Active Braze Alloys for
Metal Single Layer Grinding Technology
by
Ren-Kae Shiue
S.M. National Taiwan University, 1988
S.B. National Taiwan University, 1986
Submitted to the Department of
Materials Science and Engineering
in Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy
in Materials Engineering
at the
Massachusetts Institute of Technology
June 1996
@ 1996 Massachusetts Institute of Technology
All rights reserved
. . ...............
Signature of A uthor ............................................................
Department of Materials Science and Engineering
May 10, 1996
.. ................
76as
W. Eagar
Department of Materials Science and Engineering
Thejsj Supervisor
Certified
by
........................................
A ccepted
by
............................
I...........
...............
. .........
Michael F. Rubner
TDK Professor of Materials Science and Engineering
Chair, De artmental Committee on Graduate Students
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
MAY 2 1 1998
LIBRARIES
2
Active Braze Alloys for Metal
Single Layer Grinding Technology
by
Ren-Kae Shiue
Submitted to the Department of Materials Science and Engineering
on May 3, 1996 in partial fulfillment of the requirements for
the Degree of Doctor of Philosophy in Materials Engineering
Abstract
Components made of high-performance ceramics or superalloys are subject to strict
requirements with regard to their geometric and dimensional accuracy. The surface finish
and edge zone characteristics have a large effect on the component's performance. These
requirements can not be met directly by the sintering process used in the manufacture of
ceramic materials or traditional casting of superalloys. Grinding is both technically and
economically the number one choice when one has to consider machining these materials.
Metal Single Layer (MSL) grinding technology provides an altemative way to make use of
the superabrasives, diamond and CBN, in grinding these materials. One of the primary
challenges in MSL grinding technology is to develop suitable active braze alloy(s) which
can bond the superabrasive grits. Ticusil (Ag-Cu eutectic+4.5 wt% Ti) and 70Cu-21Sn9Ti (wt%) are two of the currently used active braze alloys. The primary failure mode of
these two MSL wheels in the grinding test is transverse fracture and debonding of the
diamond grits. The high applied load is responsible for transverse fracture of the diamond
grit, and the intermetallic phase existing at the interface between the diamond and the braze
alloy is one of the causes of the debonding of the diamond grits. Also, a finite element
analysis shows that most of the residual thermal stresses and the thermal mismatch strains
are localized at the diamond/braze alloy interface. This results in potential weakness of this
area. Moreover, the inherent defects, such as voids, and the brittle intermetallics in the
interface can cause crack initiation and propagation. Both deteriorate the life of the grinding
wheel.
The failure of the braze alloy can be divided into two categories. If the grinding process is
very abrasive, such as green concrete grinding, the wear resistance of the braze dominates
the fracture of the braze alloy. On the other hand, failure of the braze alloy can also result
from cracks at the interface. In such a case, the fatigue resistance of the braze alloy plays
an important role in determining the wheel's life. The wear resistance of the braze alloy can
be improved by introducing suitable hard particles. It was found that a braze alloy of
77Cu-23Sn-12.5Ti-7.5Zr-lOTiC-0.2C (by weight) exhibits excellent performance in a
wear test (a ten fold improvement), which is further confirmed in the grinding test (a two
fold increase in life). The fatigue resistance of the active braze alloy can be modified by
either reducing the volume fraction of the brittle intermetallic phase in the braze and/or
enhancing the ductility of the braze alloy matrix. A ductile active braze alloy can be
achieved by combining the two-layer structure and two step brazing process. To aid
dissolution and diffusion of the Cu atoms into the Cu/Sn/Ti braze alloy, a lower volume
fraction of the intermetallic phase and higher ductile matrix of the braze can be achieved.
Both have beneficial effects in modifying the ductility of the active braze alloy, and make
removal of the braze alloy from the substrate by acid etching easier.
Thesis Supervisor: Professor Thomas W. Eagar
Title: Head of the Department of Materials Science and Engineering
3
Table of Contents
Abstract
Table of Contents
List of Figures
List of Tables
List of Symbols
Acknowledgements
2
3
5
10
11
13
1.
Introduction
14
2.
Literature review
2.1 Theory and applications of reactive brazing
2.2 Reaction zone formation and its effects on mechanical properties
of the joint
2.3 Residual thermal stresses after brazing
2.4 Types of diamond wheel failure
18
18
22
Problem identification and preliminary study of currently available braze alloys
3.1 Documentation of the Failure Mode in MSL Grinding Wheels
3.2 Fundamental study of the currently used active braze alloys
3.3 Alternative methods to improve the performance of MSL wheels
Finite element analysis of the residual stresses in MSL grinding wheels
4.1 Review of the finite element analysis principles
4.2 Elastic/rate-independent plastic finite element analysis model
4.3 Elastic/rate-dependent plastic finite element analysis model
31
31
33
39
55
55
59
64
Development of abrasive-resistant active braze alloy
5.1 Developing abrasive-resistant braze alloy by introducing hard
particles
5.2 Fundamental study of the abrasive resistant braze alloys
5.3 Grinding test and cutting test of the MSL wheels
88
88
6.
Development of a ductile active braze alloy
6.1 Using alloy design to develope a ductile braze alloy
6.2 Developing a ductile active braze alloy using a two-layer structure
6.3 Grinding test of the two-layer MSL grinding wheels
6.4 Stripping test of the two-layer MSL grinding wheels
117
117
119
122
123
7.
Summary and conclusions
7.1 Summary
135
135
3.
4.
5.
24
27
95
96
4
7.2 Conclusions
8.
Future work
137
139
Bibliography
144
Appendix A: Materials property input in finite element analysis
154
Appendix B: A sample ABAQUS input program
157
Appendix C: Theoretical and measured density of the braze alloy
164
Biographical note
166
5
List of Figures
Figure 2.1:
Factors affecting the strength of ceramic to metal joint
29
Figure 2.2:
The predicted characteristic temperature differences by plane stress
and plane strain model
29
Figure 2.3:
Interactions at the grinding zone:
(a) superabrasive/work interface
(c) swarf/work interface
30
(b) swarf/bond interface
(d) bond/work interface
Figure 3.1
Fractograph of the nickel-plated MSL grinding wheel
41
Figure 3.2:
41
Figure 3.6:
Fractographs of the 70Cu-21Sn-9Ti (by weight) MSL grinding wheel
(a) fractured surface overview
(b) cracks surround the debonded diamond grain
(c) cracks situated in the radial direction of the debonded diamond
grain
Schematic diagrams of the bonded diamond grain
(a) ideal MSL bond
(b) poor bond due to insufficient wetting of the diamond grain
(c) poor bond due to over wetting of the diamond grain
Fractograph of the nickel-based braze alloy developed by Norton
Company
Fractograph of the 75Cu-25Sn-12.5Ti-7.5Zr-1OTiC-0.2C (by
weight) MSL grinding wheel
Fractograph of the high tin MSL grinding wheel
45
Figure 3.7:
Fractograph of ABRASIVE TECH's MSL grinding wheel
45
Figure 3.8:
46
Figure 3.10:
Ternary phase diagrams of Ag-Cu-Ti and the microstructure of
Ticusil
(a) Ag-Cu-Ti ternary phase diagrams
(b) Microstructure of Ticusil brazing at 875 0 C* 30minutes
Fractographs of Ticusil after tensile test and grinding test
(a) Fractograph of Ticusil after tensile test
(b) Fractograph of Ticusil MSL grinding wheel after grinding test
Fractograph of 70Cu-21Sn-9Ti (wt%) after tensile test
48
Figure 3.11:
The DSC analysis of 70Cu-2lSn-9Ti (wt%), heating cycle
48
Figure 3.12:
49
Figure 3.13:
The SEM analysis of 70Cu-21Sn-9Ti (wt%), 880*C* 30minutes
(a) The morphology of 70Cu-2lSn-9Ti
(b) The dot mapping of C, Ti, Sn, and Cu
Wetting angle measurement installations
Figure 3.14:
Wetting angle measurement test samples
50
Figure 3.3:
Figure 3.4:
Figure 3.5:
Figure 3.9:
43
44
44
47
50
6
Figure 3.15:
Figure 3.17:
Time dependent wetting angle measurement for 70Cu-2lSn-9Ti
(wt%) at 9000C
Temperature dependent wetting angle for 70Cu-21Sn-9Ti (wt%) and
Ticusil (Ag-Cu eutectic + 4.5wt% Ti) on polished graphite surface
The change of wetting angle with various Ti contents at 920"C
52
Figure 3.18:
Fractographs of 70Cu-2lSn-9Ti (wt%) after 10 thermal cycles
53
Figure 3.19:
Fractographs of Ticusil after 10 thermal cycles
54
Figure 4.1:
The process of finite element analysis
68
Figure 4.2:
The morphology of the nodes and elements in the analysis
69
Figure 4.3:
The comparison between the engineering stress-strain curve and the
true stress-strain curve of an elastic-linear work hardening material
Finite element analysis results of two different size ratio cooling from
900"C: (a) (b) (c) and (d) (e) (f)
The finite element analysis results of diamond/braze/(SS304)
combinations
(a)(b) diamond/Cu braze/Cu disk combination
(c)(d) diamond/Cu braze/200gm Cu interlayer/SS304 Combination
70
Figure 4.6:
Finite element analysis of the MSL bond with 1 mm and 3 mm Cu
interlayer
73
Figure 4.7:
The analysis of diamond/i pm TiC/Cu braze/SS304 combination
74
Figure 4.8:
The analysis result of a 50gm crack at the bottom interface
(a) Mises stress distribution (b) PEEQ distribution
The equivalent plastic strains for different brazes (a) Cu (b) Ni (c) Al
75
The accumulated plastic strain distributions in an octagonal cone of
the diamond grit
(a) lower braze alloy level
(b) higher braze alloy level
All stress components obtained from the finite element analysis
77
Figure 3.16:
Figure 4.4:
Figure 4.5:
Figure 4.9:
Figure 4.10:
Figure 4.11:
Figure 4.12:
Figure 4.13:
Figure 4.14:
Figure 4.15:
Figure 4.16:
51
52
71
72
76
78
The change of the Mises stress and the equivalent plastic strain with
temperature in element 3021
The equivalent pressure stress of a two-layer braze
(a) Ni/Cu two-layer braze
(b) Cu/Ni two -layer braze
79
The SEM backscattered image in the diamond-Cu/Sn/Ti braze
interface formed by a fast cooling rate after brazing
The creep strain rates of Cu and SS304 at 200, 400, and 600 0C with
varied Mises equivalent stresses
The currently used thermal cycle for 70Cu-21Sn-9Ti (wt%) braze
alloy
81
80
82
83
7
Figure 4.17:
Figure 4.18:
Figure 4.19:
Figure 4.20:
Figure 4.21
Figure 5.1:
Figure 5.2:
Figure 5.3:
Figure 5.4:
Figure 5.5:
The equivalent plastic strain (PEEQ) and the equivalent creep strain
(CEEQ) change with temperature at element 3021
The Mises stress variation during the cooling cycle for three different
elements
The Mises stress variations of element 3021 with different cooling
rates- 100"C/min, 10*C/min, 1PC/min, 0. 1C/min
The PEEQ and CEEQ of element 3021 for various cooling rates
(a) PEEQ: accumulated plastic strain (%)
(b) CEEQ: accumulated creep strain (%)
Overview of the Mises stress distribution around the braze alloy
(a) rate-independent plastic model (b) 10 0C/min
(c) 10C/min
(d) 0. 10C/min
Effect on abrasive wear when second phase is varied
(a) small second phase, easily removed
(b) large second phase, protection of matrix
(c) very large second phase, small abrasive channeled to matrix
Test procedures in developing abrasive resistant active braze alloys
The results of shear test and microhardness test for various particle
additions
The results of shear and microhardness tests for 75Cu-25Sn-lOTiXTiC (44 micron or 4 micron) by weight, brazing at 9000C*30
minutes
The morphology of A12 0 3 swarf after grinding test
83
84
85
86
87
100
101
102
103
104
Figure 5.6:
The results of shear and microhardness tests for 75Cu-25Sn-lOTi1OZr- 1OTiC-(0-0.7)C by weight, brazing 900*C*30 minutes
105
Figure 5.7:
The microstructure of 75Cu-25Sn-lOTi and 75Cu-25Sn-lOTi-Zr1OTiC-0.25C by weight
106
Figure 5.8:
The erosion and wear tests of 75Cu-25Sn-lOTi-X (by weight) braze
alloy
The erosion and wear tests of 75Cu-25Sn-wTi-xZr-yC-zTiC (by
weight) braze alloys
EDX analysis of 75Cu-25Sn-12.5Ti-7.5Zr-1OTiC-0.2C (by weight),
9000 C*30 minutes
(a) its morphology
(b) the dot mapping of Zr, Ti, Sn, and Cu
DSC analysis of 77Cu-23Sn-12.5Zr-10TiC-0.2C (by weight)
(a) heating cycle
(b) cooling cycle
The grinding test result of six different alloys
107
Figure 5.9:
Figure 5.10:
Figure 5.11:
Figure 5.12:
Figure 5.13:
Figure 5.14:
Fractographs of 77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C (by weight)
MSL wheel: (a) low magnification overview, (b) fractured diamond
Fractograph of a debonded surface
(a) diamond/77Cu-23Sn-IOTi (by weight)
(b) 77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C (by weight)/diamond
108
109
110
111
112
113
8
Figure 5.15:
Fractograph of a debonded surface
114
Figure 5.16:
114
Figure 6.1:
Fractograph of 77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C (by weight)
after tensile test
The morphology of two MSLwheels used in the test
(a) high density alumina grinding test
(b) green concrete grinding test
Fractographs of two MSL wheels after cutting test
(a) Cu/Sn/Ti bond after 300 meters of cutting
(b) Cu/Sn/TiiZr/TiC/C bond after 411.5 meters of cutting
Vapor pressure as a function of temperature
Figure 6.2:
The microstructure of 91Cu-4Si-5Ti in wt%, 1150 0C* 30minutes
124
Figure 6.3:
The microstructural observations of Cu/Ag/Sn/f'i active braze alloys
125
Figure 6.4:
The morphology of the interface between 70 Cu-2lSn-9Ti (wt%) and
Ni
(a) Cu-Sn binary phase diagram. Arrows indicate specimen
composition
(b) Specific Wear of Cu-Sn bronze
The SEM back scattered image displaying the interface between braze
and Fe
The EDX analysis of the interfacial phases in wt%
126
Figure 5.17:
Figure 5.18:
Figure 6.5:
Figure 6.6:
Figure 6.7:
Figure 6.8:
Figure 6.9:
Figure 6.10:
Figure 6.11:
Figure 6.12:
Figure 6.13:
The morphology of the interfaces after brazing at 900*C*30 minutes
(a) 70Cu-21Sn-9Ti (wt%)/Cu interface
(b) Cu/steel interface
The morphology of 70Cu-21Sn-9Ti (wt%) and Cu two-layer
structure after brazing
(a) 860*C*30 minutes (b) 880 0C*30 minutes (c) 9000C*30 minutes
The microstructure of 70Cu-21Sn-9Ti (wt%) and Cu two-layer
structure after brazing
(a) 860*C*30 minutes (b) 880 0 C*30 minutes (c) 900 0C*30 minutes
The microstructure of 71.4 bronze-7.2Ti-21.4Cu (wt%) brazing at:
(a) 865 0C*30 minutes (b) 880 0C*30 minutes (c) 9000C*30 minutes
(d) 865 0C*30minutes + 900"C*30 minutes
The grinding test result of three test wheels, (1), (2) and (3) as
described in section 6.3
(a) power vs. the accumulated alumina removed
(b) normal force vs. the accumulated alumina removed
Weight loss of three MSL bond wheels with different braze alloys
(1) 70Cu-21Sn-9Ti (wt%)
(2) 77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C (by weight)
(3) Two-layer structure, 76.9 wt% 77Cu/23Sn bronze-7.7 wt% Ti
15.4 wt% pure copper powder and a 50 gm pure copper
interlayer
115
116
124
126
127
127
128
129
130
131
132
133
9
Figure 6.14
The morphology of three MSL wheels after 595 minutes stripping
134
Figure 8.1:
The schematic diagrams displaying the modified transient liquid
phase bonding of the superabrasive grits
(a) before brazing
(b) first step brazing: bonding of the superabrasive grits
(c) second step brazing: dissolution and diffusion of the coated
powder into the braze alloy
143
10
List of Tables
Table 3.1:
The mechanical properties of Ticusil and 70Cu-2lSn-9Ti by wt%
34
Table 3.2:
Wetting angle at 30 minutes for various copper-base braze alloys
38
Table 4.1:
Copper and SS304
66
Table 5.1:
Physical properties of some related materials
91
Table 5.2
The cutting test result of three different wheels
98
Table 6.1:
Mechanical properties of some copper/tin alloys
117
Table 6.2:
EDX analysis of the copper-rich phase in 70Cu-2lSn-9Ti braze alloy
121
Table 8.1:
The chemical composition of some promising active braze alloys in
MSL technology
140
11
List of Symbols
Variable
A
Aw
a(Me)
(X
b
Dc
Def
Di
Dm
Dt
D,
d
E
Description
power-law creep constant
normal contact area in wear test
the activity of Me
coefficient of thernal expansion
71V
the magnitude of Burgers vector
core diffusion coefficient; DC = Doc exp-(Q]RT)
effective diffusion coefficient for power law creep
density of the component i
measured density of the braze alloy
theoretical density of the braze alloy
lattice diffusion coefficient; D,=Doexp-(Q]RT)
particle diameter
Young's modulus
normal strain (rate) tensor
elastic strain (rate) tensor
plastic strain (rate) tensor
equivalent plastic strain
total deformation tensor
elastic (inelastic) deformation tensor
yield function
the fractions of atom sites associated with core and lattice diffusion
respectively
the change in free energy
the change in free energy per unit area released by reaction of the
material
flow potential (for the ith system)
liquid-vapor surface tension
7,1
solid-liquid surface tension
YIV
Ayr
H
solid-vapor surface tension
Ha
a set of hardening parameters
h
K
Kic
the height of sample
a dimensionless number, Archard wear coefficient
fracture toughness
k
Boltzmann's constant, 1.38* 1023 J/OK
E_()
E e(l
)
EPl(tPI)
EPI
F
Fel (FP')
f
feI fV
AG
AGr
g)
the change in interfacial energy after reaction
hardness
12
shear modulus
n
V
P
p
Q, QV
q
R
Rw
O
00
creep exponent
Poisson's ratio
normal pressure
equivalent pressure stress
activation energies for core and lattice diffusion respectively
Mises equivalent stress
gas constant, 8.314 J/mole0 K
wear resistance
wetting angle
wetting angle of the liquid on the substrate absent of any reaction
0mm
the smallest contact angle possible in a reactive system
density
S
deviatoric stress tensor
stress tensor
(I.
G,
T
AT,
t
U
V
Ve
VW
v
vi
Wa
Wwawr
x
yield strength
temperature
the characteristic temperature difference which causes the onset of
plastic deformation
time
strain energy density potential
volume of the braze alloy
the volume of material removed by erosion per unit mass impacted
the volume of material removed by wear per unit sliding distance
velocity
volume fraction of the component i
the weight of the braze alloy in air
the weight of the braze alloy in water
the current spatial position
13
Acknowledgements
I am sincerely grateful to Professor Thomas W. Eagar for his instruction and support to
complete this thesis. I also deeply appreciate Norton Company financially supporting this
research, and the colleagues in the Superabrasives Department of Norton Company for
their kindly help to accomplish this project: Dr. S.T. Buljan, Dr. R.M. Andrews, B.J.
Miller, and D.R. Vujic. I am grateful to Wei-dong Zhuang in the Welding Laboratory of
MIT giving me a lot of help in the experiments. Finally, I would like to thank my dear
wife, Yunai Chou, who helps me type the draft and encourages and supports me to
complete this work.
14
1. Introduction
With the ever increasing number of ceramic materials and superalloys in the market
place, grinding is both technically and economically the number one choice when one has
to consider machining these materials. It is a cutting process using tools with multiple
cutting edges provided by randomly bonded abrasive grits of natural or synthetic origin
which remove material at high speed, mostly under interrupted cutting conditions, and
improve or modify the shape, the dimensions, and/or the surface quality of the workpiece
(Metzer, 1986; Warnecke and Wimmer, 1995).
The type of abrasive and the bonding method are two key parameters for a grinding
wheel. It was not until the nineteenth century that synthetic abrasives began to replace the
natural abrasives of sandstone, crocus rouge, emery, corundum, and diamond (Salmon,
1992). The synthetic abrasives were used due to the fact that natural abrasives contained
many impurities and varied in quality. Synthetic abrasives, however, are pure, consistent
and can be carefully controlled. The most common artificial abrasives available today, in
order of their popularity, are aluminum oxide, silicon carbide, cubic boron nitride (CBN),
and synthetic diamond. CBN and diamond are termed superabrasives due to their high
hardness (Froes, 1995).
There are three basic bonding methods - vitrified, resinoid, and metal bond
(Salmon, 1992). A vitrified bond is made of clay or feldspar which is fused at high
temperature to form a glass-like structure. During the firing operation, the clay or feldspar
melts surrounding the abrasive grain, bonding each grain to the next, and forming a
homogeneous structure. When the wheel cools, each grain is surrounded by a hard glasslike bond which has high strength and rigidity. Resin-bonded wheels are manufactured in
a very similar manner to vitrified wheels. However, the bonding medium is a
thermosetting synthetic resin. There are two divisions of metal-bonded wheels: those
which have been plated, and those which have been brazed. Many superabrasive wheels
are made with a metal bond.
For an abrasive to function properly, it must be harder than the material being
ground, and be shaped to penetrate the surface of the material to be ground and form a
swarf or particulates. Based on this criterion, two superabrasives - diamond and CBN are very suitable materials to make grinding wheels. Diamond is suited to grind tungsten
carbide, natural stone, granite, concrete, and ceramics, but unsuitable for the grinding of
steels due to the very aggressive chip formation which tends to tear the diamonds from their
bond. Also, it is postulated that diamond, being a carbon-based material, has an affinity
for iron and suffers accelerated wear by the dissolution of the diamond into the steel,
15
producing an iron carbide (Fe3C) with most unsatisfactory results. Moreover, the tendency
of the graphitization of the diamond at high temperature (above 800'C) may also prohibit
the application of diamond at elevated temperatures (Wilks and Wilks, 1991; Malkin, 1989;
Tanaka, Ikawa, and Tsuwa, 1981; Pierson, 1993). Compared with diamond, CBN is less
reactive in the presence of ferrous alloys and is thermally stable at elevated temperatures
(-1300'C). CBN, a more expensive superabrasive than diamond, is widely used in
grinding of ferrous materials like tool steel while diamond is applied in grinding of
nonferrous metals and ceramics. The application of diamond and CBN can, therefore,
compliment each other.
When compared with commercially available SiC or A12 0 3 abrasives, the
application of the superabrasives in grinding some difficult machining materials is very
encouraging (Aronson, 1994; Davis and Pearce, 1995).
Grinding time has been
significantly reduced, surface finish is improved, and there appears to be an enhancement
of surface quality. Because the superabrasives are several times harder than conventional
abrasives, they last longer during grinding, often 100 times or more. Consequently, they
offer the potential for improved production through better finish, greater part consistency,
and tighter tolerances. Moreover, the superabrasive wheel produces excellent ground
surfaces unattainable with conventional wheels, and increases fatigue strength of the
material with resulting reductions in part size and weight. This unique grinding
performance has such a great impact on part design that machine designers will have to
change their approach significantly in the very near future (Yokogawa and Yokogawa,
1992).
Metal matrices are used to bond super hard abrasives, such as diamond and CBN.
The bonds are sintered from powders or made by electroplating (Borkowski and
Szymanski, 1992). The metal powder used for wheel bonding consists of various
compositions of copper, tin, iron, aluminum, nickel, ...etc. The most popular is bronze
powder composed of copper and tin powder with various alloy additives. But quite
widespread, especially in the production of diamond wheels, is a nickel electroplated bond
which deposits on the metal tool body from a suitable electroplating bath. This deposit
bonds the diamond grains distributed over the wheel surface usually in the form of a single
layer. One of the major disadvantages for the electroplating method is its high production
cost. In order to guarantee full coverage of the diamond wheel, a huge amount of diamond
must be kept in the electroplating bath, and the cost of the superabrasives is high, on the
order of thousands dollars per pound. One alternative method is metal single layer (MSL)
produced by brazing (Aronson, 1994).
16
In MSL grinding technology the cutting wheel has a steel core and a layer of
diamonds which are brazed with a special braze alloy (Wiand, 1990). The first step is to
mix a carbide forming substance such as Ti or Cr with the traditional braze alloy powder,
and form a slurry paste with a temporary binder. Second, one applies the above coating
material to a tool substrate. Third, one adds at least a monolayer of diamond particles on
the coating material. Finally, the preform is brazed at a temperature sufficient to form a
metal carbide on the diamond and to braze the diamond to the tool substrate.
This method is less costly than the electroplating method as much less diamond is
tied up in the process. The market for metal single layer grinding technology is
consistently growing and the application of MSL grinding wheels may replace some
traditional grinding or machining technologies. Today, MSL grinding wheels are applied at
very high cutting speeds to machine materials, such as ceramics, superalloys, and magnetic
materials, which are difficult to shape.
One of the primary challenges for MSL grinding technology is to join the diamond
and the steel reliably. Brazing has a major advantage compared with many other joining
processes as the base materials do not melt (Akselsen, 1992). This allows brazing to be
applied to the joining of dissimilar materials which can not be joined by fusion processes
due to metallurgical incompatibility. In the case of brazing, ceramic-metal joints may be
obtained in two different ways: (1) indirect brazing, where the ceramic surfaces are
metallized prior to brazing with conventional filler metals; and (2) direct brazing, where the
filler alloys contain active elements such as titanium or zirconium (Hadian and Drew,
1994). Due to oxidation of the metallized ceramic surfaces, it may be more difficult to
bond diamond by indirect brazing. The oxides of many strong carbide former such as Ti,
Nb, and Cr are tenacious, and the wettability of these stable oxides is much lower than that
of the diamond. Moreover, if the diamond is coated with a less reactive element such as Ni
or W, the bond between the diamond and the coated material is not as strong as that of
direct brazing. Therefore, the second method, direct brazing diamond to the steel perform,
is to be studied in this paper.
There are several criteria that the braze alloy(s) must satisfy. First, the key issue in
the direct brazing is to develop brazing filler metals which provide the required wetting and
spreading on both the diamond and the steel. The braze alloy will show good meniscus
shape around the diamond after brazing. Second, the braze alloy should provide
reasonable ductility and wear resistance in order to extend the life of the grinding wheel.
Third, the braze alloy must be chemically and/or electrochemically stripped from the steel
core after the diamond wears out, so the grinding wheel can be recycled. Fourth,
dimensional control of the grinding wheel should be as accurate as possible, and distortion
17
of the grinding wheel must be avoided. Finally, the cost of the braze alloy must be
inexpensive in order to compete with other technologies. Generally speaking, the new
braze alloy(s) should meet the following conditions:
(1) wet both the diamond and the steel.
(2) provide good mechanical properties.
(3) be chemically and/or electrochemically stripped without altering the steel
preform.
(4) have a low brazing temperature to reduce the distortion.
(5) be inexpensive.
The goal of this research is to develop active braze alloys fitting all the above
requirements for metal single layer grinding technology.
18
2. Literature Review
2.1 Theory and Applications of Reactive Brazing
Many researchers have concentrated on reactive brazing for ceramic/metal joints
(Chattopadhyay, Chollet, and Hintermann, 1991; Kang and Kim, 1995; Russell, Oh, and
Figueredo, 1991). This is because ceramics are not wetted by most traditional filler metals,
even when their surfaces are clean. Ceramics are chemically very stable, with their atoms
strongly bonded to one another. Therefore, these materials will not react with and be
wetted by the filler unless the latter contains an active element that can attach itself to the
anionic species of the nonmetallic material. Titanium is often used as an active constituent
of brazes. Less reactive elements, such as chromium, and more reactive elements, such as
hafnium, are also used. Active metal joining is only effective if sufficiently high
temperatures, typically above 800"C, can be used for the joining operation so that the active
ingredient is able to react with the nonmetal (Humpston and Jacobson, 1993).
Wettability of the active braze alloy is the first important criterion used to choose the
proper type of braze alloy. Practical problems encountered in joining two dissimilar
materials are not only the thermal mismatch, which causes a significant residual stress at the
interface, but the chemical compatibility among the joint components and its performance at
the working temperature. The active element plays a crucial role in the braze alloy, and has
a strong effect on both the chemical compatibility and performance of the braze alloy.
There are many types of commercial active braze alloys based on aluminum, silver,
copper, nickel, and titanium. The type of active element in the braze alloy is determined by
many factors. The active element must not react strongly with the base metal, or the
activity of the active element may be decreased greatly by the formation of the intermretallic
compounds. For instance, Ti is not suitable as an active element in aluminum base braze
alloys, because a very stable intermetallic compound will be formed between Ti and Al.
Therefore, there are suitable active element(s) for different alloys. Based on previous
research, the wettability of Al base braze alloys can be enhanced by adding Mg as an active
element (Russell, Oh, and Figueredo, 1991; Ip, Kucharski, and Toguri, 1993).
Magnesium alloying decreases the contact angle of the molten aluminum drop because
evaporation of magnesium prevents formation of a thin oxide layer at the surface of the
molten drop (Kobashi, Kuno, Choh, and Shimizu, 1995). Ti is a good active element in
copper or silver base braze alloys (Scott and Nicholas, 1975; Xu and Indacochea, 1994).
The excellent compatibility of Ni-Cr alloys has already been utilized to fabricate abrasive
tools with tungsten carbide particles by liquid phase bonding (Chattopadhyay and
19
Hintermann, 1993). The use of Ni-Cr alloys containing B, Si or Si and Ti in brazing
graphite to steel has also been reported (Amato, Cappelli, and Martinengo, 1974; Lowder
and Tausch, 1975).
There are four major classes of commercially available braze alloys - Al, Ni, Ag,
and Cu base alloys. Two barriers prohibit the application of Al base braze alloys in metal
single layer (MSL) technology. Due to the chemical stability of aluminum, there is no
commercially available binder for Al base braze alloys to form a slurry paste which is a
necessary step in the MSL process. For example, Al-Si braze alloy, one of the most
popular Al base braze alloys, can not wet diamond at 800*C, because it reacts with the
binder. In addition to the chemical stability problem, these alloys are of low strength and
wear resistance and are not suitable as a braze to fabricate monolayer diamond abrasive
tools. The matrix, holding the abrasive grits, should be strong enough and should not
yield under the action of the cutting force transmitted to it by the grit (Chattopadhyay and
Hintermann, 1993).
On the other hand, the Ni base braze alloys have high yield strength and hardness,
but most of their brazing temperatures are above 1000*C (Schwartz, 1987). Because the
MSL grinding wheel is used at very high grinding speeds, the distortion of the grinding
wheel becomes an important issue. One of the most effective ways to reduce distortion is
to decrease the brazing temperature. It is reported that high brazing temperature can result
in graphitization of the diamond and decrease its strength (Wilks and Wilks, 1991). It is
preferred that the brazing temperature be less than 1000'C. Another problem encountered
in application of Ni-Cr-X braze alloys is that the Cr of the Ni base braze alloy can not wet
CBN (Chattopadhyay and Hintermann, 1993). This situation can not be improved by
increasing either the wt% of Cr or the brazing temperature, and extension of the brazing
time does not show any significant changes. Therefore, the Cr content of Ni base braze
alloys is not a solution for MSL technology. Ag base braze alloys are undesirable because
of their low strength and prohibitively high cost. Hence, the research in this paper is
concentrated on copper active base braze alloys.
At least two commercially available copper base brazing filler metals wet diamond
and CBN (Sara, 1990; Schwartz, 1989; Evens, Nicholas, and Scott, 1977). Ticusil, CuAg eutectic and 4.5 wt% Ti, with a solidus of 830*C and a liquidus of 8500 C is one of the
most popular active copper base braze alloys applied in metal-ceramic joining (Olson, 1993;
Kuzumaki, Ariga, and Miyamoto, 1990). Cu/Sn/Ti, an active braze alloy with lower
ductility and higher hardness and strength than that of Ticusil, is another good choice in
joining diamond or CBN to steel. In addition the wear resistance is superior. However,
low ductility due to a large volume fraction of intermetallic phases is a potential problem.
20
Highly active titanium or zirconium can be made available at the ceramic-metal
interface by hydride decomposition of a powder slurry on the ceramic surface. The
application of braze alloys which contain reactive metals requires that joining be performed
at a very low oxygen potential, or in a dry inert-gas atmosphere with a low dew point to
prevent the reactive elements from reacting with the atmosphere (Pearsall and Eingeser,
1949). However, the active titanium or zirconium hydride will decompose into pure metal
and release hydrogen gas below the brazing temperature. Vacuum brazing is a better choice
than inert-gas atmosphere in preventing voids in the joints after brazing. The use of
hydride can avoid oxidation of the active element powder before the process begins.
Another way to avoid oxidation of the active element is to use alloy powders instead of a
pure elemental powder mixture, but this will result in higher cost due to the chemical
instability of the active element in the process of powder formation.
A comprehensive theory of the spreading of liquids with no chemical reactions has
been developed (Howe, 1993a). Considering the fact that materials possess a free surface
energy balance, the Young-Dupre equation will exist between a liquid drop and a solid
substrate:
7.1 =7
- 71V cos
e
(2.1)
Here, y, %1, and y,, denote the liquid-vapor, solid-liquid and solid-vapor surface tension,
respectively, and 0 is the contact angle. To apply the Young-Dupre equation to nonreactive systems, the surface tension between the molten alloy and the diamond must be
measured. However, these data are scarce and are system dependent (Howe, 1993a;
Keene, 1993; Nogi, Okada, Ogino, and Iwamoto, 1994; Sugihara and Okazaki, 1993).
Seldom can we apply this equation to the practical situation.
In the case of a reactive brazing of diamonds, it becomes much more complex than
non-reactive systems. Decrease in the contact angle over time is usually taken as evidence
that the reactions are occurring between the molten drop and the diamond and that the
system is not equilibrium (Loehman and Tomsia, 1994). The active element, titanium, will
decrease the wetting angle drastically by producing a thin layer of reaction product, titanium
carbide. In addition to reaction layer formation, a precursor film, or halo, which shows up
ahead of the nominal contact line is a common phenomenon in liquid metal spreading on a
solid (Xian, 1993). The presence of titanium, zirconium or hafnium in the alloy induce the
formation of a precursor film, but niobium, vanadium and tantalum do not. A precursor
film will not form unless the critical wetting temperature is reached. This is found to be
true for Ticusil and Cu/Sn/Ti alloys. If a precursor film appears ahead of the spreading
droplet, better wettability of the liquid on the solid will be expected, because the precursor
21
film is mainly composed of reactive metals such as titanium. The transportation of the
active element into the joined surface plays an important role in determining the wettability
of the braze alloy. Surface diffusion, evaporation-condensation, and rapid adsorption then
film overflow are proposed to explain the formation of a precursor film.
Because the reactive wetting is a kinetic process, Young's equation can not be
applied. There is at present no generally accepted theory capable of describing reactive
wetting satisfactorily. However, there is an equation which can describe the material
transfer at the solid liquid interface. The smallest contact angle possible in a reactive
system is given by (Espie, Drevet, and Eustathopoulos, 1994; Kritsalis, Drevet, Valignat,
and Eustathopoulos, 1994):
cos9
=cos 0 -(Ayr)
AG)
(2.2)
where 00 is the contact angle of the liquid on the substrate absent of any reaction; and Ayr
takes into account the change in interfacial energy. AGr is the change in free energy per
unit area released by the reaction of the material contained in the "immediate vicinity of the
metal/substrate interface."
It is often stated that AG, represents the predominant
contribution of wetting, meaning that an intense reaction is required to obtain good wetting
of a liquid on a solid. However, major difficulties lie in the calculation and the
experimental determination of this term. Indeed, from a theoretical point of view the
coupling conditions of the time-dependent interfacial reaction with the kinetics of wetting
are unknown. The thickness of the zone in the immediate vicinity of the interface involved
in the reaction appears as an adjustable parameter. Moreover, a simplified thermodynamic
approach can not be a useful tool in determining AG, (Wang and Lannutti, 1995).
For
example, considering the nonideal behaviour of the liquid melt, the reaction between the
reactive element (Re) in the melt with the nonmetal (X=O, N, or C) in the ceramic (MeX )
can be generalized as follows:
V
V
Re+-MeX = Re X, +-Me
E
(2.3)
e
where v and e are the chemical stoichiometries of the ceramics. The Gibbs energy change
for the reaction is
AG= AGO(ReX,)E
AG(MeX,)+ R
E
n(
)
a(Re)6
(2.4)
22
where AG 0 (ReX,) and AG 0(MeX,) are the Gibbs energy of formation of ReX, and MeX',
respectively, and a(Me) and a(Re) are the activities of Me and Re in the liquid melt,
respectively. For most binary metal melts, these activity data at elevated temperature are
lacking, although there are many improved methods for estimating such information. For
most commercial multi-component brazing alloys, activity data are difficult to find, and
estimating of these data may result in large deviation from reality. One can realize from
equation 2.4 that reactive wetting is not only governed by the relative stability of the
reactive metal compound but is also strongly dependent on the activities of the related
species. An accurate estimation requires a knowledge of the activities of the reactive
elements in the braze alloy.
Therefore, a rigorous evaluation of AGr for a given
metal/ceramic system is at present impractical (Paulasto, Kivilahti, 1995).
2.2 Reaction Zone Formation and Its Effects on Mechanical Properties of
the Joint
When diamond is joined by an active braze alloy, a reaction layer forms at the
interface between the ceramic and the braze alloy. It is usually admitted that chemical
reaction is beneficial in achieving strong bonding (Courbiere, 1991; Prasad and Mahajan,
1994), and it is very difficult to analyze precisely the interface because of its quite different
physical and chemical properties. As a result, there are still many problems in
understanding the joining mechanism (Chung and Iseki, 1991). Interfacial phenomena in
joining of ceramics and metals by active braze alloys have been studied extensively (Howe,
1993ab; Fujii, Nakae, and Okada, 1993; Shaw, Miracle, and Abbaschian, 1995; Lee and
Lee, 1992; Treheux, Lourdin, Mbongo, and Juve, 1994; Loehman, 1994). The
mechanical properties of the brazed joint is a function of key parameters such as
temperature and time. Both are important in determining reaction zone formation. Many
research results show that the titanium does not wet and react with ceramics below 700 0 C
(Xian, and Si, 1991; Nukami and Flemings, 1995). Stasyuk (1984) studying the
interaction of diamond with titanium at high pressure proposed a high rate of carbide
formation during the initial period and retardation of the growth rate thereafter. The rate
during the initial stage of the process is determined by reaction at the interface, which is
very rapid compared with the second stage. This stage leads to the formation between the
diamond and titanium of a sublayer of carbide having low saturation with respect to carbon,
i.e., of a carbide of composition corresponding to the lower boundary of the homogeneity
region. The carbide formation process is then complicated by the diffusion of carbon
23
through the carbide layer, so that the growth rate of the reaction layer is decreased. Also,
during the reaction, the non-stoichiometric carbides are formed and the number of vacant
lattice points in the metalloid sublattice is decreased, which also retards the rate of transfer
of carbon in the carbide. Accordingly, during the second stage of the process, the growth
rate of the carbide is decreased and is rate-controlled by carbon diffusion, but the carbide
becomes more stoichiometric as well as more perfect in structure. The highest rate of
interaction takes place during the first few minutes of heating, and the interaction is then
reduced because of the decreased rate of diffusion of carbon through the layer of carbide
produced.
For diffusion controlled growth, the reaction layer thickness can be estimated by a
Johnson-Mehl type equation with a time exponent, n, of 0.5 (Howe, 1993; Akselsen,
1992; Nakao, Nishimoto, and Saida, 1989; Chidambaram, Edwards, and Olson, 1994):
x= kot" exp(-
RT
)
where t is the brazing time, ko a constant,
(2.5)
Q an
activation energy for diffusion, R the gas
constant and T is the brazing temperature.
As can be expected, the strength of a ceramic-metal joint will depend on the nature
of the interfacial reaction layer and residual stresses at the interface arising from a mismatch
in the coefficient of thermal expansion. A summary of factors affecting the tensile strength
of ceramic to metal joints is described in Figure 2.1 (Nakao, Nishimoto, Saida, and Ohishi,
1993).
When the layer forms and grows, the joint strength increases progressively up to a
maximum value for increases in the area of the interface and in the mechanical interlock
effect. However, the mechanical strength of a brittle system such as the reaction layer is
governed by three factors: the severity of pre-existent flaws, the minimum crack
propagation resistance of the material in the vicinity of that flaw, and the associated
magnitude of the local residual and imposed stresses (Evans and Lu, 1986). The
microstructure at the interface often displays arrays of dislocations, and defects,
presumably arising from thermal expansion mismatch between joined materials (Charim,
Loehman, 1990). When the reaction layer is thin, the size and quantity of the flaws in this
layer are less than those in a thicker layer, but when it becomes thicker than the optimum,
defects such as a porous zone and cracks occur. The existence of porosity in the reaction
layer was reported in many studies (Stoop and Ouden, 1995; Gupta, Lai, and Soo, 1995).
It can result from columnar-equiaxed type of solidification structure and/or the product of
reaction. Consequently, an optimal reaction layer thickness exists, as has been confirmed
in many experiments (Howe, 1993; Xu, Indacochea, 1994).
24
It has been reported that the bond strength is limited either by plastic flow or by
ductile fracture in the metal when the bond layer is thick (Dalgleish, Trumble, and Evans,
1989). Conversely, when the bond layer is thin, failure occurs in the ceramic. Conditions
for failure either by rupture of the metal or by brittle cracking in the ceramic have been
revealed as the operative failure modes, depending on the bond layer thickness and the
yield strength. Based on the previous explanation, there are optimal process variables
such as temperature and time in order to acquire the best bonding strength between
diamond and the braze alloy. Finding suitable process variables for certain active braze
alloys is one of the primary goals of this research.
2.3 Residual Thermal Stresses after Brazing:
In the last decade great interest has been aroused in the bonding of ceramics to
metals for practical applications of ceramics. There are still several problems to be solved
for ideal bonding. Thermal expansion mismatch between ceramics and metals is one of
them. When the joints are bonded at elevated temperatures, thermal expansion mismatch
produces a large stress concentration in the joints. This stress can cause fatal damage in the
joints without any applied stresses. Hence, compensation for this mismatch is needed to
obtain high strength joints (Hatakeyama, Suganuma, and Okamoto, 1986). Several
methods have been developed for this purpose. For example, multilayered structures have
been developed to reduce the thermal stress (Shen and Suresh, 1995; Nakao, Nishimoto,
Saida, Murabe, and Fukaya, 1994; Stoop and Ouden, 1995; Srolovitz, Yalisove, and
Bilello, 1995). The layered structure comprises an elastic-perfectly plastic ductile material
sandwiched between two elastic brittle materials. Candidate interlayer materials are selected
on the basis of their mechanical and physical properties, taking into account information
provided by relevant phase diagrams. The interlayers need to be ductile and should have a
low yield strength and a thermal expansion coefficient matching the material combination to
be joined (Cao, Thouless, and Evans, 1988).
Functionally Graded Materials (FGMs) offer another solution to the thermal stress
problem (Ravicha, 1995). The FGM system consists of a gradual change in the volume
fraction of constituents from one location to the other in a component. A typical FGM
structure consists of a change from fully ceramic on one side to fully metal on the other side
with the intermediate regions consisting of a mixture of both constituents, varying in
volume fraction with distance. Such a design would allow a gradual change in thermal
expansion mismatch, minimizing the thermal stresses arising from cooling or heating.
Further, metallic phases embedded in the ceramic could increase the thermal conductivity,
25
reducing the temperature gradient across the thickness and hence minimizing the
susceptibility to thermally induced shock. However, due to factors such as chemical
incompatibility, wetting problem, and manufacturing cost, these ideas are currently not
available for MSL technology.
There are several reported instants in which the fracture of ceramic/metal bonds
originates at the interface (He, Dalgleish, Lu, and Evans, 1988; He, and Evans, 1991).
Such behavior is most likely when (1) the bond is relatively thin, such that the limit load is
substantially higher than the yield strength of the metal and (2) when the bond is relatively
devoid of flaws. If these conditions are achieved, it is important to understand the behavior
of flaws near the interface. Three important factors are involved in the behavior of these
flaws: the residual stress, the mismatch in elastic properties, and plastic flow in the metal.
Residual stress exerts an influence on fracture and causes fracture in the absence of an
applied load. When the interface has a sufficiently high fracture energy, failure does not
occur at the interface. The major limitation on the strength concerns stress concentrations
in the ceramic near the edge. These stress concentrations arise because of the elastic
mismatch between the metal and the ceramic. The magnitude of the stress and of the
energy release rate at edge flaws is modified by plastic relaxation and thermal expansion
misfit. Two basic behaviors have been identified. For strong bonds, the edge flaws are
small and the stresses are large. Plastic relaxation effects dominate. Notably, the edge
failures in the ceramic near the bond can be suppressed by using a metal with a low yield
strength. In this regime, expansion misfit effects, although small, are detrimental. Very
different characteristics are obtained when the cracks are relatively large and the stresses
small, as appropriate for the assessment of crack arrest, e.g., when the loadings are
displacement dominated. In this region, the energy release rate is diminished by having
large positive expansion misfit, because of the compressive residual stresses generated near
the interface. In the case of diamond/braze alloy bonding, there is a huge positive
expansion misfit, and a compressive force is generated in the diamond near the interface. If
the bond is "strong" as described above, a low yield strength braze alloy would be
preferred in MSL technology when considering the stress distribution in the diamond.
It is important to estimate the residual stresses in the MSL grinding wheel after
brazing. A purely elastic model may be not suitable for this analysis, although there are
analytical solutions for some simple geometries (Krishna Rao and Hasebe, 1995). This is
because the braze alloy experiences plastic deformation within the process temperature
range. Considering a layered composite which is composed of layer 1 of height h, (made
of relatively weaker material, e.g., a metal) and layer 2 of height h2 (made of the relatively
stronger material, e.g., the diamond), the thermally-induced elastic deformation in a two-
26
layer structure with the same thickness can be estimated by the following equations
(Suresh, Giannakopoulos, and Olsson, 1994):
Plane stress model:
AT
t
res8
-
(2.6)
,(E1+E+14E E 2)
EIE 2 (a - a 2)(E 2 + 7E 1 )
Plane strain model:
A Titri" = a,
B=
E,
1
[B 2 ( +v1 - v)- BEIa I(1- 2v,) + Eca4]-45
[(1+ v1 )al - (1+v
(1-vl-)
x [I+ (
E2
)21
E
2 )a 2]' [7 (l
1- v2
)(
E2
-v22+14(
l-v2
E2
(2.7a)
2
)+ 1]
1v
)-(
l-v2
(2.7b)
-1
where layer 1 and layer 2 are isotropic, elastic-perfectly plastic solids of Young's moduli,
El and E2, with yield strengths, ay, and ay2 , coefficients of thermal expansion, a and a ,
1
2
and Poisson's ratios, v, and V2 . AT, is the characteristic temperature difference, which
causes the onset of plastic deformation in layer 1.
Substituting proper material properties
into equation 2.6 and 2.7,
temperature
the characteristic
differences
of various
diamond/metal combinations can be obtained as shown in figure 2.2. It is clear that plastic
deformation will be formed within a 100'C temperature change for diamond/metal joint.
Therefore, considering the elastic response of the braze alloy only is not pragmatic. It is
essential to consider plastic deformation in estimating the residual thermal stress in the
braze alloy.
In addition stress relaxation by rate-independent plastic deformation,
rate-
dependent plastic deformation such as creep also plays an important role in decreasing the
thermal stress at the interface (Pan, 1994; Paydar, Tong, and Akay, 1994).
Creep
dominates the mechanical response of the braze alloy at high temperatures (above 1/2 the
melting point of the material), and rate-independent plasticity, on the other hand, governs
the alloy behavior at low temperatures (blow 1/3 melting point of the material). Both have
no currently available analytical solutions in solid mechanics. Therefore, a finite element
approach becomes the easiest way to estimate the residual stresses in grinding wheels.
27
2.4 Types of Diamond Wheel Failure
The grinding process can be described as a machining process which is analogous
to the milling process, using a milling cutter having thousands of very small teeth.
(Salmon, 1992). Each tooth removes an extremely small chip from the surface of the
workpiece material, and produces a smooth and accurate surface finish. The grinding
process is very difficult to analyze and even more difficult to model due to its stochastic
nature.
There are generally four types of surface interactions taking place in the grinding
zone characterized as shown in figure 2.3 (Subramania, and Ramanath, 1992). The
interaction between the abrasive grain and the work material depends on the grinding
process variables, superabrasive geometry, and work material properties. There are three
frictional interactions due to the rubbing of the swarf produced against the bond matrix in
the wheel, the rubbing of the bond matrix in the wheel against the work material, and the
rubbing of the swarf against the work material. Based on the above descriptions, there are
three possible reasons which can result in failure of a superabrasive wheel:
(1) Fracture of the superabrasive itself:
Fracture of the superabrasive may result from a heavy load of the wheel or low quality
of the superabrasives. Natural diamond contains impurities and defects. Though the
diamond will not expand with increasing temperature, inclusions in the diamond will
expand at a rapid rate and destroy the grain (Salmon, 1992). Because synthetic
diamond and CBN have fewer inclusions and defects, they are much stronger than
natural diamond.
(2) Fracture at the interface between the braze alloy and the diamond:
Debonding between the diamond and the braze alloy is related to the kinetics of
interlayer formation and the residual stresses within the interface as discussed earlier.
Therefore, interfacial thickness control is important and will be studied in the
experiment.
(3) Failure of the braze alloy due to abrasion and/or fatigue:
Wear of the braze alloy may result from rubbing of the swarf against the bond matrix or
rubbing of the bond matrix against the work material. The grinding of brake pads or
concrete is a typical example of the first case. The ground particles are accumulated
next to the matrix and cause wear of the bond metal. On the other hand, the grinding of
rubber is an example of wear due to the rubbing of the bond matrix against the work
material. The wear of the bond metal results from intimate contact and friction between
the bond metal and the rubber. Consequently, rubber grinding is very abrasive. In
28
addition to wear of the braze alloy, fatigue may also result in failure of the braze alloy
which experiences cyclic loading during grinding. If there are solidification hot cracks
in the braze, they may grow due to fatigue of the braze alloy. The MSL grinding wheel
can not be dressed. The braze alloy will experience increasing load transmitted from
the grit due to blunting of the superabrasive's cutting edges. This can be observed
during grinding, because the normal force will increase with time. Therefore, the
mechanical properties of the braze alloy are an important factor in determining the
wheel's life. In the case of the MSL grinding process, the braze alloy experiences high
cycle fatigue in the initial stages of grinding, because the superabrasive grits are sharp.
Defects in the joint play an important role in determining the fatigue strength of the
joint. As they become blunt, fatigue of the braze shifts from high cycle fatigue wear to
low cycle fatigue wear, and the braze alloy deforms plastically due to higher applied
grinding load. In other words, the ability of the braze deformed plastically dominates
its fracture behavior. High ductility of the braze alloy creates higher wear resistance in
low cycle-fatigue type wear (Ikeno, Siota, Nobuki, and Nakamura, 1995). A braze
alloy with low yield strength and high toughness would be preferred in MSL grinding
technology, because it can absorb the plastic energy much easier than a braze with a
high yield strength and low toughness. The superabrasives can, therefore, be protected
by the braze alloy instead of being crushed. Both ways to improve the braze alloy will
be studied in this research.
In summary, an analysis of the reason why a superabrasive wheel fails is not an
easy task. It depends on many factors and must be studied case by case.
29
Strength of the
I I
reaction layer
Strength near the
bonding interface
.......
-[Occurrence
Bonding strength
at interface
Factors affecting
bonding strength
Residual stress
of defects]
Chemical bonding strength
(Bond strength between atoms)
Reacted bonded area
(Area of the bonding interface)
Mechanical joining strength
(Anchoring effect)
Figure 2.1 Factors affecting the strength of ceramic to metal joints
(Nakao, Nishimoto, Saida, and Ohishi, 1993)
1 Plane Stress Model U Plane Strain Model
U
E
S
S
0
S
70
7
01
50
U
-
40
*
o~O
S
301
U
204
I-
7
S
S
U
U
1~
S
0
1 0' 0 11
Ag-Diamond
Al-Diamond
Cu-Diamond
Ni-Diamond
Figure 2.2 The predicted characteristic temperature differences by plane stress
and plane strain model
30
Diamond wheel
2
1
Figure 2.3
3
_Workpiece
Interactions at the grinding zone: (a) superabrsive/work interface; (b)
swarf/bond interface; (c) swarf/work interface; (d) bond/work interface
(Subramania, and Ramanath, 1992).
31
3. Problem Identification and Preliminary Study of Currently
Available Braze Alloys
3.1 Documentation of the Failure Mode in MSL Grinding Wheels
To identify the failure mode of MSL grinding wheels, a grinding test was made
using five inch diameter test wheels with different braze alloys. High density alumina
(99.5%) blocks with dimensions of 20.32cm*10.16cm*2.54cm were used as the grinding
material. The wheel speed was 25.4 smps (surface meter per second), the longitudinal
speed was 25.4 millimeter per second, the transverse feed was 2.54 mm, and the depth of
cut was 0.432 mm. The definition of wheel failure in this test is when the normal force
increases to 2670 N (600 lb) and/or the grinding wheel can not grind anymore. Six braze
alloys were evaluated in this test as described below:
(1) NIPLATE: This is a traditional nickel-plated diamond wheel. 40/50 mesh IMG*
diamonds were used as the abrasive.
(2) NORTON: This is Norton's currently used braze alloy. Its chemical composition is
70Cu-2lSn-9Ti in wt%. 77Cu-23Sn prealloyed 325 mesh bronze powder was used with
titanium hydrite. 40/50 mesh IMG* diamonds were applied as the abrasive.
(3) NORTON-S: This was developed by Norton Company at Salt Lake City. It is a nickel
base braze alloy, and the brazing temperature is about 1030'C. 40/50 mesh IMG*
diamonds were used as the abrasive.
(4) MIT: This was made by MIT. The chemical composition is 75Cu-25Sn- 12.5Ti-7.5Zr1OTiC-0.2C by weight. 40/50 mesh IMG* diamonds were used as the abrasive.
(5) High Sn: Cu/Sn/Ti braze alloy with over 30 wt% tin content. 40/50 mesh IMG*
diamonds were used as the abrasive.
(6) ABR TECH: This was purchased from Abrasive Technology. The quality of
diamonds is unknown.
Figure 3.1 shows the fracture surface of the nickel-plated wheel. Fracture of the
diamonds is the main failure mode. Most of the diamond grits still have sharp cutting
edges. This indicates that only some of the grits contribute to the grinding process. When
the cutting edges of the working grits become blunt, the normal force goes up, and the
failure criterion of the wheel is achieved. Because there is no meniscus shape around the
diamond in the Ni-plated MSL grinding wheel, the diamond is not supported by Ni. The
superabrasive grits experience most of the cutting force. Moreover, the geometry of the
*Trademark of Tomei Company, artificial diamonds
32
diamond situated in the Ni is similar to a cantilever beam. The root of the grit supports a
huge moment due to the cutting force. This will induce a high tensile stress during
grinding. Therefore, many diamond grits fail at the root as shown by the arrows in Figure
3.1.
Figure 3.2 shows SEM fractographs of the currently used Cu/Sn/Ti MSL grinding
wheel after grinding test. Both fractured and debonded diamonds are shown in Figure
3.2(a). There are two types of the cracks observed in the debonded and fractured
diamonds. One is the cracks parallel to the diamond boundary, the other is the cracks
situated in the radial direction of diamonds. The cracks parallel to the diamond boundary
originate from high tensile stress in the braze alloy during grinding. This indicates that the
ultimate tensile strength and/or the ductility of the braze alloy is not sufficient to support the
diamond during the grinding process. Therefore, it is necessary to increase the ultimate
tensile strength and/or the ductility of the braze alloy in order to retard or eliminate the
formation of this type cracks.
The radial cracks, on the other hand, result from the mismatch of thermal
expansion coefficients between the diamond and the braze alloy. A schematic of the cross
sections of a bonded diamond grit is given in Figure 3.3. Due to the mismatch of the
thermal expansion coefficients, there is a compressive stress in the diamond, and a tensile
stress in the braze alloy after brazing as shown in Figure 3.3(a). In an ideal MSL bond, the
diamond is tightly grasped by the braze alloy. In addition to the formation of the chemical
bond between the reactive element, titanium, in the copper base braze alloy, and the
diamond, the thermal expansion mismatch stresses between the diamond and the braze
alloy provide an additional contribution to hold the diamond. If, however, the braze alloy
can not wet the diamond very well as shown in Figure 3.3(b), thermal stress will have an
adverse effect. In this case, diamond may debond and/or cracks initiate on the diamond
surface due to thermal expansion mismatch. However, if the braze alloy wets the diamond
too well as shown in Figure 3.3(c), the braze alloy covers most of the sharp cutting edge of
the diamond. The grinding wheel will become blunt, and its grinding performance is
deteriorated. The stress state in the MSL grinding wheel is very important. Therefore, a
detailed analysis of thermal stress in the grinding wheel after brazing will be performed in
the following chapter.
Figure 3.4 shows a fractograph of the nickel-based braze alloy developed by
Norton at Salt Lake City. Both fractured and debonded diamonds are observed. The Nibase braze alloy is very hard, over 60 HRC, and brittle. Some cracks can be observed as
demonstrated by an arrow in Figure 3.4. The braze alloy should be ductile enough to
absorb the thermal strain of brazing and plastic deformation during grinding. Also, it must
33
be not too hard in order to avoid crashing the grits during grinding. Debonding of the
diamond is much more pronounced than that of the previous cases.
Figure 3.5 shows the fracture surface of 75Cu-25Sn-12.5Ti-7.5Zr-1OTiC-0.2C (by
weight) wheels. Transverse fracture and debonding of the diamonds are two primary
fracture modes. The fracture mode of the braze alloy is basically brittle. No dimple was
formed in the fracture area. Figure 3.6 shows a fractograph of high tin grinding wheel.
Because it is much harder and more brittle than 70Cu-2lSn-9Ti (in wt%), many cracks in
the braze alloy can be observed in the figure. These cracks may result from thermal
stresses and/or grinding stresses. Another important observation is the diamond clustering
phenomenon. This indicates the viscosity of the braze alloy is not high enough to restrain
the diamonds during brazing. This diamond clustering phenomenon is also reported in the
Ni-Cr alloy with flame-sprayed brazing (Hintermann and Chattopadhyay, 1992).
Therefore, controlling the brazing temperature and changing the alloy composition in order
to increase the viscosity of the braze alloy are two alternative ways to reduce their
clustering. Figure 3.7 shows the fracture surface of the ABRASIVE TECH's MSL
grinding wheel. Because the quality of the diamond is unknown, the result can not be
compared with other data. However, the cracks shown in the braze alloy and debonded
grits are similar to the previous observations.
All fractographs show that only fraction of the diamonds is effective in grinding.
The grinding will become inefficient when the effective diamonds are blunt. Therefore, in
order to increase the percentage of the effective diamonds in the grinding wheel, keeping
the diamonds at the same height is very important.
3.2
Fundamental Study of the Currently Used Active Braze Alloys
There are two active braze alloys currently used by Norton in the production of
MSL superabrasive grinding wheels: one is Ticusil, Ag-Cu eutectic +4.5 wt% Ti; the other
is 70Cu-2lSn-9Ti in wt%. Ticusil is widely used in metal-ceramic joining and has been
studied extensively (Loehman and Tomsia, 1994; Pandey, Lele, and Ojha, 1995;
Suzumura, Yamazaki, Takahashi, and Onzawa, 1995). Figure 3.8 shows the ternary
phase diagrams of Ag-Cu-Ti and the microstructure of Ticusil (Villars, Prince, and
Okamoto, 1995; Petzow and Effenberg, 1988). According to the isothermal section at
700*C, there are three equilibrium phases, Ag, Cu, and y-CuTi. The microstructure shown
in Figure 3.8(b) exhibits Ag, Ag-Cu eutectic, and y-CuTi phases respectively.
The
proposed solidification process is that of primary silver and y-CuTi intermetallic phase
34
solidifying first. Next, both dendrite ripening and intermetallic compound growth proceed.
Finally, the remaining liquid cools to the eutectic point, and the eutectic phase, Ag-Cu, is
formed.
The elongation and tensile strength of Ag-Cu eutectic alloy is 35% and 154.4 MPa
(Basak, Singh, Dubey, and Mohanty, 1992). Both the primary Ag phase and Ag-Cu
eutectic alloy are ductile.
However, the inherent brittleness of y-CuTi intermetallics
deteriorates the total ductility of Ticusil. The needle-like intermetallic phase as indicated by
arrows in Figure 3.8(b) provides a possible low energy path to initiate and propagate
cracks in the braze alloy. It can not be avoided except by Ti consumed by reacting with
other element(s) other than Cu and Ag. As explained in Chapter 2, one of the primary
challenges in developing active braze alloys is to prevent and/or retard brittle intermetallic
phase formation. If it can not be avoided and/or retarded, controlling the size and
morphology of the intermetallic phase is the next choice. An unusual feature of Ticusil is
that its chemical composition is located within a miscibility gap. This will result in an
Moreover,
inhomogeneous microstructure as demonstrated in Figure 3.8(b).
microshrinkages and porosities are formed during the traditional solidification process,
caused by the lack of melt supply in the interdendritic zone (Tensi, Hooputra, Weinfurtner,
and Mayr, 1995) In fact, microshrinkages can be detected in almost all of the conventional
by cast specimens, especially in the interdendritic zone. These are responsible for the
incipient fracture. Hence, accurately evaluating the mechanical properties of Ticusil is
difficult.
Table 3.1 shows the ultimate tensile strength, elongation, and hardness of Ticusil.
As predicted before, titanium addition causes its elongation drop to about 3%. Figure
3.9(a) shows the fracture surface of Ticusil after the tensile test. The cracks initiate and
propagate from microshrinkages and the brittle intermetallic phase as indicated by arrows in
the photo. Figure 3.9(b) shows the fractograph of the Ticusil MSL grinding wheel after
the grinding test. Unlike the fractograph displayed in Figure 3.2, the primary failure mode
of the MSL wheel is the debonding of the diamonds instead of the fracture of them. This
can result from a weak interface and/or insufficient abrasive resistance of Ticusil.
Table 3.1 The mechanical properties of Ticusil and 70Cu-2lSn-9Ti in wt%
Braze Alloy
UTS (MPa)
Elongation(%)
Hardness
Ticusil
180
3
87 (HRB)
70Cu-21Sn-9Ti
211
0.6
26 (HRC)
35
The ultimate tensile strength of 70Cu-2lSn-9Ti (wt%) is 211 MPa (30.6ksi), and
its elongation is 0.6% as displayed in Table 3.1. It is stronger and harder but less ductile
than Ticusil (Ag-Cu eutectic+4.5wt%Ti). Figure 3.10 demonstrates the fractograph of the
70Cu-2lSn-9Ti (wt%) tensile test specimen. There is no Cu-Sn-Ti ternary phase diagram
available. However, at least two phases in the braze alloy can be identified: one is a
copper-rich phase and the other is a Cu/Sn/Ti intermetallic phase. According to the EDX
analysis of the copper-rich phase marked A as shown in the figure, its chemical
composition is 84.6Cu-15.3Sn-0.lTi (wt%). The chemical composition of the Cu/Sn'Ti
intermetallic phase marked B as shown in the figure is 29.3Cu-41.lSn-29.6Ti in wt%.
The cracks displayed in Figure 3.10 originate from the intermetallic phase. It can be seen
that the intermetallic compound has cracked and the crack does not follow the interface
between the intermetallic compound and the copper-rich matrix. This indicates that the
bond is coherent and strong. The fracture of blocky intermetallics where the cracks are
observed to take place inside the particles indicates the brittle nature of this phase.
Examination of the fracture surfaces shows that the failure through the copper-rich matrix is
more ductile than that through the intermetallics. Therefore, the suggested fracture
mechanism in this braze alloy is that of straining the specimen to the point where the
intermetallic phase fractures, followed shortly by failure of the matrix. This type of failure
is widely observed in metal matrix composites or alloys with hard, brittle second phase(s)
(Loretto and Konitzer, 1990; Narayanan, Samuel, and Gruzleski, 1995; Samuel and
Samuel, 1995).
Figure 3.11 shows the thermal analysis result of 70Cu-21Sn-9Ti (wt%). Because
of the high activity of titanium in the braze, it tends to react with the platinum crucible
material. The measured melting point of the alloy is only an approximate value. The alloy
was prepared by arc melting and started melting at 846.4*C. The currently used brazing
temperature is 865"C. However, 77Cu-23Sn (wt%) bronze powder and 325mesh (44 gm)
TiH2 powder are used instead of 70Cu-21Sn-9Ti (wt%) master alloy. The use of bronze
alloy powder is better than pure elemental powder based on field tests. The kinetic barrier
of melting can be minimized by using alloy powder, because the alloy powder melts at
lower brazing temperatures and forms a much more uniform liquid phase than that of the
elemental powder. Hence, better wetting, less segregation and a more homogeneous
microstructure of the braze alloy is obtained. This is consistent with the reported rapidly
solidified low-silver brazing filler alloy foils (Dev and Mohanty, 1994). This alloy shows
much better microstructural homogeneity in comparison to its conventionally cast
counterpart. This results in uniform melting and flow in the joint areas during brazing.
36
The brazed joints are free voids and segregation. In addition to these benefits in
microstructure, the dimensional accuracy of the MSL grinding wheels can be improved by
using alloy powder. 325 mesh bronze powder was used throughout the experiments.
Figure 3.12 shows the SEM morphology and dot mapping of the 70Cu-2lSn-9Ti
(wt%) alloy braze. It is clear that there is a reaction layer, TiC, between the diamond and
braze alloy. The thickness of the reaction layer is less than 1 pm. Because of electron
spreading in the specimen, the maximum lateral resolution of an EDX analysis is about 1
pm (Watt, 1985). Therefore, measurement of its thickness can only be considered as an
approximation. The reaction layer thickness of 70Cu-2lSn-9Ti (wt%) is thinner than that
of most observed Cu-(Ag)-Ti active braze alloys (Nogi, 1993; Peteves, Ceccone, Paulasto,
Stamos, and Yvon, 1996). For example, the reaction layer for joining AL 20 3/A12 0 3 by
Ticusil is about 2 pm (Hongqi, Zhihao, and Xiaotian, 1994; Hongqi, Yonglan, Zhihao,
and Xiaotian, 1995). It is also reported that the Ti segregates at the joint interface and
reduces the bonding strength between the diamond and the Ticusil (Suzumura, Yamazaki,
Takahashi, and Onzawa, 1994; Suzumura, Yamazaki, Takahashi, and Onzawa, 1995).
Fracture of the joint is prone to occur at the interface of diamond-Ti and/or TiC-Ti. Lu et
al. (1995) studied the influence of interfacial reactions on the fracture toughness of TiA120 3 interfaces. The experiment demonstrates that the interfacial fracture toughness of Ti
thin films on A12 0 3 substrates is severely degraded by the formation of cavities. Therefore,
the strongest interface is obtained when there is little reaction between the metal and the
ceramic. Based on the SEM morphology of Cu/Sn/fi as displayed in Figure 3.12, there is
no clear evidence that Ti segregates into the joint interface and the reaction layer thickness is
fairly thin. That explains why the debonding of diamonds in the Ticusil MSL wheel is
much more prominent than in Cu/Sn/Ti.
Figure 3.13 displays the wetting angle measurement installation. 1 is a He-Ne laser
generator, 2 is a vacuum furnace, and 3 is a camera to record the experimental result. Due
to the high cost of polished polycrystalline diamond films, high purity graphite platelets
were used in the test. The apparent density of T-6 graphite rod is 1.9 g/cm 3, and its ash
content is less than 200 ppm. The graphite rod was sectioned into thin slices. Because the
surface roughness of the test sample is related to its wetting, all thin slices were polished by
using 0.3 pm alumina to achieve the same surface roughness (Borgs, Coninck, Kotecky,
and Zinque, 1995; Yost, Michael, and Eisenmann, 1995; Li and Hausner, 1995; Li, 1994).
The alloys were tested by mixing metal powders and binder gel. There are two reasons to
test metal slurry pastes instead of alloys prepared by arc melting. First, certain alloy
37
compositions containing TiC particles can not be prepared by arc melting. Second, using
slurry pastes matches the actual production situation, which makes the data more useful in
determining the best alloy composition for MSL application. Some test samples and
polished graphite slices used in the wetting angle measurement experiment are displayed in
Figure 3.14.
One of the major concerns, especially in active braze alloy systems, in the sessile
drop experiment is contamination of the sample surface (Lazaroff, Ownby, and Weirauch,
1995; Li, 1993). The oxygen partial pressure can strongly affect the test result. Besides,
the sessile drop test performed in vacuum or Ar can result in different outcome. That is
why many test results show huge differences in the same alloy-ceramic system. All tests
were processed under high vacuum condition, 5*10~5 torr.
Figure 3.15 exhibits the morphology change in wetting angle with time for 70Cu21Sn-9Ti (wt%) at 900'C. Because active brazing is a kinetic process, it is strongly related
to time and temperature. The heating rate is carefully controlled by fixing all process
variables throughout the tests. Figure 3.16 displays the temperature dependence of the
wetting angle in the test for Ticusil and 70Cu-21Sn-9Ti (wt%). The wetting angle of
Cu/Sn/Ti at 920'C is much less than that at 900'C. A precursor film can be observed at
920 0C, but does not exist at 900"C. The precursor film contains a layer of continuous thin
film adhering to the substrate as described in Section 2.1, and the continuous thin film is
composed mainly of the active element such as Ti in our case (Xian, 1991; Xian and Si,
1991). Because formation of the bond is strongly related to the transport of the active
element, better wettability of the liquid on the solid will be expected if a precursor film
appears ahead of the spreading droplet. This explains why the wetting angle at 920'C is
much less than that at 9000C for 70Cu-21Sn-9Ti (wt%).
It is clear that Ticusil wets diamonds much better than Cu/Sn/Ti alloy. The wetting
angle drops below 100 in 10 minutes at 9000C. However, there is no clear relationship
between the wetting angle and the bond strength. Based on the grinding test result at
Norton, the bond strength in Ticusil MSL grinding wheels is inferior to that in 70Cu-21Sn9Ti (wt%). The wetting angle of 70cu-21Sn-9Ti (wt%), the currently used braze alloy, is
48*. This wetting angle is very high for general brazing, but works well for the MSL
application.
It has been widely considered that a low metal contact angle (0<300), as observed
in sessile drop experiments, is a prerequisite for the formation of a strong bond except
bonds between ceramics and ductile metals (Dalgleish, Saiz, Tomsia, Cannon, and Ritchie,
1994). As discussed in Section 2.2, there are many factors which affect bond strength.
38
These include interfacial chemistry, elastic mismatch, metal yield strength, and thickness
which influence residual stress distributions, flaw populations at the interface, and
interfacial fracture resistance. Good wetting is only one of the criteria to form a good
bond. For example, localized plasticity can blunt the interface flaws and limit stress
concentrations which develop at and/or near the interface and can induce premature brittle
fracture of either the interface or ceramic. Hence, a braze alloy with good mechanical
properties can greatly contribute to the bond strength. 70Cu-2lSn-9Ti (wt%) has higher
hardness, higher tensile strength, and less microstructural inhomogenuity than Ticusil.
These properties compensate for its poorer wetting ability.
Figure 3.17 displays the change of wetting angle with different Ti content at 9200 C.
Table 3.2 shows the wetting angle at 30 minutes for various copper-based braze alloys. It
demonstrates that the Ti content in Cu/Sn/Ti alloys has a significant effect on both wetting
phenomena and the melting point of the braze alloy. If the Ti content is less than 7 wt%,
the braze alloy will not fully melt below 940'C. Increasing the Ti content from 8.3 wt% to
Table 3.2 Wetting angle at 30 minutes for various copper-base braze alloys
Alloy Composition (in weight percent)
Ticusil (Ag-Cu eutectic + 4.5 Ti)
77Cu-23Sn-2.5Ti (75.lCu-22.4Sn-2.4Ti)
77Cu-23Sn-5Ti (73.3Cu-21.9Sn-4.8Ti)
77Cu-23Sn-7.5Ti (71.6Cu-21.4Sn-7Ti)
77Cu-23Sn-lOCu-lOTi (72.5Cu-19.2Sn-8.3Ti)
77Cu-23Sn-lOTi (70Cu-21Sn-9Ti)
77Cu-23Sn-lOTi (70Cu-21Sn-9Ti)
77Cu-23Sn-lOTi (70Cu-2lSn-9Ti)
77Cu-23Sn-lOCu-15Ti (69.6Cu-18.4Sn-12Ti)
77Cu-23Sn-15Ti (67Cu-2OSn-13Ti)
77Cu-23Sn-7.5Ti-7.5Hf (67Cu-2OSn-6.5Ti-6.5Hf)
77Cu-23Sn-7.5Ti-5Zr (68.4Cu-20.4Sn-6.7Ti-4.4Zr)
77Cu-23Sn-12.5Ti-7.5Zr (64.2Cu-19.2Sn-10.4Ti-6.2Zr)
77Cu-23Sn-lOZr-5Ti (67Cu-2OSn-8.7Zr-4.3Ti)
77Cu-23Sn-lOTi-5Zr-lOTiC (61.6Cu-18.4Sn-8Ti-4Zr-8TiC)
77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C
(59.2Cu- 17.7Sn-9.6Ti-5.8Zr-7.7TiC-0. 15C)
* partially melted
Temperature("C) Wetting Angle
940
3
not melted
not melted
46*
920
880
900
55
48
51
900
940
940
920
920
920
940
920
940
23
27.5
27
not melted
24*
940
920
24.5*
39*
20*
940
21*
39
9 wt% can drastically decrease the wetting angle. Increasing the Ti content further has no
benefit on the wetting process. This results from a huge volume fraction of intermetallic
compound formation. Because increasing the Ti content can impair the ductility of the
braze alloy, 9 wt% Ti is considered as an optimal value in the Cu/Sn/Ti alloy.
Ticusil and 70Cu-2lSn-9Ti (wt%) were chosen to verify the effect of accumulated
plastic deformation. All samples experienced 10 thermal cycles ranging between room
temperature and 6000 C. The average heating rate was about 15 0C/min, and the average
cooling rate was about 40C/min. All test specimens show poor resistance to thermal
fatigue. Figure 3.18 exhibits SEM fractographs of the present used braze alloy, 70Cu2lSn-9Ti (wt%). Many cracks can be observed at the interface. The braze tends to peel
from the diamond. This demonstrates that the interface experiences the largest thermal
strain and is a weak area in the bond. Some cracks at the diamond side are indicated by the
arrows. This is consistent with crack growth in the A20 /Al alloy system under cyclic
loading (Cannon, Dalgleish, Dauskardt, Oh, and Ritchie, 1991). The crack growth may
occur either in the ceramic or in the metal within a few microns of the interface.
Figure 3.19 shows the fractographs of the most widely used active braze alloy,
Ticusil. It is observed that Ticusil wets the diamond very well, and no alloy peels off from
the diamond. A braze alloy with lower yield strength protects the diamond from fracture.
However, the cracks can still be observed at high stress edges and corners. Although this
alloy has 3% elongation in the monotonic tensile test, its strain hardening rate is high due to
the existence of the inherent dendritic structure and the brittle intermetallic phase as shown
by the arrows in the SEM back scattered image.
3.3
Alternative Methods to Improve the Performance of MSL Wheels
Fracture of the diamond grits was the major failure mode in the test. This indicates
that the normal and horizontal applied force is too large for the diamonds to support. The
superabrasive grits in the test are IMG 40/50 artificial diamonds. They are basically strong,
defect-free and of high quality. Changing the grinding material and/or using a lower feed
rate in the test are the optimal ways to avoid the fracture of diamond.
Diamonds are the least compressible material in the world. One of the major
characteristics in differentiating brittle and ductile materials is their fracture made. For
brittle material, due to the insufficient ability of plastic deformation, it fails when the stress
exceeds its ultimate stress. Hence, overall stress is an important criterion in determining
fracture of these brazes, but it is not a sensitive factor in determining fracture of ductile
40
brazes due to its ability to deform inelastically. Ductile brazes fail when the total plastic
deformation exceeds a critical value. In the case of MSL grinding wheel, both the diamond
and the braze alloy display more brittle fracture than ductile fracture. In other words, they
both lack the ability to deform plastically. Moreover, the residual thermal stresses
concentrate at the interface region due to the high mismatch of thermal expansion
coefficients as demonstrated in the next chapter. This makes the interface the weakest area
in wheel, and explains the reason why the diamond debonds as will be further discussed in
Chapter 5.
Another explanation in debonding of diamonds is that the braze alloy is not
sufficiently abrasive and/or fatigue resistant. For example, Ticusil is softer than the
Cu/Sn/1i braze as displayed in Table 3.1. The braze alloy can not hold the diamond grits
anymore when worn out. This is observed by comparing the fractographs in Figure 3.5
and Figure 3.9(b). Debonding of the diamond grits is much more pronounced in the
Ticusil MSL wheel than that in the Cu/Sn/Ti one.
In addition to wear of the braze alloy, fatigue of the braze alloy is another possible
reason causing the debonding of diamond grits. The number of cycles to failure in the test
is about 2.5*10'. This is far below 10' cycles. Therefore, the current test can not evaluate
the fatigue properties of the braze alloy. Decreasing the feed rate in the future tests is the
best way to make the grinding test more practical. As discussed in the previous chapter,
there are many defects such as voids and dislocations at the interface. Also, the brittle
intermetallic phase in the braze is another weak area in the bond. The diamond and braze
alloy experience cyclic loading in the grinding process. The above weak area can initiate
and propagate the crack during cyclic loading. Finally, the braze fails and the diamond
debonds.
Abrasive resistance can be improved by introducing hard particles into the braze
alloy, and the fatigue resistance can be modified by using a ductile active braze alloy with
few defects. These two methods will be demonstrated in Chapter 5 and Chapter 6.
41
Figure 3.1 Fractograph of the nickel-plated MSL grinding wheel
|(a)
Figure 3.2 Fractographs of the 70Cu-2lSn-9Ti (bywt%) MSL grinding wheel
(a) Fractured surface overview
(b) Cracks surround the debonded diamond grain
(c) Cracks situated in the radial direction of the debonded diamond grain
42
Figure 3.2 (continued)
43
Diamond
C
C
T
T
T
C
T
T
Braze Alloy
(a)
Diamond
Braze Alloy
(b)
Diamond
Braze Alloy
(c)
Figure 3.3 Schematic diagrams of the bonded diamond grain
(a) ideal MSL bond (C: compression, T: tension)
(b) poor bond due to insufficient wetting of the diamond grain
(c) poor bond due to over wetting of the diamond grain
44
Figure 3.4 Fractograph of the nickel-based braze alloy developed by NortonCompany
Figure 3.5 Fractograph of the 75Cu-25Sn-12.5Ti-7.5Zr-1OTiC-0.2C (byweight) MSL
grinding wheel
45
Figure 3.6 Fractograph of the high tin MSL grinding wheel
Figure 3.7 Fractograph of ABRASIVE TECH's MSL grinding wheel
46
Ag
grid in at.
%
axes inmas
Liquidus surface:
970,
CU
10M/-r1
Ti
Isothermal section at 700'C:
Ag
grid inat. %
axes in mass %
(Ag)
(Ag) *jo+
X\V//N,
(a)
(.A )+y
iffl
Ti
I,
(hi)
(CU)
\
/
'/CU
4OOPim
(b)=
TM!T
Figure 3.8 Ternary phase diagrams of Ag-Cu-Ti and the microstructure of Ticusil
(a) Ag-Cu-Ti ternary phase diagrams
(b) Microstructure of Ticusil brazing at 875'C * 30 minutes
47
(a)
(b)
Figure 3.9 Fractographs of Ticusil after tensile test and grinding test
(a) Fractograph of Ticusil after tensile test
(b) Fractograph of Ticusil MSL grinding wheel after grinding test
48
Figure 3.10 Fractograph of 70Cu-2lSn-9Ti after tensile test
0.000 mg
3C
<Sa!Ip Ing>
_____________
LO see
13 25-
0.,
:n
C
3 '37-
1,1
600
MIT Center
Tor tAateria1 1
S
700
cie
-60
n
9 6 m
800
I.Le C tHeating)
900
1000
Figure 3.11 The DSC analysis of 70Cu-2lSn-9Ti (wt%), heating cycle
49
(a)
(b)
Figure 3.12 The SEM analysis of 70Cu-2lSn-9Ti (wt%), 880 0C*30 minutes
(a) The morphology of 70Cu-2lSn-9Ti
(b) The dot mapping of C, Ti, Sn, and Cu
50
2i
Figure 3.13 Wetting angle measurement installations
Figure 3.14 Wetting angle measurement test samples
51
5 min.
10 min.
15 min.
20 min.
25 min.
30 min.
40 min.
45 min.
Figure 3.15 Time dependent wetting angle measurement for 70Cu-2lSn-9Ti at 900 0C
52
*70Cu-21Sn-9Ti,920C M 70Cu-21Sn-9Ti,900C XTicusil,900C
90
80
e 70
60
-
50
-
#U
a
< 40
e
Ux
30
20
10
0
10
0
20
40
30
60
50
Time(min)
Temperature dependent wetting angle for 70Cu-2lSn-9Ti (wt%) and
Ticusil (Ag-Cu eutectic + 4.5wt% Ti) on polished graphite surface
Figure 3.16
*72.5Cu-1 9.2Sn-8.3Ti U 7OCu-21 Sn-9Ti
90
80
70
-
-
-
60
*350
40
U
*4
30
20
10
0
0
10
20
30
40
50
60
Time(min)
Figure 3.17
The change of wetting angle with various Ti contents at 9200 C
53
SEI
169 F1.0
2 2 0X
00001
10 0pM
Figure 3.18 Fractographs of 70Cu-2lSn-9Ti (wt%) after 10 thermal cycles
(BEI: back scattered image, SEI: secondary electron image)
54
Figure 3.19 Fractographs of Ticusil after 10 thermal cycles
(BEI: back scattered image, SEL: secondary electron image)
55
4. Finite Element Analysis of Residual Stresses in MSL
Grinding Wheels
4.1 Review of Finite Element Analysis Principles
The finite element method is widely used to solve physical problems in engineering
analysis and design. Figure 4.1 summarizes the process of finite element analysis (Bathe,
1996). The physical problem typically involves an actual structure subjected to certain
loads. The idealization of the physical problem to a mathematical model requires certain
assumptions that together lead to differential equations governing the mathematical model.
The finite element analysis solves this mathematical model. Since the finite element
solution technique is a numerical procedure, it is necessary to assess the solution accuracy.
If the accuracy criteria are not met, the finite element solution has to be repeated with
refined solution parameters, such as finer meshes, until a sufficient accuracy is reached.
It is clear that the finite element solution will solve only the selected mathematical
model and that all assumptions in this model will be reflected in the predicted response.
We can not expect any more information in the prediction of physical phenomena than the
information contained in the mathematical model. Hence the choice of an appropriate
mathematical model is crucial and completely determines the insight into the actual physical
problem that we can obtain through the analysis.
Once a mathematical model has been solved accurately and the results have been
interpreted, we may consider a refined mathematical model in order to increase our insight
into the response of the physical problem. Furthermore, a change in the physical problem
may be necessary, and this in turn will also lead to additional mathematical models and
finite element solutions.
The key step in engineering analysis is choosing appropriate mathematical models.
These models will be selected depending on what phenomena are to be predicted. In the
case of diamond-braze alloy joining, a purely elastic model is too far removed from the
actual situation as demonstrated in Section 2.3. Therefore, the first attempt of a model in
this thesis is the elastic/time-independent plastic model.
ABAQUS is a
A finite element analysis was performed using ABAQUS.
displacement-based finite element formulation. The principle of virtue work is its
fundamental approach method. In ABAQUS, the elastic and inelastic responses are
distinguished by separating the deformation into recoverable (elastic) and nonrecoverable
56
(inelastic) parts (Hibbitt, Karlsson, and Sorensen, 1994abc). This separation is based on
the assumption that there is an additive relationship between the strain rates:
i=
(4.1)
jel +
where e is the total strain rate tensor, eiel is the rate of change of the elastic strain tensor,
and i is the rate of change of inelastic strain tensor. A more general assumption is that
the total deformation tensor, F, is made up of inelastic deformation tensor followed by
purely elastic deformation tensor:
F =
(4.2)
-FP
pel
Equation 4.1 is an approximation to Equation 4.2 if
(1) The total strain rate measure used in equation 4.1 is the rate of deformation:
i = sym(
-F-1) = sym(-)
where v is the velocity, x is the current spatial position of a material point, and sym (F -F )
is the symmetric part of the dot product of the rate of deformation and a rate of rotation.
(2) The elastic strains are small. They always remain small for many materials of practical
interest-- for example, the yield stress of a metal is typically three orders of magnitude
smaller than its elastic modulus, indicating elastic strains of order 10'.
Equation 4.3 is the simplest expression of linear elasticity:
o-= Del
(4.3)
:Eel
where Dd is a matrix that may depend on the temperature but does not depend on the
deformation. Also, a more general type of nonlinear elastic response is assumed to be
derivable from an elastic strain energy density potential, so that the stress is defined by:
dU
-
del
)(4.4)
=
where U is the strain energy density potential. Since we assume that, in the absence of
plastic straining, the variation of strain is the same as the rate of deformation, conjugacy
arguments define the stress measure, a, as the "true" stress. All stresses in ABAQUS are
output in this form.
The plasticity models provided in ABAQUS are written as rate independent models
or as rate dependent models. A rate independent model is one in which the constitutive
response does not depend on the rate of deformation -- the response of many metals at low
temperature relative to their melting point and at low strain rates, is effectively rate
57
independent. In a rate dependent model the response does depend on the rate at which the
material is strained. An example of such a model is a creep model.
The rate independent plasticity model in ABAQUS has a region of purely elastic
response. The yield function, f, defines the limit to this region of purely elastic response,
and is written so that:
f(u, T, Ha) < 0 for purely elastic response
where T is the temperature, H. are a set of hardening parameters, and the range of the
subscript a is not specified until a particular plasticity model is defined.
The hardening
parameters are state variables that are introduced to allow the models to describe some of
the complexity of the inelastic response of real materials. In the simplest plasticity model,
perfect plasticity, the yield surface acts as a limit surface and there are no hardening
parameters at all. Complex plasticity models usually include a large number of hardening
parameters (Suresh, 1992).
Stress states that cause the yield function to have a positive value cannot occur in
the rate independent plasticity model. In the rate independent model, we have the yield
constraint: fi = 0 during inelastic flow. When the material is flowing inelastically, the
inelastic part of the deformation is defined by the flow rate, which we can write as:
dep' = I d).j -(g
i
(4.5)
da
where gj(a,T,Hj.) is the flow potential for the ith system, and dXi is a scalar measuring the
amount of plastic flow rate in the ith system, whose value is determined by the requirement
to satisfy the consistency condition fi =0, for plastic flow of a rate independent model.
The final ingredient in the plasticity model is the set of evolution equations for the
hardening parameters:
(4.6)
dHi,a = dAi -hi,a (q,T, Hi,)
where hl' is the hardening law for Hi,,.
Isotropic hardening was used in the analysis.
Then, applying the Euler method to the flow rule gives:
AEc' = I AA) -(g)
i
da
(4.7)
and applying it to the hardening evolution equation gives:
AHia = AAj -hi,a
The strain rate decomposition is integrated over a time increment as:
(4.8)
58
(4.9)
Ae = Aeel + Aep
where Ae is defined by the central difference operator:
Ae = sym[
dAx
d(x, + 0.5Ax)
]
(4.10)
We integrate the total values of each strain measure as the sum of values of that strain at the
start of the increment, and rotate to account for rigid body motion during the strain
increment. This integration allows the strain rate decomposition to be integrated into:
From a computational viewpoint, the problem is now algebraic. We must solve the
integrated equations of the constitutive model for the state at the end of the increment. The
set of equations that define the algebraic problem is the strain decomposition, Equation
4.11; the elasticity, Equation 4.4; the integrated flow rule, Equation 4.7; and the integrated
hardening laws, Equation 4.8. For the rate independent model, the yield constrains
(4.12)
f1 = 0
For rate independent models with a single yield system, the algebraic problem is
considered to be a problem in the components of AEN. Once these have been found, the
elasticity together with the integrated strain rate decomposition defines the stress. The flow
rule defines AX and the hardening laws define the increments in the hardening variables.
According to the equations above, we can derive the equations for Newton's solution of the
integrated problem for the case of rate independent plasticity with a single yield system.
The Mises stress potential for isotropic behavior is used as the metal plasticity model
throughout the analysis.
The rate dependent problem with a single yield system can be solved in a similar
way. The explicit method, forward Euler, is often satisfactory as an integrator for the flow
rule. Combining the integrated flow rule:
AeP' = At -
(4.13)
da
with the integrated strain rate decomposition and linear elasticity gives:
(4.14)
da
All of the terms on the right-hand side of Equations 4.13 and 4.14 are known when the
St+At=Del:(Et
-e'pI i-At-I)
constitutive integration is done, so that the above equations define at+,t explicitly.
59
The stress states of the MSL wheel will be analyzed by an elastic/rate-independent
plastic model first. Next, a more elaborate elastic/rate-dependent plastic model will be
performed. Finally, a conclusion from the above analysis and recommendations for further
optimizing the current braze alloy will be made.
4.2 Elastic/Rate Independent Plastic Finite Element Analysis Model
Figure 4.2 is one example showing the morphology of the nodes and elements in
the analysis. It is reasonable to use a fine mesh at the diamond/braze alloy interface, and a
coarse mesh away from this area. There are two shapes of diamond chosen in this
analysis. One is a regular polygon of eight sides cross-section as displayed in Figure 4.2;
the other is a square cross-section diamond. The axisymmetric elements, defined in the RZ plane with R as the first coordinate, are used in the calculation. The Z-axis is the axis of
symmetry. Any radial displacement in an axisymmetric solid induces a hoop strain, in the
circumferential direction. Coordinate 1 is R, coordinate 2 is Z, and coordinate 3 is 0.
Coordinate 1 should be greater than or equal to zero.
Since the motion is purely
axisymmetric, only four components of the strain are non-zero: radial (E1), axial (e 2 2 ),
hoop (e33) and shear in the R-Z plane (C12). Similarly, four output stress components can
be obtained in the analysis. They are radial (an), axial (a 22), hoop (G
(a 12 ).
33
), and shear stress
In addition to those stresses and strains, three extra parameters are also derived in
the output process as described below:
(1) PRESS: Equivalent pressure stress, defined as p =
-
a / 3 This is important for the
nucleation of voids in the material when p <0.
(2) MISES: Mises equivalent stress, defined as (McClintock and Argon,1966):
q=
2
S: S
(4.15)
where S is the deviatoric stress tensor, defined as S = a + p I, where a is the stress, p
is the equivalent pressure and I is a unit matrix. In index notation,
q=
-S..S..
2
(4.16)
where Sij = crij +p 8ij, where p = - oi / 3 and 8ij is the Kronecker delta. The MISES
60
stress defines the isotropic yield criterion of the materials.
(3) PEEQ: Equivalent plastic strain. It is defined as:
PEEQ =e
=
3d
(4.17)
This is the total accumulation of plastic strain typically used in an isotropic hardening
plasticity theory to define the yield surface size.
The following assumptions are made in the finite element analysis:
Isotropic linear elastic material: Anisotropy of the materials is not considered.
(1)
(2) No Bauschinger effect: The compressive yield stress is smaller than the initial yield
stress in tension. This is known as the Bauschinger effect (Reed-Hill and
Abbaschian, 1992). In other words, the inelastic deformation induced anisotropy is
not considered. This is true in our case, because monotonic loading is applied in this
analysis.
(3) Incompressible material, this is true in both the plastic part of the deformation and the
small elastic strain.
(4) No rate dependent effect, e.g., creep, is considered in the analysis.
Young's modulus, Poisson's ratio, and the linear thermal expansion coefficient at
different temperatures are necessary input properties to calculate the elastic response of the
material. True stress-strain curves and linear thermal expansion coefficients at various
temperatures are essential input properties to compute the plastic response of the material.
Diamond is the least compressible material of all, and its brazing temperature is much lower
than its melting point. Therefore, it is reasonable to assume that there is no plastic flow of
the diamond during the brazing process. In this analysis, only the elastic response of the
diamond is considered, although in other cases both elastic and plastic response are
considered.
Because there are no currently available mechanical properties of the braze alloy at
the relevant temperatures, the mechanical properties of pure metals are used as an
approximation in this analysis. For example, the mechanical properties of copper are used
to replace those of copper base braze alloys, and the mechanical properties of nickel are
used to replace those of nickel base braze alloys. Due to differences of the mechanical
properties between the pure metal and the braze alloy, the output stresses can only be
considered as an estimation of the stress distribution in the braze alloy. However, the
output strains, if their elastic part is small, can be considered as an index of the thermal
expansion misfit between the diamond and the braze alloy. The diamond wheel preform is
made of stainless steel 304 which is one of the materials currently used in MSL grinding
wheels.
61
The true stress aY"* is expressed in terms of the engineering stress a*" by
atrue
= a"
(4.18a)
"(en"
+1)
and the true strain E " can be determined from the engineering strain E*" by
Etrue = Jn(en" + 1)
(4.18b)
In addition to requiring true stress and true strain input data, ABAQUS requires that the
value of strain at the yield point be zero. Therefore, the linear portion of strain must be
subtracted from total strain as follows (Vaughan and Schonberg, 1995):
eng
Etrue ___eng +(1)
(a
)4.18c)
E
However, the engineering stress-strain curve is an good approximation to the true stressstrain curve when the total strain is less than 2% as displayed in Figure 4.3. In this
analysis, the engineering stress-strain curves are used as input properties. All input
properties of these materials are shown in Appendix A.
The Z-axis symmetry at r=0 is the only fixed boundary condition throughout the
analysis. All other surfaces are free, i.e. no traction and no displacement constraint. The
actual morphology of the analysis is a small diamond brazed in a huge stainless steel disk.
In order to simulate the actual situation, the size of the disk is at least five times larger than
that of the diamond in both the radial and the axial directions as shown in Figure 4.2.
The initial condition depends on what kind of braze alloy is used. Typical values are
900 *C for copper, 1000 'C for nickel, and 600 "C for aluminum. However, there is
almost no hot strength for copper until 600 0C, thus 600 0C was used as the initial
condition for some analyses. All samples cool down to room temperature, 20 *C, after
brazing. Appendix B displays an example of the ABAQUS input program.
Figure 4.4 shows the analysis results of two different diamond/disk size ratios
cooling from 9000C. The position of the diamond, braze alloy, and steel disk are displayed
in Figure 4.2. The size of the diamond is 25 mesh, 0.707 mm, throughout the analysis.
The size of the steel disk in figure 4.4(a)-(c) is 0.707 mm in radius and 2 mm in length.
The steel disk in Figure 4.4(d)-(f) is 2 mm in radius and 3.5 mm in length. All output
stresses are in MPa, and there is no unit for output stains. The Mises stress and equivalent
plastic strain (PEEQ) are very similar in these different diamond/disk size ratios. In order
to simulate the actual application, the larger disk size, 2 mm in radius and 3.5 mm in
height, was used throughout the remaining analysis.
The interface between the diamond and braze alloy experiences most of the thermal
expansion mismatch. Therefore, the interface has the highest stress and strain. This
62
indicates that the interface between the diamond and the braze alloy is a weak area from the
viewpoint of mechanics. Based on Figure 4.4(c) and 4(f), the region of highly
concentrating stress and strain is about the order of 100 jim in width. The ratio of the
diamond size and the above region is approximately 1/7. The equivalent plastic strain
induced by thermal expansion mismatch between Cu and SS304 is about 1.7% as
displayed in Figure 4.2(f).
Figure 4.5(a)(b) displays the analysis results of a diamond/Cu braze/Cu disk
combination. There is no mismatch between the braze alloy and the disk. All stresses and
strains result from the mismatch between the diamond and the copper. The largest
equivalent plastic strain is at the top of the interface, and is greatly reduced at the bottom of
the interface. However, introducing a thin layer of copper beneath the diamond can not
relieve the interfacial stress and strain in exactly the same way as shown in Figure 4.5
(a)(b). That is because the mismatch between the Cu and SS304 disk can cause
deterioration of the stress and the strain distribution at the interface. The thin layer of
copper will be stretched by the steel after brazing, and this will negate a part of its beneficial
effect. Figure 4.5(c)(d) shows the result of adding a 200 pm Cu layer between the SS304
and the braze alloy. A thin copper interlayer can partially reduce the interfacial equivalent
plastic strain, especially at the bottom part of the diamond. Figure 4.6 further demonstrates
the above argument. The position of element 3021 is shown in Figure 4.2. There is about
0.1% accumulated plastic strain difference for 1 mm and 3 mm thick copper interlayers.
The Mises stresses, on the other hand, experience no clear change. This can be explained
by the small amount of work hardening of the material. Therefore, the change in the Mises
Stresses is not as obvious as the change in the accumulated plastic strains.
In the case of adding a thin layer, 1 jm, of TiC between the diamond and the braze
alloy as displayed in Figure 4.7, the Mises stresses in the TiC interlayer are too high to be
realistic. Due to the property discontinuity at the interface, singular points will be created
during the analysis. Therefore, the computed results very close to the interface are not
reliable, and they are mesh dependent. The finite element analysis can not be applied to
estimate the state of stress and strain at the reaction layer by a simple plastic deformation
model.
Figure 4.8 shows the analysis result of a 50 jm crack at the bottom interface. The
Mises stress demonstrates that the stress concentration can not be totally eliminated by
simply introducing an internal crack at the interface. Consequently, the crack tip can
63
propagate during cyclic loading, and this may, finally, result in debonding of the diamond
grit.
Figure 4.9 estimates the effect of thermal expansion mismatch for different braze
alloys, Cu, Ni and Al. The Al braze has the highest equivalent plastic strain, although it
has the lowest brazing temperature. The equivalent plastic strain is about the same in Cu
and Ni. However, the mismatch between copper and steel is greater than that between
nickel and steel. Based on this information, copper and nickel base braze alloys are
superior to aluminum base braze alloy.
Figure 4.10 shows the accumulated plastic strains for different diamond shapes.
Figure 4.10(a) is the bonded diamond grit with a lower depth of the braze, and Figure
4.10(b) is the bonded diamond grit with a higher depth of braze. They are similar to the
previous results. The plastic strain reaches the maximum value at the diamond corner.
Strains in the interface are smaller than those of corner. The rest of the braze experiences
less strains than those of the interface. Therefore, thermal stresses and strains concentrate
at the diamond-braze interface. Also, the depth of the diamond covered by the braze alloy
has an effect on the final stress and strain states. The more coverage of the diamond by the
braze, the higher the Mises stress and the equivalent plastic strain that can be induced. The
analysis result of an octagonal cone is closer to the actual situation because this shape is
similar to that of the diamond.
The Mises stress does not differentiate tensile or compressive stress. It is known
that tensile stress is more destructive than compressive stress, especially for brittle
materials. Figure 4.11 shows all stress components acquired from the finite element
analysis. In most cases, the braze alloy is under tensile stress. The stress state of the
diamond, however, is divided into two parts. The diamond covered by the braze alloy
experiences a compressive stress, and the diamond which is not covered by the braze alloy
experiences a tensile stress. The compressive stress will grasps the diamond. It is
beneficial as long as it is not large enough to cause diamond fracture during grinding.
When the diamond is grinding, there is a bending moment applied at its upper point. Both
the applied moment and the thermal mismatch can induce a tensile stress in the upper part of
the diamond. This results in transverse fracture of the diamond grits as shown in Figure
3.2-3.7, and explains why good wetting of the diamond grits is a necessary condition in
order to obtain a good MSL bond. The tensile stress in the diamond induced by the applied
moment can be greatly reduced if the coverage of the diamond by the braze is increased.
Another important conclusion can be derived from observing the hoop stress, S33.
The radial direction of cracks around the diamond as shown in Figure 3.2(c), 3.9(b), 3.18,
and 3.19 results from the tensile hoop stress induced by the thermal expansion mismatch
64
between the diamond and the braze. In reality, there are many different phases in the braze
alloy. The hoop stress will do the greatest damage to the weakest phase in the alloy.
Because the intermetallic phase is difficult to avoid in active brazing as explained earlier, the
cracks will initiate within it. Figure 3.2(c) and Figure 3.19 display a backscattered image
of the fracture surface. This demonstrates that cracks initiate from the brittle phase. These
cracks propagate during the grinding process, and damage the braze. The thermal strain is
difficult to eliminate, so another way to avoid this type of damage is to make the braze alloy
tougher. This goal can be achieved by decreasing the volume fraction of intermetallic
phase(s) and/or increasing the ductility of the matrix. Both will be discussed in Chapter 6.
Figure 4.12 shows the change of Mises stress and the equivalent plastic strain with
temperature in element 3021. It is obvious that the Mises stress is negligible until the
sample cools to 600 0C. The melting point of pure copper is 1084.6"C which is higher than
that of the Cu/Sn/Ti braze alloy. It is reasonable to assume that thermal stress is not
prominent until the sample cools to 600 0 C. Therefore, all the following calculations of the
copper braze are based on the temperature difference between 600C and 20'C.
Figure 4.13 displays the equivalent pressure stress of a two-layer braze. The
thermal expansion coefficient of Ni is smaller than that of Cu. The Cu layer experiences a
tensile stress, and the Ni layer has a compressive stress after brazing. Therefore, the top
layer of a Ni-Cu braze has a compressive stress. It is helpful to prevent crack initiation at
the surface. However, the tensile stress existing in the lower part of the braze, Cu layer,
can cause crack initiation and delamination of the Cu layer. On the contrary, the top copper
layer results in a tensile stress at the junction between the diamond and the braze. This
stress state deteriorates when a cyclic grinding load is applied. The stress distribution in
Figure 4.13(a) is better than that in Figure 4.13(b) from the viewpoint of fracture
mechanics.
4.3
Elastic/Rate Dependent Plastic Finite Element Analysis Model
The elastic/rate independent plastic finite element analysis can only exhibit the
mismatch plastic strain which is independent of the cooling cycle. In other words, the
stress states of the bond have no relation to its cooling rate. This is not consistent with the
experimental observation. Figure 4.14 shows an SEM backscattered image in the
diamond-Cu/Sn/Ti braze interface formed by a fast cooling rate after brazing. The crack
shown in the figure does not exist in a sample with a normal slower cooling rate.
Therefore, the rate dependent plastic deformation of the braze alloy plays an important role
in determining the final stress states after brazing. Based on the mechanical properties
65
displayed in Appendix A, copper shows very limited strength above 600'C. This also
indicates that creep of the copper should be included in the analysis. On the other hand, the
preform, stainless steel 304, and the diamond show almost no creep effect below 600'C.
This can be verified by using a creep model to estimate the creep rate at relevant
temperatures, as will be demonstrated latter.
The previous section shows that the Mises stress increases rapidly as the
temperature decreases. According to the deformation-mechanism map of copper, the
primary creep mechanism for copper is power law creep (Frost and Ashby, 1982).
Therefore, a power law creep model is used to simulate the creep response of copper. The
following equation shows a power-law creep by dislocation climb-plus-glide:
=
(4.19)
A -Dpb (qJ
kT
- _
where s is normal creep strain rate, A is power-law creep constant, D, is lattice diffusion
coefficient, b is the magnitude of the Burger's vector, g is shear modulus, k is
Boltzmann's constant, q is the Mises equivalent stress, and T is temperature. In this simple
form, Equation 4.19, is incapable of explaining certain experimental facts, notably an
increase in the exponent n and a drop in the activation energy for creep at low temperatures.
It is necessary to assume that the transport of matter via dislocation core diffusion
contributes significantly to overall diffusion transport of matter , and, in some cases, it
becomes the dominant transport mechanism. The contribution of core diffusion is included
by defining an effective diffusion coefficient (Frost and Ashby, 1982):
(4.20)
Deff = Dvf, + Dcfc
where D. is the core diffusion coefficient, and f, and f, are the fractions of atom sites
associated with each type of diffusion. By substituting proper values into Equation 4.20,
the effective diffusion coefficient becomes:
Deff = D,[1+
b
aC( q ) 2(c)]
(4.21)
Fp
Dv
Inserting Equation 4.21 into 4.19, a more general rate-equation for power-law creep:
ADeff pb q
- p
kT
4.22)
Equation 4.22 contains two rate-equations. At high temperatures and low stresses, lattice
diffusion is dominant. At lower temperatures or higher stresses, core diffusion becomes
dominant, and the strain rate varies as qn2 instead of q".
66
Table 4.1 shows the relevant constants in Equation 4.19 and 4.22. Substituting
these values into the above equations, the creep strain rates varied with the Mises stresses at
200, 400 and 6000C can be derived as displayed in Figure 4.15. It is clear that the creep
stain rates of copper are several orders of magnitude larger than those of SS304.
Moreover, the thermal strain of copper, due to the mismatch of the joined materials, is
much larger than that of the preform, SS304. Therefore, it is reasonable to consider the
creep of copper only, throughout the analysis.
Table 4.1 Copper and SS304 (Frost and Ashby, 1982)
Variables
Burger's vector, b(m)
Copper
SS304
2.56*10-10
2.58*10-10
Core diffusion
Pre-exponential, aD.(m,/s)
Activation energy,
Q. (KJ/mole)
Lattice diffusion
Pre-exponential, D.,(m2/s)
Activation energy, Q,(KJ/mole)
Power-law creep exponent, n
Power-law creep constant, A
1.0* 10-24
-__
117
---
2.0* 10 5
197
3.7* 10-5
280
4.8
7.5
7.4*10 5
1.5*10"
Figure 4.16 shows the currently used thermal cycle for the 70Cu-21Sn-9Ti (wt%)
braze. The cooling rate is approximately 10 0C/min. A cooling cycle with different cooling
rates, 100*C/min, 10*C/min, 1"C/min, and 0.1*C/min, will be modeled in this section. The
forward Euler method, an explicit method, was used in the finite element analysis, and the
accuracy of the equivalent strain for each step is below 5* 10-6. Figure 4.17 displays the
equivalent plastic strain (PEEQ) and the equivalent creep strain (CEEQ) change with
temperature at element 3021. This demonstrates that the creep strain is dominant when the
temperature is above 200'C. Creep has a very little effect on relieving the thermal stress
below 100'C.
Figure 4.18 shows the Mises stress variation during the cooling cycle for three
different elements. The yield strength for Cu at room temperature used in the analysis is
420 MPa. The closer the element to the diamond, the higher the Mises stress which is
induced. However, highly dense diamond grits are used in most of the MSL grinding
wheels. This indicates that the thermal stress in the braze exceeds its yield strength in most
cases. Once the braze has yielded, strain hardening behavior becomes an important issue.
67
Most of the braze alloys show same strain hardening effect. The inelastic strain is formed
after brazing and the hardening effect can be further enhanced during grinding. This finally
results in failure of the braze. Both the rate-independent plastic strain and the creep strain
are inelastic deformation. They are not recoverable once formed. Pau (1994) studied the
critical accumulated strain energy failure criterion for thermal cycling fatigue of solder
joints, and found that creep is the predominant factor in deciding fatigue life. Creep
accounts for 51 to 97 percent of the total accumulated strain energy, depending on the
cycling profiles. This is consistent with this analysis. The magnitude of the creep strain is
about two times larger than that of rate-independent plastic strain as demonstrated in Figure
4.17 under the condition of 10*C/min cooling rate.
Figure 4.19 displays the Mises stress variation with different cooling rates 100*C/min, 10*C/min, 1"C/min, and 0.1 0C/min. This demonstrates that the stresses in the
braze will be greatly decreased by creep if the temperature is above 150*C. The creep effect
does not work very well in relieving thermal stresses below 150'C. Therefore, the final
Mises thermal stress keeps the same value for different cooling rates. However, the
accumulated plastic strain (PEEQ) and the accumulated creep strain (CEEQ) display great
differences as shown in Figure 4.20(a) and (b). There are very limited rate-independent
plastic strains for 1*C/min and 0.1 0C/min cooling rates. Over 85% of the plastic strain is
creep strain. On the other hand, the creep strain only contributes about 50% of the total
plastic strain for the case of 100C/min and 10*C/min cooling rates. Thus cooling rates
should be carefully controlled in brazing. Although there is only very limited strength for
the braze alloy above 600'C, a slower cooling rate at elevated temperatures can cause
growth of undesirable brittle intermetallic phases. This deteriorates the fatigue resistance of
the braze alloy. Using a slower cooling rates between 200'C and 600'C improves the
stress states of the braze alloy. It is not economical to reduce the rate-independent plastic
strain via creep below 150*C.
The above analysis is based on element 3021 only which is very close to the
diamond/braze interface. There is a high thermal expansion mismatch at this location, and
the final Mises stress does not show any differences for various cooling rates. This is not
true for elements far away from the interface. Figure 4.21 shows an overview of the Mises
stress distribution around the braze alloy with different cooling rates. This demonstrates
that creep effect can decrease the Mises stress in the braze. Creep can alleviate most of the
thermal stress in the areas with low thermal expansion mismatch. The Mises stress
distribution shown in Figure 21(b) provides another approach to the real stress distribution
after brazing. Based on this simulation, the thermal stresses between the braze alloy and
the steel substrate are greatly reduced by rate-dependent plastic deformation.
68
I
Change of
physical
problem
Physical problem
Mathematical model
Governed by differential equations
Assumptions on
. Geometry
"Kinematics
"Material law
"Loading
"Boundary conditions
- Etc.
r-
of
mathematical
model
Improve
mathematical
-------------------------------------------Finite element solution
Choice of
. Finite elements
"Mesh density
"Solution parameters
Representation of
"Loading
"Boundary conditions
"Etc.
Finite
element
solution
4---
Refine mesh,
solution parameters,
etc.
Assessment of accuracy of finite
element solution of mathematical model
I----
Interpretation of results
Design improvements
Structural optimization
Figure 4.1
The process of finite element analysis (Bathe, 1996)
69
Rome
*
2
3O21 3 121:
-4
I
Figure 4.2 The morphology of the nodes and elements in the analysis
I
70
Engineering Stress-Strain ------ True Stress-Strain
500'
450'
-----------------------------------------------------------
400 m
350v
C,-
C,
300 s
250"
150 "
1001"
50 -
CD 200'
n.
0
Figure 4.3
I
M
1
2
3
4
U
-
5
Strain
6
7
8
9
10
(%)
The comparison between the engineering stress-strain curve and the true
stress-strain curve of an elastic-linear work hardening material.
71
Figure 4.4 Finite element analysis results of two different sizes of steel disks cooling
from 900'C: (a)(b)(c) 0.707mm in radius, 2mm in length, (d)(e)(f) 2mm in
radius, 3.5mm in length
72
Figure 4.5 The finite element analysis results of diamond/braze/(SS304) combinations
(a)(b) diamond/Cu braze/Cu disk combination
(c)(d) diamond/Cu braze/200%tm Cu interlayer/SS304 Combination
73
Element
I
3021
1 mm (MPa)
3mm (MPa) -
450
400
S
a. 350
300
S
S
0
1~
S
S
S
250
200
150
100
50
0
200
100
0
Temperature
-
400
300
500
600
(C)
3mm (%)-U-1mm (%)
4
2
0. 8
0. 6
0.
0. 4
.
2
0'
0
100
200
400
300
Temperature
500
600
(C)
Figure 4.6 Finite element analysis of the MSL bond with 1 mm and 3 mm Cu interlayer
74
Figure 4.7 The analysis of diamond/1pim TiC/Cu braze/SS304 combination
75
(a)
(b)
Figure 4.8 The analysis result of a 50pm crack at the bottom interface
(a) Mises stress distribution (b) PEEQ distribution
76
Figure 4.9 The equivalent plastic strains for different brazes (a) Cu (b) Ni (c) Al
77
Figure 4.10 The accumulated plastic strain distributions in an octagonal cone of the
diamond grit (a) lower braze alloy level (b) higher braze alloy level
78
Figure 4.11 All stress components obtained from the finite element analysis
79
FEM53-3021 ELEMENT
MISES(MPa) ------
PEEQ(%)
450
4.00
400
3.50
350
3.00
300
a
2.50
250
2.00
200
1.50
150
1.00
1 00
0.50
50
0
0
200
400
600
800
0.00
1000
TEMPERATURE(C)
Figure 4.12 The change of the Mises stress and the equivalent plastic strain with
temperature in element 3021
80
(a)
(b)
Figure 4.13 The equivalent pressure stress of a two-layer braze
(a) Ni/Cu two-layer braze (b) Cu/Ni two-layer braze
81
Figure 4.14 The SEM backscattered image in the diamond-Cu/Sn/Ti braze interface
formed by a fast cooling rate after brazing
82
Copper
Cu 400 C -A--
-4-- Cu 200 C 1.00E-01
1.00E-02
1.OOE-03
1.OOE-04
1.OOE-05
1.OOE-06
'S'
1.OOE-07
U
1.OOE-08
I1.OOE-09
1.OOE-10
C)CL
1.OOE-1 1
1.OOE-12
1.OOE-13
Cu 600 C
m,
0
50
100
150
Mises Stress
250
200
300
350
(MPa)
SS304
-4-200 C --
U
I-
600 C
400 C -A-
1.OOE-04
1.OOE-06
1.OOE-08
1.00E-10
1.OOE-12
1.OOE-14
1.OOE-16
1.OOE-18
1.OOE-20
1.OOE-22
1.OOE-24
1.OOE-26
0
50
100
150
200
Mises Stress
250
300
350
400
(MPa)
Figure 4.15 The creep strain rates of Cu and SS304 at 200, 400, and 600 0C with varied
Mises equivalent stresses
83
The Thermal Cycle of Cu/Sn/Ti Bond
900 800 -
5 700
-
600 500 0.
E
400 300 200 100 -
0
Time
200
150
100
50
0
250
(min)
Figure 4.16 The currently used thermal cycle for 70Cu-2lSn-9Ti (wt%) braze alloy
Cooling Rate = 10 C/sec:
I
*
PEEQ (%) --
U-
CEEQ (%)
0.01
0.009
0.008
0.007
0.006
0.005
kA A
-&A
- -
L-
.0.004
0.003
0.002
0.001
0
0
100
200
400
300
Temperature
500
600
(C)
Figure 4.17 The equivalent plastic strain (PEEQ) and the equivalent creep strain (CEEQ)
change with temperature at element 3021
84
Cooling Rate = 10
-
C/min
element 3121 -A-
element 3021 -
element 3701
450
400
350
2 300
250
200
150
100
50
0
0
1 00
200
300
Temperature
400
500
600
(C)
Figure 4.18 The Mises stress variation during the cooling cycle for three different
elements
85
-+
100 C/min ---
10 C/min -A-
1 C/min -X-
0.1 C/min
450
400
350
a. 300
250
200
150
100
50
0
0
100
200
400
300
Temperature
500
600
(C)
Figure 4.19 The Mises stress variations of element 3021 with different cooling rates 100*C/min, 10"C/min, 1*C/min, 0. 1"C/min
86
Element
1
100 C/min
M 10 C/min
3021
A
1 C/min
X
0.1 C/min
0.8
0.7
0.6
a 0.4
Lu
0.3
0.2
0.1
0
0
100
200
300
400
Temperature
-0-100 C/min --
10 C/min
A
500
600
(C)
1 C/min-X-0.1
C/min
1.6
1 .4
1 .2
1
0.8
'
'
0 0.6
0.4
0.2
0
0
100
200
300
Temperature
400
500
(C)
Figure 4.20 The PEEQ and CEEQ of element 3021 for various cooling rates
(a) PEEQ: accumulated plastic strain (%)
(b) CEEQ: accumulated creep strain (%)
600
87
Figure 4.21 Overview of the Mises stress distribution around the braze alloy
(a) rate-independent plastic model (b) 10*C/min (c) 1*C/min (d)
0.1 C/min
88
5. Development of Abrasive-Resistant Active Braze Alloy
5.1 Developing Abrasive-Resistant Braze Alloy by Introducing Hard
Particles
According to the previous section's discussion, the MSL grinding wheel's life can
be extended by improving the abrasion resistance of the bond matrix. Because the braze
alloy can not be solution treated in a vacuum brazing process, introducing hard particles is
one of the most convenient ways to improve the wear resistance of the bond metal. With
reactive brazing, the reactive element, titanium in our case, reacts with the superabrasive as
described in the previous chapter. Also, the reactive element can react with the hard
particles. This will result in consuming the reactive element and a deterioration of the
wettability of the braze alloy. Moreover, the size and morphology of the hard particles also
play an important role in determining the strength, toughness, and abrasive resistance of the
braze alloy.
It is necessary to understand the mechanism of abrasive wear in order to improve
the wear behavior of the braze alloy. There is a simple yet nevertheless still valuable
expression for the volume of ductile material removed by wear known as Archard's
equation (Powell, 1986; Zhang, Zhang, and Mai, 1994).
V =
H
(5.1)
where V is the volume of material removed by wear per unit sliding distance, K is a
dimensionless number known as the Archard wear coefficient, A, is the normal contact
area, P is the normal pressure, and H is the indentation hardness of the softer material. The
wear resistance, R is simply defined as the reciprocal of the wear volume:
1
R, = 1(5.2)
VW
The wear property of a material is improved by producing a hard second phase in
the matrix. Figure 5.1 exhibits the effect of the size ratio of the abrasive grain to the hard
particles in the matrix. The small coherent particles are often sheared during plastic
deformation, and the incoherent particles fail to block the dislocations that are generated.
As a result, precipitation treatments are not generally a useful way to decrease abrasive
wear. Larger, hard incoherent precipitates or particles such as carbides can be useful in
decreasing abrasive wear if they are well bonded within the matrix. For large particle size,
dislocation cross-slip or climb is not easy.
Large amounts of particles diminish the
89
flexibility of dislocations. In both cases, dislocation cell structures are not formed, and
neither are wear particles. Basically, the particle characteristics that work best for wear
protection are hard, tough, and blocky. A high hardness value makes them harder to cut.
Toughness gives them resistance to breakage. Blocky particles, versus those that are plate
or rod shaped, also reduce crack propagation and breakage. For example, the role of the
hard second phases in the mild oxidation wear mechanism of high-speed steel-based
materials was reported (Vardavoulias, 1994). The size of the hard second-phase particles
is the most important parameter which determines the possibility of the particles providing
protection against oxidation wear of the matrix. Particles of a size less than or equal to the
oxide thickness are carried away when the oxide breaks up. Particles larger than the oxide
thickness remain in place. In this case, their ability to protect the metallic matrix is
determined by the loads imposed on the second-phase particles as well as the strength of
their cohesion with the metallic matrix.
It is important to note that brittle material has an additional mode of abrasive wear,
namely, microfracture. This occurs when the applied stress exceeds the fracture strength of
the material. Therefore, the fracture toughness, K1 c, of the material is important in
determining abrasive wear of ceramics.
Provided that the reinforcement is well bonded to the matrix, ceramic-reinforced
metal-matrix composites (MMCs) generally show much better resistance to unlubricated
sliding wear than the unreinforced matrix (Hutchings, 1994). For example, SiC or A12 0 3
particles are widely used in strengthening the aluminum matrix (Venkataraman and
Sundararajan, 1996ab; Redsten, Klier, Brown, and Dunand, 1995; Ames and Alpas, 1995;
Axen, Alahelisten, and Jacobson, 1994). All reported test results are consistent with the
previous discussion, i.e., the reinforced composites were more wear resistant than the
unreinforced Al sample. However, a little increase in coefficient of friction and a huge
decrease in ductility of the composite was observed in these cases.
It is considered that there are three possible mechanisms for ceramic particles to
break from the matrix: (1) brittle fracture; (2) debonding from the matrix; (3) being carried
away with the matrix alloy.
Because more microcracks are inherently present in a larger ceramic particle, a
catastrophic brittle fracture is more likely to be triggered. Consequently, ceramic particles
become progressively weaker as their size increases. In the case of brittle fracture
prevailing, the composite with coarser ceramic particles can result in poorer wear
resistance. The size of ceramic particles in a composite has an opposing effect when
comparing items (1) and (3). So, the size of the ceramic particles should be determined
case by case depending on the size of the abrasive. The active braze alloy contains
90
titanium. In general, the bond strength can be enhanced by chemical reaction (Tewari,
Asthana, Tiwari, Bowman, and Smith, 1995). The debonding of ceramic particles from
the matrix seldom occur except for the existence of a weak interface such as A14 C3 . The
abrasive wear resistance of a ceramic reinforced metal composite may be up to five or even
ten times that of the metal alone, but only if fracture and removal of the reinforcement are
avoided. These conditions are favored by small abrasive particles. If the conditions are
more severe as in so-called high stress abrasion, widespread fracture of the reinforcing
phase occurs and the wear resistance may be no different from that of the unreinforced
phase.
On the other hand, fracture of the reinforcement occurs readily and most MMCs
show poor resistance in erosive wear (Hutchings, 1994). The composite shows good
erosion resistance if it contains a very high volume fractions of ceramic. This is because
the erosion of brittle materials is distinct from that of ductile materials. The mechanism of
material removal involves cracks initiated by brittle fracture. The erosion rate of ceramics
is given by (Blau et al., 1991):
Ve oc vO -d-
p" -K
-H
(5.3)
where v0 , d, and p are particle velocity, diameter, and density, respectively, H is material
hardness, KIC is material toghness, and V, is the volume loss by erosion per unit mass
impacted. Equation 5.3 explains why introducing some very hard ceramic particles can not
produce improved erosion resistance. The fracture toughness of the material plays the most
important role in determining the erosion rate. It demonstrates that the hard, brittle second
phase particles can actually be detrimental to erosion resistance.
Figure 5.2 shows the current test procedure used in developing abrasive resistant
active braze alloys. First, samples with different chemical compositions were brazed at
different temperatures (880-920"C). Next, each sample is examined by stereo microscope
in order to inspect for any solidification cracks and a meniscus shape around the diamond.
An optical microscope was used for general metallurgical observations. A shear test can
evaluate the bonding strength between the diamond and the braze alloy, and hardness test
can be an indirect index of the wear resistance of the braze alloy. After completing this first
stage examination, qualified braze alloys were chosen for further wear and erosion tests in
order to evaluate their wear resistance more accurately. Finally, the best braze alloy
systems will be selected for grinding tests.
Metal matrix composites containing a high volume fraction of carbide, nitride,
boride, and/or oxide particles are frequently the materials of choice for applications which
require high wear resistance. Table 5.1 shows physical properties of some related hard
91
materials. Suitable particles introduced into the braze can not be judged based on their
hardness only. Chemical stability, metallurgical compatibility, and toughness should also
be considered. Some refractory materials, such as Mo and W, possess excellent erosion
resistance (Blau, et al., 1991). These should also be included in the test. 75Cu-25Sn-lOTi
(by weight) braze with Mo, W, TiC, SiC, and WC additions was evaluated in the
experiment. Figure 5.3 displays the averaged shear and microhardness test results for
75Cu-25Sn-10Ti-X+(by weight) braze alloys. 30/40 mesh natural diamonds were used
throughout the shear test. Some experimental data deviated from the averaged value are
observed in both the shear and the microhardness test. The deviation in shear test
originates from different cross-sections of the diamonds. However, the averaged values
can be used as an indication of bond strength between the diamond and various braze alloys
Table 5.1 Physical properties of some related materials
hardness**
Reference
3150(-)
2260(K)
Schwartz (1989)
2350
2898(-)
2800(K)
Schwartz (1989)
3.48
3227
--
4500(K)
DeVries (1972)
3.52
3550
9000(-)
6900-
Field (1990)
9000(K)
Wilk (1991)
density
m.p.
Strength*
(g/cm 3)
(C)
(MPa)
Al
3.96
2050
B4C
2.50
CBN
Diamond
material
Mo
10.22
2610
600(+)
350 (H,)
Davis (1990)
SiC
3.20
2650
840(-)
1875-
Field (1990)
3980(K)
Schwartz (1989)
Si 3 N4
3.20
1900
432-632(-)
9.0(M)
Schwartz (1989)
TiC
4.90
3140
763(-)
3200(K)
Schwartz (1989)
TiN
5.40
2900
987(-)
1770(K)
Schwartz (1989)
W
19.25
3387
375-400(+)
400 (H,)
Davis (1990)
WC
15.8
2777
---
2000(K)
Schwartz (1989)
* "+" stands for the tensile test, and "-" stands for the compression test
**
"K" stands for Knoop hardness (kg/mm 2), H, stands for Vickers hardness, and
"M" stands for Mohs hardness
+ proportion by weight
92
On the other hand, the inhomogeneous microstructure of the braze and porosity formed
during the brazing process are responsible for the deviation in the hardness test.
The hardness improvement of the braze with Mo additions is not very effective. If
the Mo addition is greater than 15.4 wt% ((20/(75+25+10+20)* 100%), the bond between
the diamond and the braze will deteriorate. Adding W powder will increase the braze alloy
hardness while maintaining acceptable bonding force between the diamond and the braze.
Adding TiC below 15.4 wt% provides the best result so far. It possesses both the highest
hardness and the highest bond strength. A poor bond is observed for all samples
containing SiC particles. The optimal value of WC particle additions is below 8 wt%.
Titanium is thermodynamically favored to reduce WC or SiC (Kingery, Bowen,
and Uhlmann, 1991). It is reported that titanium can react with SiC and form TiC and
TisSi 3 sequentially as shown below (Lee, Hwang, and Lee, 1993; Warrier and Lin, 1995):
SiC(g)+ Ti -+TiC(.)+ Si
(5.3a)
3Si + 5Ti
(5.3b)
-+ Ti5 Si 3 (s)
Consequently, SiC and WC are not useful hard particles for this application.
Based on experiments, TiC displays the best metallurgical compatibility in Ti
containing copper-base braze alloy, and this is consistent with other test results (Ho and
Loretto, 1994). It is also reported that the additions of titanium carbide can greatly improve
the abrasion resistance of iron alloys (Dogan and Hawk, 1995). As the volume fraction of
TiC increases, the mean free path between the carbide particles decreases. The ability of
the abrasive to deform the softer matrix and to remove it through wear mechanism is much
reduced. Therefore, it is expected that higher volume fractions of TiC display better
abrasion resistance under the conditions of material removal via micro-plowing and microcutting. However, the bond strength deteriorates as the concentration of TiC particles
exceeds 15.4 wt%. Consuming the active element and decreasing the ductility of the braze
are two possible explanations for this phenomenon. Great hardness improvement can not
be acquired by a low volume fraction of ceramic particle addition. A large volume fraction
can result in deteriorating the bond strength. There is an optimal quantity of each ceramic
particles. The following compositions (by weight) were selected for further erosion tests:
(1) 75Cu-25Sn-1OTi-(5-20)TiC
(2) 75Cu-25Sn-lOTi-(l0-30)W
(3) 75Cu-25Sn-lOTi-10WC
(4) 75Cu-25Sn-lOTi-lOMo
The ceramic particles tend to cluster during brazing. Agglomeration of the ceramic
particles is also observed in Al/SiC composites (Sukumaran, Pillai, Pillai, Kelukutty, Pai,
93
Satyanarayana, and Ravikumar, 1995). Chung and Hwang (1993) suggest that the
agglomerated SiC particles appear to have been crushed during wear and have become
loose. The relatively low binding force among the clustered particles certainly reduces their
effectiveness in enhancing wear resistance. Based on the test result, the clustering effect of
TiC can be reduced with a larger and a higher volume fraction TiC particles addition.
Figure 5.4 shows the results of shear test and microhardness test for 44 pm and 4 gm TiC
additions with difference in the volume of TiC particles. The bonding forces decrease as
the size of TiC particles decreases. This is consistent with the previous discussion. The
surface area of TiC increases as it becomes smaller. This can have effects on the reaction
kinetics of the braze.
As discussed in the previous section, the strength of ceramic particles can be
decreased due to the possibility of defects in them. On the other hand, the size of the hard
particles should be larger than that of the swarf of the grinding material in order to obtain
the maximum protection from matrix wear. Figure 5.5 displays the A120 3 swarf in the
grinding test.
Its size is below 10pm.
Therefore, 1Opm-44pm (325mesh) ceramic
particles were chosen throughout the experiments.
Another way to increase the hardness of the braze is to form carbide via chemical
reaction. There are two potential hindrances which may suppress carbide formation. First,
a strong carbide forming element, i.e., Ti in our case, can also react with other element(s)
in the braze, and form intermetallic compound(s). That is to say, these reactions compete
with each other. Second, the Cu-C binary phase diagram shows very limited solubility of
C in Cu (Massalski, 1990). This indicates that the flux of C atoms in Cu is low, and the
process will be rate controlled by diffusion of C atoms. A series of experiments were made
in order to verify the kinetics of these reactions. Based on the test results, carbide formers,
such as Ti, Cr, W, and Si, do not improve the hardness very much after carbide formation
in the braze at 9000 C. Zr is the only element which has a measurable effect in enhancing
the hardness of the braze by carbide formation. It is also observed that there is a greater
extent of carbide formation with finer carbon powder additions. Therefore, the finest
carbon black powder (<1 pm) was used throughout the experiment.
The braze with 75Cu-25Sn-l0Ti-l0Zr-0.5C (by weight) provides both good
hardness and bond strength, and it needs further optimization of its chemical composition.
Moreover, the hardness of the braze can be further improved by combining both TiC
particle additions and carbide formation by chemical reaction. Figure 5.6 displays the shear
test and microhardness test of 75Cu-25Sn-l0Ti-l0Zr-(0-0.7)C by weight. Excellent
bonding between the diamond and the braze alloy can be obtained if the carbon content is
94
below 0.38 wt%. However, the hardness increase by adding carbon into the braze alloy is
not very effective. The TiC distribution in the above alloy is much more uniform than that
in 75Cu-25Sn-lOTi-10TiC as shown in Figure 5.7. This will greatly improve the
mechanical properties.
Further wear and erosion tests of the above alloys were performed. The erosion
test was performed by a steady nitrogen gas flow with 80 psig, 0.25 inch distance, and 30
degrees impingement angle for 60 seconds.
Number 320 grit, 32 tm-44ptm, dry SiC
particles with a flow rate of 1.07 g/min was used as erosion particles throughout the
experiment. The wear test was performed by using a cross section of 0.0625 in 2 rod,
0.282 inch in diameter, ground by a number 180 SiC paper with a constant load of 10 N.
The weight loss of the test sample was measured each minute. The braze alloys with
different compositions have different densities. However, the results of erosion test and
wear test are measured by mass loss. In order to make all data comparable, every datum
must be calibrated by the braze alloy density, and transferred into volume loss. The
measured braze alloy densities, D, show in appendix C are used in the following sections
to calibrate the experimental results.
Figure 5.8 exhibits the erosion and wear test of 75Cu-25Sn-lOTi-X (by weight).
75Cu-25Sn-lOTi-lOZr-lOTiC-0.4C (by weight) has the best wear resistance in the wear
test, if brittle fracture is not the primary wear mechanism as described in the previous
sections. The wear resistance of Cu/Snfli/Zr/TiC/C alloy is about ten times better than that
of Cu/Sn/Ti. Some data do not change in linear, because the microstructure of these alloys
is not homogeneous. Clustering of the introduced particles is responsible for it.
Introducing hard, brittle particles, however, can not improve the erosion resistance of the
braze alloy, because the erosion rate of composites is strongly related to both fracture
toughness and hardness as discussed before. Based on these result, tough, hard particles,
such as W, improve the erosion resistance more effectively than brittle, hard ones.
75Cu-25Sn-lOTi-lOZr-lOTiC-0.4C (by weight) has the best abrasive resistance of
any alloy developed. Before further tests are made, another problem was encountered.
The viscosity of the braze was too high to form a good meniscus shape around the larger
size of diamond, e.g., 20/30 mesh (0.841-0.595 mm). Phase separation and micro voids
occurred after brazing. The viscosity is a critical issue for brazing, especially in the case of
MSL grinding technology. The viscosity should be low enough to form a good meniscus
shape around the diamond, but it can not be so low that it will not hold the braze alloy on
the wheel during brazing. Two possible methods may overcome this barrier: one is to
increase the brazing temperature; the other to change the chemical composition of the braze
95
alloy. Based on the experimental results, increasing the brazing temperature is not an
effective way to reduce the viscosity of the braze alloy when introducing hard particles.
Therefore, changing the composition of the braze alloy is a necessary step to reduce the
viscosity of the braze alloy.
In order to get better meniscus shape around the larger diamond, a series of
experiments have been made. Based on the optical microscope observations, adding
carbon powder can avoid the formation of micro voids in the matrix. It also results in a
more uniformly distributed matrix, but, unavoidably, increases the viscosity of the braze.
Decreasing the carbon content in the braze is a good way to lower its viscosity. Further
optimization of this alloy was performed. Figure 5.9 displays the erosion and wear test of
The wear resistance of
75Cu-25Sn-xTi-yZr-zTiC-*C (by weight) braze alloy.
Cu/Sn/Ti/Zr/TiC/C alloys is in good agreement with the previous wear test. All these
alloys exhibit great abrasive wear resistance in the experiment. 77Cu-23Sn-12.5Ti-7.5Zr1OTiC-0.2C brazing at 920'C shows good wear resistance as well as excellent wetting
around diamonds. Therefore, this alloy was chosen for the grinding test.
5.2 Fundamental Study of the Abrasive Resistant Braze Alloys
Figure 5.10 displays the EDX analysis of 75Cu-25Sn-12.5Ti-7.5Zr-lOTiC-0.2C
(by weight). The thickness of the TiC reaction layer is about 1 pm, which is thicker than in
the 77Cu-23Sn-lOTi braze. At least three phases can be identified from Figure 5.7 and
5.10(a). They are TiC particles, the copper-rich phase, and the Ti/Zr/Sn intermetallic
compound. Based on the X-ray analysis, copper, TiC, and a small amount of ZrC were
identified. Only a limited amount of Zr reacts with the carbon. This may result from the
low brazing temperature which is not high enough for formation of zirconium carbide.
Other phases, unfortunately, can not be identified by reviewing all currently existing crystal
structure files (Jenkins et al., 1986).
The zirconium has a much stronger tendency to associate with tin than copper does.
An important contribution of adding Zr into the braze is that the Sn content in the copperrich phase can be decreased. If the Zr content is decreased, a high tin bronze phase would
be formed as demonstrated in Section 3.2. This can result in a more brittle braze than the
current one. Because the pure copper has excellent ductility, a continuous high purity
copper phase is beneficial to the toughness of the braze. It is an ideal composite by
combining hard, brittle phases with a ductile matrix if the interfacial bond is strong enough.
96
Figure 5.11 shows a thermal analysis (DSC) of the above alloy. The alloy starts
melting at 871.4"C. Its melting point is higher than that of Cu/Sn/Ti one. The range of the
heating cycle is between 25-1000*C in the test. However, there is no clear solidification
This results from the chemical reaction
temperature observed in Figure 5.11(b).
proceeding at high temperature and forming intermetallics during heating. In most cases,
the intermetallic phases have high melting points. Therefore, they will not melt in the
braze. Moreover, the melting point of the remaining liquid becomes higher because the
solute is consumed by intermetallic formation. The melting point of the alloy shifts to
higher temperatures as the reaction proceeds. Consequently, there is no liquid phase left
after the heating cycle.
Similarly, isothermal solidification is performed during the brazing process. This is
the primary reason that increasing the brazing temperature can not enhance the viscosity of
the melt effectively. Solid phase formation makes the remaining liquid more viscous
during brazing. According to Figure 5.11(a), the minimum brazing temperature is about
9000 C, and the recommended brazing temperature is 9200C.
5.3
Grinding Test and Cutting Test of the MSL Wheels
The grinding test is described in Section 3.1. Figure 5.12 shows the grinding test
result. The 77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C wheel exhibits the best grinding
performance. Its grinding life is about twice the current one. The power used in grinding
is lower than that of any other wheels. Figure 5.13 shows the fractographs after the
grinding test. Transverse fracture and debonding of diamonds are two primary fracture
modes as shown in Figure 5.13(a). It is also noted that the cracks close to transverse
fractured diamond are observed as shown in Figure 5.13(b). The most probable reason for
this type of failure is fatigue.
As diamonds become blunt, a larger applied force is necessary to grind. Once the
applied stress exceeds the yield strength of the braze, cracks initiate and propagate
throughout the alloy. Finally, the diamond may be either fractured or debonded. The
fracture of diamonds simply results from the high tensile stresses in the diamond induced
by thermal expansion mismatch and applied grinding stresses. However, the debonded
diamond grits may result from many reasons. The inherent strength and thickness of the
reaction layer are two significant factors in determining their bond strength as discussed in
Section 2.2, and another important factor must also be included in this case.
The strong effect of the interfacial intermetallic phase on fracture resistance of
A120Al-Cu alloy interfaces were confirmed (Zhang and Shang, 1996; Liu and Shang,
97
1996). Based on this investigation, interfacial toughness depends on the microstructure of
the metal as well as the interface formed by solid-state phase transformations, such as
intermetallic phases. Interfacial phases considerably weaken the fracture resistance of the
interface. Peak toughness of the interface scales with the yield strength of the metal and is
relatively insensitive to variations in interfacial microstructure. Initiation toughness of the
interfaces, on the other hand, varies greatly with the interfacial microstructure. For
precipitate-covered interfaces, the toughness is directly related to the ratio of the spacing
and the size of the precipitates. The interfacial microstructures of Cu/SnfIi and
Cu/Sn/Ti/Zr/TiC/C are displayed in Figure 5.14. Intermetallic phases can be clearly
observed at the interfaces. Therefore, the cracks, developed either by thermal stresses or
by cyclic applied grinding load, are initiated at the interfaces between these brittle phases
and the diamond grit. Next, they propagate into the braze, and finally, the diamond grit is
debonded. According to the fractographs of the debonded surface as demonstrated in
Figure 3.2 and 3.5, there is very limited plastic deformation in the braze, and brittle fracture
can be observed in these figures. However, the crack tip can be blunted by plastic
deformation of the braze alloy. The peak toughness of the interface will be improved by a
ductile braze alloy. Therefore, decreasing the volume fraction of the intermetallic phases
and increasing the toughness of the braze alloy are two primary methods to ameliorate the
fatigue resistance of the bond.
Another important phenomenon that was noticed was that some cracks in the radial
direction of debonded diamond as observed in Figure 5.15. This can be explained by the
thermal hoop strain close to the interface as discussed in Chapter 4. The SEM back
scattered image shows that the crack is inside a particle. Because the size of introduced TiC
particles is between 10-44 gm, the size of the broken particle in Figure 5.15 is below 10
gm. Therefore, a reasonable deduction is that the cracks initiate within the intermetallic
phase instead of TiC. This argument can further be demonstrated by examining the
fractograph of a tensile test specimen as shown in Figure 5.16. All cracks initiate in the
intermetallic phase instead of in the particles. These cracks do not propagate into the TiC.
Therefore, the Cu/SnIi/Zr intermetallic phase is the weakest one in the alloy. The copperrich phase shows a certain extent of ductility as displayed in the figure. Consequently, the
braze itself is similar to a composite, copper matrix with hard brittle phases. The dominant
wear mechanism of the braze in grinding depends on many factors such as the materials to
be ground, density of the abrasive, distribution of the abrasive...etc. For this test, there is
more erosion than abrasive wear. Therefore, further test of this alloy in abrasive dominated
wear is necessary.
98
To verify the abrasive resistance of the new alloy, a more abrasive cutting test was
performed. Figure 5.17 shows two types of the MSL test wheels. Figure 5.17(a) is the
grinding wheel used in the previous test, and Figure 5.17(b) is the cutting wheel used in
this test. There are thme wheels used in this test. The first is a laser-welded diamond
wheel. The second is a 77Cu-23Sn-lOTi (by weight) MSL bond diamond wheel. The
third is a 77Cu-23Sn-12.5Ti-7.5Zr-lOTiC-0.2C (by weight) MSL bond diamond wheel.
Each diamond wheel is 22.86 cm in diameter and 0.159 cm in thickness. Green concrete
blocks with the dimension of 30.48cm*30.48cm*701cm were used as material to be cut in
the test, and the depth of cut is 2.54cm. The cutting test result is summarized in Table 5.2.
Table 5.2 The cutting test result of three different wheels
wheel type
meters of cutting
304
laser-welded diamond wheel
Cu/Sn/Ti bond MSL diamond below 300
wheel
Cu/Snfri/Zr/TiC/C bond MSL 411.5
failure mode
wear of the wheel substrate
debonding of the diamonds and wear
of the substrate
wear of the wheel substrate
diamond wheel
The cutting process is highly impactive and abrasive. The laser-welded diamond
wheel failed at 304 meters of cutting due to wear of the wheel substrate. The thickness of
the test wheel is 0.159 cm. To avoid catastrophic failure during grinding, the thickness of
the wheel can not be too thin to support the diamond blade. Therefore, the cutting test was
stopped at 304 meters of cutting.
The second MSL wheel with Cu/Sn/Ti bond failed below 300 meters of cutting due
to diamond debonding and wear of the steel substrate. The third MSL wheel with
Cu/Sn/Ti/Zr/TiC/C bond failed at 411.5 meters of cutting due to wear of the steel substrate.
Figure 5.18 shows the fractographs of the above two MSL wheels after the cutting test.
Wear of the Cu/Sn/Ti braze can be observed in Figure 5.18 (a). Both MSL wheels are
about the same diamond weight. However, the diamond concentration in Figure 5.18(b) is
much higher than that in Figure 5.18 (a). Debonding of the diamond grits is a possible
explanation for the higher diamond losing rate from the Cu/Sn/Ti alloy. The wear of the
Cu/Sn/Ti alloy during cutting results in deteriorating the bonding force between the
diamond and the braze alloy due to the decrease of the bonding area. Therefore, the
diamond grits debond throughout the Cu/Sn/Ti bond wheel. The wavy surface in the
fractographs demonstrates that the wear resistance of the Cu/Sn/Ti braze is inferior to that
99
of the Cu/SnrTi/Zr/TiC/C braze alloy. On the other hand, the Cu/Sn1i/Zr/TiC/C braze
remains bonded to the diamond grits very well after 411.5 meters of cutting. All of the
remaining diamond grits were still fmnly bonded by the braze alloy, and there is no
evidence of the diamond grits debonding.
The primary reason for the Cu/Snri/TZrfiC/C bond working better than the
Cu/Sn/Ti bond can be attributed to the improved wear resistance of the braze alloy. Wear
of the braze alloy during the cutting process results in exposing the diamond grits.
Therefore, the bonding force decreases due to reduction of the bond area. Finally, the
braze alloy can not hold the diamond anymore, and the diamond grits debond. The wearresistant braze alloy extends the wheel's life and changes the failure mode of the MSL
cutting wheel from debonding of the diamond to wear of the steel substrate. Moreover, it
is expected that the wheel's life can be further improved by choosing an improved (i.e.
harder) substrate material.
100
o
t
0
0
0
0
0
110
0
0
o 0
K
0
o
0
So
0
to 0
0
*
0
(a)
/
/
(b)
(c)
Figure 5.1 Effect on abrasive wear when second phase is varied (Blau et al. 1994)
(a) small second phase, easily removed
(b) large second phase, protection of matrix
(c) very large second phase, small abrasive channeled to matrix
101
Samples with various alloy compositions
Brazing
Stereo microscope
Optical microsope
Shear test
Hardness test
No Z
Reject
Wear test
Erosion test
No
Reject
Yes
T
Grinding test
N o
Yes
Product
Figure 5.2 Test procedures in developing abrasive resistant active braze alloys
102
Shear Test
50 -
46
45
3
43
o 40 n 38
34
36
43
42
36
37
28
30
27
U20
21
-
-
8.6 8.3
10"+"
0
20
-
-
-_
0
0
_
_
OC*
0
00000
0
Cf)
CqJ
LO
0
-r-
0
CM
0
(in
75Cu-25Sn-1OTI-X
Microhardness
UL)
C
V)
0
0
0
0
C\1
0
M~
weight)
Test
573
6001
570
483
500
431
398 417
385
346 366
306 324 345 346
400
285
265
264
300
200
100
0
LO
0
0
C- i
CV)
75Cu-25Sn-10TI-X
LO
0
(
In
0
0
LO
LO
0
0
weight)
Figure 5.3 The results of shear test and microhardness test for various particle
additions, brazing at 9000C*30 minutes
0
103
Shear Test
50'
U
45. .
.0
0
U.
43
43
42
40
40- "
35. "
30m "
25- 20 m"
15 m10 a 5 . -
35
34
30
27
0 M
)
0
0)
0
N
0)
0
'4.
'4.
'4.
'4-
TIC
(micron,
0)
0
CM
cv,
1-i
0f)
cm
1-
'4.
1-i
gram)
Microhardness Test
600. .
573
483
500
417
400
380
453
443
414
338
z 300
200
100 +I
I
I
0
0)
In
I
0)
0
I
0D
0
(V.,
'4.
'4.
N
0)
I
n
'4O
0)
0
I
I
0)
0t
0)
it
'4.
'4.
TIC
(micron,
gram)
Figure 5.4 The results of shear and microhardness tests for 75Cu-25Sn-lOTi-XTiC(44
micron or 4 micron) in weight, brazing at 9000C*30 minutes
104
Figure 5.5 The morphology of A12 0 3 swarf after grinding test
105
in
75Cu-25Sn-1 OTi-1 OZr-1 OTiC-XC
50
-
50-
43
42
47
41
-
-40
48
weight
34
32
e- 3
30
U
00 20 I
0
10 - -
--+---
0 .2 C
.1 C
0c
.3 C
I
.4 C
M
.5 C
I
1
.6 C
.7 C
X grams Carbon
Microhardness
450
400
Test
I.
414
a"
350
350
337
364
367
365
.2C
.3C
.4 C
367
382
300
30
250
2001
1501
1 00
50*
I
0
OC
II
.1C
.5 C
.6 C
.7 C
X grams C
Figure 5.6 The results of shear and microhardness tests for 75Cu-25Sn-lOTi-lOZr1OTiC-(0-0.7)C in weight, brazing at 900 0C*30 minutes
106
75Cu-25Sn-1 OTI-1Zr-10TiC-O.25C
Figure 5.7 The microstructure of 75Cu-25Sn-1OTi and 75Cu-25Sn-1OTi-1OZr-1OTiC 0.25C by weight
107
Erosion
0.7'
1'
0.606
0.6' "
0.492
r 0.5
E
Test
0.541
0.515
0.493
0.446
0.441
0.415
*0.4'
0.472
0.356
0
0.3'
IE
0.20.1
0 I
0
i.
C)CMC
0
U)
75Cu-25Sn-1 OTI-X
(in
6
weight)
Wear Test
100
90
80
5TiC
---- +- 1 TiC
-015TiC
E.
E
70
60
E
50
6 20W
-O--30W
-0-1 OWC
-1 OMo
-X- 1 OZr-1 OTiC-0.4C
40
30
20
10
60
120
180
240
300
360
420
480
Time (second)
Figure 5.8 The erosion and wear tests of 75Cu-25Sn-1OTi-X (in weight) braze alloy
108
Erosion
1-
Test
U
0.874
0.8" "
0.9'
.739
E 0.7E
0.60
E
0.5'
0.49
-
0.568
2
0.483
0.649
0.623
0.58
0.472
0.44
-
0.3 ' "
0.2 ' 0.1 " 0.4 '
06
1=
0
NO
)
U!=
p
oM
N
N'-
0' C
0
75Cu-25Sn-wTi-xZr-yC-zTIC
0.
r-o
U
r0
.±-
.2.-
weight)
(In
Wear Test
140
UM
I-rn
120
E
E
--4-1
-4-1
100
--
80
--
0
--
60
E
77Cu23Sn1 OTi
OZr
OZr.4C
1OZr OTiC
1OZr.4C20W
1 OZr.25C1 OTiC
OZr.2C1 2.5TiC
-1
1 OZr.4C1 OTiC
--X-12.5Ti7.5Zr.4C10TiC
-X- 12.5Ti7.5Zr.2C1 OTiC
40
20
0
60
120
180
240
300
360
420
480
Time (second)
Figure 5.9 The erosion and wear tests of 75Cu-25Sn-wTi-xZr-yC-zTiC (in weight) braze
alloys
109
(a)
(b)
Figure 5.10 EDX analysis of 75Cu-25Sn-12.5Ti-7.5Zr-lOTiC-0.2C (byweight),
9000 C*30 minutes
(a) its morphology, (b) the dot mapping of Zr, Ti, Sn, and Cu
110
i .0 sec
35
-70
139 .6
12.52
20-
0
871.4 C
N
-70
.543 min
-10
V1IT Center
for
645
-140
915
825
735
materiaIs Science
TEMP C
1005
(Heating)
(a)
1 0 SeL
-10
MIT Center
(a) hetn yce()coln
~25L
645
735
for Materials Science
40
-
yl
-2
825
TEMP C
915
1005
(Cooling)
(b)
Figure 5.11 DSC analysis of 77Cu-23Sn-12.5Ti-7.5Zr-LOTiC-0.2C (by weight)
(a) heating cycle
(b) cooling cycle
0
E
111
NIPLATE -U-
--
NORTON
A
NORTON-S -X-
MIT -3
HIGH TIN
0
ABR TECH
1000
900
800
700
.0
600
U
500
-
400
E
300
z
200
100
0
1
0
-I-
2
NIPLATE -0-
4
3
Number of Grinds
NORTON -A-
NORTON-S -X-
5
MIT -2-
6
7
HIGH TIN -0-
8
ABR TECH
1400
1200
1000
800
0
CL
600
400
200
0
0
1
2
3
4
5
6
Number of Grinds
Figure 5.12 The grinding test result of six different alloys
7
8
112
(a)
(b)
Figure 5.13 Fractographs of 77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C (byweight) MSL
wheel: (a) low magnification overview, (b) fractured diamond.
113
(a)
(b)
Figure 5.14 The interfacial morphology between the braze alloy and the diamond
(a) diamond/77Cu-23Sn-lOTi(by weight)
(b) 77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C(byweight)/diamond
114
Figure 5.15 Fractograph of a debonded surface
Figure 5.16 Fractograph of 77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C (byweight) after
tensile test
115
(a)
(b)
Figure 5.17 The morphology of two MSLwheels used in the tests
(a) high density alumina grinding test
(b) green concrete cutting test
116
(a)
(b)
Figure 5.18 Fractographs of two MSL wheels after cutting test
(a) Cu/Sn/Ti bond after 300 meters of cutting
(b) Cu/Sn/Ti/Zr/TiC/C bond after 411.5 meters of cutting
117
6. Development of a Ductile Active Braze Alloy
6.1 Using Alloy Design to Develope a Ductile Braze Alloy
Table 1 shows the mechanical properties of some Cu-Sn-(Zn) alloys (Davis et al.,
1990). The ductility will drastically decrease if the tin content exceeds 14 wt%. To join
dissimilar materials with large thermal expansion mismatch, an ideal brazing filler metal
should have sufficient ductility to accommodate this mismatch as described in chapter 4. In
our case, a low yield strength of the braze alloy can avoid crushing the diamonds, and a
high ultimate tensile strength can prevent the braze alloy from fracture by plastic
deformation. According to Table 6.1, all these criteria can be satisfied if the tin content in
the alloy is decreased. Because the copper-rich phase is a continuous phase in the 70Cu21Sn-9Ti (wt%) alloy, its mechanical properties can be improved by increasing the ductility
of the copper-rich phase. However, the low tin content of the Cu/Sn/Ti alloy has a high
brazing temperature and it is difficult to wet the diamond.
Table 6.1 Mechanical properties of some copper/tin alloys (Davis et al., 1990)
UTS [MPa(ksi)]
YS [MPa(ksi)]
Elongation(%)
Hardness (HB)
98.7Cu-1.3Sn
276(40)
76(11)
47
---
94.8Cu-5Sn-0.2P
330(48)
130(19)
47
---
93Cu-7Sn
262(38)
110(16)
30
70(500kg)
88Cu-lOSn-2Zn
310(45)
152(22)
25
75(500kg)
89Cu-11 Sn
303(44)
152(22)
20
80(500kg)
87Cu-13Sn
276(40)
138(20)
15
90(500kg)
85Cu-14Sn-lZn
221(32)
172(25)
2
105(500kg)
84Cu-16Sn
241(35)
172(25)
2
135(3000kg)
8lCu-19Sn
241(35)
207(30)
0.5
170(3000kg)
Composition
An alternative way is to replace part or all of the tin with other element(s). Great
efforts have been made to develop a new active braze alloy with lower tin content. There
are several requirements that the melting point depressant(s) must meet. Because this is a
vacuum brazing process, the adding element(s) should have a low vapor pressure at the
118
brazing temperature. This requirement excludes the possibility of adding Zn, Pb, Bi, Cd,
Sb, Mn, and Mg as shown in Figure 6.1 (Olson, Siewert, Liu, and Edwards, 1993).
Next, the added element must depress the melting point of copper effectively. Several
candidates can be found by consulting the binary phase diagrams of copper (Massalski,
1990). Four elements are chosen as discussed below:
(1) Ag addition: Silver is a good choice to replace part of tin in the braze. In fact, 75Cu15Ti-lOAg, 75Cu-10Ti-l5Ag, and 80Cu-lOTi-lOAg (wt%) exhibit good wetting of both
diamond and steel.
(2) Al addition: Aluminum can be a melting point depressant for copper. However, based
on experimental results, Al and Ti form intermetallic compounds during brazing which
severely reduces the activity of titanium. This can decrease the wettability of the braze alloy
with the diamond. Moreover, Al tended to react with the binder during the test. Therefore,
Al is not a suitable element to replace Sn.
(3) Indium addition: Indium is expensive and forms a tenacious oxide. This prohibit
further applying it into the copper-based braze alloy.
(4) Si addition: Silicon can lower the melting point of copper very effectively. However,
there are three major barriers to hinder the application of Si in Cu/Sn/Ti. First, it is
necessary to use alloy powder instead of pure Si powder in the braze, because the melting
point of Si is much higher than that of Cu. Second, Si reacts with Ti to form titanium
silicide (Nishino and Ural, 1991). This lowers the activity of Ti and makes the braze alloy
more brittle. Third, there is some porosity in the braze alloy close to the steel substrate as
indicated by the arrows in Figure 6.2. They are related to the Kirkendall shift due to the
fast diffusion of Si into steel. This has been reported in studies of other alloy systems
containing Si (Shaw, Miracle, and Abbaschian, 1995). These porosities can result in a low
fracture energy of the interfacial region due to crack propagation along these weak paths.
Therefore, Si is not a suitable adding element in the copper base braze alloy.
In summary, Ag is the best candidate to substitute for part of the Sn in the Cu/Sn/Ti
alloy. A series of tests were made in order to evaluate the possibility of replacing part of
the Sn in the Cu/Sn/Ti alloy by Ag. Figure 6.3 shows the microstructural observations of
Cu/Ag/Sn/Ti active braze alloys. All alloys were prepared by arc melting and were brazed
to high purity graphite disks to evaluate their wettability. Figure 6.3(a) and (b) are the
microstructures of the Ag-Cu eutectic alloy and 9OCu-lOSn (wt%) bronze. Figure 6.3(c)
shows the microstructure of Ag-Cu eutectic + 4.5Ti. The major difference between Figure
6.3(a) and (c) is the needle-like intermetallic phase in the Ti containing active braze alloy.
This results in decreases in both the ductility and the fatigue strength of the braze alloy.
Figure 6.3(d) and (e) show the microstructure of two Cu/Ag/Sn + -4 wt% Ti alloys.
119
Needle-like intermetallics can still be observed in these photos. Based on these
experimental results, a little nickel, 0.7 wt%, was found to greatly retard intermetallic
formation as shown in Figure 6.3(f). However, these alloys do not wet the polished
graphite very well. Good wetting can be obtained by increasing the titanium and/or silver
content in the braze alloy, but the needle-like intermetallic phase forms again as displayed in
A little Zr addition can retard the formation of the needle-like
Figure 6.3(g)(h).
intermetallics as shown in figure 6.3(i). The compositions displayed in Figure 6.3(h) and
(i) produce the best wetting on the graphite surface.
The vapor pressure of Ag is about 10' torr at 900*C as shown in Figure 6.1. It is
necessary to use a partial pressure and/or an alloy powder during brazing to avoid silver
loss. Moreover, the brittle phase can not be totally eliminated by adding Ag into the braze
alloy. Therefore, no further test was performed on the Cu-Ag-Sn-Ti system.
6.2
Developing a Ductile Active Braze Alloy Using a Two-Layer Structure
An alternative way to decrease the tin content in the alloy is to use a two-layer
structure to dilute its concentration by dissolution and solid state diffusion. As discussed
in Section 2.3, functionally graded materials or multilayered structures can greatly decrease
the residual thermal stress in the material by influencing the thermoelastoplastic properties
of the interfacial layers (Williams, Arnold, and Pindera, 1993; Shalz, Dalgleish, Tomsia,
and Glaeser, 1994) Copper, chromium, nickel, and silver can easily be plated on the steel
(Cotell, Sprague, and Smidt, 1994). The plated thin layer should not react with titanium in
the Cu/Sn/Ti braze, because the intermetallic layer will greatly retard the dissolution
process. For example, a Ni plated layer will react with Ti and is not a good interlayer
candidate as shown in Figure 6.4. High ductility, low yield strength, and good
metallurgical compatibility with the Cu/Sn/fi braze makes copper an ideal interlayer. At
least three beneficial effects can be achieved from a thin copper interlayer:
(1) The residual thermal stresses and strains are decreased when a copper layer is
introduced between the diamond and the SS304 substrate as discussed in Chapter 4.
Moreover, the stresses in the braze, developed either by an applied load or by thermal
mismatch of the materials, can be alleviated by plastic deformation of the low yield
strength, high ductility interlayer.
(2) Dissolution of the interlayer copper into the Cu/Sn/Ti braze during brazing results in a
decrease in the tin content of the copper-rich phase. This will contribute to an increase in
the ductility of the braze, and, therefore, promotes fatigue resistance of the bond.
Moreover, the dissolution process will not deteriorate the wear resistance of the braze. It is
120
reported that the wear resistance of tin bronze is greatly affected by the tin content in the
alloy as shown in Figure 6.5 (Sasada, Ban, Norose, and Nakano, 1992; Eliezer, Ramage,
Rylander, Flowers, and Amateau, 1978). The wear resistance of the alloy decreases
rapidly as the tin content in the bronze is reduced. However, dissolution of the pure copper
interlayer is limited by diffusion. Consequently, a copper-rich phase with high tin content
is formed at the outer part of the wheel, and a low tin content copper-rich phase is located
close to the braze-substrate interface. The outer part of the braze, experiencing the most
severe wear in grinding, still has the same wear resistance as compared to the original
braze. The benefit of a tough inner part of the braze is that it makes the braze more fatigue
resistant. For example, as the material experiences surface traction, voids and cracks can
nucleate under the surface. Delamination of the subsurface area may result in failure of the
material (Suh, 1986). Therefore, a tough material can blunt the crack tip and retard
propagation of the crack. In the case of an MSL grinding wheel, the applied load is
transmitted into the inner part of the braze via diamond grits. A void may be nucleated if
the braze does not have sufficient ductility to be deformed plastically. A soft inner braze is
a good way to improve such a situation.
(3) As described in Chapter 1, the braze alloy should be chemically and/or
electrochemically stripped without jeopardizing the steel substrate. The currently used
70Cu-2lSn-9Ti (by weight) braze can not be easily stripped from the steel substrate. One
of the primary barriers to do this is the Ti/Fe/Cu intermetallic phase formation at the brazesubstrate interface as shown in figure 6.6. This phase is difficult to remove by chemical
stripping. Electrochemical stripping and sand blasting must be used in order to recycle the
wheels. Figure 6.7 shows the EDX analysis of the interfacial phases, respectively. It is
clear that Fe, dissolves into the braze and forms a solid solution and intermetallics. This
can be avoided if a copper interlayer is introduced. The copper layer works as a barrier
layer to block the Fe dissolution into the braze. There is no intermetallic phase formed
between the braze alloy/Cu and Cu/Fe as demonstrated in Figure 6.8.
Figure 6.9 shows the morphology of 70Cu-2lSn-9Ti (wt%) and the Cu two-layer
structure after brazing. No clear dissolution layer can be observed in the low magnification
stereo microscope if the brazing temperature is below 880*C. The width of the dissolution
layer is about 300 gm at 900*C. There is no clear difference by varying the brazing time
from 30 minutes to 120 minutes. The diamond can be easily brazed between 865*C and
880'C, but only very limited dissolution between the copper and Cu/SnfI'i is achieved
below 880 *C. This means that diamond can be first brazed at 880 'C or lower, then heated
up to 900 *C to dilute the tin content of the alloy.
121
A finite element analysis shows that there is a high misfit at the bottom interface.
Decreasing the hardness of the bottom part of the braze alloy has little effect on the wear
and/or erosion resistance of the braze alloy during the grinding process as discussed earlier.
Therefore, plating a thin layer of copper between the braze alloy and the steel wheel may
improve the low cycle fatigue resistance of the braze. It is necessary to perform a grinding
test in order to verify the above statement.
Figure 6.10 shows the microstructure of the two-layer structure after brazing for
various temperatures and times. The braze alloy is not totally melted until 9000 C.
Although the braze alloy can work very well in the MSL grinding wheel at 880 0 C, it is
recommended that the braze alloy should be brazed above its melting point in order to avoid
inhomogeneity in the alloy. Fewer voids and a more homogeneous microstructure can be
obtained if the alloy is brazed at 900 0C.
Table 6.2 displays the EDX analysis of the copper-rich phase in 70Cu-2lSn-9Ti
(wt%). The dissolution of copper is much more prominent at 900 "C than that at 880 0 C.
The tin content in the copper-rich phase is less than 13 wt% for the sample brazed at 9000 C
Table 6.2 EDX analysis of the copper-rich phase in 70Cu-2lSn-9Ti braze alloy
Temperature ("C) Time (minute)
Position* (gm)
Composition (wt%)
880
30
-30
95.4Cu-4.3Sn-0.3Ti
880
30
+30
87.7Cu-12.lSn-0.2Ti
880
30
+1000
84.5Cu-14.4Sn-1.lTi
900
30
+75
88.7Cu-l0.9Sn-0.4Ti
900
30
+1000
87.lCu-12.6Sn-0.3Ti
900
120
-70
98.7Cu-l.lSn-0.2Ti
900
120
-23
96.8Cu-2.9Sn-0.3Ti
900
120
+200
88.7Cu-l1.lSn-0.2Ti
900
120
+1000
89.5Cu-10.7Sn-0.3Ti
position=0 at the copper/braze interface, position > 0 at the braze alloy side, and
position <0 at the copper side.
for 30 minutes. Therefore, a thin layer of plated copper applied to the wheel before brazing
may be a good way to improve the ductility of the Cu/Sn/Ti. The interfacial bond strength
*
122
among copper and steel, and the optimal thickness of the plated copper layer needs further
study.
The toughness of the Cu-rich phase can be further improved by introducing pure
copper powder into the braze alloy paste. For example, 71.4 wt% bronze powder, 7.2
wt% Ti powder, and 21.4 wt% Cu powder (325 mesh) were mixed into the paste. Figure
6.11 shows the microstructure of the above alloy composition after brazing at 8650 C,
880*C, and 900'C for 30 minutes. All alloys wet the diamonds well. A special feature,
This can be explained by isothermal
microvoids, is observed in Figure 6.11(c).
solidification of the braze alloy. The dissolution of pure copper into the braze alloy is much
more prominent at 900*C than that at 880'C or 8650 C as demonstrated earlier. When Cu
atoms dissolve into the braze alloy, a new alloy with a higher melting point can be
expected. This causes a higher viscosity of the alloy, and some porosities are formed
during isothermal solidification. However, this can be improved by a two-step brazing.
The diamonds are first brazed at 865*C for 30 minutes. Good wettability and fluidity of the
braze alloy can be achieved at this stage. Next, the system heats up to 900'C for 30
minutes in order to enhance the dissolution of the pure copper powder. Figure 6.11(d)
exhibits this microstructure. It is obvious that both the intermetallic phase and the porosity
are greatly decreased. It is expected that the fatigue-resistance of the braze alloy is further
improved. Moreover, the braze alloy is easier to strip from the steel substrate due to its
lower Sn and Ti content.
6.3 Grinding Test of the Two-Layer MSL Grinding Wheels
The grinding test procedures are described in Section 3.1. Three tested wheels are
described below:
(1) The present alloy, 70Cu-21Sn-9Ti (wt%), brazing at 8650C*30 minutes.
(2) The braze with the alloy composition 76.9 wt% 77Cu/23Sn bronze-7.7 wt%
Ti- 15.4 wt% pure copper powder, brazing at 8650 C*30 minutes, then heating
up at 10C/min to 895 0 C*5 minutes.
(3) Two-layer structure, 76.9 wt% 77Cu/23Sn bronze-7.7 wt% Ti-15.4 wt% pure
copper powder and a 101.6 gm pure copper interlayer, brazing at 865*C*30
minutes, then heating up at 10C/min to 8950 C*5 minutes.
Figure 6.12 shows the grinding test results. All three wheels behave similarly.
The power and the tangential force are at the same level. Fracture of the diamond grits and
flat spots on the diamond grain are the primary failure mode. Very limited diamond
123
debonding, less than 5 grits per wheel, are observed in the stereo microscope. This
indicates that diamonds are well bonded by these braze in the test. Due to the short test
period for each wheel, the fatigue resistance of these braze alloys can not be examined in
this experiment. Using lower hardness grinding material such as Mullite and/or lowering
the feed speed are alternatives to complete the test. However, it takes a much longer time to
finish the test. No more grinding test will be processed at this stage.
6.4 Stripping Test of the Two-Layer MSL Grinding Wheels
There are five criteria that the MSL bond braze alloy should meet as discussed in
Chapter 1. One of the criteria is that the braze alloy should be chemically and/or
electrochemically stripped without altering the steel preform. The currently used Cu/Sn/Ti
alloy is difficult to remove from the substrate. However, the two-layer braze with pure Cu
powder addition can make stripping the braze alloy easier than stripping Cu/Sn/Ti braze
alloy due to its lower Sn content and absence of a reaction layer between the braze alloy and
the steel. Therefore, three alloys were chosen for the strip test as described below:
(1) The present alloy, 70Cu-21Sn-9Ti (wt%), brazing at 8650 C*30 minutes.
(2) The wear-resistant alloy, 77Cu-23Sn-12.5Ti-7.5Zr-lOTiC-0.2C (by weight),
brazing at 9200 C*30 minutes.
(3) Two-layer structure, 76.9 wt% 77Cu/23Sn bronze-7.7 wt% Ti-15.4 wt% pure copper
powder and a 50 gm pure copper interlayer, brazing at 865*C*30 minutes, then
heating up at 10C/min to 8950 C*5 minutes.
Figure 6.13 shows the weight loss for three different alloys. The stripping speed
for the two-layer structure is much faster than the other wheels. Figure 6.14 shows the
morphology of these MSL wheels after 595 minutes stripping. Both the braze alloy and the
diamonds are totally removed from the steel substrate in sample (3). There is no reaction
on the substrate surface, so the recycled wheel is ready to use without machining. On the
other hand, wheels number (1) and (2) still contain numerous diamonds. The ease of
stripping two-layer braze from the MSL wheel is an importance economic factor in MSL
technology.
124
Temperature. OF
32
392 752
1472
2192
2912
3632
4352
5072
Boiling point: all substances at 1 atm
---- -
105
A34
-Zn- -- M 1-B
-
Pb --
r
M.
Ni-
Cl
103
V- 10
103
rTh
00
AS4
--
-
00
10-1
Hg
t
01
Mde
Ta
l-
Nb
10-3
A
-g
Thh
ft
10W-
/
/
10-1
10-5
IL
Pb
-
10-5
1 O-7
- -
10-7
10-9
- - ----
(a
s
0-'3
0
----
-1f-I
Cd
MIn
C
-
10-11
1
--
200
-
-
u Fe S1 , Pt
I V
rI Zr
hi
400 800 800 1000
1400
--
10-9
10-l
0
-ain point
I
10-1,
1800
2200
2800
3000
Temperature. *C
Figure 6.1 Vapor pressure as a function of temperature (Olson, Siewert, Liu, and
Edwards, 1993)
steel
Figure 6.2 The microstructure of 9lCu-4Si-5Ti in wt%, 1150 0 C*30 minutes
125
Figure 6.3 The microstructural observations of Cu/Ag/Sn/Ti active braze alloys
(a) 72Ag-28Cu in wt%, 880*C*30min, 10OX
(b) 90Cu-lOSn in wt%, 1050 0 C*30min, 10OX
(c) 69Ag-27Cu-4Ti in wt%, 880*C*30min, 10OX
(d) 68Cu-l2Sn-l6Ag-4Ti in wt%, 875 0C*30min, 200X
(e) 58.6Cu-10.4Sn-27.6Ag-3.4Ti in wt%, 880 0 C*30min, 200X
(f) 58.2Cu-10.3Sn-27.4Ag-3.4Ti-0.7Ni in wt%, 875*C*30min, 10OX
(g) 51.5Cu-9.1Sn-36.4Ag-3Ti in wt%, 880 0 C*30min, 10OX
(h) 57.6Cu-10.2Sn-27.lAg-5.lTi in wt%, 875 0 C*30min, 10OX
57.2Cu-10.lSn-26.9Ag-5.1Ti-0.7Zr in wt%, 875 0C*30min, 200X
(i)
126
Braze
Ni
100pm
Figure 6.4 The morphology of the interface between 70Cu-2lSn-9Ti(wt%) and Ni
10-4
20
1100
1.000
30
{
40
50
1
60
Allov
0
Alloy Disk
in
%
Sn Wt.
10
0
70n
80
90
101
[
40
900
U
800
9
-
700C-
U
600-
10-
6
I.
U
i
Ln
I
50C
400
10-7?
300
0
200
Cu
+Fi r +
' 0
40
50
03
60
50
70
60
Sn Atomic
i
80
90
Sn
1P
0O
0
0
50
Cu
Atomic
(a)
I of Sn
(b)
Figure 6.5 (a) Cu-Sn binary phase diagram. Arrows indicate specimen composition.
(b) Specific Wear of Cu-Sn bronze (Sasada et al.,1992)
Sn
127
all
Braze
Fe
Figure 6.6 The SEM back scattered image displaying the interface between braze and Fe
35Ti-1OFe-1OCu-45Sn
85Cu-15Sn
5Ti-lFe-59Cu-35Sn 29Ti-59Fe-1OCu-2Sn
KI
I
Figure 6.7 The EDX analysis of the interfacial phases in wt%
128
IUU
1 Ipm
Cu
70Cu-21Sn-9Ti(wt%)
(a)
CU
Steel
(b)
Figure 6.8 The morphology of the interfaces after brazing at 900 0C*30minutes
(a) 70Cu-2lSn-9Ti(wt%)/Cu interface (b) Cu/steel interface
129
Figure 6.9 The morphology of 70Cu-2lSn-9Ti(wt%) and Cu two-layer structure after
brazing (a) 860"C*30 minutes (b) 880*C*30 minutes (c) 900'C*30 minutes
130
-
9
Figure 6.10 The microstructure of 70Cu-2lSn-9Ti(wt%) and Cu two-layer structure after
brazing (a) 860 0 C*30 minutes (b) 880*C*30 minutes (c) 9000 C*30 minutes
131
T.wi
All
(a)
(d)
(b 880 0 *Oius()90
*3O
04.1e
+900
P6OC*Oinue
85 0C*Omintes
0
/1Ominte
132
1 M2 A3
1400
1200
1000
800
A
600
0
IL
400
200
0
0
60
40
20
Accumulated
80
Volume (cubic Inch)
(a)
01 02 A3
800
700
600
500
A
U.
o
400
-i 300
E
0 200
z
100
0
0
20
40
60
80
Accumulated Volume (cubic inch)
(b)
Figure 6.12 The grinding test result of three test wheels, (1), (2) and (3)
as described in section 6.3
(a) power vs. the accumulated alumina removed
(b) normal force vs. the accumulated alumina removed
133
Stripping Test
----
1 -M-
2 -A--3
16
14
12
IM
0j
10
8
IM
//A
6
4
2
0
0
400
200
Time
600
800
(min)
Figure 6.13 Weight loss of three MSL bond wheels with different braze alloys
(1) 70Cu-2lSn-9Ti (wt%)
(2) 77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C (by weight)
(3) Two-layer structure, 76.9 wt% 77Cu/23Sn bronze-7.7 wt% Ti-15.4
wt% pure copper powder and a 50 gm pure copper interlayer
134
Figure 6.14 The morphology of three MSL wheels after 595 minutes stripping
135
7.1 Summary and Conclusions
7.1 Summary
Whether fatigue is the rate-controlling mechanism of the MSL wheel's failure is
determined by the material to be ground.
For certain hard materials grinding such as
alumina and Si 3N 4 grinding, diamond grits fail before the braze alloy fractures.
In these
cases, fatigue is not the only primary factor in determining the MSL grinding wheel's life,
as the bond strength of the braze alloy is also important. On the other hand, fatigue will
become the dominant factor in determining the wheel's life when a softer material such as
mullite is ground. It is expected that an extended life can be obtained by a tougher bond
under the same test condition.
Failure of the MSL bond grinding wheel is strongly related to the material to be
ground. When grinding softer materials, the diamond cutting edges are sharp during initial
grinding, and the failure mode produces high cycle fatigue of the braze alloy. Braze alloys
with higher toughness can prevent and/or retard crack nucleation and growth at the bond
interface. As the cutting edges of the diamond grits become blunt, a larger applied force
and power is necessary to continue the grinding process. With increased stress, the fatigue
mechanism of the braze alloy shifts from high cycle fatigue to low cycle fatigue.
Thus,
both toughness and strength of the braze alloy are important factors to avoid crack
nucleation and growth.
In addition to the fatigue properties of the braze alloy, the wear resistance of the
braze alloy also plays an important role in deciding the life of an MSL bond wheel.
For
example, the concrete cutting process is very abrasive. Wear of the braze alloy results in
debonding of the diamond grits. A wear-resistant braze alloy improves the life of MSL
bond cutting wheels. Therefore, the performance of the braze alloy in MSL bond is
materials dependent, and should be studied case by case.
Based on the alumina grinding test, transverse fracture and debonding of the
diamond grits are the two primary fracture modes in the MSL wheel's tests. The transverse
fracture of the diamond results from high tensile stresses during grinding. The debonding
of the diamonds can be explained by insufficient abrasive/fatigue resistance of the braze
alloy, stress states at the bond interface, and the brittle intermetallic phases at the diamond
interface.
The existence of interfacial intermetallic phases considerably weakens the
fracture resistance of the interface. The cracks, developed either by thermal stresses or by
cyclic applied grinding stresses, initiate at the interface, and propagate into the braze.
Ultimately, the diamond grits are debonded.
136
There are two types of cracks observed in the debonded and fractured diamonds.
One cracks parallel to the diamond boundary, the other cracks radially from the diamond.
The first type of crack originates from high tensile stresses in the braze alloy during
grinding, and the second type of crack results primarily from the thermal expansion
mismatch between the diamond and the braze alloy. Both indicate that a stronger and
tougher braze alloy is preferred to avoid braze alloy failure.
Good wetting between the diamonds and the braze alloy is only one of the
prerequisites of forming a good MSL bond. However, there is no strong relation between
the bond strength and the wetting angles. For example, Ticusil (Ag-Cu eutectic + 4.5wt%
Ti) demonstrates the best wetting behavior in the wetting angle test, but the grinding
performance of 70Cu-2lSn-9Ti (wt%) alloy is better than that of Ticusil. The bond
strength between the diamond and the braze alloy is affected by many factors such as the
inherent strength and thickness of the reaction layer, stresses and defects at the interface,
and the mechanical properties of the braze alloy. A thin reaction layer is preferred with
active brazing as it produces fewer defects at the interface. The thickness of the TiC
reaction layer for 70Cu-2lSn-9Ti (wt%) and 77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C (by
weight) is about 1 pm.
The intermetallic phases in both 70Cu-2lSn-9Ti (wt%) and 77Cu-23Sn-12.5Ti7.5Zr-1OTiC-0.2C (by weight) alloy are weak, as demonstrated by tensile tests. The
suggested fracture mechanism in the tensile test is that of straining the specimen to the point
where the intermetallic phase fractures, followed shortly by failure of the copper-rich
matrix. The cracks initiate within the intermetallic phase and propagate into the matrix.
Therefore, removing or decreasing the volume fraction of the intermetallic phase in the
braze alloy is important in order to modify the mechanical properties of the braze alloy and
improve the joint strength.
According to the finite element analysis results, most of the thermal stresses and
strains are localized at the diamond/braze alloy interface. The higher diamond concentration
in the MSL wheels will result in greater thermal mismatch, and, therefore, higher residual
thermal stresses after brazing. Part of the thermal stresses can be relaxed by rate dependent
plastic behavior, i.e. creep, at temperatures between 200 0 C and 600'C created by delayed
cooling. However, it is not economical to decrease the thermal stresses via creep below
150*C as the times become excessive. According to the results of the analysis, a slower
cooling rate between 200*C and 600*C improves the stress state of the braze alloy. Creep
strains account for 50% to 85% of the total plastic strain for the case of 100*C/min,
10*C/min, 1*C/min, and 0.1*C/min cooling rates.
137
The rate independent plastic model shows that a thin copper interlayer can partially
reduce the interfacial equivalent plastic thermal strain, especially at the bottom of the
diamond grit. Consequently, it is possible to absorb the thermal mismatch between the
steel and the braze alloy by introducing a low yield strength copper interlayer.
The abrasion resistance of the braze alloy can be greatly improved by introducing
hard and blocky particles such as TiC. However, improving the erosion resistance of the
braze alloy can not be achieved in this way. The erosion resistance of the braze alloy is
strongly related to both the toughness and hardness of the alloy. Therefore, there is no
great improvement in erosion resistance by introducing hard but brittle particles. Based on
the experimental results, the 77Cu-23Sn-12.5Ti-7.5Zr-lOTiC-0.2C (by weight) braze
displays excellent wear resistance. With this braze the grinding and cutting performance is
improved both in the alumina grinding and green concrete cutting test.
The volume fraction of the intermetallic phase is greatly decreased for Cu/Sn/Ti
braze alloys by a two-layer structure with 15.4wt% pure copper powder addition and a
two-step brazing. The alumina grinding test demonstrates that this wheel has the same
grinding performance as the currently used 70Cu-2lSn-9Ti (wt%) alloy. However, the
alumina grinding test can not provide information about the fatigue resistance of the braze
alloy. Further tests using softer grinding materials and slower feed rates is necessary in
order to avoid fracture of the diamond grit, and compare the fatigue resistance of these
alloys. The stripping test of the above alloy is very successful. Due to a lower Sn and Ti
content in the braze alloy and a thin Cu interlayer to retard the reaction between the braze
alloy and steel substrate, the new braze alloy is much more easily stripped from the wheel
substrate than the present 70Cu-2lSn-9Ti (wt%) braze alloy.
7.2 Conclusions
The following conclusions can be derived from this work:
*
The failure mode of the MSL bonded wheel is strongly related to the material to be
ground. For different grinding materials, fracture of the braze alloy is controlled by
fatigue and/or wear resistance of the braze alloy depending on the material being
ground.
"
The cracks observed in the debonded (or fractured) diamonds result from both grinding
stresses and the thermal expansion mismatch between the diamond and the braze alloy.
138
*
Wettability of the braze alloy is only one of the prerequisites for obtaining a good MSL
bond. Based on the experimental data, there is no relation between the bond strength
and the wetting angles.
*
The finite element analysis demonstrates that most of the thermal stresses are
concentrated at the diamond/braze interface, and part of the thermal stresses can be
relaxed by rate dependent plastic deformation at temperatures between 2000C and
6000 C. However, it is not economical to decrease the thermal stresses by creep below
150 0 C.
*
77Cu-23Sn-12.5Ti-7.5Zr-1OTiC-0.2C (by weight) provides excellent resistance in the
wear test, and the MSL bond grinding and cutting wheel performance is further
confirmed in grinding alumina and green concrete cutting tests.
*
The volume fraction of the intermetallic phase is greatly decreased for Cu/Sn/Ti braze
alloy by a two-layer structure with 15.4wt% pure copper powder addition and two-step
brazing. This structure more easily stripped from the steel wheel than the present alloy.
139
8. Future Work
The growth of the brittle intermetallic phases during brazing or soldering is an
important issue because it affects the mechanical properties of the joint (Yang, Messler, and
Felton, 1995; Frear and Vianco, 1994). Excessive intermetallic growth and the brittleness
of the intermetallic layer are detrimental to the joint reliability. When the intermetallic phase
is thin, fracture occurs in the braze alloy. As the interfacial intermetallics thicken, the
fracture path moves into the intermetallic layer. Moreover, the morphology of the
intermetallic phase in the braze alloy is strongly related to its fatigue resistance. If
intermetallics can not be avoided in brazing, large, needle-like intermetallics are inferior to
small, round ones. Therefore, it is important to control both the quantity and the
morphology of these intermetallic phases. However, the intermetallic phases are difficult to
avoid. The active element in the braze tends to react with other elements, and forms
thermodynamically stable intermetallic compounds. These can not be removed during
traditional heat treatment such as aging.
Partial transient liquid phase bonding provides a way to manipulate intermetallic
formation (Duvall, Owczarski, and Paulonis, 1974). Combining active brazing and partial
transient liquid phase bonding (PTLP) improves the mechanical properties of the braze
alloy. The benefit of PTLP bonding is that a bond free of brittle and segregated phases can
be achieved. It is reported that Si 3N4 can be joined by using Au coated Ni-22Cr (wt%)
foils (Ceccone, Nicholas, Peteves, Tomsia, Dalgleish, and Glaeser, 1996). The average
flexture strength is 272 MPa at room temperature. Moreover, the microstructures and
strength of joints produced by the best processing conditions examined are equivalent to
those obtained by optimized diffusion bonding practices. However, a thin interlayer with
the specific composition and melting point used in PTLP bonding is not suitable for a paste
process in MSL technology. Certain changes must be made in order to meet the
requirements of the MSL process.
Figure 8.1 displays the modified PTLP bonding process. A specially designed
alloy powder coated with a thin barrier layer is mixed with the braze alloy paste. The braze
alloy wets and bonds the superabrasive grits well at the first stage of brazing. In this stage,
the coated powder is protected by its barrier layer, and does not react with the braze alloy.
After the superabrasives are well wetted by the alloy, the second stage of the brazing starts.
The specially designed alloy powder dissolves into the braze alloy via diffusion, and forms
a brand new alloy composition with the desired mechanical properties. Many preliminary
studies must be made before completing such a joint.
140
For example, the selection of a coated layer for Cu/Sn/Ti active braze alloy and the
alloy composition of the coated powder should be carefully designed. The dissolution
kinetics of the barrier layer and alloy powder also needs further study. There are two
possible functions of the coated powder in the braze. One is its reaction with the active
element; the other is to improve the mechanical properties of the braze alloy. The Ti/Cu/Sn
intermetallic phase is soft and brittle as confirmed by the experiment. It is possible to form
other stronger and/or harder intermetallics such as TiAl, TiNi3 or Ti5 Si 3 by reaction of the
coated powder and braze (Kosolapova, 1990). Moreover, the morphology of the newly
formed intermetallic phase can be controlled by the shape of the coated powder, because the
formation of the intermetallic phase is a diffusion controlled process. The coated powder
provides the possibility of adjusting the mechanical properties of the bond. As described
earlier, the optimal properties of the braze depend on the specific application of the MSL
grinding wheel. A hard braze is necessary for certain abrasive grinding processes, and a
tough braze is essential for some cyclic fatigue applications. Once the mechanical
properties of the active braze alloy can be modified by introducing a coated powder, a better
performance braze alloy can be achieved.
Table 8.1 The chemical composition of
some promising active braze alloys in MSL technology
Composition (wt%)
Brazing Temperature (*C)
75.6Cu-14.9Sn-9Ti-0.5Ni
1000
75.6Cu-14.9Sn-9Ti-0.5Zr
1000
74.5Cu-8.3Sn-6.9Ni-4.6Cr-5.7Ag
980
60Cu-29.6Mn-7.2Ni-3.2Cr
920
57.6Cu-10.2Sn-27.lAg-5.lTi
875
57.2Cu- 10.1 Sn-26.9Ag-5. lTi-0.7Zr
875
Alloy powder production is another important issue in developing active braze
alloys. The currently used Cu/Sn/Ti paste contains 77Cu-23Sn (wt%) prealloyed powder
and TiH 2 powder. The reason for using TiH 2 powder instead of pure Ti powder is that
pure Ti tends to react with the binder and the Ti oxide is tenacious. Both deteriorate the
activity of Ti in the braze alloy. Better dimensional control and lower brazing temperatures
141
can be achieved by using prealloyed powder for the rest of the elements in the braze. Many
active braze alloys developed in this research as displayed in Table 8.1. These show
excellent wetting behavior and uniform microstructure, but no further tests have been
performed due to absence of a commercially available alloy powder. The melting point of
the powder mixture can be drastically decreased, especially in the case of elements in the
braze with a large difference in melting point.
There are many methods to produce alloy powders as described below (Klar et al.,
1984):
Gas and water atomization:
(1)
High-quality powders, from aluminum, brass, and iron powders to stainless steel,
tool steel, and superalloy powders, have been made successfully. Water-atomized
powders generally are quite irregular in shape and have relatively high surface
oxygen contents. Gas-atomized powders, on the other hand, generally are more
spherical or round in shape. If atomized by inert gas, lower oxygen contents in
(2)
(3)
the powder are expected.
Chemical method:
Chemical and physiochemical methods of metal powder production allow great
variations in powder properties. Powders made by reduction of oxides,
precipitation from solution or from a gas, thermal decomposition, and hydride
decomposition belong in this classification.
Milling of brittle and ductile materials:
Milling of materials, whether hard and brittle or soft and ductile, is of prime
However,
interest and of economic important in powder production.
contamination of the metal powder during the milling process is the primary
concern in using this method. Both crucible and balls can contaminate the alloy
powder. The heat generated during the milling process causes oxidation of the
powder. Therefore, it is not a proper production method for this research.
Based on the above description, inert gas atomization is the best choice for
production of the alloy powder in developing active braze alloys. It is reported that many
aluminum alloy powders are successfully made by inert-gas atomization (Lavernia, Ayers,
and Srivatsan, 1992). The rapid extraction of thermal energy permits large deviations from
equilibrium which offers the following advantages:
(1) the extension of solid solubility, often by orders of magnitude
(2) a reduction in grain size
(3) a reduction in both the number and size of segregated phases
(4) production of new non-equilibrium alloy phase
142
According to the above discussion, an inert-gas atomizing facility should be constructed in
order to produce alloy powders for further improving the active braze alloys.
143
Superabrasives
/
Coated powder
0
0
0
0
0
Braze
alloy
E
0
0 paste
0
00
0
0
0
0
Substrate
(a)
Braze alloy
0
0
0
0
411111
0
0
U
0
0O 0
0
0
0
0
0
0
0
00
0
Co ated powder
1/or
1 40.0400 /0
0'000
(b)
Braze alloy with uniform microstructure
-7777777
(c)
/7/
Figure 8.1 The schematic diagrams displaying the modified transient liquid phase
bonding of the superabrasive grits
(a) before brazing
(b) first step brazing: bonding of the superabrasive grits
(c) second step brazing: dissolution and diffusion of the coated powder
into the braze alloy
144
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154
Appendix A
Materials property input in finite element analysis ( Battelle, 1979; Davis, et. al.,
1990; Frost and Ashby, 1982; Holt, Mindlin, and Ho, 1994; Rosenberg, 1968; Simmons
and Wang, 1971; Touloukian, Kirby, Taylor, and Desai, 1977; Touloukian, Kirby,
Taylor,and Lee, 1977; Wilks and Wilks, 1991)
DIAMOND
*
-*
thermal e xpansion coeff.(10E-6) -AM-Young's modulus(1000GPa)
Poisson's ratio(/10)
6
5
4
3
2
1
0
200
0
1000
800
600
400
1400
1200
TEMPERATURE(C)
TiC
[
---
A
thermal expansion coeff.(1 OE-6)
Poisson's ratio(/10)
-UX
Young's modulus(1 OOGPa)
U.T.S.(100MPa)
9
10
8
3
0
-E
0
200
400
600
800
TEMPERATURE(C)
1000
1200
1400
I
155
COPPER
-'--
-A--
thermal expansion coeff.(10E-5) -NPoisson's ratio(/10)
X
4--U.T.S.(1 OOMPa)
Young's modulus(100GPa)
Y.S.(100MPa)
elongation(/1 0)
j
0
400
200
K
600
800
1000
1200
TEMPERATURE(C)
SS304
-*
thermal e xpansion coeff.(1 OE-5) -MIYoung's modulus(100OGPa)
-A- Poisson's ratio(/10)
-X- Y.S.(100MPa)
-XU.T.S.(1 OOMPa)
-0 elo ngat ion(/10)
K
X
~Z
0
200
low
400
600
TEMPERATURE(C)
800
1000
1200
156
ALUMINUM
Young's modulus(10GPa)
Y.S.(10 MPa)
elongation(/10)
-*-- thermal expansion coeff.(10E-5) +
-X-A- Poisson's ratio(/10)
-0-E- U.T.S.(10MPa)
9
8
-------
7
6
5
4
3
2
-
A~~
1
0
0
100
200
300
400
500
600
700
TEMPERATURE(C)
NICKEL
-4- thermal expansion coeff.(1 OE-5) -§U- Young's modulus(1 OOGPa)
-X- Y.S.(100MPa)
A Poisson's ratio(/10)
-0-elongation
-lI-U.T.S.(100MPa)
4.5
4
3.5
3
2.5
2
1.5 '
1'
0.5
0
0
200
40
800
600
TEMPERATURE(C)
1000
1200
157
Appendix B
A sample ABAQUS input program
*HEADING
FEM74.INP
DIAMOND (25MESH, R=0.707) - CU (COLD DRAWN) - SS304 (ANNEALED)
RESIDUAL THERMAL STRESS ANALYSIS (600C-20C)
REGULAR POLYGON OF 8 SIDES DIAMOND
FREE BC'S, 0.1MM DEPTH, HIGHER BRAZE ALLOY
CREEP ONLY MODEL, 10 C/MIN, 3480SEC. ACCURACY=5E-6
**NODE AND ELEMENT GENERATION
**PART 1 DIAMOND
*NODE
1, 0.0, 0.0
30, 0.0, 0.707
2001, 0.1352786, 0.0
2010, 0.326591, 0.1913127
2020, 0.326591, 0.4618697
2030, 0.1352786, 0.707
*NGEN, NSET=ND1
1, 30, 1
*NGEN, NSET=ND2
2001, 2010, 1
*NGEN, NSET=ND3
2010, 2020, 1
*NGEN, NSET=ND4
2020, 2030, 1
*NGEN, NSET=ND5
ND2, ND3, ND4
*NFILL, BIAS=1.00, NSET=ND6A
ND1, ND5, 40, 50
*ELEMENT, TYPE=CAX4
1, 1, 51, 52, 2
*ELGEN, ELSET=ED6A
1, 40, 50, 50, 29, 1, 1
*NSET, NSET=ND7, GENERATE
1, 1801, 200
**PART 2 BRAZE ALLOY: CU
*NODE
1998, 0.707, 2.27
1999, 0.707, 2.0
3001, 0.1352786, 0.0
3010, 0.326591, 0.1913127
3701, 0.707, 0.0
3710, 0.707, 0.15174116
4000, 0.0, 0.0
4010, 0.1352786, 0.0
4015, 0.707, 0.0
5000, 0.0, -0.1
5010, 0.1352786, -0.1
5045, 0.707, -0.1
5065, 2.0, -0.1
158
3091, 2.0, 0.0
3910, 2.0, 0.15174116
4065, 2.0, 0.0
10010, 0.326591, 0.1913127
10045, 0.707, 0.15174116
10065, 2.0, 0.15174116
11010, 0.326591, 0.4618697
11045, 0.707, 0.42228623
11065, 2.0, 0.42228623
*NGEN, NSET=NB1
3001, 3701, 20
*NGEN, LINE=C, NSET=NB2
3010, 3710, 20, 1999
*NFILL, BIAS=1.0, NSET=NB3A
NB1, NB2, 9, 1
*ELEMENT, TYPE=CAX4
3001, 3001, 3021, 3022, 3002
*ELGEN, ELSET=EB3A
3001, 9, 1, 1, 35, 20, 20
*NGEN, NSET=NB4, GENERATE
3001, 3010, 1
*MPC
TIE, ND2, NB4
*NGEN, NSET=NB5
4000, 4010, 1
*NGEN, NSET=NB6
4010, 4045, 1
*NGEN, NSET=NB7
NB5, NB6
*NGEN, NSET=NB8
5000, 5010, 1
*NGEN, NSET=NB9
5010, 5045, 1
*NGEN, NSET=NB10
NB8, NB9
*NGEN, NSET=NB5-1, GENERATE
4000, 4009, 1
*MPC
TIE, ND7, NB5-1
*MC
TIE, NB1, NB6
*NFILL, BIAS=1.0, NSET=NB11A
NB7, NB10, 10, 100
*ELEMENT, TYPE=CAX4
4000, 4000, 4100, 4101, 4001
*ELGEN, ELSET=EB 1 1A
4000, 10, 100, 100, 45, 1, 1
*NGEN, NSET=NB12
3701, 3710, 1
*NGEN, NSET=NB13
3901, 3910, 1
*NFILL, BIAS=1.0, NSET=NB14A
NB12, NB13, 20, 10
*ELEMENT, TYPE=CAX4
159
3701, 3701, 3711, 3712, 3702
*ELGEN, ELSET=EB14A
3701, 20, 10,10,9,1, 1
*NGEN, NSET=NB15
4045, 4065, 1
*NGEN, NSET=NB15-1, GENERATE
4046, 4065, 1
*NGEN, NSET=NS 1
5045, 5065, 1
*NFILL, BIAS=1.0, NSET=NB16A
NB15, NS1, 10, 100
*ELEMENT, TYPE=CAX4
4045, 4045, 4145, 4146, 4046
*ELGEN, ELSET=EB 16A
4045, 10, 100, 100, 20, 1, 1
*NGEN, NSET=NB17, GENERATE
3711, 3901, 10
*MPC
TIE, NB17, NB15-1
*NGEN, LINE=C, NSET=NB20
10010, 10045, 1, 1999
*NGEN, LINE=C, NSET=NB21
11010, 11045, 1, 1998
*NFILL, BIAS=1.0, NSET=NB22
NB20, NB21, 10, 100
*ELEMENT, TYPE=CAX4
10010, 10010, 10011, 10111, 10110
*ELGEN, ELSET=EB22A
10010, 10, 100, 100, 35, 1, 1
*NGEN, NSET=NB23
10045, 10065, 1
*NGEN, NSET=NB24
11045, 11065, 1
*NFILL, BIAS=1.0, NSET=NB25A
NB23, NB24, 10, 100
*ELEMENT, TYPE=CAX4
10045, 10045, 10046, 10146, 10145
*ELGEN, ELSET=EB25A
10045, 10, 100, 100, 20, 1, 1
*NSET, NSET=NB26, GENERATE
10110, 11010, 100
*NSET, NSET=ND3-1, GENERATE
2011, 2020, 1
*MPC
TIE, ND3-1, NB26
*NSET, NSET=NB2-1, GENERATE
3010, 3690, 20
*NSET, NSET=NB20-1, GENERATE
10010, 10044, 1
*MPC
TIE, NB2-1, NB20-1
*NSET, NSET=NB27, GENERATE
3710, 3910, 10
*MPC
160
TIE, NB23, NB27
**PART 3 PERFORM: SS304
*NODE
7500, 0.0, -3.6
7510, 0.1352786, -3.6
7545, 0.707, -3.6
7565, 2.0, -3.6
*NSET, NSET=NS2
NB8, NB9, NS1
*NGEN, NSET=NS3
7500, 7510, 1
*NGEN, NSET=NS4
7510,7545, 1
*NGEN, NSET=NS5
7545, 7565, 1
*NSET, NSET=NS6
NS3, NS4, NS5
*NFILL, BIAS=1.0, NSET=NSS304
NS2, NS6, 25, 100
*ELEMENT, TYPE==CAX4
5000, 5000, 5100, 5101, 5001
*ELGEN, ELSET=ESS304
5000, 25, 100, 100, 65, 1, 1
**PART 4 WHOLE SET
*NSET, NSET=NDIAMOND
ND6A
*ELSET, ELSET=EDIAMOND
ED6A
*NSET, NSET=NBRAZE
NB3A, NB11A, NB14A, NB16A, NB22A, NB25A
*ELSET, ELSET=EBRAZE
EB3A, EBI1A, EB14A, EB16A, EB22A, EB25A
*NSET, NSET=NB18, GENERATE
4000, 5000, 100
*NSET, NSET=NS8, GENERATE
5000, 7500, 100
*NSET, NSET=NCENTER
ND1, NB18, NS8
*NSET, NSET=NALL
NDIAMOND, NBRAZE, NSS304
*ELSET, ELSET=EALL
EDIAMOND, EBRAZE, ESS304
**PRINT OUTPUT DESCRIPTION
*NSET, NSET=NBSHOW
3021, 3121, 3321, 3701, 4050, 4065
*NSET, NSET=3021
3021
*ELSET, ELSET=EBSHOW
3021, 3121, 3321, 3701, 4050, 4065
**MATERIAL'S PROPERTIES INPUT
*SOLID SECTION, ELSET=EDIAMOND, MATERIAL=DIAMOND
*SOLID SECTION, ELSET=EBRAZE, MATERIAL=CU
*SOLID SECTION, ELSET=ESS304, MATERIAL=SS304
*MATERIAL, NAME=DIAMOND
161
*ELASTIC
1050000.0, 0.2, 20.0
1050000.0, 0.2, 1000.0
*EXPANSION
1.OE-6, 20.0
1.5E-6, 77.0
1.8E-6, 127.0
2.3E-6, 227.0
2.8E-6, 327.0
3.2E-6, 427.0
3.7E-6, 527.0
4.OE-6, 627.0
4.4E-6, 727.0
4.7E-6, 827.0
5.OE-6, 927.0
5.2E-6, 1027.0
5.4E-6, 1127.0
5.6E-6, 1227.0
5.8E-6, 1327.0
5.8E-6, 1377.0
*MATERIAL, NAME=CU
*ELASTIC
110400, 0.367, 20.0
107600, 0.369, 77.0
105500, 0.370, 127.0
103400, 0.372, 127.0
101200, 0.373, 227.0
99100, 0.374, 277.0
97000, 0.376, 327.0
94800, 0.377, 377.0
92700, 0.379, 427.0
90600, 0.38, 477.0
88400, 0.382, 527.0
72000, 0.382, 900.0
*PLASTIC
420, 0.0, 20.0
430, 0.26, 20.0
385, 0.0, 100.0
395, 0.24, 100.0
320, 0.0, 200.0
330, 0.18, 200.0
250, 0.0, 300.0
260, 0.22, 300.0
125, 0.0, 400.0
150, 0.38, 400.0
30, 0.0, 500.0
60, 0.3, 500.0
10, 0.0, 600.0
40, 0.48, 600.0
0.01, 0.0, 700.0
20.0, 0.52, 700.0
0.01, 0.0, 800.0
10, 0.6, 800.0
0.01, 0.0, 900.0
162
*EXPANSION
16.5E-6, 20.0
17.6E-6, 127.0
18.3E-6, 227.0
18.9E-6, 327.0
19.5E-6, 427.0
20.3E-6, 527.0
21.3E-6, 627.0
22.4E-6, 727.0
24.9E-6, 927.0
25.8E-6, 1027.0
*CREEP, LAW=USER
*USER SUBROUTINES
C
SUBROUTINE CREEP (DECRA, DESWA, STATEV, SERD, ECO, ESWO, P,
1 QTILD, TEMP, DTEMP, PREDEF, DPRED, TIME, DTIME, CMNAME,
2 LEXIMP, LEND, COORDS, NSTATV, NOEL, NPT, LAYER, KSPT, KSTEP,
3 KINC)
C
INCLUDE 'ABAPARAM.INC'
C
CHARACTER*8 CMNAME
C
DIMENSION DECRA(5), DESWA(5), STATEV(*), PREDEF(*), DPRED(*),
1 TIME(2), COORDS(*)
C
C DEFINE CONSTANTS
C
BACDOC=1E-24
BQC=1 17E3
BDOV=2E-5
BQV=197E3
BB=2.56E-10
C
BACDC=BACD0C*EXP(-BQC/(8.314*(TEMP+273)))
BDV=BDOV*EXP(-BQV/(8.314*(TEMP+273)))
BYOUNG= 1 10400-(TEMP-20)/580*252 10
BNEW=0.367+(TEMP-20)/580*0.015
BSHEAR=BYOUNG/2/(1+BNEW)
BDEFF=BDV*(1+10*BACDC/BB**2/BDV*(QTILD/1.73205/BSHEAR)**2)
DECRA(1)=7.4E5*BDEFF*BSHEAR* 1E6BB/1.38 1E-23/(TEMP+273)*
1 (QTILD/BSHEAR)**4.8*DTIME
RETURN
END
*MATERIAL, NAME=SS304
*ELASTIC
192400, 0.30, 20.0
186880, 0.31, 149.0
183430, 0.312, 204.0
179300, 0.315, 260.0
176500, 0.318, 316.0
170330, 0.319, 371.0
166190, 0.32, 427.0
159990, 0.32, 482.0
163
155160, 0.32, 538.0
150330, 0.322, 593.0
145500, 0.326, 649.0
140680, 0.328, 704.0
133780, 0.33, 760.0
124800, 0.332, 816.0
111370, 0.338, 900.0
*PLASTIC
410.0, 0.0, 20
669.0, 0.665, 20
331.0, 0.0, 205
483.0, 0.365, 205
290.0, 0.0, 425
472.0, 0.355, 425
265.0, 0.0, 540
427.0, 0.345, 540
214.0, 0.0, 650
324.0, 0.35, 650
162.0, 0.0, 760
207.0, 0.445, 760
112.0, 0.0, 870
119.0, 0.585, 870
66.0, 0.0, 980
68, 0.755, 980
*EXPANSION
11.8E-6, 20.0
13.4E-6, 127.0
14.4E-6, 227.0
15.1E-6, 327.0
15.7E-6, 427.0
16.2E-6, 527.0
16.4E-6, 627.0
16.6E-6, 727.0
16.7E-6, 827.0
16.8E-6, 912.0
23.3E-6, 913.0
23.3E-6, 1377.0
**HISTORY INPUT
*RSTART, WRITE, FREQ=90000
*INITIAL CONDITIONS, TYPE=TEMPERATURE
NALL, 600.0
*STEP, AMPLITUDE=RAMP, INC=90000, NLGEOM
*VISCO, CETOL=5E-6, EXPLICIT
0.01, 3480.0, 0.0000001, 100
*TEMPERATURE, OP=MOD
NALL, 20.0
*BOUNDARY, TYPE=DISPLACEMENT
7500,2
*NCENTER, 1
*EL PRINT, ELSET=EBSHOW, POSITION=CENTROIDAL, FREQUENCY=1
TEMP, MISES, PEEQ, CEEQ, SENER, PENER, CENER
*NODE PRINT, NSET=3021, FREQUENCY=90000
NT
*END STEP
164
Appendix C
Theoretical and measured density of the braze alloy
If the braze alloy is assumed to be an ideal solution, with no volume change after
brazing, the theoretical density of the braze alloy can be calculated by the following
equation:
(C. 1)
Dt = Y, vi Di
where Dt is the theoretical density of the braze alloy, g/cm 3 , vi is the volume fraction of the
component i, and Di is the density of the component i, g/cm 3 . To illustrate the calculation
procedure, here is one example of 75Cu-25Sn-lOTi-10WC by weight:
vC = (75/8.9) / (75/8.9 + 25/7.3 + 10/4.5 + 10/15.0) = 0.5710
VS, = (25/7.3) / (75/8.9 + 25/7.3 + 10/4.5 + 10/15.0) = 0.2329
vTi = (10/4.5) / (75/8.9 +25/7.3 + 10/4.5 +10/15.0) = 0.1508
vw= (10/15) / (75/8.9 + 25/7.3 + 10/4.5 + 10/15.0) = 0.0453
Dt = I vi Di = 0.5710*8.9 + 0.2329 * 7.3 + 0.1508 * 4.5 + 0.0453 * 15 = 8.1580 (g/cm 3)
Table C.1 shows densities of different elements, and these data are used to calculate the
theoretical density of various braze alloys.
Table C.1 The density of some elements used in the braze alloy
Ag
Cu
Graphite
Mo
Sn
TI
TiC
W
WC
Zr
Density (g/cm3)
10.5
8.9
2.3
10.2
7.3
4.5
4.9
19.3
15
6.5
Note
20 0C
20 0C
20 0C
15 0 C
20 0C
The experimental measurement of the density can be performed by the following
equation:
Dm= Wj / V = Wf / (W - W.)
(C.2)
where Dm is the measured density of the braze alloy, g/cm 3, V is the volume of the braze
alloy, cm 3, Wi is the weight of the braze alloy in air, g, and Wa.t is the weight of the
braze alloy in water, g.
There is a possible error when equation C.2 is applied to measure the braze alloy
density. If there are some porosities in the sample, the measured density will deviate from
165
the real one. Based on equation C.1 and C.2, the density of the braze alloy with different
compositions can be obtained and shown in table C.2.
Table C.2 The theoretical and measured density of the braze alloys with different
chemical compositions
Composition (by weight)
75Cu-25Sn-1OTi
75Cu-25Sn-1OTi-5TiC
75Cu-25Sn-lOTi-lOTiC
75Cu-25Sn-lOTi-15TiC
75Cu-25Sn-1OTi-10W
75Cu-25Sn-1OTi-20W
75Cu-25Sn-1OTi-30W
75Cu-25Sn-1OTi-10WC
75Cu-25Sn-1OTi-lOMo
75Cu-25Sn-lOTi-lOZr
75Cu-25Sn- 1OTi- lOZr-0.4C
75Cu-25Sn-lOTi-lOZr-lOTiC
75Cu-25Sn-lOTi-1OZr-2OTiC
75Cu-25Sn-lOTi-lOZr-1OTiC-0.4C
75Cu-25Sn-lOTi-lOZr-1OTiC-0.25C
75Cu-25Sn-lOTi-lOZr-12.5TiC-0.2C
75Cu-25Sn- 12.5Ti-7.5Zr- 1OTiC-0.4C
75Cu-25Sn-12.5Ti-7.5Zr-1OTiC-0.2C
75Cu-25Sn-lOTi-lOZr-20W-0.4C
75Cu-15Ti-1OAg
75Cu-15Ti-lOAg-lOTiC
75Cu-15Ti-lOAg-15TiC
75Cu-15Ti-lOAg-25W
68.8Ag-26.7Cu-4.5Ti (Ticusil)
65.96Ag-26.22Cu-7.72Ti
D, (g/cm 3)
3
Dm (/cm )
7.8332
7.6346
7.4146
7.3082
8.2407
7.9193
7.6604
7.566
7.3642
8.0575
8.6202
8.9741
8.158
7.9878
7.7021
7.6733
7.3776
8.5339
8.9796
8.2095
8.1367
7.5727
8.1201
7.4147
7.1204
7.3268
7.3457
7.2834
7.2572
7.282
8.3592
7.0989
7.6506
7.574
7.4612
7.6354
7.5525
8.6812
7.793
7.2937
7.2112
8.3493
9.2556
7.8859
7.4721
7.3055
8.9422
9.4814
9.1433
9.3891
(D-11)*100%
1.10%
0.34%
2.04%
0.77%
-2.22%
-1.00%
0.06%
-0.63%
1.86%
-1.86%
5.82%
0.50%
-0.30%
4.42%
3.11%
2.44%
5.21%
3.71%
3.85%
-1.18%
-2.39%
-1.29%
-6.63%
-2.38%
2.69%
166
Biographical Note
Ren-Kae Shiue
Education:
MS in Materials Engineering, National Taiwan University, 1988.
BS in Mechanical Engineering, National Taiwan University, 1986.
Experience:
Superabrasives Department, Norton Company, Worcester, Massachusetts,
Summer 1995.
Taichung Power Plant, Taiwan Power Company, Taichung, Taiwan,
June 1991 - July 1992.
Industrial Technology Research Institute, Hsingchu, Taiwan,
February 1991 - May 1991.
Publications:
Shiue, R.K. and Chen, C. (1992). "Laser Transformation Hardening of
Tempered 4340 Steel," Metallurgical Transactions, 23A, pp. 163-170.
Shiue, R.K. and Chen, C. (1991). "Microstructural Observations of the
Laser-Hardened 1045 Steel," Scripta Met., 25, pp. 1889-1894.
Professional
Association:
Member of Sigma Xi Honor Society, American Welding Society, and The
Minerals, Metals and Materials Society.