0.4>
-
0.6
0.20
0.4-
A=ON
0.2- c = 0.20
0.0
0
2
MCS (101)
c
4
0.50
2
MCS (107)
c
4
0.80
2
MCS (107)
4
Figure 2.11 - Evolution in order parameter a during simulations following a cooling
trajectory while shearing, using the A's and c's indicated. Note that with increasing c, a
large difference in strength is no longer sufficient for preventing mixing: when c equals
0.8, all of the simulations homogenize by 230 K.
Results from several simulations are shown in Figure 2.11 and two features are immediately
apparent. First, adding a strength mismatch depresses the onset temperature for deformationinduced mixing, and for small c's, large differences in strength prevent mixing altogether. From
inspection of the microstructure, the A clusters in these latter simulations essentially behave like
unshearable dispersoids. Second, the relationship between A and the onset of mixing becomes
less significant as c increases. Above a threshold c, all of the simulations mix at roughly the
same temperature regardless of A because the atoms become geometrically constrained to codeform and mix. This trend is consistent with the experiments of Gaffet and coworkers [82] who
mechanically alloyed several compositions of W and Cu, a couple with an 80% difference in
strength when both metals are nanocrystalline [130,131].
The authors found that although the
powder remained dual phase after milling, more Cu dissolved in the W as the volume fraction of
W in the starting charge increased.
The link between c, A, and the amount of mixing is also
consistent with the behavior of dual phase metallic materials with coarse microstructures, in
which co-deformation becomes more likely as the volume fraction of the harder phase increases.
Co-deformation and atomic mixing should also occur more easily at all c's as the phase strength
mismatch decreases, as is the case in our simulations and in experiments.
For example,
nanocrystalline Fe and Cu have an ~8 GPa difference in hardness [132,133], less than half that of
W-Cu, and when the two are mechanically alloyed, they torm a solid solution at all compositions
other than FeCu(I\) (60 < x < 80) [134].
Based on these observations, we conclude that the only requirement for a stable dual phase
rnicrostructure in these simulations is that there be two "easy glide" planes parallel to each axis.
The most trivial approximation of this condition would be if the easy glide planes comprised
only B atoms, for which we can calculate a maximum concentration of A atoms, cvax, as
C
8
L
24
L
2
3
L=--+
32
(2.8)
L
where L is the number of atoms along an edge of the simulation cell; Eqn. 2.8 gives 0.76 for our
simulations, which agrees reasonably with the simulation output in Figure 2.11, where at higher
concentrations near c ~ 0.7, mixing is geometrically forced no matter the strength mismatch. In
an experimental context there may be no threshold concentration above which mixing is forced,
because the geometric constraint on deformation-induced mixing is not as strict in reality as it is
in our simulations: when non-planar slip is possible, plastic deformation can deflect around the
harder phase as suggested by the pileup pattern in W50 Zr5 Oin Figure 2.8.
Finally, in Figures 2.12a-d, we summarize and generalize our simulation results for four different
values of A by first scaling the temperatures at which the atoms completely mixed by TH and
then plotting them as a function of the concentration of the harder A atoms, which can be
compared with the concentration (or volume fraction) of W in our experiments. The data points
here, and more specifically the shaded regions below them, delineate the combinations of
temperature and concentration for which the simulations formed solid solutions.
First examining the case where no strength mismatch is employed, i.e., A = 0 in Figure 2.12a, we
observe that homogeneously mixed states are produced at all concentrations, when the
temperature is low enough to prevent diffusional phase separation. The boundary separating the
dual phase and solid solution regions is symmetric about a volume fraction of 0.5, and resembles
the re-entrant miscibility gap that Martin [36] and Enrique and Bellon [135] predicted for
irradiated alloys with a miscibility gap. This behavior is expected, because without a significant
difference in strength, shearing, like irradiation, affects both phases equally.
However, the
limiting case of zero phase strength mismatch is not one often occurring in experimental alloys,
and none of the present experiments are comparable to this simulated condition.
1.5 - a.
=0
1.5
bA
=
0.3
dual phase
TT1.0-
TH 1.0
0
0
solid solution
0.2
0.4
0.6
0.2
0.8
0.6
0.4
1.5 - C.
A=0.4
1.5
d.
A=0.7
W50 Hf50
+
1.0
T1.0
TH
W
W5Nb
0.2
0.6
0.4
C
0
WZr
TH
0.5
0.8
C
C
0.8
0.5
0.2
0.4
0Ni
0.6
0.8
C
Figure 2.12 - Dynamical phase diagrams for systems studied as a function of temperature
and composition. The regions below the lines correspond to the temperatures at which
the various simulations homogenized during the simulated anneals. With increasing
phase strength mismatch A, a two-phase region opens up where certain couples remain
segregated if they start as such. The open circles on the x-axis indicate compositions that
remained dual phase over the range of temperatures studied. Experimental compositions
are placed on these diagrams at their expected locations based on the strength differential
in a fine nanocrystalline structure from Figure 2.7.
Figure 2.12b illustrates the mixing behavior of couples with A = 0.3, which can be reasonably
compared with the W-Cr system, which has a 30% strength mismatch in the fine nanocrystalline
regime (cf. Figure 2.7b). Near the terminal compositions, the data in Figure 2.12b also show the
development of a re-entrant miscibility gap, much as we saw in Figure 2.12a.
However, the
strength mismatch suppresses the ability of the system to mix for some intermediate
compositions between about 40 and 50% A atoms; the open data points show systems that
remained phase separated in a steady-state condition even at low temperatures. The emergence of
a low temperature dual phase region bookended by solid solution regions is encouraging because
most mechanically alloyed transition metal couples exhibit this type of mixing behavior [24]. It
also supports Xu et al.'s hypothesis that the positions of such phase boundaries in a dynamical
phase diagram are partly determined by the mechanical properties of the constituent phases [90].
What is more, it reasonably compares with our observations for the W-Cr system, which is the
most closely comparable to these simulations among our experiments. As shown by the arrow at
the bottom of Figure 2.12b, W5 OCr5 O lies within the region of the map where mixing is expected,
as indeed it is seen to occur in the experiments (cf. Figure 2.3b).
Figures 2.12c and 2.12d expand the discussion to larger phase strength mismatches of A = 0.4
and 0.7, respectively. These values are comparable to that of our W-Nb couple, and the three
couples W-Zr, W-H f, and W-Ni, respectively. The tendency of strain partitioning increases with
A, expanding the range of the dual phase region to a compositional width of about 20% at A
0.4, and to a width of ~50% at A = 0.7. The dual phase region also becomes more asymmetrical
with A, skewing towards the A-lean side of the diagram. These simulations correctly align with
the experimental observations that the W 5oZr5 O, W50 Hfso, and W50Ni5O couples should remain
dual phase during mechanical alloying. According to these simulations, a couple with W 5ONb 5 O's
strength mismatch and volume fraction of W should remain dual phase, which is nominally at
odds with what we found experimentally. However, this apparent discrepancy is explained by
the accumulation of Fe in the as-milled powder, which after 25 hrs of milling consists of 25 at%
Fe (cf. Figure 2.1). The presence of Fe is expected to promote homogenization of the W and Nb
because it decreases the volume fraction of W, thereby shifting the position of the W 5oNb50
couple in Figure 2.12c from c ~ 0.46 to ~ 0.38, bringing it closer to the A-lean solid solution
region.
Dissolution of Fe into both the Nb and W should also promote homogenization by
decreasing A due to solid solution strengthening and softening effects in the W and Nb,
respectively. For example, in the powder milled for 25 hrs containing 25 at% Fe, if the Fe
completely dissolved in equal proportions in nanocrystalline W and Nb, then A would decrease
from 0.4 to -0.3 [113].
When both the change in the W concentration and the expected
decrease in A are accounted for, then the W50Nb 5 O couple lies in the solid solution region of the
dynamical phase diagram in Figure 2.12b, which brings alignment between the experiments and
the model.
2.5. Concluding Remarks
The objective of this research was to clarify the effects of a phase strength mismatch between the
input materials on the steady state chemical mixity during extensive plastic straining of alloys;
some alloy pairs mix during straining and others do not, and the steady-state after large strains
was explored here in several W-transition metal couples treated by high energy ball milling.
Two contrasting sets of behavior were observed: the W-Cr/Nb couples formed homogeneous
solid solutions after 15 hours of milling, whereas the W-Zr/Hf/Ni couples remained dual phase
even after 25 hours of milling. In the latter couples, the mixing kinetics appeared to be
asymmetric in that more W dissolved in the alloying element than alloying element dissolved in
W.
A more in-depth investigation of the evolution in the W5 oCr5 o and W 5 oZr5o couples' hardness
and microstructure demonstrated that the root cause of the two groups' disparate mixing
behaviors was the magnitude of the strength mismatch between the phases.
In the W 5 oCr5 O
couple a comparatively small fractional difference in phase strength encouraged co-deformation
and consequent mixing. That the W and Cr were co-deforming was indirectly evidenced by the
lamellar phase morphology in the as-milled, WsoCr 5 O powders. In contrast, nanocrystalline W
and Zr's large difference in strength led to strain localization in the softer Zr phase and a
consequent lack of deformation-induced mixing.
To further explore the effects of a strength mismatch in the context of a driven alloy framework,
we adapted a kinetic Monte Carlo simulation of mechanical alloying to account for differences in
phase strength in a model system. The simulations were able to reproduce several salient features
of our experimental results, such as the asymmetric mixing kinetics of the W-Zr/Hf/Ni couples
and the particulate morphology of the W regions in the W 50 Zr50 powder.
The simulations also
enabled a more general, parametric study of the effects of composition and processing
parameters on the development of a solid solution.
The dynamical phase diagrams of
mechanically alloyed pairs tend to show re-entrant miscibility at low temperatures, where
diffusion is suppressed and mechanical strain tends to promote mixing.
Phase strength
mismatch, however, works against mechanical mixing, and decreases the degree of re-entrant
miscibility; the trends seen in the dynamical phase diagrams also align with the experimental
results for the various W-TM couples. These dynamical phase diagrams and the emergence of
multi-stability and path-dependent steady states in simulations of couples with a large strength
mismatch highlight the need to appropriately modify the classical driven alloy framework when
describing systems in which the potency of the mixing process is environment dependent.
3. Guidelines for the Microstructure Design of Mechanically Alloyed
Materials
In the preceding chapter, we demonstrated that A, or the fractional difference in the alloying
elements' strengths when they are nanocrystalline, is related to the degree of strain localization
during mechanical alloying.
We also showed that the degree of strain localization in turn
determines the as-milled powder's steady state chemical mixity.
In this chapter, we further
explore the relationships between A, plastic strain localization, and the steady-state chemical
mixity of mechanically alloyed powders through a survey of the grain size strengthening and
mechanical alloying literature. This survey was motivated by the abundance of relevant data in
the open literature: there have been mechanical alloying studies on nearly 100 different metalmetal couples, and the strengths needed to calculate A for most of these couples can be estimated
using results from Hall-Petch studies.
To begin, we summarize the results from mechanical alloying studies on positive heat of mixing
couples in Table 3.1.
Included in Table 3.1 are descriptions of the microstructures that the
different couples developed after long milling times, and based on these mixing behaviors, we
divided the couples into two groups. The couples labeled mechanically immiscible are ones that
remain dual-phase across a wide range of compositions even after long milling times. By
contrast, the couples labeled mechanically miscible are either ones shown to mix completely at
all of the compositions studied, or couples that contain alloying elements with dissimilar crystal
structures and that are therefore dual-phase over a small range of compositions as they transition
between the crystal structures of the two terminal solid solutions.
Table 3.1 - Mechanical alloying behaviors reported for positive heat of mixing metal-metal couples.
Compositions
Couples
Coup
Studied (at%
(A-B)
B)
mechanically
immiscible
Mixing Behavior
Refs.
SAED patterns collected from as-milled powders suggest dual-phase
microstructures at all compositions studied
[136]
______________________________
Ag-Co
40, 80, 94
Ag-Fe
50
Ag-Ni
XRD measurements of the Ni lattice parameter indicate that only the
Ag-95Ni alloy homogenizes
SEM micrographs show W particles in a Ag matrix
XRD indicates that the Al phase can dissolve up to 20 at% Zn
[121,136,141]
Ag-W
Al-Zn
30, 50, 70, 90,
95
60
1, 4, 78
Cd-Zn
16,30,42
XRD measurements revealed that the as-milled powder is still dual-
[145]
Cr-Cu
30, 50, 70
Cu-Mo
1, 7, 70
Cu-Nb
Cu-Ta
Mossbauer spectroscopy indicate Fe nanograins sit dispersed in an
[137-140]
Ag matrix
'__'_phase,
[142]
[143,144]
but that there is enhanced solid solubility
XRD of powders milled in argon reveal that the alloy is still dual-
[146,147]
XRD reveals Bragg peaks due to both Mo and Cu
[148,149]
1, 5, 10, 20, 50
XRD reveals that the alloy is still dual phase but that the FCC Cu
phase can
[150-153]
10, 30, 50, 70,
90
XRD reveals that the alloy remains dual phase after milling for long
times. Some studies claimed the alloy amorphizes during milling but
phase at all compositions tested
dissolve up to 10 at% Nb
[83,154,155]
this is likely due to contamination by the milling atmosphere
Cu-V
30, 50, 70
Cu-W
2, 4, 6, 10, 13,
18, 25, 30, 50,
60, 75
XRD patterns reveal 2 sets of Bragg peaks corresponding to
nanocrystalline W and nanocrystalline Cu
Fe-Mg
5, 10, 15, 20,
80
XRD and Mossbauer spectroscopy show that the Mg can dissolve up
to 5 at% Fe and that up to 15 at% Mg can dissolve in the Fe but that
8
[156]
[82,157-160]
[161-163]
I the alloy is otherwise dual-phase
15, 20, 65, 85, XRD measurements of the lattice parameter show that up to 3 at%
90, 95
I Mg-I ,i I
I Mg can dissolve in the Ti but that the alloy remains dual-phase at
,
_______Mg-Ti
EXAFS and XRD reveal that this alloy is dual-phase when milled in
Ar
I
[164-169]
I
I
I
Ag-Cu
20 30, 40, 50,
60, 70, 80
Ag-Pd
5, 10, 15, 30,
50, 60, 70, 80,
85
10, 25, 60, 75,
90, 100
Co-Cu
most compositions
XRD, FIM, and DSC measurements indicate that the alloy forms a
single-phase FCC solid solution at all compositions. Alloy must be
milled at liauid nitrogen temperatures to suppress phase separation.
XRD indicates that the alloy forms a single phase solid solutionn at
all compositions
XRD, TEM, and atom probe all indicate that Cu-Co form a
metastable FCC solid solution at all compositions, though some
magnetic measurements indicate that the alloy is dual-phase at the
[75,91,106,170,
171]
[172,173]
[80,106,174180]
nanoscale.
mechanically
miscible
Co-Ni
30, 40, 50, 60,
XRD results indicate that this alloy forms single phase solid solution
[181-184]
Cr-Mo
25, 50, 75
Lattice parameter measurements with XRD indicate that the alloy is
[185]
Cr-Ni
60, 80
XRD patterns suggest the formation of a single-phase solid solution
[186]
Cr-W
50
70
chemically homogeneous
XRD and electron microscopy indicate that the alloy mixed
atomically
Chapter 2
Cu-Fe
30, 40, 50, 70,
90
XRD, Mossbauer, and EXAFS show that the alloy forms a single
phase FCC solid sol'n with up to 60 at% Fe dissolved in the Cu, is
dual-phase between between 60 and 80 at% Fe, and forms a single
phase BCC solid solution with up to 20 at% Cu in Fe
[25,118,134,13
8,187,188]
CuNi
10, 30, 50, 60,
Lattice parameter measurements with XRD indicate that the alloy is
[189191]
Fe-V
40, 50, 60
XRD and Mossbauer spectroscopy have shown that the alloy
[192-195]
Mo-W
13, 25, 50, 75,
87
XRD suggests that all compositions homogenize during mechanical
alloying
XRD measurements indicate that the alloy mixes to a chemically
[196,197]
70, 80, 90
Nb-Zr
I
at all compositions
I
40, 45, 50
chemically homogeneous
homogenizes during mechanical alloying
I homogeneous state
[189__91]
[198]
A first approach to explaining the disparate mixing behaviors in Table 3.1 can be made with the
classic Bellon-Averback framework, which ignores strain localization effects. According to this
framework, thermally activated phase separation and shear-induced chemical mixing compete to
Which of these two processes
determine the alloy's steady state chemical mixity [199].
dominates is indicated by the dimensionless quantity e/(Deff/b2 ), where b is the Burgers
vector, Detf is an effective diffusivity that accounts for grain-boundary, short-circuit diffusion,
Since grain boundary diffusion
and t is the average macroscopic plastic strain rate [69].
dominates lattice diffusion over the range of grain sizes and temperatures typically encountered
during mechanical alloying, DeI can be estimated as follows
Deff f=Dgb
(3.1)
where Dgh is the grain boundary diffusivity, L the grain size, and t the grain boundary thickness,
which we approximate as being twice the average of the two alloying elements' Burgers
vectors. The activation energy and pre-factor that are required to calculate Dgb can be estimated
from lattice diffusivity data: the grain boundary diffusivity's activation energy is typically half
that of the lattice diffusivity, while the pre-factors of the lattice and grain boundary diffusivities
are roughly the same [200,201]. According to the classic Bellon-Averback framework, when an
alloy is processed such that t/(Deff/b 2 ) >> 1, the rate of shear-induced chemical mixing is
expected to be greater than that of thermally activated phase separation, and as a result, the alloy
should chemically homogenize even if it would energetically prefer to de-mix [70].
mechanically immiscible
100
I
I I
iCO
Cu-Ag
Ag-Pd
Ni-Cu
I
1010
ICo-Cu
1 IW-Cr
2
a, i/D~
Ui(D,/b2
|
W-Fe
)
4&I
Cr-Cu Cu-Nb
Ni-Ag
Fe-Ag
Cd-Zn
Zn-Al
I
1M5
1
T = 100 *C
i = 104 s-
Cu-W
Mo-Cr
mechanically miscible
Figure 3.1 - ei/(D/b 2 ) of binary alloys processed by high-energy ball milling. All of
the couples are expected to form single phase solid solutions. While experiments show
that the couples colored red do in fact form solid solutions, the couples colored blue
form simple mechanical mixtures.
62
Figure 3.1 shows values of 9/(Deff/b 2 ) for the transition metal couples in Table 3.1 when they
are mechanically alloyed in a SPEX high energy ball mill. The couples in Figure 3.1 were
selected because their interdiffusivity data are available in the open literature. In this figure, 9 is
taken as 104 s4 and the ambient temperature used to calculate Dej is 100 'C, in line with
estimates of the t and temperature rise encountered during ball milling [18,92]. In Figure 3.1,
-
those couples with t/(Deff/b 2 ) >> 1 are all - including the mechanically immiscible ones
expected to homogenize according to the Bellon-Averback framework [24]. Since Figure 3.1
shows that this expectation is not realized in experiments, we conclude that /(Deff/b 2 )
> 1
is a necessary condition for two elements to mechanically alloy, but it is not sufficient.
1.5
A 0.5
1.0
Cu
0
Ag
0.5
0
0.1
0.2
1 2
D-
0.3
0.4
(nM 1 2
)
0
Figure 3.2 - Aggregated Hall-Petch data for pure Cu and Ag. The solid dots indicate the
maximum strength of pure, as-milled Cu and Ag.
In light of this clear discrepancy between the classic Bellon-Averback metric and the
experimental results, we next correlate the mixing behaviors in Table 3.1 with the couples'
respective A values. To calculate A for each of these couples, we first reviewed the mechanical
alloying literature to identify the steady state grain size of the pure metals when they are
mechanically alloyed at room temperature.
Subsequently, we estimated the strength of the
63
metals at this grain size with data from Hall-Petch studies. Figure 3.2, for example, shows the
aggregated Hall-Petch data for pure copper and silver, and the solid dots indicate the expected
strength of the pure, as-milled powders. These strengths were the values used to calculate this
couple's A. For metals that do not have Hall-Petch data at the finest grain sizes, we estimated
the as-milled powder's strength by extrapolating the available grain size strengthening data.
Table 3.2 lists the strengths used to calculate A in the following discussion, and Appendix I
includes the aggregated Hall-Petch data for each of the metals in this Table.
Table 3.2 - Steady state grain sizes of pure metals during high energy ball milling at
room temperature and estimated strength of the pure, as-milled powders from their grain
size strengthening data. Grain sizes were either taken from 121,22,2021 or estimated
using the trends reported in those References.
Element
Ag
Al
Au
Be
Cd
Co
Cr
Cu
Fe
Mg
Mo
Nb
Ni
Pd
Ta
Ti
V
W
Zn
Zr
Grain Size
(nm)
25
25
17
11
30
14
9
21
10
39
9
9
14
8
7
14
8
7
25
13
Strength
(GPa)
0.4
0.6
0.7
5.3
0.08
1.7
5.3
0.8
2.9
0.3
6.2
4
2.3
1
5
1.8
3.8
7.3
0.2
1.8
Figure 3.3 shows values of A for couples with t/(Deff/b2 ) >> I when they are mechanically
alloyed. Here, the mechanically miscible and immiscible couples separate into two regions that
overlap only slightly: couples with A less than 0.6 are all mechanically miscible, those with A
greater than 0.75 are mechanically immiscible, while in the range 0.6 < A < 0.75, there are both
64
mechanically miscible and immiscible couples. This Figure demonstrates that A and /(Deff/
b 2 ) can be used together to identify a couple's mixing behavior.
mechanically immiscible
Mb-Cu
Fe-Ag
,u
0511
)
0.
T1V-Fe V-Ag
Ni-Co
W-Mo
Mo-Cr
Cu-Cr
i
I M o-Cu
W-Ag
Ni-g
1.0
Zr-Nb
Cu-Co Pd-Ag
Cu-Ag Ni-Cr Ni-Cu
mechanically miscible
Figure 3.3 - A values for various metal-metal couples whose mixing behaviors have
been studied in detail.
In order to facilitate the microstructure design of mechanically alloyed materials, we calculated
A for all of the binary combinations of the metals listed in Table 3.2 and aggregated these A
values in Figure 3.4.
Each square in Figure 3.4 corresponds to a specific couple and the
square's color indicates whether that couple is mechanically miscible (A < 0.6), immiscible (A >
0.75), or indeterminate (0.6 < A < 0.75).
With this table, it is possible to predict the mixing
behaviors of couples that have yet to be studied.
65
> ZI--mom
ON M<«<Q..O-NZW
W
Mo
Cr
Be
Ta
Nb
V
Fe
Ni
Zr
Ti
Co
Pd
Cu
Au
Ag
Mg
Zn
Cd
UA < 0.6 (mech.
__0.75<
miscible)
0.6 < A < 0.75
A (mech. immiscible)
Figure 3.4 - A values for all metals whose grain size strengthening behavior has been
studied. The red and blue squares indicate couples expected to be either mechanically
miscible or immiscible, respectively. The grey squares indicate couples that could
exhibit either behavior.
Returning our attention to Figure 3.3, we can use results from continuum plasticity to explain
why the transition between the mechanically miscible and immiscible couples occurs at A's
between 0.6 and 0.75. Support for using continuum plasticity to describe the micromechanics
of plastic deformation in a mechanically alloyed material is provided by the nanoindentation
experiments described in the previous chapter. These tests showed that the hardness of the asmilled W5 oZr5o powder was nearly identical to that of the as-milled Zr powder after long milling
times, despite the fact that the alloy powder contained nearly 50 vol% tungsten in the form of 10
nm diameter dispersoids.
Such a complete lack of dispersion-strengthening, while initially
surprising because it departs from the behavior of traditional, microcrystalline materials, is
actually consistent with the theorems of limit analysis in continuum plasticity and their
prediction of the limit load for a composite material featuring isolated rigid particles in an
elastic-perfectly plastic matrix.
These W-Zr powders - and possibly other powders of
mechanically immiscible couples prepared by high energy ball milling - might behave like such
idealized particulate composites for three main reasons.
First, dislocations cannot accumulate
in the nanoscale grains of the matrix so that the matrix exhibits minimal work-hardening and is
66
therefore nearly elastic-perfectly plastic. Second, much higher stresses are required to nucleate
and propagate dislocations in the W nanoparticles than in the Zr matrix so that the particles are
effectively rigid. Third, and most importantly, the length of the dislocations in the matrix and
the distance that they travel is limited by the grain size of the matrix. This is why the matrix
behaves like a plastic continuum even at the nanoscale.
In materials with A smaller than that of W-Zr, the second justification listed above can break
down and the particles may deform along with matrix. In this case, the nanocomposite can still
be described using continuum plasticity, but instead of approximating the particles as rigid, they
can be modeled as elastic-perfectly plastic. Such dual-phase particulate composites in which
both the dispersoid and the matrix are elastic-perfectly plastic have been studied in detail by
Bao et al. using finite element simulations, and their results can help explain the trends in
Figure 3.3 [203]. These investigators showed that the plastic strain is uniform throughout the
composite regardless of the volume fraction of the hard phase when A is less than 0.5, that the
strain starts to localize in the softer phase when A is greater than 0.5, and that the particles stop
deforming altogether when A is larger than 0.6. Comparing these results with Figure 3.3, we
therefore speculate that the transition from mechanically miscible to immiscible behavior
starting at a A of roughly 0.6 can be explained by modeling mechanically alloyed materials as
dual-phase elastic-perfectly plastic particulate composites.
The survey conducted in this chapter showed that predicting the mixing behavior of a given
binary alloy requires knowledge of both A and /(Deff/b 2 ).
In light of this, we aggregated the
data needed to calculate A for most metal-metal couples into a heat map that can help guide
alloying decisions during the microstructure design of mechanically alloyed materials.
In
addition, we explained certain features of this map with the help of continuum plasticity results.
67
4. Powder-Route Synthesis and Mechanical Testing of Ultrafine Grain
Tungsten Alloys
As mentioned in the Introduction, ultrafine grain tungsten's high density, compressive strength,
and propensity for shear banding make it an attractive material for penetration applications, but
the amount of available data supporting its unique mechanical properties remains limited due to
processing constraints [204,205]. One major constraint has been the limited dimensions of W
specimens whose grain sizes are refined by severe plastic deformation techniques such as wire
drawing and high pressure torsion [99,206-209]. For example, Wei and coworkers used high
pressure torsion to prepare a W specimen whose grain size was refined to about 170 nm, but this
technique is limited to specimen geometries of -1
mm thickness and ~10 mm diameter
[209,210], while much higher aspect ratio specimens are required for traditional ballistic testing
[211]. Furthermore, severe plastic deformation techniques capable of yielding larger specimens
(e.g., cold rolling and equal channel angular extrusion) have generally produced W specimens
with coarser ultimate grain sizes (>500 nm) [208,212,213]. It is thus of interest to synthesize
ultrafine grain W specimens using more readily scalable methods, for example based on powder
processing.
Previous efforts to synthesize ultrafine grain W articles using powder processing have generally
found that pressure-assisted sintering and alloying are necessary for achieving high relative
densities without grain growth [208,214-221]. Hot isostatic pressing, for example, was used to
consolidate 50 nm W particles to >95% relative density between 1093 and 1193 K [222].
Because these temperatures are below the grain growth onset temperature of unalloyed tungsten
(1273-1373 K), grain growth was suppressed, and the compacts retained grain sizes as small as
150 nm [223].
Attempts to replicate these results with other pressure-assisted sintering
techniques such as field assisted sintering (FAS) used lower stresses: the hot isostatic pressing
study used an isostatic pressure of I GPa, whereas the maximum uniaxial stress reported in FAS
studies is 266 MPa [208,218-221]. Consequently, these FAS studies generally required higher
soak temperatures (>1273 K) or longer hold times to achieve similar relative densities. Despite
FAS's fast ramp rates, the higher thermal excursion led to coarse (>1 pm) grains and
68
commensurately degraded mechanical properties. Hence, pressure-assisted sintering and rapid
ramp rates, although beneficial, cannot guarantee low porosity and ultrafine grains.
In addition to merely increasing consolidation pressure and thermal excursion, it is also
desirable to consider W alloys containing elements that accelerate densification at lower
temperatures and/or retard grain growth, thereby decreasing the necessary soak temperature and
allowing longer hold times at higher temperatures. This, in turn, can reduce the need for very
high consolidation pressures. Accordingly, this is the approach that we took in this chapter, in
which we describe a specific nanocrystalline, W-based alloy powder (W-7Cr-9Fe, at%) that can
consolidate to high relative densities without excessive grain growth during FAS. Because of
their relatively small fractional differences in strength, W, Cr, and Fe mix to a chemically
homogeneous state when mechanically alloyed and then phase separate on heating. Two-phase,
ultrafine grain compacts made from the powder exhibit high hardness and dynamic compressive
strengths, as well as a tendency to shear localize. Examination of the structure and properties of
these materials also provides directions for the improvement of future generations of ultrafine
grain W-based materials.
4.1. Materials and Methods
4.1.1.
Powder Processing and Consolidation
Nanocrystalline powder with a W to Cr atomic ratio of 10:1 was prepared by milling the
appropriate ratio of feedstock powders (99.95% W, -200+325 mesh; 99+% Cr, -325 mesh) in a
SPEX 8000 high energy ball mill. For comparison purposes, initially unalloyed W was milled
as well. The W and W-Cr powders were milled for up to 20 hours in a hardened steel vial with
steel media and a ball-to-powder ratio of 5:2 (20 g of powder). In order to prevent oxidation,
milling was conducted in a glovebox kept under an ultra-high purity argon atmosphere. The
amount of Fe pickup in the powder due to abrasion of the vial and media was measured using
energy dispersive spectroscopy (EDS) in a JEOL 661 OLV scanning electron microscope (SEM)
operated at 20 kV.
Prior to compaction, the as-milled powder's homogeneity and microstructure were assessed
using X-ray diffraction (XRD) and transmission electron microscopy (TEM). The grain size
and lattice parameter were calculated from XRD profiles collected using Cu-Ka radiation in a
Panalytical X'Pert Pro diffractometer.
The grain size was measured from the XRD pattern
69
using a Williamson-Hall analysis of the peak broadening after correcting for instrumental
broadening using a NIST LaB6 standard. The Williamson-Hall method was used in the present
work because it has been shown to measure the grain size more accurately than techniques that
do not account for microstrain, i.e. the Scherrer equation, which tend to underestimate the grain
size [224]. The lattice parameter of the BCC W phase was measured using Rietveld refinement.
TEM was used to confirm the XRD grain size. TEM specimens were prepared by mixing the
powder in epoxy, manually grinding a powder-epoxy disk until it was less than 10 tm thick,
and then argon ion polishing the disk to electron transparency in a Fischione 1010 ion mill.
During ion polishing, the specimen was cooled to 183 K using a liquid nitrogen cold finger.
Bright field TEM micrographs were collected in a JEOL 2010F operating at 200 kV. Individual
grains were manually traced and their spherical-equivalent diameters measured.
The milled powders were subsequently consolidated in a Dr. Sinter SPS-515S hot pressing
(FAS) apparatus, using various soak times and temperatures to identify the optimal processing
parameters for minimizing both porosity and grain growth.
Except for samples used
subsequently for micropillar compression and Kolsky bar tests, all of the samples were
consolidated using an 8 mm diameter graphite punch and die set.
The Kolsky bar and
micropillar compression specimens were machined from a larger compact consolidated with a
20 mm punch and die set. Both the 8 and 20 mm compacts were consolidated under a uniaxial
stress of 100 MPa. During consolidation, the temperature was ramped from room temperature
to 843 K (570 'C) in 3 minutes and then from 843 K to the soak temperature at 100 K/min. The
soak temperature was systematically varied from 1373 to 1673 K in increments of 100 K, and
soak times of I and 20 minutes were used at each temperature. During consolidation, the hot
zone was held under a vacuum of at least 0.2 mbar. Following consolidation, the temperature in
the water-cooled consolidation chamber initially decreased at a rate of ~200 K/min, eventually
slowing to <40 K/min after dropping below 1073 K. The compacts were rough ground to
remove any carbide from their surfaces and sectioned using electro discharge machining (EDM)
for microstructural characterization and mechanical testing.
4.1.2. Microstructural Characterization
The porosity, volume fraction of phases present, and mean grain size of the W-rich BCC phase
were quantified in as-compacted samples using standard stereological techniques. A section of
70
each compact was mounted, ground, and polished prior to collecting SEM images for
stereological measurements.
Metallographic preparation concluded with a suspension of
colloidal silica in dilute chromic acid (0.03 M) to enhance grain boundary relief.
The
micrographs used for grain size measurements were taken in secondary electron mode, whereas
those used for volume fraction and porosity measurements were taken in backscatter electron
mode. The volume fraction of intermetallic was manually measured using the point counting
technique described in ASTM standard E562-11 [225]. The porosity was measured following
the image analysis procedure outlined in ASTM E1245-03 [226].
The mean grain size was
measured in accordance with the circular intercept procedure for specimens containing two
phases as described in ASTM standard El 12-12 [227].
To validate the stereological porosity measurements, the compacts' relative densities were also
estimated. Their specific gravities were measured using the Archimedes method in deionized
water. Each sample's specific gravity was measured five times giving a relative uncertainty of
0.5%. The compacts' theoretical densities were calculated by summing the product of each
phase's theoretical density and stereological volume fraction.
4.1.3. Mechanical Testing
Microhardness was measured using a Leco DM-400FT Microhardness Tester with a 1 kg load
and a 15 s hold time. Compact as well as individual phase mechanical properties were measured
by instrumented nanoindentation using a MTS Nanoindenter XP with a diamond Berkovich tip.
The tip's area function was calibrated on a fused silica standard. Indentations were performed
at a nominal strain rate of 0.05 s- to a maximum depth of 1 ptm. The hardness and reduced
modulus were calculated from the load-displacement data using the Oliver-Pharr method [228].
The Young's modulus was then calculated using standard values for the elastic properties of
diamond and the Poisson's ratio of W (vw = 0.28) [229].
Select specimens were subjected to additional small scale mechanical testing. After polishing
the sample's surface, micropillars with diameter and length of 5 and 10 pm, respectively, were
fabricated using the lathe technique in a FEI Nova 600i dual-beam focused ion beam [230].
The micropillars were compressed in the same MTS Nanoindenter XP with a square, 30 x 30
tm flat punch diamond tip. The loading rates in the load-controlled nanoindenter were
prescribed to provide nominal strain rates of ~104 s-1. Engineering stress and strain for each
71
test were calculated from the applied load and cross-head displacement data collected by the
nanoindenter. In addition, the samples were observed post-mortem using an SEM.
High strain rate uniaxial compression experiments were conducted on select samples using a 3/8
inch diameter maraging steel Kolsky bar system. Details of a comparable experimental setup
can be found in Reference [29]. For these experiments, cuboidal samples were cut from the bulk
materials using a wire EDM and polished to a cross sectional geometry of 2.2 x 2.2 mm and
lengths from 1.8-2 mm. Impedance-matched tungsten carbide platens were used to protect the
ends of the bars due to the test specimens' high strengths. In addition, Cu pulse shapers were
used to produce ramped loading conditions in order to ensure stress equilibrium was achieved
within the sample prior to failure. Several specimens were recorded during loading using an
Imacon 200 high speed camera. The specimens were illuminated by a Photogenic Powerlight
2500DR flash, and the images were captured with a 2 pis exposure time at a framing rate of 2.2
pts.
4.2. Powder Characterization
Abrasive wear of the steel vial and media during milling was the source of iron in the present
alloys; milling changed the average stoichiometry of the W 9 oCrio and W powders to
W 84.1 Cr7.1 Fe8 .8 and W 90.5Fe9 .5, as measured by EDS. The two alloys are referred to as W-7Cr9Fe and W-9Fe for simplicity. Previous studies on mechanical alloying of W reported similar
Fe pickup and so this was expected [114]. Here, the addition of Fe modified the equilibrium
phases present at the soak temperatures used. Inspection of the ternary W-Cr-Fe phase diagram
shows that W and W-IOCr lie in a single-phase, BCC solid solution field at temperatures greater
than 1373 K; W-7Cr-9Fe and W-9Fe alloys lie in a two-phase field linking the BCC solid
solution with a pt-phase intermetallic [231].
The intermetallic p-phase precipitated during
consolidation.
XRD patterns of the feedstock W- I OCr powder and the W-7Cr-9Fe powder milled for 10 and
20 hours are shown in Figure 4. 1a. The elemental W and Cr powders diffract differentiable sets
of BCC Bragg peaks. With increasing time milled, the Cr peaks disappear, while the W peaks
broaden due to grain refinement and shift to higher 20 indicating a change in lattice parameter.
The disappearance of the Cr peaks and the change in W's lattice parameter suggest that the W,
Cr, and Fe form a metastable solid solution, in line with previous reports on mechanically
72
alloyed W-Cr and W-Fe couples and as expected based on the map (Figure 3.2) presented in
Chapter 3 [232,233].
Similarly to the W-7Cr-9Fe powder, the W lattice parameter in the
initially pure W powder changes as Fe dissolves into the W lattice.
a.
* tungsten
v chromium
feedstock powder
Cd
milled 10 hrs
milled 20 hrs
*
I
*
I
100
80
60
40
.
Position (020)
b.
60
- W-7Cr-9Fe
o W-9Fe
E
N
''C
40
20
,3.16
3.15
a.
.1
3.13
0
I-
.1
I
*
5
10
*
03.14
15
20
Time Milled (hrs)
Figure 4.1 - a) Set of XRD scans taken from the feedstock and W-7Cr-9Fe powder
milled for 10 and 20 hrs. Note the disappearance of the Cr (110) Bragg peak in the
highlighted region after 10 hrs of milling. This, along with the change in W lattice
parameter, suggests the formation of a solid solution. b) Williamson-Hall and Rietveld
analysis give the W-rich BCC phase's grain size and lattice parameter as a function of
milling time for both alloys.
73
Figure 4. 1b shows the change in the W-rich solid solution lattice parameter and grain size with
time milled for the W-7Cr-9Fe and W-9Fe powders. The evolution in both powders' micro
strain, as measured using the Williamson-Hall method, is in agreement with that previously
reported by Wagner et al. for mechanically milled W, plateauing after 10 hrs of milling at -0.8
% [234]. Both samples' rate of grain size reduction slowed after 10 hrs of milling; however,
their lattice parameters, indicators of the powder's chemical homogeneity, only started to
change appreciably after 10 hrs of milling.
20 hrs of milling was chosen as a suitable
compromise between achieving a terminal grain size, chemically homogenizing the powder, and
avoiding excessive Fe pickup. The mean grain sizes of the 20 hr milled W-7Cr-9Fe and W-9Fe
powders were 17 5 and 15 5 nm, as measured using TEM (Figure 4.2). These values were
validated by the XRD measurements of grain size by the Williamson-Hall method (Figure
4.1b).
The as-milled powders' grain sizes are in line with what has been reported in other
studies of high energy ball milled W (-5 to 15 nm) [10 1,234-237].
b.
Figure 4.2 - Representative TEM micrographs of the as-milled a) W-7Cr-9Fe and b) W9Fe powders illustrating the powders' nanocrystalline grain structure. The inset electron
diffraction patterns feature the uniform rings characteristic of nanocrystalline materials.
74
4.3. Compaction and Compact Microstructure
Punch displacements measured during some typical consolidation runs with both alloys are
shown in Figure 4.3. The curves were collected while ramping from 843 to 1673 K at 100 K/s
under a compaction pressure of 100 MPa.
The onset of significant punch displacement at
around 1173 K indicates that both alloys are beginning to densify, and the densification
accelerates before slowing at ~1448 K where, presumably, full density is being approached.
Although both alloys densify over the same temperature range, the Cr-free alloy appears to
densify more rapidly at lower temperatures than the Cr-bearing alloy.
W-9Fe
W-7Cr-9Fe
--
0.6
-
E
E 0.40,2
/
~0.2
0.0S
1100
I
1200
*
I
1300
*
I
1400
*
I
1500
Temperature (K)
Figure 4.3 - Punch displacement curves measured during the heating ramp-up phase for
the two alloys, under an applied stress of 100 MPa.
The trends in the punch displacement data noted above agree with the stereological porosity
versus soak temperature curves presented in Figure 4.4. As expected, the samples consolidated
at soak temperatures of 1473 K or higher all had less than 2 vol% porosity and so were nearly
full density. In addition, the W-9Fe alloy densified more rapidly at lower temperatures. Each
compact's specific gravity, porosity measured using stereology, and porosity calculated from its
relative density are shown in Table 1. For clarity, the two measures of porosity are presented in
adjacent columns; the agreement is good.
75
-
8
1 min
-W-7Cr-9Fes-
6
a_1
min
W-9Fes-
-
0
0
4
0)
0
u)2
20 min
-W-7Cr-9Fem1- \W-9Feww ------
.
0
1300
1400
1500
1600
Temperature (K)
Figure 4.4 - Stereological porosity after compaction experiments at a variety of soak
temperatures and two soak times, I and 20 minutes.
Although Figure 4.4 shows that the samples compacted at 1373 K for 20 minutes had porosities
equivalent to those of samples consolidated at higher temperatures, we found that they were
relatively friable and not well bonded at interparticle interfaces. In light of this, 1473 K at 1
minute was identified as the combination of time and temperature that minimized the thermal
excursion while still achieving near full relative density and good interparticle bonding.
76
Table 4.1 - Compact properties after densification, including specific gravity, p (relative
uncertainty: 0.5%), porosity measured using stereology (relative uncertainty: 50%), and
porosity calculated from the relative density (relative uncertainty: 20%) for each
compact.
Alloy, Die
Temp.
Time
p
Porosity
100*(]-p/pi)
Diameter
(K ("C))
(min.)
(g/cc)
(%)
(%)
1
17.7
4.5
3.5
20
18.1
0.5
1.1
1
18.1
0.6
1.1
20
18.1
0.3
1.4
1
18.1
1
1.3
20
18.1
0.8
1.4
1
18.1
1
1.4
20
18.1
1.3
1.5
1
16.1
7
8.5
20
17.3
0.9
1.5
1
17.3
0.5
1.8
20
17.3
0.8
1.5
1
17.3
1.1
1.5
20
17.4
0.8
1.2
1
17.5
0.9
0.9
20
17.6
1
0.6
1
17.0
1.7
3.3
1373
1473
W-9Fe,
8 mm
1573
1673
1373
1473
W-7Cr-9Fe,
8 mm
1573
1673
W-7Cr-9Fe,
20 mm
1473
Rapid, low temperature densification comparable to that reported above has been previously
observed in two other studies of ball milled W and W alloys [215,238]. Oda and coworkers ball
milled pure W powder and subsequently FAS consolidated the as-milled powder to near full
density at 1273 K (1000 'C) and 50 MPa for 30 minutes [215]. Oda et al. did not assess the
extent of Fe pickup after milling; however, in an independent W-Fe mechanical alloying study
that used milling equipment similar to Oda et al.'s, Herr and Samwer observed that the Fe
77
pickup increased linearly with milling time and reached -70 at% after 80 hrs of milling
whenever there was less than 70 at% Fe in the starting charge [239]. Thus, after accounting for
the difference in ball to powder ratio used in the two studies, we estimate that there might be as
much as perhaps -20 at% Fe in the powders made by Oda et al. after milling for 100 hrs.
In
addition, Xiang et al. mechanically alloyed a mixture of W, Ni, and Fe (W-7Ni-3Fe wt%)
powders that they consolidated to 95% relative density using the same pressure, 50 MPa, but
holding for only 8 minutes at a higher temperature, 1473 K [238]. The present results are in line
with these other reports, although we achieve higher relative densities than Xiang et al. and use
a significantly shorter soak time than Oda et al.
The p-phase intermetallic precipitated during consolidation and was present in all of the
compacts along with the majority BCC solid solution phase.
EDS was performed on the
samples consolidated at 1673 K for 20 minutes to determine both phases' compositions. In the
W-7Cr-9Fe samples, the intermetallic and BCC phases had respective stoichiometries of
W 4 6Cr1 6 Fe38 and W 92 Cr3Fe 5 , whereas
in the W-9Fe compacts, the same phases had
compositions of W5 oFe5o and Wq 8 Fe2 .
In addition, we performed nanoindentation on the
intermetallic in these samples to measure its hardness, which was determined to be about 17.4
GPa averaging over 8 indents.
a.
b.
BCC
solid sol'n
p-phas
10 pm
10_pm
Figure 4.5 - Backscatter electron micrographs of a) W-7Cr-9Fe and b) W-9Fe compacts
78
consolidated at 1673 K (1400 C) for 20 minutes. These samples had the coarsest
microstructures of all the compacts. The p-phase precipitates in both samples are
generally darker than the BCC solid solution due to the lower W content. The precipitates
are also distributed randomly throughout the BCC solid solution, which itself is
composed of many individual grains. The black dots in both micrographs are residual
pores.
There was a larger volume fraction of the p-phase in the Cr-bearing samples, but both alloys'
compacts had qualitatively similar microstructures: regions of the W-rich, BCC solid solution
phase containing many individual grains were interspersed with intermetallic precipitates as
demonstrated by the micrographs in Figure 4.5. For soak temperatures greater than 1373 K, the
volume fraction of the pt-phase that precipitated during compaction was, within error, equal to
that predicted by the equilibrium phase diagram (as assessed by THERMOCALC software)
given the alloys' stoichiometries (Figure 4.6) [240]. For the samples consolidated at 1373 K,
the intermetallic volume fraction was greater than 10% but could not be more accurately
measured because of difficulties resolving the two phases. The residual porosity, also evident in
the micrographs in Figure 4.5, was located predominantly at triple junctions in the W-rich, BCC
solid solution phase, the intermetallic-BCC phase boundaries, and the centers of larger regions
of intermetallic. The samples consolidated at 1673 K for 20 minutes shown in Figure 5 had the
coarsest microstructures of all of the compacts, and most of the other samples had similar
microstructures, albeit on a finer length-scale.
In the samples consolidated at 1373 K for 1
minute, individual powder particles were separated by pockets of porosity and could be clearly
delineated.
79
W-7Cr-9Fe THERMOCALC
0.20-
CL
t
-
W-7Cr- 9Fe
1 min 0
2min
020 rmin 0-0
0
L-0.15E20Ominmm
W-9Fe
1 mino-E
E
w
W-9Fe THERMOCALC
0.10
1
1400
1500
1600
Temperature (K)
Figure 4.6 - Volume fraction intermetallic predicted by THERMOCALC and measured
using stereology for compacts consolidated at temperatures greater than 1373 K. All of
the predicted and experimental volume fractions are within 3 vol% of each other, which
is reasonable given uncertainties in the global stoichiometry of the powder and the
stereology measurements.
The compacts' grain sizes (D) are plotted against their soak temperatures in Figure 4.7. Even at
the lowest soak temperature and shortest hold time (1373 K for 1 min), the grain size in both
alloys was considerably larger than for the as-milled powder.
The observed onset of grain
growth at temperatures below 1373 K is in agreement with past reports of grain boundary
migration in heavily worked W alloys [99,207].
In a study of warm-drawn, K-doped W wire,
for example, Meieran and Thomas observed grain boundary migration at temperatures as low as
1 73 [99].
In our samples, the grain boundaries are sufficiently mobile by 1673 K that the
grains rapidly coarsen to micron dimensions.
It is also evident from the results in Figure 4.7 that Cr supports a finer grain structure in the W-
7Cr-9Fe samples relative to the W-9Fe samples. Cr appears to slow grain growth most at the
lower soak temperatures.
For example, the W-7Cr-9Fe samples consolidated at 1373 K for 1
and 20 minutes have 50% smaller mean linear intercept grain sizes than the similarly processed
W-9Fe samples, whereas by 1673 K, the W-7Cr-9Fe and W-9Fe samples have effectively the
same grain size. Additionally, one prior study of Cr-doped W reported that a W-30Cr alloy
compact had a -5x smaller grain size than similarly processed pure W compacts after sintering
80
[232]. The Cr can inhibit grain growth in two ways. First, Cr is expected to segregate to grain
boundaries in W and thereby lower the driving force for grain growth as well as the grain
boundary mobility; this is specifically the case at 1373 K [11]. Second, if the p-phase exerts a
pinning force on mobile grain boundaries in the W-rich, BCC phase, the larger volume fraction
of p-phase in the Cr-bearing sample would result in more sluggish grain growth.
20 min
*-W-9Fe
2.0
-'W-7Cr-9Fe
E 1.5
1 min
-
EJ-QW-9Fe
ioW-7Cr-9Fe
(.
0.5
01
-As-milled
n
0
Powder U
I
1500
1600
Temperature (K)
-
300
1 400
S
1700
*
0
1800
Figure 4.7 - Grain sizes of compacts made from both alloys and consolidated at various
soak temperatures and two soak times, I and 20 minutes. Also shown for comparison is the
grain size of the as-milled powder.
From a practical perspective, it is of interest that the grain growth kinetics are sufficiently slow
in the Cr-bearing sample that the powders can be consolidated at 1473 K for I minute to near
full density and still retain ultrafine grains (D ~130 nm).
These samples are therefore singled
out for the micropillar compression and Kolsky bar experiments described later. We include
additional low- and high-magnification SEM micrographs of this material in Figure 4.8 to
illustrate the distribution of the intermetallic, the porosity, and the refined grain structure.
81
Figure 4.8 - a) Low- and b) high-magnification secondary electron micrographs of the
optimized W-7Cr-9Fe compact consolidated using the 20 mm die at 1473 K for 1 min.
The low-magnification micrograph illustrates the distribution of porosity (black regions)
and the p-phase internetallic (darker grey contrast). The high-magnification micrograph
illustrates this sample's ultrafine grain structure (D -130 nm).
4.4. Mechanical Properties
4.4.1. Strengthening Contributions
Consistent with other reports of grain-size strengthening in W and W alloys, the compacts'
microhardnesses conform to a Hall-Petch scaling, as shown in Figure 4.9.
For comparison
purposes, the data collected in this study are plotted alongside microhardness measurements on
nominally pure W compacts fabricated by hot isostatic pressing W nanopowders from
82
Reference [20].
Numerical values for the Hall-Petch slopes are shown in the figure, and the
extrapolation of the trend to infinite grain size is shown at the y-intercept.
The slopes are
similar among the three alloys, and the y-intercepts suggest that the W-7Cr-9Fe and W-9Fe
compacts are respectively about 1.6 and 1.0 GPa harder than a nominally pure W compact,
independently of grain size effects.
4.00
14
Grain Size (prm)
0.44
0.25
1.00
0.16
0 W-7Cr-9Fe
,12
M
E
W-9Fe
W, [20]--
E
)10-,''
3.2
4.'
0.0
3.2 G P ap M1
. I
0.5
I
1.0
1.5
2.0
2.5
plot for compacts made with both alloys, from samples
Figure 4.9 -Hall-Petch
compacted at various times and temperatures to densities in excess of 98%.
Microhardness values from Vashi et al. on nominally pure W compacted to 95% relative
density are also presented for comparison [222]. According to Vashi et al., the hardness
of their W specimens was independent of load between loads of 0.2 and 2 kgf, and the
data shown is the average of the hardnesses measured using loads of 0.2, 0.3 and 2 kgf.
The data point labeled with a star is the hardness of the W-7Cr-9Fe sample consolidated
with the 20 mm die.
One possible explanation for the higher hardness of the Fe- and Cr- bearing alloys is classical
solid solution strengthening of the BCC W-rich phase.
using the Fleischer equation:
83
We estimate solid solution hardening
3/2
1
AH=33
12 G~cl
700
dG
G, d
dG
1
1
2G, dc
(4.1)
3 da
a dc
where the 33/2 prefactor is used to convert shear stress to hardness, Gw is W's shear modulus, G
is the alloy's shear modulus, a is the lattice parameter, and c is the solute concentration [241].
If we assume that there are no solute-solute interactions so that the strengthening effects of Fe
and Cr are additive, then using the solute concentrations given earlier and the material
properties listed in References [44] and [45], we estimate that solid solution strengthening
would increase the hardness in both the W-7Cr-9Fe and W-9Fe compacts by ~20 MPa relative
to a nominally pure W compact. The solid solution strengthening contribution is thus two orders
of magnitude too small to explain the >1 GPa hardening seen in the present alloys. Although
solid solution strengthening effects have been found to be dramatically enhanced in extremely
fine grain nanomaterials [113], the grain sizes in the present alloys are too big to permit such an
explanation here.
A more likely explanation for the high hardnesses of our alloys relative to pure W is the
presence of the hard intermetallic pt-phase.
This intermetallic's hardness (~17 GPa) is much
higher than that of even the hardest nominally pure W compacts from the study of Vashi et al.
in Figure 4.9 (~1 3 GPa). Its presence at volume fractions up to 20% can adequately explain the
alloy hardness; using the model of Gurland and Lee [242] we can estimate the hardening factor
as:
AH = (H, - Hf,)f.m C,.
(4.2)
where H, is the intermetallic's hardness, Hw is the hardness of pure W, fim is the volume
fraction of the intermetallic (equal to 14 and 20% in the W-9Fe and W-7Cr-9Fe alloys,
respectively), and Cim is a contiguity parameter for the intermetallic (defined in Reference [48]
and estimated as CIM z 0.6 based on its volume fraction and the random, homogeneous, and
isotropic microstructure) [243]. Using the y-intercept from Vashi et al.'s data, i.e., Hw = 3.7
GPa, the AH values for the W-7Cr-9Fe and W-9Fe compacts are 1.6 and 1.2 GPa, respectively.
These align with the measured values of 1.6 and 1.0 reasonably well.
84
We conclude that the
alloy compacts are clearly substantially strengthened because of grain size refinement (cf.
Figure 4.9), but with a non-negligible contribution from the presence of the intermetallic.
4.4.2. Micropillar Compression
Micropillar compression tests were used to measure the yield strength and study the
deformation behavior of the ultrafine grain BCC phase. We therefore made efforts to avoid
larger p-phase precipitates and pores when machining the microcompression pillars, but cannot
rule out the possible presence of some p-phase content in them. Engineering stress-strain
curves from several microcompression experiments are shown in Figure 4.10. The Young's
modulus, taken from a linear fit of the elastic region of the stress-strain curve, was ~50% of the
nanoindentation value (~355 GPa). This difference is ascribed to the compliance of the pillar's
base and a non-zero angle (< 1) between the pillar's longitudinal axis and the platen's face
normal [244]. Although micropillar compression experiments are generally not well suited for
accurate measurement of the Young's modulus, the engineering stress and yield strength values
can be reliably measured. The average 0.2% offset yield strength was 5.15 GPa, with apparent
hardening to an ultimate engineering stress of about 6 GPa followed by a plateau in the stressstrain response. The plateau is associated with the development of a single shear band within the
pillar. An example of a shear offset, captured just before failure at an applied stress level of 6.3
GPa, is shown in the inset of Figure 4.10.
-
6
cc
C
4-
U)Shear
Offset
C
0)
2
'5
C
w
0
0.02
0.04
0.06
Engineering Strain
85
0.08
Figure 4. 10 - Some typical engineering stress-strain curves from micropillar compression
tests on pillars preferentially milled from the BCC solid solution phase. Inset shows a
shear offset in a micropillar loaded to 6.3 GPa.
We are not aware of any other reports on the micropillar compression testing of ultrafine grain
W, but our pillars are large (~5x10 pm) compared to the grain size (0.13 prm) and can thus be
compared to bulk compression tests. It is particularly instructive to highlight two differences
between our results and those from quasi-static compression tests on bulk coarse and ultrafine
grain W specimens. First, the pillars' average yield strength of 5.15 GPa is substantially higher
than the 3.1 GPa yield strength exhibited by a high pressure torsion specimen reported by Wei
et al. [209] This increment in strength is most likely due to better alignment of our specimen
with the loading axis, as the high pressure torsion specimen had a similar grain size (170 nm)
and microhardness (11 GPa), and Wei et al. reported issues with specimen misalignment and
buckling during loading [209]. Second, the shear localization observed in our micropillar
compression specimens is consistent with another recent report by Butler et al. of shear
localization during quasi-static compression testing of bulk ultrafine grained WI-Re, (x = 5, 10,
25 at%) compacts [245]. These W-Re compacts were also synthesized by powder processing
and had porosities similar to our Kolsky bar specimens', but had slightly larger grain sizes (200
to 350 nm). Although Butler et al.'s W-Re samples exhibited lower yield strengths than ours,
their post-mortem analysis of the compression
specimens showed evidence of shear
localization.
Apart from the work by Butler et al. described above, W test specimens with grain sizes ranging
from 50 prm to 170 nm were reported to have only deformed by homogeneous plastic
deformation and axial cracking along grain boundaries [209,212,246]; the only other reports of
shear localization in W were from high strain rate tests of ultrafine grain specimens
[208,209,212,213,247].
In such high strain rate tests, the shear localization has been most
commonly attributed to adiabatic heating that causes localized softening on planes of maximum
shear stress. The low strain rates used in both Butler et al.'s and our quasi-static tests are not
consistent with this kind of adiabatic shear localization, and instead argue for a structural origin
of shear softening.
This more closely resembles that seen during quasi-static compression
86
testing of ultrafine grain Fe [248], Ta [249], and Fe-lOCu [250]. In these other materials, shear
localization occurs because grain rotation leads to geometric softening [251,252].
4.4.3. High Strain Rate Deformation
A representative engineering stress versus time curve from a Kolsky bar test conducted at a
strain rate of 600 s-1 is shown in Figure 4.11. Note that engineering strain values are not
reported because these specimens failed at very low strains, which are difficult to measure
accurately with a Kolsky bar system. The specimen was loaded until failure, followed by rapid
unloading. Accompanying the stress-time curve are images collected using high-speed
videography, which serve to illustrate the specimen's brittle mode of failure at 76 pIs. The
average failure stress was 4.14 GPa, which is in rough agreement with the Tabor estimate based
on the measured microhardness value reported earlier (a ~ H/3 = 13.5 / 3 GPa = 4.5 GPa).
4-
3
q
Ca)
2
U)
1
(1
0
20
40
Time (ps)
60
Figure 4.11 - An engineering stress-time curve collected during a Kolsky bar test
conducted at a strain rate of 600 s-1. The test specimen was cut from the W-7Cr-9Fe
87
compact consolidated at 1473 K using the 20 mm die. The accompanying high speed
photographs were taken at the times indicated by the lines. The arrows next to the first
frame indicate the loading direction, and the test specimen's orientation is the same in all
of the photographs.
Coarse-grained W strained at high rates deforms by a combination of homogeneous plastic
deformation and axial cracking [246], and ultrafine grain W has been reported to exhibit
adiabatic shear localization [208,209,212,213,247].
In our samples, the residual pores act as
stress risers and crack nucleation sites, while the brittle intermetallic p-phase lowers the
compact's toughness.
Together, these two microstructural features likely contributed to the
onset of fracture events at high rates. Based on our samples' grain size and the micropillar
compression results on the W-rich BCC phase reported in the previous section, we speculate
that the BCC phase would favor shear localization under both quasi-static and high strain rate
testing.
This is because other ultrafine grain BCC metals that exhibit structural shear
localization during quasi-static compression tests also typically exhibit shear localization in
high strain rate tests [248]. Therefore it is expected that further tuning of the alloy composition
and consolidation schedule to reduce the volume fraction of the intermetallic and the porosity
could permit some tuning of the propensity for shear localization versus cracking.
4.5. Concluding Remarks
Nanocrystalline W-rich alloy (W-9Fe and W-7Cr-9Fe) powders have been synthesized via
mechanical alloying, and the microstructure and mechanical properties of compacts made from
the powder systematically investigated. The main results of this work are as follows:
"
Ultrafine grain W-rich compacts with high relative densities were achieved by suppressing
the rate of grain growth during consolidation, by (1) minimizing the thermal excursion
during consolidation, thereby slowing thermally activated grain growth, and (2) alloying
with Cr, an element expected to reduce grain boundary energy and mobility in W. Dense
compacts with grain sizes as small as 130 nm were synthesized.
" The ultrafine grain compacts' hardnesses were greater than 12 GPa due to grain size
strengthening in the W-rich, BCC phase, and followed the Hall-Petch scaling. A second
significant contribution to their hardnesses (-1-2 GPa) came from the hard intermetallic tphase that precipitated during compaction.
88
*
The ultrafine grain compacts exhibited very high quasi-static and dynamic compressive
failure strengths measured using micropillar compression and Kolsky bar tests, respectively.
During micropillar compression experiments, pillars that were ion-milled out of a compact
began to yield at 5 GPa and eventually failed by shear localization upon loading to 6 GPa.
During Kolsky bar tests on bulk specimens machined out of the same compacts, the samples
failed at an average stress of 4.14 GPa.
89
5. Sub-Scale Ballistic Testing of an Ultrafine Grained Tungsten Alloy
The high-density, ultrafine grain alloys described in the previous chapter possesses a unique set
of mechanical properties that make them very attractive kinetic penetrator materials for rigid
body penetration into concrete and geomaterials. Their high strengths, for instance, suggest that
they should remain elastic at striking velocities where penetrators made from softer materials,
e.g., high strength steels, start to deform plastically [209,253,205,208,254-256,2].
In this
chapter, we evaluate the ballistic performance of these ultrafine grain tungsten alloy using subscale ballistic tests into concrete targets. This sub-scale test method departs from many of the
standard protocols for characterizing penetration performance, which call for penetrators with
large dimensions. For example, the classic Forrestal framework for evaluating the performance
of rigid body penetrators into concrete was originally developed for penetrators with lengths
upwards of 9 cm and diameters of at least 1 cm [257]. Our results demonstrate the potential of
sub-scale ballistic testing as a means of characterizing next-generation kinetic penetrator
materials as well as the potential of this specific tungsten alloy in ballistic applications.
5.1. Experimental Methods
We studied the ballistic performance of two different penetrator materials: a tungsten carbide
cermet (WC-12Co, wt%) and a powder-processed, ultrafine-grained W alloy. A schematic of
the cemented carbide penetrator is shown in Figure 5.1 a. We used these conical nose cemented
carbide rounds to calibrate the penetration equations described below. Quasi-static compression
tests on specimens machined from these cemented carbide rounds gave an average failure stress
of 3.8 GPa, with the samples failing by brittle fracture.
90
a.
10.4 mm
4.0 mm
550
14.2 mm
b.
8.0 mm
4.0 mm
R, 10.0 mm
14.0 mm
Figure 5.1 - Schematics of the a) cemented carbide and b) W-8Cr-4Fe penetrators.
We also prepared sub-scale rounds from an ultrafine-grained W-Cr-Fe alloy whose chemistry
and processing schedule are related to the optimized alloy described in Chapter 4. The material
used in this study was prepared by 6 hours of attrition milling of elemental feedstock powders
of W and Cr (99.95 pct W -100 mesh; 99+ pct Cr, -325 mesh) with an initial stoichiometry of
W-lOCr, at%.
Milling was performed under an Ar atmosphere using 200 g of powder, steel
media, and a ball to powder ratio of 10:1. The final chemistry of the as-milled powder was W8Cr-4Fe, at% as measured by energy dispersive spectroscopy, where the Fe was introduced due
to abrasion of the milling equipment.
Note that this is a different chemistry from that reported
in Chapter 4 and this difference is due to the fact that we used attritor mill, as opposed to a
SPEX mill, to produce larger quantities of powder for these ballistic tests. We consolidated the
as-milled powder using a Dr. Sinter SPS-515S hot press, a graphite punch and die having a
diameter of 24 mm, and the preferred consolidation parameters identified in Chapter 4: a ramp
rate of 100 K/min, a consolidation pressure of 100 MPa, a soak time of 1 min, and a soak
temperature of 1200 'C.
We centerless ground samples electro-discharge machined from the
center of these compacts into ogive nose rounds with the dimensions given in Figure 5.1b.
We mounted in epoxy, cross-sectioned, and polished one of these W-8Cr-4Fe rounds using
standard metallographic techniques, and characterized the microstructure of this cross-sectioned
round using a JEOL 6610LV scanning electron microscope (SEM) operated at 20 kV and
equipped with an energy dispersive spectrometer.
91
We also measured this cross-sectioned
round's Vickers microhardness using a LECO microhardness tester with a load of 50 gf and a
hold time of 15 s. These microstructural investigations revealed that the W-8Cr-4Fe penetrators
had a bimodal grain size distribution: approximately 85 vol% of the penetrator had a grain size
of 200 nm, while the remaining material was coarse grained, with an average grain size
exceeding 10 tm. As a result of their different grain sizes, the coarse- and fine-grained regions
had different mechanical properties, with the fine grained regions having an average Vickers
hardness of 10.8 GPa, more than double the Vickers hardness of the softer, coarse-grained
regions. The coarse- and fine-grained regions also had different chemistries, with the coarsegrained regions containing no solute and the fine grained regions containing Fe and Cr, with an
average stoichiometry of W-IOCr-6Fe as measured by energy dispersive spectroscopy. That
only the fine grained regions contained Fe and Cr supports our claim in Chapter 4 that these
alloying elements are critical for retaining a fine grain size.
This penetrator's average
stereological porosity was 6%, and its density was 16.1 g/cm 3 as measured by the Archimedes
method using high purity water as a reference liquid.
We fired the projectiles from a 5.56 mm diameter powder gun with a 1:7 twist and a 0.5 m long
barrel, and varied the incident velocity between 500 to 1100 m/s by using different amounts of
gun powder. We monitored the incident velocity as well as the pitch and yaw at impact using
flash x-radiography [258].
Based on these measurements, we adjusted the muzzle-to-target
distance between 3.3 and 3.9 m to minimize the pitch and yaw at impact, and only included tests
with angles of incidence less than 4' in our analysis.
We fired all of the shots into targets prepared from the same batch of well-cured concrete. The
concrete had a density of 2.2 g/cm 3 and contained aggregate with a volume-average, circular
equivalent diameter of 2 mm. Cylindrical compression specimens with a 5 cm diameter and an
aspect ratio of 2.5 that were cored from several targets had an average, unconfined compressive
failure strength of 48 MPa. The concrete targets had cross-section dimensions of 20 by 20 cm
and a thickness of 13 cm. The maximum depth of penetration was roughly half the thickness of
the target and there was no scabbing seen on the back face of the target after impact, so these
targets could be approximated as semi-infinite.
The reported depths of penetration are the
average of two measurements from radiographs taken at right angles to one another, which were
always in good agreement.
92
l+g[
]+4R
5.2. Sub-Scale Ballistic Testing into Concrete
Forrestal and coworkers used experiments and theory to develop a framework describing rigid
body penetration into concrete and geomaterials [257,259-270].
Using penetrators with on-
board accelerometers [267,268,270], these researchers showed that the axial force on a
projectile during impact can be described by the following relationships:
4R
(5.la)
z > 4R
(5.1b)
z
F = -cz
F = -7rR
2 (US
+ NpV 2 )
where Eqns 5.1 a and 5.1 b describe the force equations during the cratering and tunneling phases
of impact, respectively, and with z the instantaneous depth of penetration, R the radius of the
penetrator, U the unconfined compressive stress of the concrete target, p the density of the
concrete, and V the instantaneous velocity of the penetrator. The pre-factor c in Eqn 5.1 a is a
constant that depends on the incident velocity, VsK, as follows:
(5.2)
C = wR Sa + mVsNp
4
m
+ 47rR3Np)
The constant N accounts for the shape of the penetrator's nose. For conical-nose penetrators, N
is given by
N = sin(p) 2
(5.3)
where (p is half the nose angle [271], and for ogive-nose penetrators, N is calculated using
N =
(5.4)
81P-1
241p2
where ip = r/2R with r being the ogive radius [257]. Table 1 summarizes the properties of the
cemented carbide and W-8Cr-4Fe penetrators that are necessary for evaluating Eqns 5.1 to 5.4.
The constant S in Eqns 5.la, 5.1b, and 5.2 is a fitting parameter that accounts for the
strengthening of the concrete due to the hydrostatic compressive stress and high strain rates at
the tip of the penetrator. Evaluating the equations of motion using Eqn 5.1a and 5.1b and the
initial condition that V = V, at z = 0 gives the following relationship between the incident
velocity and the depth of penetration
_____
(5.5)P =
2
27rR pN
Sum+NpmVS
3
Sa(m+47R Np)
1
93
which can be fitted to experimental data to calibrate S.
Table 5.1 - Properties of the cemented carbide and tungsten alloy penetrators.
m (g)
N
WC-Co
2.1
0.21
W-8Cr-4Fe, at%
2.3
0.13
Forrestal and coworkers have shown that Eqns 5.1 through 5.5 apply to penetrators with lengths
ranging from 9 to 53 cm and diameters between 1.3 and 8 cm [257,267,268,270]. To test if they
apply to sub-scale penetrators as well, we compared their predictions with the behavior of the
much smaller cemented carbide penetrators.
Because these cemented carbide penetrators are
two orders of magnitude stronger than the concrete targets, it was expected that they would
remain elastic during impact given the incident velocities used in this study. This expectation
was confirmed by radiographs of these cemented carbide rounds embedded in concrete targets,
like those shown in Figure 5.2a, which reveal a lack of plastic deformation (though there is
evidence of fracturing which we discuss later). These radiographs also reveal distinct cratering
and tunneling regions in the wake of the penetrator, with the average depth of the craters being
I cm, or roughly twice the diameter of the penetrator. The morphology of this impact zone is
consistent
with
Forrestal
et
al.'s
previous
reports
of penetration
into
concrete
[257,263,264,268].
In Figure 5.2b, we plotted the cemented carbide penetrators' incident velocities against their
depths of penetration, as well as a best fit to these results using Eqn 5.4.
The agreement
between the fit and the results is quite good, confirming that the Forrestal equations work very
well even with these small-caliber penetrators.
From this fit, we found S= 24, which is twice
that predicted by Forrestal et al. for concrete with a compressive strength of 48 MPa
[257,264,266]. The reason for this discrepancy is the small ratio of the penetrator diameter to
aggregate diameter in our work; the smaller this ratio, the larger S is for a given strength
concrete, as noted by Beth [272] and others [267].
94
b.
a. Y=
cemented carbide shots
-
10
720 m/s
-00
C
Rigid body
penetration, Eqn 5.5
j_
1>
crater
82-
820m~0
1 M C
4-5
-W
910 m/s
~00
0.6
0.8
1.0
1.2
Incident Velocity (km/s)
Figure 5.2 - a) Radiographs of cemented carbide rounds that struck the targets at the
velocities indicated. The crater region is highlighted in the radiograph of the penetrator
that had an incident velocity of 720 m/s. b) Cemented carbide rounds' depths of
penetration as a function of incident velocity. The dashed line is the best fit to the data
using Eqn 5.4, and the grey shaded region indicates the 95% confidence intervals.
In light of these cemented carbide results, we next evaluated the penetration behavior of the W8Cr-4Fe rounds, which still performed well in these ballistic tests despite their processing
defects, e.g., porosity, regions of coarse-grained material, and chemical heterogeneity. Figure
5.3a shows a set of radiographs of the concrete targets containing embedded W-8Cr-4Fe
penetrators, which have dimensions similar to those of the as-received penetrators, excluding
the 620 m/s shot. To test for rigid body behavior, we plotted the W-8Cr-4Fe penetrator's depth
of penetration as a function of incident velocity alongside the depth of penetration predicted by
Eqn 5.5 in Figure 5.3b.
Aside from a slight deviation between the predicted and measured
depths of penetration at the highest striking velocity, which we can ascribe to the larger angle of
incidence of that penetrator at impact (~2.5o), the measured and predicted values agree quite
well, confirming rigid body penetration and attesting to the high strength of this ultrafine
grained alloy.
95
b.
ultrafine grain W shots
10
620 msC-
Rigid body
penetration, Eqn 5.5
4).
5
1070 ms
01
0.6
1 CIncident
0.8
1.0
Velocity (km/s)
1.2
Figure 5.3 - a) Radiographs of W-8Cr-4Fe rounds embedded in the concrete targets. b)
Depth of penetration of the W-8Cr-4Fe penetrators as a function of incident velocity.
The rigid body depth of penetration predicted using Eqn 5.4 is shown as well.
Of more engineering significance is the fact that the W-8Cr-4Fe penetrators appear to be more
tolerant of oblique impact at high velocities than the cemented carbide penetrators.
This is
illustrated by Figures 5.4a and 5.4b which show radiographs of shattered cemented carbide
penetrators and the angle of incidence versus the incident velocity of the different penetrators,
respectively.
In Figure 5.4b, the cemented carbide penetrators that fractured during impact are
indicated by crosses. Figure 5.4b suggests that the cemented carbide rounds are more likely to
fracture than the W-8Cr-4Fe penetrators under equivalent or less severe impact conditions (i.e.,
either smaller angles of incidence or lower incident velocities or both), though the data is
limited and a direct comparison between the cemented carbide and W-8Cr-4Fe penetrators is
complicated by their different nose geometries.
96
a. WC-Co penetrators, V = 820 m/s
b.
* W-8Cr-4Fe
* WC-Co
X shattered WC-Co
3
X
930 m/s
CD
CD
1
1030 m/s
ee
00
0
0.6
1 cm
X
I
I
0.8
1.0
Incident Velocity (km/s)
1.2
Figure 5.4 - a) Radiographs of cemented carbide penetrators that shattered on impact. b)
Incident velocity versus angle of incidence, y, of the W alloy and cemented carbide shots
with the cemented carbide shots that fractured indicated by crosses.
We can use the results from these sub-scale ballistic tests to compare the different penetrator
materials by estimating limit velocities above which these small scale penetrators should
transition from rigid body to eroding behavior. From Eqns 5.1 a and 5.1 b, we can estimate the
forces acting on the rounds during penetration. By normalizing these forces by the penetrator's
cross-sectional area, we can then estimate the nominal stresses that the rounds experience. The
maximum nominal stress that the rounds experience during impact is then given by
Gmax
=
Sm + mVs2 Np
3
(5.6)
m + 47rR Np
Setting Eqn 5.6 equal to the yield strength of the penetrator material and solving for V gives a
rough estimate of the limit velocity, Vmax. Note that this V,,x represents an optimistic estimate
since it assumes perfectly normal incidence; in reality, fracture or plastic flow may occur at
lower velocities due to bending moments generated by oblique impact, for example. With Vnax,
we can then calculate a kinetic energy density, p(Vjax)2 , where p is the density of the penetrator
material. This kinetic energy density can be used as a figure of merit for comparing different
penetrator materials.
97
As an example of how to apply these concepts, we use them to compare our W-8Cr-4Fe
material with high strength steel, the standard material used in concrete penetration. Our
ultrafine grained W-8Cr-4Fe alloy has a dynamic compressive strength of 2.8 GPa as measured
by Kolsky pressure bar experiments, so penetrators made from this alloy with the geometry
shown in Figure 5.1b should start to yield at incident velocities of 2.2 km/s. By contrast, high
strength steel penetrators with the same geometry and a yield strength of 1.5 GPa should start to
yield at much lower incident velocities, around 1.2 km/s. Combined with the ~8 g/cc density of
steel, these limit velocities indicate that penetrators made from our ultrafine grained W-8Cr-4Fe
alloy should be capable of delivering 7 times the kinetic energy of a high strength steel round
before transitioning from rigid body to eroding behavior.
5.3. Concluding Remarks
Sub-scale ballistic tests into concrete have been performed using cemented carbide and ultrafine
grained tungsten alloy penetrators.
We found that the penetration behavior of these small-
caliber rounds was well-described by the Forrestal equations.
After calibrating the fitting
parameter in these equations, we were able to evaluate the performance of the ultrafine grained
tungsten alloy penetrators and quantitatively demonstrate that they essentially behave as a rigid
body penetrators over the range of velocities tested. In addition, this tungsten alloy appears to
be less likely to fracture due to oblique impact at high velocities than the cemented carbide
calibrant penetrators. These results together demonstrate the promise of this particular tungsten
alloy as well as the potential of sub-scale ballistic testing as a tool for rapidly screening novel
ballistic materials.
98
6. Conclusions
High energy ball milling is not a new processing technique; it was developed in the late 1960's
and is currently used to manufacture large quantities of oxide dispersion strengthened
superalloys [17].
Despite this, the process's effects on microstructure are still poorly
understood, so using it to synthesize materials with tailored microstructures remains a trial-anderror endeavor. The same is true for most of the other severe plastic deformation processing
techniques such as high-pressure torsion and equal channel angular pressing. Removing some
of the empiricism associated with these techniques was the main objective of this thesis. A
second, related objective was using this improved understanding of mechanical alloying to
guide the microstructure design of a powder capable of being consolidated into bulk ultrafine
grained parts. The following summary highlights the main contributions of this thesis:
" The process of mechanical alloying has been studied in several tungsten-transition metal
couples in order to develop a better understanding of phase strength effects on shearinduced chemical mixing. One group of binary alloys (W 5 oCr5 o, W 5oNb5 O) is found to
rapidly mix to a chemically homogeneous state, while a second group (W5oNi 5o,
W 5 oHf5 o, W5 oZr5o) is found to remain dual-phase despite prolonged milling.
The two
groups' disparate mixing behaviors are directly linked to strain localization due to
differences in the base alloying elements' relative strengths using nanoindentation
experiments on individual power particles and SEM observations of the pile-up around
these nanoindentations.
These experiments also revealed asymmetric mechanical
mixing in the couples that remained dual-phase, wherein some W dissolved in the
second alloying element while the W remained relatively pure.
" The results from these experiments are incorporated into classical Bellon-Averback type
kinetic Monte Carlo simulation of mechanical alloying so that they better account for
strain localization effects.
With these improved simulations, we reproduce the
asymmetric mixing and channeling behaviors observed during the high energy ball
milling of W 50 Ni50 , W 50 Hf5 0 , and W5 oZr50
strength.
-
couples with large fractional differences in
We also use these simulations to generate dynamical phase diagrams which
99
feature an asymmetric dual-phase region with a width that is directly proportional to the
alloying elements' fractional difference in strength.
Finally, we demonstrate with
simulations of low-temperature mechanical alloying that couples with large fractional
differences in strength should exhibit path-dependent steady state microstructures.
Though such a path dependence has been observed in other dissipative systems, it has
not previously been demonstrated in mechanically alloyed materials.
This result also
runs counter to the conventional wisdom of Martin's rule of corresponding states, which
holds that a driven alloy has a unique steady state chemical mixity under a given set of
processing conditions.
" An analysis is introduced that builds on insights from these mechanical alloying
experiments and simulations and that enables one to predict the microstructures that will
emerge in extensively deformed materials.
This analysis is calibrated using studies
available in the open literature, and takes into account the effects of strain localization as
well as the competition between shear-induced mixing and thermally activated phase
separation. With the output of this analysis, it is straightforward to identify mechanically
immiscible, mechanically miscible, and nanopatterning couples.
"
We describe a nanocrystalline tungsten-based alloy powder that forms a homogeneous
solid solution during high energy ball milling, and explore the consolidation behavior of
this nanocrystalline powder in detail, demonstrating that it can be compacted into dense
ultrafine grained articles under one set of processing conditions.
Using a battery of
characterization techniques, we also show that compacts prepared with this optimized
set of processing parameters exhibit a suite of properties - high strength, specific
gravity, and relative density - that make this alloy ideal for penetration applications.
*
The penetration performance of this material is evaluated with sub-scale ballistic testing
into concrete targets.
Despite defects in the rounds, they still perform favorably,
remaining rigid body at the highest striking velocities, ~1100 km/s.
As the preceding summary illustrates, the topics explored in this thesis run the gamut from
materials science (e.g., the theory of mechanically driven alloys) to materials engineering (e.g.,
the synthesis and testing of a new and improved ballistic material).
Possible avenues for future
research in each of the topics covered in this thesis are summarized below:
100
*
It would be interesting to experimentally verify that there are path dependent steady
state microstructures in mechanically alloyed materials.
The best candidates for
exhibiting this behavior are the mechanically immiscible couples identified in the map in
Chapter 3.
*
The dynamical phase diagrams should be further calibrated with additional mechanical
alloying experiments.
To systematically test the effects of temperature on the steady
state chemical mixity, I have developed jackets capable of maintaining the vial at
temperatures between 77 and 500 K and plan to conduct variable temperature milling
experiments in the future.
It would also be interesting to experimentally identify the
volume fraction at which alloys become "geometrically constrained" to co-deform and
mix. Studying how this volume fraction varies with A could shed light on the length
scales associated with plastic deformation in particulate, nanocomposite materials.
"
With a better understanding of strain localization in nanocomposites, it should be
possible to improve the analysis in Chapter 3. Here one possible research direction will
be to describe plastic deformation in these nanocomposite materials, which have
negligible capacity to work-harden, with load-bounding or slip line field theories.
" The ultrafine grain tungsten compacts described in Chapter 4 possess a suite of very
attractive properties; however, their ductility and, relatedly, toughness should be
improved if large penetrators made from this alloy are to survive high-angle, oblique
impact or the relief stress pulses generated during penetrator launch. It will be important
to improve these properties without sacrificing relative density, specific gravity, or
strength, and one way to go about doing this is to minimize the volume fraction of the
intermetallic.
*
More ballistic testing is needed in order to fully evaluate the effects of obliquity, nose
shape, target material, etc. on the performance of the small-caliber rounds described in
Chapter 5.
101
......
.........
..
.....
Appendix A: Aggregated Hall-Petch Data
Al
Cu
(DMAn
4
4
(DMA~min
3
3
a-
0Omax
0
-- ------
02
2
Omax
1
1
UP
0 .0
0.3
.
a
0.2
0.1
0.2
0.3
0.4
D112 (nm"2)
(nm r)
D-1/
Au
Ni
----------------
4
0.1
0.0
0.4
(DMA min
4
-
Omax
3
3
b 2
02
0~
00max
1
(DA
(D)MA min)
nI
0.0
1
2
0
0.3
0.2
2
D-1
(nM-1
).0
0.4
(D MAm )
0.4
4
11 2
3
3
-
-
Omax
0
0 2
I
(DMA,m n
Omax
---
-- - - - - - - -
-
- - - -
I
1
ni
0.0
0.3
Pd
4
0 2
0.2
D12 (M-1/)
Ag
0
0.1
2
)
0.1
0.1
0.2
0.3
U
0.0
0.4
I
0.1
0.2
0.3
0.4
0.5
0.6
D" 2 (nm-1 2)
D" 2 (nm-1 2
)
----L-------------
1
--
Figure A. 1 - Hall-Petch data for the FCC metals. The horizontal grey line indicates the
102
metal's theoretical strength and the vertical gray line indicates the grain size that the pure
as-milled powders will develop.
103
8 -
I
I
I
I
Cr
I
I
I
I
I
8
iI
0
.max
- 0 Max
6
6
4
0-4
(DMAmi
2
1/2
I-
2.
(DMAmn
0.1
0.4
0.2
0.3
D-1 2 (nm 1 2
0.1
8
0.2
D-1
)
0.0
Nb
0.3
0.4
(nm-1 2
)
00.0
Oh
112:
-V
8
(DMAm)12
(DMAmi)
6
6
0
0-4
4
0
0max
0.1
0.2
12
D-
8
0.3
-
0
0 .0
0.1
0.2
D 1 /2
---
0.3
1
(nm- 2
0.4
Mo
8
m)'2
---
-
- -
-F
Ta
(D
2
0.4
(nm-" 2
--
)
0
0. 0
)
2
------------------- Max-- -- -- -- -- -- -- -- -
0
7 max
-
6
-------
-
6
- -- - - - - -- - - -
A-----
0-
Omax
4
112
(DMA.Mi)1
2
2
o
0.0
/
Al
0.1
0.2
0.3
0.0
0.4
12
D- (nm-')
a
a
3
3
0.1
0.2
a
3
0.3
1 2
D- (nm" 2
)
0
4
Figure A.2 - Hall-Petch data for the BCC metals.
104
0.4
......
.................................
x..
.........
Fe
8
-
6
a.
0,max
2 -(DM
0.1
0.2
0.3
D- 2
12
(nm
112
0.4
)
0
0.0
minY
Figure A.3 (cont.) - Hall-Petch data for the BCC metals.
105
. ..........................
.......
...........
..
.............
I
II
Be ----____-_-.-------- ----
Mg
-
8_
I
aOmax
4
(D MA.mtn))1I2
6
-. 3
0
0
(4'-4
02
-
0
COmax
2
1 -- -
--- ----
- - ------
(DMAmn)1/2
'.r-7---
0
0.0
0.1
0.3
0.2
0
0.4
0.3
0.2
D-1 2 (nm- 12
0.1
).0
)
Ti
Co
4
0.4
)
D" 2 (nm-" 2
4
CY,max
3
-
D
-3
CL
0
C0
0
0max
02
2
1
I
1
1-2
:(DMA minY
(DMA mm)
a
0
0 .0
0.1
0.2
2
a
0.4
0
D.0
0.3
0.2
2
D-" (nm")
0.1
(nm 112
)
D"
a
0.3
1/ 2
0.4
Zr
Zn
4
-
4
(D MAim) 112
3
-3
-
0 1!
0 2
0Omax
--
-
omax
-
0
02
1
0
0.1
0.2
D-1 2
0.3
0.0
0.4
(nm-1 2
Figure A.4 - Hall-Petch data for the HCP metals.
106
. .........
1/
(DMAmi1
A
0.1
0.3
0.2
D"
)
0.0
V
2
(nm-"2)
0.4
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
E.O. Hall, The Deformation and Ageing of Mild Steel: 11 Discussion of Results, Proc.
Phys. Soc. Sect. B. 64 (1951) 747.
Z.C. Cordero, E.L. Huskins, M. Park, S. Livers, M. Frary, B.E. Schuster, et al., PowderRoute Synthesis and Mechanical Testing of Ultrafine Grain Tungsten Alloys, Metall.
Mater. Trans. A. 45 (2014) 3609-3618.
G.E. Dieter, Mechanical Metallurgy, 2nd ed., McGraw-Hill, New York, NY, 1976.
F.A. McClintock, A.S. Argon, Mechanical behavior of materials, McGraw-Hill, New
York, NY, (1966).
V.Y. Gertsman, R. Birringer, On the room-temperature grain growth in nanocrystalline
copper, Scr. Metall. Mater. 30 (1994).
R.M. German, Liquid phase sintering, Springer Science & Business Media, 2013.
R.M. German, Z.A. Munir, Enhanced low-temperature sintering of tungsten, Metall.
Trans. A. 7 (1976) 1873-1877.
M. Park, C.A. Schuh, Accelerated sintering in phase-separating nanostructured alloys,
Nat. Commun. 6 (2015).
J.R. Trelewicz, C.A. Schuh, Grain boundary segregation and thermodynamically stable
binary nanocrystalline alloys, Phys. Rev. B. 79 (2009) 094112.
A.J. Detor, C.A. Schuh, Grain boundary segregation, chemical ordering and stability of
nanocrystalline alloys: Atomistic computer simulations in the Ni-W system, Acta Mater.
55 (2007) 4221-4232.
T. Chookajom, H.A. Murdoch, C.A. Schuh, Design of Stable Nanocrystalline Alloys,
Science. 337 (2012) 951-954.
M. Hillert, B. Sundman, A treatment of the solute drag on moving grain boundaries and
phase interfaces in binary alloys, Acta Metall. 24 (1976) 731-743.
S.A. Humphry-Baker, C.A. Schuh, Suppression of grain growth in nanocrystalline Bi2 Te3
through oxide particle dispersions, J. Appl. Phys. 116 (2014) 173505.
J.S. Benjamin, T.E. Volin, The mechanism of mechanical alloying, Metall. Trans. 5
(1974) 1929-1934.
P.S. Gilman, J.S. Benjamin, Mechanical alloying, Annu. Rev. Mater. Sci. 13 (1983) 279300.
J.S. Benjamin, Fundamentals of mechanical alloying, in: Mater. Sci. Forum, Trans Tech
Pub], 1992: pp. 1-18.
J.S. Benjamin, Dispersion strengthened superalloys by mechanical alloying, Metall.
Trans. 1 (1970) 2943-2951.
D.R. Maurice, T.H. Courtney, The physics of mechanical alloying: A first report, Metall.
Trans. A. 21 (1990) 289-303.
D. Maurice, T.H. Courtney, Modeling of mechanical alloying: Part I. deformation,
coalescence, bdand fragmentation mechanisms, Metall. Mater. Trans. A. 25 (1994) 147158.
T.H. Courtney, D. Maurice, Process modeling of the mechanics of mechanical alloying,
Scr. Mater. 34 (1996) 5-11.
F.A. Mohamed, Y. Xun, Correlations between the minimum grain size produced by
milling and material parameters, Mater. Sci. Eng. A. 354 (2003) 133-139.
107
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
F.A. M ohamed, A dislocation model for the minimum grain size obtainable by milling,
Acta Mater. 51 (2003) 4107-4119.
D.M. Goodrich, M. Atzmon, Microstructural Evolution in Ball-Milled Iron Powder,
Mater. Sci. Forum. 225-227 (1996) 223-228.
C. Suryanarayana, Mechanical alloying and milling, Prog. Mater. Sci. 46 (2001) 1-184.
L.B. Hong, B. Fultz, Two-phase coexistence in Fe-Cu alloys synthesized by ball milling,
Acta Mater. 46 (1998) 2937-2946.
R.B. Schwarz, R.R. Petrich, C.K. Saw, The synthesis of amorphous Ni-Ti alloy powders
by mechanical alloying, J. Non-Cryst. Solids. 76 (1985) 281-302.
W.L. Johnson, Thermodynamic and kinetic aspects of the crystal to glass transformation
in metallic materials, Prog. Mater. Sci. 30 (1986) 81-134.
F. Haider, P. Bellon, G. Martin, Nonequilibrium transitions in driven AB3 compounds on
the fee lattice: A multivariate master-equation approach, Phys. Rev. B. 42 (1990) 82748281.
P. Bellon, G. Martin, Irradiation-induced formation of metastable phases: A masterequation approach, Phys. Rev. B. 38 (1988) 2570-2582.
R. Landauer, Motion out of noisy states, J. Stat. Phys. 53 (1988) 233-248.
R. Landauer, Stability in the dissipative steady state, Phys. Today. 31 (2008) 23-30.
M.S. EI-Eskandarany, K. Aoki, K. Sumiyama, K. Suzuki, Cyclic phase transformations
of mechanically alloyed Co 75Ti 25 powders, Acta Mater. 50 (2002) 1113-1123.
M.S. EI-Eskandarany, A. Inoue, Solid-state crystalline-glassy cyclic phase
transformations of mechanically alloyed Cu 33 Zr6 7 powders, Metall. Mater. Trans. A. 33
(2002) 135-143.
R.S. Nelson, J.A. Hudson, D.J. Mazey, The stability of precipitates in an irradiation
environment, J. Nucl. Mater. 44 (1972) 318-330.
H.J. Frost, K.C. Russell, Particle stability with recoil resolution, Acta Metall. 30 (1982)
953-960.
G. Martin, Phase stability under irradiation: Ballistic effects, Phys. Rev. B. 30 (1984)
1424-1436.
J.W. Cahn, J.E. Hilliard, Spinodal decomposition: A reprise, Acta Metall. 19 (1971) 151161.
H.E. Cook, D. De Fontaine, J. e Hilliard, A model for diffusion on cubic lattices and its
application to the early stages of ordering, Acta Metall. 17 (1969) 765-773.
K.C. Russell, Phase stability under irradiation, Prog. Mater. Sci. 28 (1984) 229-434.
P. Pochet, E. Tominez, L. Chaffron, G. Martin, Order-disorder transformation in Fe-Al
under ball milling, Phys. Rev. B. 52 (1995) 4006-4016. doi:10.1 103/PhysRevB.52.4006.
T. Klassen, U. Herr, R.S. Averback, Ball milling of systems with positive heats of
mixing: Effect of temperature in Ag-Cu, Acta Mater. 45 (1997) 2921-2930.
G. Nicolis, I. Prigogine, Self-organization in nonequilibrium systems, (1977).
S. Banerjee, K. Urban, Kinetics of Order-Disorder Transformation in Alloys under
Electron Irradiation, Phys. Status Solidi A. 81 (1984) 145-162.
S. Banerjee, K. Urban, M. Wilkens, Order-disorder transformation in Ni 4 Mo under
electron irradiation in a high-voltage electron microscope, Acta Metall. 32 (1984) 299311.
108
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
[53]
[54]
[55]
[56]
[57]
[58]
[59]
[60]
[61]
[62]
[63]
[64]
F. Haider, P. Bellon, G. Martin, Nonequilibrium transitions in driven AB3 compounds on
the fcc lattice: A multivariate master-equation approach, Phys. Rev. B. 42 (1990) 82748281.
F. Haider, P. Bellon, N.V. Doan, G. Martin, Stochastic description of compound stability
under irradiation: Temperature, flux and cascade size effects, J. Nucl. Mater. 179-181,
Part 2 (1991) 1023-1025.
P. Bellon, F. Soisson, G. Martin, F. Haider, Stability of driven compounds: stochastic and
deterministic descriptions, Solid State Phenom. 23-24 (1992) 169-179.
S. Katz, J.L. Lebowitz, H. Spohn, Nonequilibrium steady states of stochastic lattice gas
models of fast ionic conductors, J. Stat. Phys. 34 (1984) 497-537.
J.M. Gonzalez-Miranda, P.L. Garido, J. Marro, J.L. Lebowitz, Nonequilibrium phase
diagram of Ising model with competing dynamics, Phys. Rev. Lett. 59 (1987) 1934-1937.
J.S. Wang, K. Binder, J.L. Lebowitz, Computer simulation of driven diffusive systems
with exchanges, J. Stat. Phys. 56 (1989) 783-819.
J.S. Wang, J.L. Lebowitz, Phase transitions and universality in nonequilibrium steady
states of stochastic Ising models, J. Stat. Phys. 51 (1988) 893-906.
P. Bellon, Y. Grandjean, M. Przybylowicz, F. Soisson, G. Martin, Phase evolution under
irradiation: Monte Carlo and mean-field modelings, Nucl. Instrum. Methods Phys. Res.
Sect. B Beam Interact. Mater. At. 102 (1995) 72-76.
E. Salomons, P. Bellon, F. Soisson, G. Martin, Dynamical lattice models for binary alloys
under irradiation: Mean-field solutions and Monte Carlo simulations, Phys. Rev. B. 45
(1992) 4582-4593.
L.B. Hong, B. Fultz, Effects of ballistic atom movements on ordering transitions of
binary alloys, Phys. Rev. B. 51 (1995) 2687-2693.
L. b. Hong, L. Anthony, B. Fultz, B2 and B32 ordering transformations of equiatomic bcc
alloys with ballistic and thermal atom movements, J. Mater. Res. 10 (1995) 126-132.
L.B. Hong, B. Fultz, Phase diagrams of bcc alloys at low temperatures with ballistic atom
movements, Phys. Rev. B. 52 (1995) 6230-6237.
R. A. Enrique, P. Bellon, Phase stability under irradiation in alloys with a positive heat of
mixing: Effective thermodynamics description, Phys. Rev. B. 60 (1999) 14649-14659.
R.A. Enrique, P. Bellon, Effective Interactions Approach to Phase Stability in Alloys
Under Irradiation, in: Symp. J - Multiscale Model. Mater., 1998.
R.A. Enrique, K. Nordlund, R.S. Averback, P. Bellon, Simulations of dynamical
stabilization of Ag-Cu nanocomposites by ion-beam processing, J. Appl. Phys. 93 (2003)
2917-2923.
J. Ye, J. Liu, R.A. Enrique, P. Bellon, Compositional and order patterning in driven
alloys: the role of external-forcing characteristic lengths, Scr. Mater. 49 (2003) 969-975.
R.A. Enrique, P. Bellon, Nonequilibrium fluctuations, effective temperature, and
effective interactions driven by irradiation of alloys, Phys. Rev. B. 70 (2004) 224106.
R.A. Enrique, P. Bellon, Compositional Patterning in Systems Driven by Competing
Dynamics Of Different Length Scale, Phys. Rev. Lett. 84 (2000) 2885-2888.
P. Bellon, R.A. Enrique, Interface stability and self-organization of precipitates under
irradiation, Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. At. 178
(2001) 1-6.
R.A. Enrique, P. Bellon, Compositional patterning in immiscible alloys driven by
irradiation, Phys. Rev. B. 63 (200 1) 134111.
109
[65]
J. Ye, J. Liu, R.A. Enrique, P. Bellon, Compositional and order patterning in driven
alloys: the role of external-forcing characteristic lengths, Scr. Mater. 49 (2003) 969-975.
[66] J. Ye, P. Bellon, Nanoscale patterning of chemical order induced by displacement
cascades in irradiated alloys. 1. A kinetic Monte Carlo study, Phys. Rev. B. 70 (2004)
094104.
[67] S.W. Chee, B. Stumphy, N.Q. Vo, R.S. Averback, P. Bellon, Dynamic self-organization
in Cu alloys under ion irradiation, Acta Mater. 58 (2010) 4088-4099.
[68] B. Stumphy, S.W. Chee, N.Q. Vo, R.S. Averback, P. Bellon, M. Ghafari, Irradiationinduced patterning in dilute Cu-Fe alloys, J. Nucl. Mater. 453 (2014) 66-74.
[69] D. Schwen, M. Wang, R.S. Averback, P. Bellon, Compositional patterning in immiscible
alloys subjected to severe plastic deformation, J. Mater. Res. 28 (2013) 2687-2693.
[70] P. Bellon, R.S. Averback, Nonequilibrium Roughening of Interfaces in Crystals under
Shear: Application to Ball Milling, Phys. Rev. Lett. 74 (1995) 1819-1822.
[71] K. Differt, U. Essmann, H. Mughrabi, Models of particle destruction in fatigued
precipitation-hardened alloys, Phys. Status Solidi A. 104 (1987) 95-106.
[72] J.K. Lee, S.P. Bhat, R. de ]a Veaux, C. Laird, Mechanisms of cyclic softening in
precipitation-hardening alloys-A ball model approach and tests at 78 K, Int. J. Fract. 17
(1981) 121-141.
[73] S. Zghal, M.J. H tch, J.P. Chevalier, R. Twesten, F. Wu, P. Bellon, Electron microscopy
nanoscale characterization of ball-milled Cu-Ag powders. Part I: Solid solution
synthesized by cryo-milling, Acta Mater. 50 (2002) 4695-4709.
[74] F. Wu, P. Bellon, A.J. Melmed, T.A. Lusby, Forced mixing and nanoscale decomposition
in ball-milled Cu-Ag characterized by APFIM, Acta Mater. 49 (2001) 453-461.
[75] F. Delogu, Forced chemical mixing in model immiscible systems under plastic
deformation, J. Appl. Phys. 104 (2008) 073533.
[76] S. Odunuga, Y. Li, P. Krasnochtchekov, P. Bellon, R.S. Averback, Forced Chemical
Mixing in Alloys Driven by Plastic Deformation, Phys. Rev. Lett. 95 (2005) 045901.
[77] Y. Ashkenazy, N.Q. Vo, D. Schwen, R.S. Averback, P. Bellon, Shear induced chemical
mixing in heterogeneous systems, Acta Mater. 60 (2012) 984-993.
[78] N.Q. Vo, R.S. Averback, Y. Ashkenazy, P. Bellon, J. Wang, Forced chemical mixing at
Cu-Nb interfaces under severe plastic deformation, J. Mater. Res. 27 (2012) 1621-1630.
[79] N.Q. Vo, J. Zhou, Y. Ashkenazy, D. Schwen, R.S. Averback, P. Bellon, Atomic Mixing
in Metals Under Shear Deformation, JOM. 65 (2013) 382-389.
[80] M. Baricco, N. Cowlam, L. Schiffini, P.P. Macri, R. Frattini, S. Enzo, Copper-cobalt
f.c.c. metastable phase prepared by mechanical alloying, Philos. Mag. Part B. 68 (1993)
957-966.
[81] F. Delogu, M. Pintoref, S. Enzott, F. Cardellini, V. Contini, A. Montone, et al.,
Mechanical alloying of immiscible elements: Experimental results on Ag-Cu and
Co[sbnd]Cu, Philos. Mag. Part B. 76 (1997) 651-662.
[82] E. Gaffet, C. Louison, M. Harmelin, F. Faudot, Metastable phase transformations induced
by ball-milling in the Cu-W system, Mater. Sci. Eng. A. 134 (1991) 1380-1384.
[83] J. Xu, J.H. He, E. Ma, Effect of milling temperature on mechanical alloying in the
immiscible Cu-Ta system, Metall. Mater. Trans. A. 28 (1997) 1569-1580.
[84] S. Ankem, H. Margolin, A rationalization of stress-strain behavior of two-ductile phase
alloys, Metall. Trans. A. 17 (1986) 2209-2226.
110
[85]
[86]
[87]
[88]
[89]
[90]
[91]
[92]
[93]
[94]
[95]
[96]
[97]
[98]
[99]
[100]
[101]
[102]
[103]
S. Ankem, H. Margolin, C.A. Greene, B.W. Neuberger, P.G. Oberson, Mechanical
properties of alloys consisting of two ductile phases, Prog. Mater. Sci. 51 (2006) 632709.
M.H. Poech, H.F. Fischmeister, Deformation of two-phase materials: a model based on
strain compatibility, Acta Metall. Mater. 40 (1992) 487-494.
K. Cho, J. Gurland, The law of mixtures applied to the plastic deformation of two- phase
alloys of coarse microstructures, Metall. Trans. A. 19 (1988) 2027-2040.
C.W. Sinclair, J.D. Embury, G.C. Weatherly, Basic aspects of the co-deformation of
bcc/fcc materials, Mater. Sci. Eng. A. 272 (1999) 90-98.
M. Atzmon, J. Xu, H.H. Tian, On the coupling between mechanical behavior and phase
stability in mechanically milled alloy powder, J. Metastable Nanocrystalline Mater. 10
(2001)311-316.
J. Xu, G.S. Collins, L.S.J. Peng, M. Atzmon, Deformation-assisted decomposition of
unstable Fe50Cu5O solid solution during low-energy ball milling, Acta Mater. 47 (1999)
1241-1253.
U. Herr, T. Klassen, R.S. Averback, Modeling of the Mechanical Alloying Process in
Binary Systems, MRS Online Proc. Libr. 400 (1995).
R.B. Schwarz, C.C. Koch, Formation of amorphous alloys by the mechanical alloying of
crystalline powders of pure metals and powders of intermetallics, Appl. Phys. Lett. 49
(1986) 146-148.
C. Yuan, R. Fu, F. Zhang, X. Zhang, F. Liu, Microstructure evolution and mechanical
properties of nanocrystalline zirconium processed by surface circulation rolling
treatment, Mater. Sci. Eng. A. 565 (2013) 27-32.
E. Underwood, Quantitative Stereology, Addison-Wesley Publishing Co., Reading, MA,
1970.
G.B. Skinner, H.L. Johnston, Thermal Expansion of Zirconium between 298'K and
16000 K, J. Chem. Phys. 21 (2004) 1383-1384.
P. Duwez, The Allotropic Transformation of Hafnium, J. Appl. Phys. 22 (2004) 11741175.
C.S. Barrett, T.B. Massalski, Structure of metals, 3rd ed., McGraw-Hill, New York, NY,
1966.
L.A. Giannuzzi, F.A. Stevie, eds., Introduction to Focused Ion Beams: Instrumentation,
Theory, Techniques, and Practice, Springer, New York, 2005.
E.S. Meieran, D.A. Thomas, Structure of Drawn and Annealed Tungsten Wire, Trans Met
Soc AIME. 233 (1965) 937-43.
W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic
modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7
(1992) 1564-1583.
A.O. Aning, Z. Wang, T.H. Courtney, Tungsten solution kinetics and amorphization of
nickel in mechanically alloyed Ni-W alloys, Acta Metall. Mater. 41 (1993) 165-174.
G. Cocco, S. Enzo, N.T. Barrett, K.J. Roberts, Structural investigation of the
amorphization reaction by mechanical alloying of the Mo1Ni'o system, J. Common Met.
154 (1989) 177-186.
G. Cocco, S. Enzo, N.T. Barrett, K.J. Roberts, X-ray analysis of changes to the atomic
structure around Ni associated with the interdiffusion and mechanical alloying of pure Ni
and Mo powders, Phys. Rev. B. 45 (1992) 7066-7076.
111
[104] F. Delogu, G. Cocco, The size refinement of Cu crystallites under mechanical processing
conditions: a phenomenological modeling approach, J. Mater. Sci. 42 (2007) 4356-4363.
[105] F. Delogu, G. Cocco, Crystallite size refinement in elemental species under mechanical
processing conditions, Mater. Sci. Eng. A. 422 (2006) 198-204.
[106] F. Delogu, G. Cocco, Kinetics of structural evolution in immiscible Ag-Cu and Co-Cu
systems under mechanical processing conditions, Mater. Sci. Eng. A. 402 (2005) 208-
214.
[107] R. BrOning, K. Samwer, C. Kuhrt, L. Schultz, The mixing of iron and cobalt during
mechanical alloying, J. Appl. Phys. 72 (1992) 2978.
[108] M. Wang, R.S. Averback, P. Bellon, S. Dillon, Chemical mixing and self-organization of
Nb precipitates in Cu during severe plastic deformation, Acta Mater. 62 (2014) 276-285.
[109] E.H. Ekiz, T.G. Lach, R.S. Averback, N.A. Mara, I.J. Beyerlein, M. Pouryazdan, et al.,
Microstructural evolution of nanolayered Cu-Nb composites subjected to high-pressure
torsion, Acta Mater. 72 (2014) 178-191.
[110] E. Cerreta, C.A. Yablinsky, G.T. Gray 111, S.C. Vogel, D.W. Brown, The influence of
grain size and texture on the mechanical response of high purity hafnium, Mater. Sci.
Eng. A. 456 (2007) 243-251.
[111] G.D. Hughes, S.D. Smith, C.S. Pande, H.R. Johnson, R.W. Armstrong, Hall-Petch
strengthening for the microhardness of twelve nanometer grain diameter electrodeposited
nickel, Scr. Metall. 20 (1986) 93-97.
[112] Z.C. Szkopiak, The Hall-Petch parameters of niobium determined by the grain size and
extrapolation methods, Mater. Sci. Eng. 9 (1972) 7-13.
[113] T.J. Rupert, J.C. Trenkle, C.A. Schuh, Enhanced solid solution effects on the strength of
nanocrystalline alloys, Acta Mater. 59 (2011) 1619-1631.
[114] T.H. Courtney, Z. Wang, Grinding media wear during mechanical alloying of Ni-W
alloys in a SPEX mill, Scr. Metall. Mater. 27 (1992) 777-782.
[115] P. Bellon, R.S. Averback, Preface to viewpoint set on: materials under driving forces,
Scr. Mater. 49 (2003) 921-925.
[116] A. Da Pozzo, S. Palmas, A. Vacca, F. Delogu, On the role of mechanical properties in the
early stages of the mechanical alloying of Ag5oCuso powder mixtures, Scr. Mater. 67
(2012) 104-107.
[117] P.P. Macri, P. Rose, R. Frattini, S. Enzo, G. Principi, W.X. Hu, et al., A study of
Cu50Fe5O produced by mechanical alloying and its thermal treatment, J. Appl. Phys. 76
(1994) 4061.
[118] J. Eckert, J.C. Holzer, C.E. Krill, W.L. Johnson, Mechanically driven alloying and grain
size changes in nanocrystalline Fe-Cu powders, J. Appl. Phys. 73 (1993) 2794.
[119] E. Ma, M. Atzmon, F.E. Pinkerton, Thermodynamic and magnetic properties of
metastable FeCuIoo-, solid solutions formed by mechanical alloying, J. Appl. Phys. 74
(1993)955-962.
[120] C.C. Koch, O.B. Cavin, C.G. McKamey, J.O. Scarbrough, Preparation of "amorphous"
Ni60 Nb40 by mechanical alloying, Appl. Phys. Lett. 43 (1983) 1017-1019.
[121] J. Xu, U. Herr, T. Klassen, R.S. Averback, Formation of supersaturated solid solutions in
the immiscible Ni-Ag system by mechanical alloying, J. Appl. Phys. 79 (1996) 39353945.
112
[122] J. Zhou, R.S. Averback, P. Bellon, Stability and amorphization of Cu-Nb interfaces
during severe plastic deformation: Molecular dynamics simulations of simple shear, Acta
Mater. 73 (2014) 116-127.
[123] D. Wu, J. Zhang, J.C. Huang, H. Bei, T.G. Nieh, Grain-boundary strengthening in
nanocrystalline chromium and the Hall-Petch coefficient of body-centered cubic metals,
Scr. Mater. 68 (2013) 118-121.
[124] F.R. De Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, A.K. Niessen, Cohesion in
Metals: Transition Metal Alloys. Vol. 1, Elsevier Sci. Publ. B V 1988. (1988) 758.
[125] P. Gordon, Principles of phase diagrams in materials systems, Krieger, 1983.
[126] M. Athenes, P. Bellon, G. Martin, Effects of atomic mobilities on phase separation
kinetics: a Monte-Carlo study, Acta Mater. 48 (2000) 2675-2688.
[127] J. Cowley, Short- and Long-Range Order Parameters in Disordered Solid Solutions, Phys.
Rev. 120 (1960) 1648-1657.
[128] F. Wu, D. Isheim, P. Bellon, D.N. Seidman, Nanocomposites stabilized by elevatedtemperature ball milling of Ag 5oCu5 o powders: An atom probe tomographic study, Acta
Mater. 54 (2006) 2605-2613.
[129] S. Zghal, R. Twesten, F. Wu, P. Bellon, Electron microscopy nanoscale characterization
of ball milled Cu-Ag powders. Part II: Nanocomposites synthesized by elevated
temperature milling or annealing, Acta Mater. 50 (2002) 4711-4726.
[130] M.C. Yang, F. Ye, X.C. Sun, X.K. Sun, W.D. Wei, Study on microhardness of bulk
nanocrystalline copper, Nanostructured Mater. 9 (1997) 481-484.
[131] X. Sun, R. Reglero, X. Sun, M.J. Yacaman, Microhardness of bulk and higher density
nanocrystalline copper obtained by hot compaction, Mater. Chem. Phys. 63 (2000) 8287.
[132] D. Jang, M. Atzmon, Grain-size dependence of plastic deformation in nanocrystalline Fe,
J. Appl. Phys. 93 (2003) 9282-9286.
[133] T.R. Malow, C.C. Koch, Mechanical properties, ductility, and grain size of
nanocrystalline iron produced by mechanical attrition, Metall. Mater. Trans. A. 29 (1998)
2285-2295.
[134] P.J. Schilling, J.H. He, R.C. Tittsworth, E. Ma, Two-phase coexistence region in
mechanically alloyed Cu-Fe: an X-ray absorption near-edge structure study, Acta Mater.
47 (1999) 2525-2537.
[135] R. A. Enrique, P. Bellon, Phase stability under irradiation in alloys with a positive heat of
mixing: Effective thermodynamics description, Phys. Rev. B. 60 (1999) 14649-14659.
[136] D. Bonyuet, J. Ochoa, G. Gonz6'lez, Mechanical Alloying in the Immiscible Systems AgM (M = Fe, Co, Ni), J. Metastable Nanocrystalline Mater. 20-21 (2004) 225-230.
[137] M. Angiolini, A. Deriu, F. Malizia, G. Mazzone, A. Montone, F. Ronconi, et al.,
Structural Refinement of Ag-Fe Blends during High Energy Ball Milling, Mater. Sci.
Forum. 269-272 (1998) 397-402.
[138] E. Ma, J.-H. He, P.J. Schilling, Mechanical alloying of immiscible elements: Ag-Fe
contrasted with Cu-Fe, Phys. Rev. B. 55 (1997) 5542-5545.
[139] J. Kuyama, H. Inui, S. Imaoka, S. Nasu, K.N. Ishihara, P.H. Shingu, Nanometer-Sized
Crystals Formed by the Mechanical Alloying in the Ag-Fe System, Jpn. J. Appl. Phys. 30
(1991) L854-L856.
113
[140] M. Angiolini, M. Krasnowski, G. Mazzone, A. Montone, M. Urchulutegui, M. Vittori
Antisari, Electron Microscopy Characterization of Cu-Fe and Ag-Fe Alloys Obtained by
Plastic Deformation, Mater. Sci. Forum. 195 (1995) 13-18.
[141] S. Zghal, P. Bhattacharya, R. Twesten, F. Wu, P. Bellon, Structural and Chemical
Characterization of Cu-Ag and Ni-Ag Nanocomposites Synthesized by High-Energy Ball
Milling, Mater. Sci. Forum. 386-388 (2002) 165-174.
[142] F.A. da Costa, A.G.P. da Silva, F. Ambrozio Filho, U.U. Gomes, Solid state sintering of a
W-25 wt% Ag powder prepared by high energy milling, Int. J. Refract. Met. Hard Mater.
26(2008)318-323.
[143] Y. Xun, F.A. Mohamed, E.J. Lavernia, Synthesis of nanocrystalline Zn-22 Pct Al using
cryomilling, Metall. Mater. Trans. A. 35 (2004) 573-58 1.
[144] M. Iqbal, M.A. Shaikh, J.I. Akhter, M. Ahmad, M. Akhtar, M.J. Moughal, Synthesis by
ball milling and characterization of Al-Zn alloys, J. Mater. Sci. 39 (2004) 4255-4262.
[145] D.K. Mukhopadhyay, C. Suryanarayana, F.H. Froes, Extended solid solutions in Cd-Zn
powders by mechanical alloying, Scr. Metall. Mater. 30 (1994) 133-137.
[146] Y. Ogino, S. Murayama, T. Yamasaki, Influence of milling atmosphere on amorphization
of chromium and Cr-Cu powders by ball milling, J. Common Met. 168 (1991) 221-235.
[147] D.G. Morris, M.A. Morris, Rapid solidification and mechanical alloying techniques
-til I oys, M ater. Sci. Eng. A. 104
applied to Cu
[148] C.-H. Lee, S.-H. Lee, Nanocrystalline Formation in Immiscible Cu-Mo System Subjected
to Mechanical Alloying, J. Nanosci. Nanotechnol. 7 (2007) 4057-4060.
[149] S. Xi, K. Zuo, X. Li, G. Ran, J. Zhou, Study on the solid solubility extension of Mo in Cu
by mechanical alloying Cu with amorphous Cr(Mo), Acta Mater. 56 (2008) 6050-6060.
[150] A. Benghalem, D.G. Morris, Structural evolution during intense ball milling of copperniobium mixtures, Scr. Metall. Mater. 27 (1992) 739-744.
[151] A. Benghalem, D.G. Morris, Microstructure and mechanical properties of concentrated
copper-niobium alloys prepared by mechanical alloying, Mater. Sci. Eng. A. 161 (1993)
255-266.
[152] E. Botcharova, M. Heilmaier, J. Freudenberger, G. Drew, D. Kudashow, U. Martin, et al.,
Supersaturated solid solution of niobium in copper by mechanical alloying, J. Alloys
Compd. 351 (2003) 119-125.
[153] E. Botcharova, J. Freudenberger, L. Schultz, Mechanical alloying of copper with niobium
and molybdenum, J. Mater. Sci. 39 (2004) 5287-5290.
[154] T. Venugopal, K. Prasad Rao, B.S. Murty, Mechanical and electrical properties of Cu-Ta
nanocomposites prepared by high-energy ball milling, Acta Mater. 55 (2007) 4439-4445.
[155] K.A. Darling, A.J. Roberts, Y. Mishin, S.N. Mathaudhu, L.J. Kecskes, Grain size
stabilization of nanocrystalline copper at high temperatures by alloying with tantalum, J.
Alloys Compd. 573 (2013) 142-150.
[156] M. Baricco, L. Battezzati, S. Enzo, I. Soletta, G. Cocco, X-Ray absorption spectroscopy
and diffraction study of miscible and immiscible binary metallic systems prepared by ball
milling, Spectrochim. Acta Part Mol. Spectrosc. 49 (1993) 1331-1344.
[157] T. Aboud, B.-Z. Weiss, R. Chaim, Mechanical alloying of the immiscible system W-Cu,
Nanostructured Mater. 6 (1995) 405-408.
[158] S.N. Alam, Synthesis and characterization of W-Cu nanocomposites developed by
mechanical alloying, Mater. Sci. Eng. A. 433 (2006) 161-168.
114
[159] M.H. Maneshian, A. Simchi, Z.R. Hesabi, Structural changes during synthesizing of
nanostructured W-20 wt% Cu composite powder by mechanical alloying, Mater. Sci.
Eng. A. 445-446 (2007) 86-93.
[160] M.A. Atwater, D. Roy, K.A. Darling, B.G. Butler, R.O. Scattergood, C.C. Koch, The
thermal stability of nanocrystalline copper cryogenically milled with tungsten, Mater. Sci.
Eng. A. 558 (2012) 226-233.
[161] A. Hightower, B. Fultz, R.C. Bowman Jr, Mechanical alloying of Fe and Mg, J. Alloys
Compd. 252 (1997) 238-244.
[162] Y. Yoneda, H. Abe, T. Ohshima, H. Uchida, Phase transformation of Mg-Fe alloys, J.
Appl. Phys. 107 (2010) 093505.
[163] E.P. Yelsukov, A.L. Ulyanov, G.A. Dorofeev, Comparative analysis of mechanisms and
kinetics of mechanical alloying in Fe-Al and Fe-Si systems, Acta Mater. 52 (2004)
4251-4257.
[164] C. Suryanarayana, F.H. Froes, Nanocrystalline titanium-magnesium alloys through
mechanical alloying, J. Mater. Res. 5 (1990) 1880-1886.
[165] E. Zhou, C. Suryanarayana, F.H. Froes, Effect of premilling elemental powders on solid
solubility extension of magnesium in titanium by mechanical alloying, Mater. Lett. 23
(1995) 27-31.
[166] G. Liang, R. Schulz, Synthesis of Mg-Ti alloy by mechanical alloying, J. Mater. Sci. 38
(2003) 1179-1184.
[167] S. Rousselot, M.-P. Bichat, D. Guay, L. Rou6, Structural and Electrochemical Hydriding
Characteristics of Mg-Ti-Based Alloys Prepared by High Energy Ballmilling, J.
Electrochem. Soc. 156 (2009) A967-A973.
[168] M. Phasha, K. Maweja, C. Babst, Mechanical alloying by ball milling of Ti and Mg
elemental powders: Operation condition considerations, J. Alloys Compd. 492 (2010)
201-207.
[169] H. Zhou, L. Hu, H. Sun, X. Chen, Synthesis of nanocrystalline Mg-based Mg-Ti
composite powders by mechanical milling, Mater. Charact. 106 (2015) 44-51.
[170] K. Uenishi, K.F. Kobayashi, K.N. Ishihara, P.H. Shingu, Formation of a super-saturated
solid solution in the Ag-Cu system by mechanical alloying, Mater. Sci. Eng. A. 134
(1991) 1342-1345.
[171] R. Najafabadi, D.J. Srolovitz, E. Ma, M. Atzmon, Thermodynamic properties of
metastable Ag-Cu alloys, J. Appl. Phys. 74 (1993) 3144.
[172] L. Aymard, A. Delahaye-Vidal, F. Portemer, F. Disma, Study of the formation reactions
of silver-palladium alloys by grinding and post-milling isothermal annealing, J. Alloys
Compd. 238 (1996) 116-127.
[173] L. Aymard, B. Dumont, B. Beaudoin, F. Portemer, Influence of size and shape of metallic
silver and palladium powders on the Ag70Pd3O solid solution formation by mechanical
alloying, J. Mater. Chem. 6 (1996) 1543-1547.
[174] J.G. Cabafias-Moreno, V.M.H. L6pez, H.A. Calder6n, J.C. Rend6n-Angeles, Mechanical
alloying of Co-Cu powder mixtures, Scr. Metall. Mater. 28 (1993) 645-650.
[175] C. Gente, M. Oehring, R. Bormann, Formation of thermodynamically unstable solid
solutions in the Cu-Co system by mechanical alloying, Phys. Rev. B. 48 (1993) 1324413252.
115
[176] J.Y. Huang, Y.K. Wu, A.Q. He, H.Q. Ye, Direct evidence of nanocrystal enhanced
complete mutual solubility in mechanically alloyed Co-Cu powders, Nanostructured
Mater. 4 (1994) 293-302.
[177] P.P. Macri, S. Enzo, N. Cowlam, R. Frattini, G. Principi, W.X. Hu, Mechanical alloying
of immiscible Cu 7oTM 30 alloys (TM = Fe, Co), Philos. Mag. Part B. 71 (1995) 249-259.
[178] R. Busch, F. Gartner, C. Borchers, P. Haasen, R. Bormann, High resolution
microstructure analysis of the decomposition of CuqoCojo alloys, Acta Mater. 44 (1996)
2567-2579.
[179] S.W. Mahon, R.F. Cochrane, M.A. Howson, GMR and precipitation kinetics in
mechanically alloyed Cu90Co10, Nanostructured Mater. 7 (1996) 195-204.
[180] R. Elkalkouli, R. Morel, J.. Dinhut, Microstructure and Magnetic Hysteresis of
Co80Cu2O Mechanically Alloyed Powders, Nanostructured Mater. 8 (1997) 313-320.
[181] T.D. Shen, C.C. Koch, The Influence of Dislocation Structure on Formation of
Nanocrystals by Mechanical Attrition, Mater. Sci. Forum. 179-181 (1995) 17-24.
[182] L. Aymard, B. Dumont, G. Viau, Production of CoNi alloys by mechanical-alloying, J.
Alloys Compd. 242 (1996) 108-113.
[183] N.E. Fenineche, R. Hamzaoui, 0. El Kedim, Structure and magnetic properties of
nanocrystalline Co-Ni and Co-Fe mechanically alloyed, Mater. Lett. 57 (2003) 41654169.
[184] S. Guessasma, N. Fenineche, Structure and magnetic properties of mechanically alloyed
Co and Co-Ni, J. Magn. Magn. Mater. 320 (2008) 450-457.
[185] J.D. Hahn, F. Wu, P. Bellon, Cr-Mo solid solutions forced by high-energy ball milling,
Metall. Mater. Trans. A. 35 (2004) 1105-1111.
[186] A.N. Streletskii, T.H. Courtney, Kinetic, chemical and mechanical factors affecting
mechanical alloying of Ni-bcc transition metal mixtures, Mater. Sci. Eng. A. 282 (2000)
213-222.
[187] A.R. Yavari, P.J. Desrd, T. Benameur, Mechanically driven alloying of immiscible
elements, Phys. Rev. Lett. 68 (1992) 2235-2238.
[188] C. Kuhrt, L. Schultz, Magnetic properties of nanocrystalline mechanically alloyed Fe-M
(M=Al, Si, Cu), IEEE Trans. Magn. 29 (1993) 2667-2669.
[189] K.J. Kim, K. Sumiyama, K. Suzuki, Formation of nanocrystalline and amorphous phases
in Cu8 oP20 , Ni8 2P 8 and Cu 8 7Ni mechanically alloyed systems, J. Non-Cryst. Solids. 168
(1994) 232-240.
[190] T. D. Shen, C. C. Koch, T. Y. Tsui, G. M. Pharr, On the elastic moduli of nanocrystalline
Fe, Cu, Ni, and Cu-Ni alloys prepared by mechanical milling/alloying, J. Mater. Res. 10
(1995) 2892-2896.
[191] L. Durivault, 0. Brylev, D. Reyter, M. Sarrazin, D. Belanger, L. Roue, Cu-Ni materials
prepared by mechanical milling: Their properties and electrocatalytic activity towards
nitrate reduction in alkaline medium, J. Alloys Compd. 432 (2007) 323-332.
[192] B. Fultz, G. Le CaUr, P. Matteazzi, Mechanical alloying of Fe and V powders:
Intermixing and amorphous phase formation, J. Mater. Res. 4 (1989) 1450-1455.
[193] T. Koyano, K. Chatani, T. Fukunaga, U. Mizutani, Magnetic properties of Fe-V powders
produced by mechanical alloying, Mater. Sci. Eng. A. 181-182 (1994) 1277-1280.
[194] H. Yang, H. Bakker, Formation of amorphous and metastable phases from the T phase by
ball milling, Mater. Sci. Eng. A. 181-182 (1994) 1207-1211.
116
[195] G.L. Car, T. Ziller, P. Delcroix, C. Bellouard, Mixing of iron with various metals by
high-energy ball milling of elemental powder mixtures, Hyperfine Interact. 130 (2000)
45-70.
[196] R. Ohser-Wiedemann, U. Martin, A. MUller, G. Schreiber, Spark plasma sintering of
Mo-W powders prepared by mechanical alloying, J. Alloys Compd. 560 (2013) 27-32.
[197] G. Gonzalez, A. Sagarzazu, D. Bonyuet, L. D'Angelo, R. Villalba, Solid state
amorphisation in binary systems prepared by mechanical alloying, J. Alloys Compd. 483
(2009) 289-297.
[198] N. Al-Aqeeli, C. Suryanarayana, M.A. Hussein, Formation of an amorphous phase and its
crystallization in the immiscible Nb-Zr system by mechanical alloying, J. Appl. Phys.
114 (2013) 153512.
[199] S.N. Arshad, T.G. Lach, M. Pouryazdan, H. Hahn, P. Bellon, S.J. Dillon, et al.,
Dependence of shear-induced mixing on length scale, Scr. Mater. 68 (2013) 215-218.
[200] R.W. Balluffi, On measurements of self-diffusion rates along dislocations in F.C.C.
Metals, Phys. Status Solidi B. 42 (1970) 11-34.
[201] A.M. Brown, M.F. Ashby, Correlations for diffusion constants, Acta Metall. 28 (1980)
1085-1101.
[202] F.A. Mohamed, Correlation between the behavior of nanocrystalline HCP metals and the
dislocation model for the minimum grain size obtainable by milling, Mater. Sci. Eng. A.
527 (2010) 2157-2162.
[203] G. Bao, J.W. Hutchinson, R.M. McMeeking, The flow stress of dual-phase, nonhardening solids, Mech. Mater. 12 (1991) 85-94.
[204] B.E. Schuster, J.P. Ligda, Z.L. Pan, Q. Wei, Nanocrystalline refractory metals for
extreme condition applications, JOM. 63 (2011) 27-31.
[205] Q. Wei, K.T. Ramesh, B.E. Schuster, L.J. Kecskes, R.J. Dowding, Nanoengineering
opens a new era for tungsten as well, JOM. 58 (2006) 40-44.
[206] D.B. Snow, The recrystallization of heavily-drawn, Metall. Trans. A. 7 (1976) 783-794.
[207] D.B. Snow, The recrystallization of commercially pure and doped tungsten wire drawn to
high strain, Metall. Trans. A. 10 (1979) 815-821.
[208] L.J. Kecskes, K.C. Cho, R.J. Dowding, B.E. Schuster, R.Z. Valiev, Q. Wei, Grain size
engineering of bcc refractory metals: Top-down and bottom-up-Application to tungsten,
Mater. Sci. Eng. A. 467 (2007) 33-43.
[209] Q. Wei, H.T. Zhang, B.E. Schuster, K.T. Ramesh, R.Z. Valiev, L.J. Kecskes, et al.,
Microstructure and mechanical properties of super-strong nanocrystalline tungsten
processed by high-pressure torsion, Acta Mater. 54 (2006) 4079-4089.
[210] A.P. Zhilyaev, T.G. Langdon, Using high-pressure torsion for metal processing:
Fundamentals and applications, Prog. Mater. Sci. 53 (2008) 893-979.
[211] L.S. Magness Jr., High strain rate deformation behaviors of kinetic energy penetrator
materials during ballistic impact, Mech. Mater. 17 (1994) 147-154.
[212] Q. Wei, L.J. Kecskes, K.T. Ramesh, Effect of low-temperature rolling on the propensity
to adiabatic shear banding of commercial purity tungsten, Mater. Sci. Eng. A. 578 (2013)
394-401.
[213] Q. Wei, T. Jiao, K.T. Ramesh, E. Ma, L.J. Keeskes, L. Magness, et al., Mechanical
behavior and dynamic failure of high-strength ultrafine grained tungsten under uniaxial
compression, Acta Mater. 54 (2006) 77-87.
117
[214] A.K. Srivastav, B.S. Murty, Dilatometric analysis on shrinkage behavior during nonisothermal sintering of nanocrystalline tungsten mechanically alloyed with molybdenum,
J. Alloys Compd. 536, Supplement 1 (2012) S41-S44.
[215] E. Oda, K. Ameyama, S. Yamaguchi, Fabrication of Nano Grain Tungsten Compact by
Mechanical Milling Process and Its High Temperature Properties, Mater. Sci. Forum.
503-504 (2006) 573-578.
[216] H. Wang, Z.Z. Fang, K.S. Hwang, H. Zhang, D. Siddle, Sinter-ability of nanocrystalline
tungsten powder, Int. J. Refract. Met. Hard Mater. 28 (2010) 312-316.
[217] R. Sarkar, P. Ghosal, M. Premkumar, A.K. Singh, K. Muraleedharan, A. Chakraborti, et
al., Characterisation and sintering studies of mechanically milled nano tungsten powder,
Powder Metall. 51 (2008) 166-170.
[218] T.S. Srivatsan, K. Manigandan, M. Petraroli, R.M. Trejo, T.S. Sudarshan, Influence of
size of nanoparticles and plasma pressure compaction on microstructural development
and hardness of bulk tungsten samples, Adv. Powder Technol. 24 (2013) 190-199.
[219] B.R. Klotz, F.R. Kellogg, E.M. Klier, R.J. Dowding, K.C. Cho, Characterization,
Processing, and Consolidation of Nanoscale Tungsten Powder, 2009.
[220] K.C. Cho, R.H. Woodman, B.R. Klotz, R.J. Dowding, Plasma Pressure Compaction of
Tungsten Powders, Mater. Manuf. Process. 19 (2004) 619-630.
[221] 0. EI-Atwani, D.V. Quach, M. Efe, P.R. Cantwell, B. Heim, B. Schultz, et al.,
Multimodal grain size distribution and high hardness in fine grained tungsten fabricated
by spark plasma sintering, Mater. Sci. Eng. A. 528 (2011) 5670-5677.
[222] U.K. Vashi, R.W. Armstrong, G.E. Zima, The hardness and grain size of consolidated
fine tungsten powder, Metall. Trans. 1 (1970) 1769-1771.
[223] C. Agte, J. Vacek, Tungsten and molybdenum, NASA Trans., 1963.
[224] H.H. Tian, M. Atzmon, Comparison of X-ray analysis methods used to determine the
grain size and strain in nanocrystalline materials, Philos. Mag. A. 79 (1999) 1769-1786.
[225] E04 Committee, Test Method for Determining Volume Fraction by Systematic Manual
Point Count, ASTM International, 2011.
[226] E04 Committee, Practice for Determining the Inclusion or Second-Phase Constituent
Content of Metals by Automatic Image Analysis, ASTM International, 2008.
[227] E04 Committee, Test Methods for Determining Average Grain Size, ASTM International,
2012.
[228] W.C. Oliver, G.M. Pharr, Measurement of hardness and elastic modulus by instrumented
indentation: Advances in understanding and refinements to methodology, J. Mater. Res.
[229]
[230]
[231]
[232]
19 (2004) 3-20.
ASM International, Handbook Committee, ASM handbook. Volume 2, Volume 2, ASM
International, Materials Park, OH, 1990.
M.D. Uchic, D.M. Dimiduk, J.N. Florando, W.D. Nix, Sample Dimensions Influence
Strength and Crystal Plasticity, Science. 305 (2004) 986-989.
P. Gustafson, An experimental study and a thermodynamic evaluation of the cr- fe- w
system, Metall. Trans. A. 19 (1988) 2531-2546.
S. Telu, A. Patra, M. Sankaranarayana, R. Mitra, S.K. Pabi, Microstructure and cyclic
oxidation behavior of W-Cr alloys prepared by sintering of mechanically alloyed
nanocrystalline powders, Int. J. Refract. Met. Hard Mater. 36 (2013) 191-203.
118
[233] M.S. EI-Eskandarany, K. Sumiyama, K. Suzuki, Crystalline-to-amorphous phase
transformation in mechanically alloyed Fe5oW5o powders, Acta Mater. 45 (1997) 11751187.
[234] C.N.J. Wagner, E. Yang, M.S. Boldrick, The structure of nanocrystalline Fe, W and NiAl
powders prepared by high-energy ball-milling, Nanostructured Mater. 7 (1996) 1-11.
[235] H.J. Fecht, E. Helistern, Z. Fu, W.L. Johnson, Nanocrystalline metals prepared by highenergy ball milling, Metall. Trans. A. 21 (1990) 2333-2337.
[236] R. Malewar, K.S. Kumar, B.S. Murty, B. Sarma, S.K. Pabi, On sinterability of
nanostructured W produced by high-energy ball milling, J. Mater. Res. 22 (2007) 12001206.
[237] D. Oleszak, P.H. Shingu, Nanocrystalline metals prepared by low energy ball milling, J.
Appl. Phys. 79 (1996) 2975-2980.
[238] D.P. Xiang, L. Ding, Y.Y. Li, J.B. Li, X.Q. Li, C. Li, Microstructure and mechanical
properties of fine-grained W-7Ni-3Fe heavy alloy by spark plasma sintering, Mater. Sci.
Eng. A. 551 (2012) 95-99.
[239] U. Herr, K. Samwer, Formation of nanocrystalline and amorphous phases by mechanical
alloying in the system W-Fe, Nanostructured Mater. 1 (1992) 515-521.
[240] J.O. Andersson, T. Helander, L. H6glund, P. Shi, B. Sundman, Thermo-Calc & DICTRA,
computational tools for materials science, Calphad. 26 (2002) 273-312.
[241] D. Peckner, The strengthening of metals, Reinhold Pub. Corp., 1964.
[242] H.C. Lee, J. Gurland, Hardness and deformation of cemented tungsten carbide, Mater.
Sci. Eng. 33 (1978) 125-133.
[243] Z. Fan, A.P. Miodownik, P. Tsakiropoulos, Microstructural characterisation of two phase
materials, Mater. Sci. Technol. 9 (1993) 1094-1100.
[244] H. Zhang, B.E. Schuster, Q. Wei, K.T. Ramesh, The design of accurate microcompression experiments, Scr. Mater. 54 (2006) 181-186.
[245] B. Butler, E. Klier, D. Casem, A. Dwivedi, M. Gallagher, J. Hays, Demonstration of
Shear Localization in Ultrafine Grained Tungsten Alloys via Powder Metallurgy
Processing Route, DTIC Document, 2012.
[246] A.M. Lennon, K.T. Ramesh, The thermoviscoplastic response of polycrystalline tungsten
in compression, Mater. Sci. Eng. A. 276 (2000) 9-21.
[247] Q. Wei, K.T. Ramesh, E. Ma, L.J. Kesckes, R.J. Dowding, V.U. Kazykhanov, et al.,
Plastic flow localization in bulk tungsten with ultrafine microstructure, AppI. Phys. Lett.
86 (2005) 101907-101907-3.
[248] D. Jia, K.T. Ramesh, E. Ma, Effects of nanocrystalline and ultrafine grain sizes on
constitutive behavior and shear bands in iron, Acta Mater. 51 (2003) 3495-3509.
[249] J.P. Ligda, B.E. Schuster, Q. Wei, Transition in the deformation mode of nanocrystalline
tantalum processed by high-pressure torsion, Scr. Mater. 67 (2012) 253-256.
[250] J.E. Carsley, A. Fisher, W.W. Milligan, E.C. Aifantis, Mechanical behavior of a bulk
nanostructured iron alloy, Metall. Mater. Trans. A. 29 (1998) 2261-2271.
[251] S.P. Joshi, K.T. Ramesh, Rotational diffusion and grain size dependent shear instability
in nanostructured materials, Acta Mater. 56 (2008) 282-291.
[252] S.P. Joshi, K.T. Ramesh, Grain size dependent shear instabilities in body-centered and
face-centered cubic materials, Mater. Sci. Eng. A. 493 (2008) 65-70.
119
[253] K. Cho, L. Kecskes, R. Dowding, B. Schuster, Q. Wei, R.Z. Valiev, Nanocrystalline and
Ultra-Fine Grained Tungsten for Kinetic Energy Penetrator and Warhead Liner
Applications, 2007.
[254] Q. Wei, L.J. Kecskes, Effect of low-temperature rolling on the tensile behavior of
commercially pure tungsten, Mater. Sci. Eng. A. 491 (2008) 62-69.
[255] Q. Wei, B.E. Schuster, S.N. Mathaudhu, K.T. Hartwig, L.J. Kecskes, R.J. Dowding, et
al., Dynamic behaviors of body-centered cubic metals with ultrafine grained and
nanocrystalline microstructures, Mater. Sci. Eng. A. 493 (2008) 58-64.
[256] Q. Wei, Z.L. Pan, X.L. Wu, B.E. Schuster, L.J. Kecskes, R.Z. Valiev, Microstructure and
mechanical properties at different length scales and strain rates of nanocrystalline
tantalum produced by high-pressure torsion, Acta Mater. 59 (2011) 2423-2436.
[257] M.J. Forrestal, B.S. Altman, J.D. Cargile, S.J. Hanchak, An empirical equation for
penetration depth of ogive-nose projectiles into concrete targets, Int. J. Impact Eng. 15
(1994) 395-405.
[258] T.E. Ehlers, B.J. Guidos, D.W. Webb, Small-Caliber Projectile Target Impact Angle
Determined from Close Proximity Radiographs, DTIC Document, 2006.
[259] M.J. forrestal, Penetration into dry porous rock, Int. J. Solids Struct. 22 (1986) 14851500.
[260] V.K. Luk, M.J. Forrestal, Penetration into semi-infinite reinforced-concrete targets with
spherical and ogival nose projectiles, Int. J. Impact Eng. 6 (1987) 291-301.
[261] M.J. Forrestal, V.K. Luk, H.A. Watts, Penetration of reinforced concrete with ogive-nose
penetrators, Int. J. Solids Struct. 24 (1988) 77-87.
[262] M.J. Forrestal, V.K. Luk, Dynamic Spherical Cavity-Expansion in a Compressible
Elastic-Plastic Solid, J. Appl. Mech. 55 (1988) 275-279.
[263] M.J. Forrestal, V.K. Luk, Penetration into soil targets, Int. J. Impact Eng. 12 (1992) 427444.
[264] M.J. Forrestal, D.J. Frew, S.J. Hanchak, N.S. Brar, Penetration of grout and concrete
targets with ogive-nose steel projectiles, Int. J. Impact Eng. 18 (1996) 465-476.
[265] M.J. Forrestal, D.Y. Tzou, A spherical cavity-expansion penetration model for concrete
targets, Int. J. Solids Struct. 34 (1997) 4127-4146.
[266] D.J. Frew, S.J. Hanchak, M.L. Green, M.J. Forrestal, Penetration of concrete targets with
ogive-nose steel rods, Int. J. Impact Eng. 21 (1998) 489-497.
[267] M.J. Forrestal, D.J. Frew, J.P. Hickerson, T.A. Rohwer, Penetration of concrete targets
with deceleration-time measurements, Int. J. Impact Eng. 28 (2003) 479-497.
[268] D.J. Frew, M.J. Forrestal, J.D. Cargile, The effect of concrete target diameter on
projectile deceleration and penetration depth, Int. J. Impact Eng. 32 (2006) 1584-1594.
[269] S.A. Silling, M.J. Forrestal, Mass loss from abrasion on ogive-nose steel projectiles that
penetrate concrete targets, Int. J. Impact Eng. 34 (2007) 1814-1820.
[270] T.L. Warren, M.J. Forrestal, P.W. Randles, Evaluation of Large Amplitude Deceleration
Data from Projectile Penetration into Concrete Targets, Exp. Mech. 54 (2013) 241-253.
[271] M.J. Forrestal, K. Okajima, V.K. Luk, Penetration of 6061-T651 aluminum targets with
rigid long rods, J. Appl. Mech. 55 (1988) 755-760.
[272] R.A. Beth, Concrete Penetration, 1946.
120