Acta Materialia 55 (2007) 4233–4241
www.elsevier.com/locate/actamat
The role of annealing twins during recrystallization of Cu
D.P. Field
a
a,*
, L.T. Bradford
a,1
, M.M. Nowell b, T.M. Lillo
c
Washington State University, P.O. Box 642920, Pullman, WA 99164-2920, USA
b
EDAX/TSL, 392 E. 12300 Street, Draper, UT 84020, USA
c
Idaho National Laboratory, Idaho Falls, ID, USA
Received 17 November 2006; received in revised form 15 March 2007; accepted 17 March 2007
Available online 15 May 2007
Abstract
The texture and grain boundary structure of recrystallized materials are dependent upon the character of the deformed matrix and the
selective nucleation and growth of crystallites from the deformation structure. Annealing twin boundary formation in materials of low to
medium stacking fault energy is not only a product of the recrystallized structure, but also plays an important role in the recrystallization
process itself. In situ and ex situ recrystallization experiments were performed on pure copper (99.99% pure) previously deformed by equal
channel angular extrusion. Intermittent characterization of the structure on the surface of bulk specimens was accomplished using electron
backscatter diffraction. The character of the structure where nucleation preferentially occurs is presumed to be in heavily deformed regions
as nuclei were first observed in such microstructures as viewed from the specimen surface. Grain growth is observed to be heavily dependent upon twinning processes at the low temperatures used for in situ experiments, with twinning occurring to aid the recrystallization
process. It is shown at these temperatures that the slowest growing grains obtain the highest fraction of twin boundaries as the new twin
orientations presumably increase the boundary energy at positions where there is insufficient driving force to continue growth.
2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Copper; Recrystallization; EBSD; ECAE; Twin boundaries
1. Introduction
The microstructures that evolve during recrystallization
of deformed polycrystals are dependent upon the character
of the deformed matrix (including stored energy content
and local chemistry), the orientation relationship between
the deformed structure and the growing grains, and the
annealing temperature and ambient conditions. Of primary
importance in this process are the local and neighboring
lattice orientations and the dislocation density distribution.
In low stacking fault energy materials, annealing twins
develop that complicate the recrystallization process. The
twinned structure generally alters the energy and mobility
of a mobile interface, thereby either enhancing or retarding
*
Corresponding author. Tel.: +1 509 335 3524.
E-mail address: dfield@wsu.edu (D.P. Field).
1
Present address: Boeing Commercial Airplanes, Seattle, Washington
98124, USA.
the growth of a given orientation [1]. Many researchers
have investigated the recrystallization process and have
described oriented nucleation and oriented growth and
their impact on the evolving microstructures [1–4]. The
effects of annealing twinning on recrystallization texture
and the resulting grain boundary character distribution
have also been described [5–8]. Since texture and grain
boundary structure affect various properties of polycrystalline metals, it is important to better understand these
structures.
Many researchers have demonstrated that materials
with a high fraction of certain ‘‘special’’ types of boundaries exhibit superior ductility, corrosion resistance, fracture toughness, etc. The coincident site lattice (CSL)
model [9] is the most common analysis used to identify
such boundaries. Since the suggestion of grain boundary
design by Watanabe in 1984 [10], grain boundary engineering (GBE) has been a topic of much research and debate.
The promotion of twin boundaries in grain boundary
1359-6454/$30.00 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.actamat.2007.03.021
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D.P. Field et al. / Acta Materialia 55 (2007) 4233–4241
engineered materials of medium to low stacking fault
energy is typically important as it tends to lower the overall
energy of the interface network, albeit indirectly [10–16].
One thermomechanical process that leads to high fractions
of twin boundaries in the microstructures of annealed
materials with moderate to low stacking fault energies consists of small plastic deformations followed by annealing
treatments, a process known as strain annealing or strain
recrystallization. The relatively low energy in the system
(from the low plastic strain level) motivates annealing twins
to form preferentially, thereby improving certain material
properties [15,16]. The core idea behind GBE is to increase
the mechanical, chemical and/or electrical performance of
a material by increasing the fraction of special boundaries
present in the microstructure. Special boundaries are
defined simply as those with superior properties for a given
application and will vary from one material to the next and
from one application to another. Grain boundary engineered fcc metals with low to moderate stacking fault energies tend to have a preponderance of annealing twin
boundaries up to a limiting value dictated by the twin-limited microstructure described by Palumbo et al. [11]. As
indicated in reviews by Aust [12] and later by Randle
[13], the role of twin boundaries in GBE is likely indirect,
but the twins are often necessary in ultimately obtaining
the desired properties. Fullman and Fisher [14] speculated
over 50 years ago that one driving force for annealing twin
boundary development was to reduce the overall boundary
energy of the system. For these reasons, there has been considerable effort to design processes that promote twin
boundaries, with strain annealing (or strain recrystallization) proving to be an effective GBE tool [15,16]. Triple
junctions and the grain boundary network play a major
role in the determination of grain boundary statistics [17].
It is actually this overall boundary network and the spatial
arrangement of grain boundaries (including percolation of
special boundaries) that control boundary specific material
behavior.
With GBE having a potentially large impact on material
properties, research into the mechanisms of twin boundary
formation continues to be important. The objective of the
present work was to observe in situ the recrystallization
of heavily deformed pure copper and to identify mechanisms of both nucleation and growth processes to the
extent possible. This has led to a better understanding of
annealing twin boundary formation and twin-dominated
structure evolution during recrystallization of these heavily
deformed microstructures.
2. Experimental procedures
Oxygen free, high-conductivity (OFHC) copper billets
(99.99% pure) were deformed by a four-pass equal channel
angular extrusion (ECAE, also referred to as ECAP) process using the B processing route (90 rotation between
deformation passes) [18,19]. The cross-sectional area of
the billets was 25 · 25 mm2 and specimens were machined
from only the center part of the billets. Samples 2 mm
in thickness with areal dimensions of 10 · 5 mm2 or
10 · 10 mm2 were cut using a slow-speed diamond saw
with liberal application of lubricant for cooling. Each specimen was cold-mounted into a quick drying acrylic epoxy
to prevent any structural changes in the sample while curing. The copper samples were ground and mechanically
polished up to 0.02 lm colloidal silica on a vibratory polisher and then removed from their mounts.
Electron backscatter diffraction (EBSD) patterns and
automated scans were obtained in a Schottkey field emission source scanning electron microscope (SEM) using
standard procedures. Several in situ recrystallization experiments were performed using a heating stage designed specifically for in situ EBSD analysis. Some of the higher
temperature recrystallization experiments were performed
by ex situ EBSD subsequent to salt bath annealing followed by water quenching. Thermocouples were positioned
against the sample surfaces in the heating stage for the
in situ experiments to monitor heat treating temperatures.
Since the sample thickness was small and conductivity of
the specimens high, only a negligible temperature gradient
was assumed to exist in the specimens during heating. Temperatures of 155, 160, 165, 170 and 175 C were used for
in situ analysis and 200 and 400 C for ex situ experiments.
For the in situ experiments the time to reach the specified
temperature was 3–5 min, while the salt bath anneals presumably brought the specimens to the desired temperatures
within a second or so. Temperature of the salt bath solutions was controlled to within ±1 C, while the in situ
experiments were performed at constant temperature to
within ±3 C after the initial heating period. The EBSD
analyses for the ex situ specimens were performed on the
surface of the specimens so as to obtain a reasonable comparison with those samples annealed in the SEM chamber.
Specimens were later sectioned and polished to compare
the bulk structure with that of the surface regions. The
average grain diameter of internal sections was smaller
than that observed on the surface, but the twin boundary
content was similar to that observed on the surface.
Orientation imaging scans were collected from an analysis area of 18 · 18 lm2 for the in situ analysis and
80 · 80 lm2 for specimens analyzed at room temperature.
The scans were made over a regular hexagonal grid using a
step size of 0.2 lm. EBSD patterns were collected over each
analysis area at rates of 70 patterns per second for the
in situ experiments yielding scan times of 2–3 min per scan.
Therefore, EBSD images were essentially collected every
3 min during annealing to monitor the recrystallization
process. This rapid scan rate was necessary for the recrystallization process to be accurately observed. At temperatures above 170 C, the recrystallization rate was too
fast for in situ observation by EBSD, so the salt bath
anneals were employed. Fiducial marks were made on the
specimen surface of each sample to ensure that the EBSD
scans were made on the same region of the specimen surface for the initial scan and all subsequent scans. Due to
D.P. Field et al. / Acta Materialia 55 (2007) 4233–4241
drift while the SEM stage temperature achieved equilibrium, the samples were repositioned to the correct analysis
position before each scan. This re-positioning required
image correction of as much as 1 lm for the first scans at
high temperature, but rapidly equilibrated to where virtually no re-positioning was required between subsequent
scans. This process of repeated imaging was continued
until recrystallization neared completion for all samples.
In the interpretation of the data, we assumed that the
images provide a snapshot in time of the true structure,
so analysis of a single image yields the fraction recrystallized at that given time. In reality, there is approximately
a 2 min time difference between the top of the EBSD image
and the bottom of the image for the specimens annealed
in situ. For the low annealing temperatures used, this relatively small amount of time is presumed to be insignificant.
3. Results and analysis
3.1. The deformed microstructure
Two representative EBSD orientation maps of the
deformed, polycrystalline copper specimen are shown in
Fig. 1. These images were taken from a cross-section
through the ECAE billet where the output extrusion direction was aligned normal to the specimen surface. Care was
taken to analyze only the center portion of the billets, thus
avoiding end effects and irregularities near the surfaces.
The shading indicates the pole orientation with respect to
the sample surface normal direction. Dark regions indicate
a {1 0 0} pole aligned normal to the specimen surface with
progressively lighter shading to 45 away from {1 0 0}. The
deformed microstructures contained a high component of
geometrically necessary dislocations (GNDs, or excess dislocation content), as determined by EBSD data [20–22].
These are the dislocations that exist in the microstructure
to account for the curvature of the crystallite lattice. The
gradient in shading seen in the images of Fig. 1 is an indi-
4235
cation of this dislocation content. Of course, the information obtained from a single plane EBSD scan necessarily
retrieves only the components of the curvature tensor relating to the directions of the specimen lying in the section
plane analyzed. The curvature changes in the normal direction are neglected only because there is no information
obtained in that direction. The relationship between the
dislocation density tensor, a, and the lattice curvature, j,
was given by Nye [23] as
aij ¼ jij dij jjj
ð1Þ
The lattice curvature is defined simply as the gradient in the
rotation of the lattice, or
jij ¼
d/i
dxj
ð2Þ
with /i indicating the angular rotation about an axis of
direction i. In more direct terms, the dislocation density
tensor is given in terms of individual orientation measurements by
aij ¼ eikl gjl;k
ð3Þ
where g is the direction cosine matrix that rotates the reference, or specimen, coordinate frame into that defined by
the crystallite lattice. The dislocation density tensor is also
defined directly by
a¼
K
X
qk bk zk
ð4Þ
k¼1
where qk is the dislocation density for dislocations of type k
for all K possible dislocation types. The Burgers vector is
given by band the dislocation line direction by z. Dislocation densities are then obtained by equating the right-hand
side of Eq. (3) with the right-hand side of Eq. (4) using the
minimum possible combination of dislocation densities. A
more complete discussion of this method is found in the
work of Sun et al. [20].
Fig. 1. EBSD orientation maps of the deformed microstructures, such that dark regions have the {1 0 0} pole aligned normal to the specimen surface with
increasingly lighter shading to 45 away from {1 0 0}. Boundaries are indicated for misorientations >10.
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D.P. Field et al. / Acta Materialia 55 (2007) 4233–4241
A proper analysis of excess dislocation content would
require three-dimensional information not available from
single plane sections such as those observed in the present
study. In addition, it is presumed that a grain boundary
exists at locations for which misorientation angles greater
than 15 between neighboring measurements are observed.
The GND density is determined with the assumption of no
curvature across the boundary for these positions. The
overall average GND density of the heavily deformed
microstructures determined by this technique was just
under 1015/m2. Fig. 2 contains a map of the excess dislocation content for the sample shown in Fig. 1a. This particular sample was later annealed at 155 C. The numbers in
Fig. 2, labeled in bold on the image, indicate the regions
where recrystallization nuclei were first observed. It is
assumed that nucleation typically took place below the
observation surface and that the structure surrounding
the nuclei as it appears on the surface is only an estimate
of that where nucleation took place. In some instances a
new grain would first appear as two or more islands that
later coalesced into a crystallite of a single orientation making it apparent that the grain was growing up to the surface
from a single nucleus that originated below the plane of
observation. For our purposes the microstructure just
below the surface is assumed to be similar to that observed
on the surface in terms of excess dislocation density. Therefore, it could be presumed that nucleation occurred in
regions of relatively high GND density as determined from
the EBSD data. It should be noted that using the excess
dislocation content to describe the dislocation density gives
no information on the statistically stored component of the
dislocation structure. It is assumed in this study that the
GND component scales somewhat to the statistically
stored component of the dislocation structure for these
specimens. Some evidence in support of this assumption
has been observed in lightly deformed aluminum alloys
[24].
Fig. 2. Excess dislocation density map from the region shown in the
orientation image of Fig. 1a.
3.2. Annealing microstructure and recrystallization kinetics
Fig. 3 contains several EBSD orientation maps of the
microstructure of the sample annealed at 155 C obtained
in situ during the heating stage recrystallization experiments. These images were created from the EBSD data
using thin lines to characterize low angle grain boundaries
(1–10 misorientations) and thicker lines to characterize
high angle grain boundaries (>10). The development and
migration of the high angle grain boundaries is evident in
the maps as the growing grains sweep into regions of high
dislocation density while new grains and annealing twins
form. The area fraction of recrystallized grains in each of
the samples was determined from the measure of grain orientation spread (GOS). The GOS can only be used to
determine the fraction of recrystallized structure if the
grain definition parameters are selected properly. In this
case, a grain was defined by a minimum misorientation
angle of 5 and the minimum grain size was set to 10 contiguous measurement points. GOS is given by the following
equation:
GOS ¼
1
N
h
i
13 9
1
=
trace gave ðhi gA Þ
1
A5
min 4cos1 @
:
;
2
A¼1
8
N <
X
2
0
ð5Þ
where A indicates the Ath measurement point in a grain
consisting of N measurements, gave is the average orientation of the grain, gA is the orientation measured at the
Ath position within the grain and hi is the appropriate symmetry element yielding the minimum misorientation angle
between the average orientation and the Ath measurement.
In essence, the GOS is the average difference in orientation
between the average grain orientation and all measurements within a single grain. This value usually increases
for increasingly deformed microstructures, but is small
for recrystallized grains since it is simply the noise or uncertainty in the EBSD orientation determination (0.5).
There is essentially no step size dependence for the GOS
parameter as long as there are several measurements within
the grain, making it a nice measure to use in determining
the fraction of recrystallized structure. Analysis of the partially recrystallized structures indicated two well-separated
peaks for the GOS value of grains that were recrystallized
and free from dislocation structure as compared with those
from deformed grains. A criterion of 2 or less was used for
the GOS tolerance to indicate a recrystallized grain, but
anything from 1 to 3 gives similar results for these
structures.
Using the definition that recrystallized grains have a
GOS value <2, the kinetics of the recrystallization process
were determined and are shown in the standard fraction
recrystallized vs. log time plot shown in Fig. 4 for all temperatures except 400 C, where there were not enough data
D.P. Field et al. / Acta Materialia 55 (2007) 4233–4241
4237
Fig. 3. Orientation images of the sample during several stages of recrystallization while at a temperature of 155 C. Low angle grain boundaries (1–10)
are shown as thin lines, with high angle boundaries shown as thick lines.
error bars shown on the data since each point indicated
was obtained from a single set of EBSD data. For all of
the in situ measurements, the observation area is reasonably small, and is not necessarily representative of the
recrystallization kinetics in heavily deformed pure copper.
Compared with experimental results from the literature,
however, it appears that the kinetic data shown here are
reasonable for recrystallization of pure copper [1,25–27].
3.3. Observation of annealing twin boundary development
Fig. 4. Recrystallization kinetics for various temperatures as measured
using the GOS parameter.
points to reliably retrieve the recrystallization kinetics. At
temperatures of 170 and 175 C, recrystallization had significantly progressed before the first elevated temperature
EBSD map could be obtained for the in situ experiments.
The data in the regions where the recrystallization fractions
approach unity can be reasonably ignored because the
GOS parameter will always slightly underestimate the
recrystallization fraction due to the quality of the data.
For example, positions of low confidence EBSD data, such
as those around the fiducial marks on the specimen surfaces, are ignored in the GOS calculation, but are included
in the overall area determination. Thus, complete recrystallization will not be observed using this measure. The data
obtained are reasonably regular, however, and typical sigmoidal recrystallization curves are retrieved. There are no
A preponderance of boundaries with twin type misorientation relationships, R3n, was observed in all recrystallized
structures regardless of annealing temperature. The average number of twin grains within a parent grain was calculated by determining the number of grains in the region
both including and excluding twin boundaries as defining
individual grains. The quotient of these values gives the
average number of twin grains for each parent grain. The
grain definitions for this calculation defined a grain using
a 5 minimum misorientation angle and a minimum grain
size of 10 measurement points. The twin boundaries that
were excluded in the calculation of the numerator were
both R3 and R9 boundary types to within a tolerance of
3. Table 1 shows the relationship between the average
number of twins per grain vs. annealing temperature once
recrystallization was near completion. In this analysis,
grains were defined using a misorientation angle of 5
and twins were not included as separate grains. It is evident
from these data that the number of twins that developed
per grain generally increased as the annealing temperature
decreased. These numbers were obtained from EBSD data
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D.P. Field et al. / Acta Materialia 55 (2007) 4233–4241
Table 1
The average number of twins per grain for each temperature when the
specimens were at near-complete recrystallization
Temperature
(C)
Twins per
grain
Average grain
size
(twins are
grains) (lm)
Twin length per unit
area (lm1)
155
160
165
170
175
200
400
6.4
4.9
5.0
3.6
4.8
4.3
3.2
2.4
2.6
2.3
2.2
1.8
1.9
2.2
1.62
1.76
1.47
1.03
1.08
1.11
0.86
obtained over larger regions than those observed in situ,
with 80 · 80 lm2 images obtained. The 400 C scans covered 200 · 200 lm2 in an attempt to include roughly the
same number of grains for each annealing temperature.
The data show a reasonably consistent trend, with the
exception of the specimen annealed in situ at 170 C. Even
the specimens annealed in the salt baths appear to follow
the same trend, even though the recovery before recrystallization must have been much more prevalent in the samples annealed in situ. Also shown in Table 1 is the total
twin boundary length per unit area observed on the plane
sections. A similar trend is observed where more twin
boundary length per unit area is seen at the lower annealing temperatures. Another interesting observation is that
grain size generally decreases with increasing annealing
temperature for twin grains being defined as individual
grains. This may occur because the higher temperature
anneals were performed by rapidly heating the specimen,
thereby restricting the amount of recovery that would
occur. The higher temperatures would also provide a
higher driving force for nucleation so the growing grains
would impinge upon one another at a smaller grain size.
At lower temperatures, fewer nuclei would form because
the structure was allowed to recover at lower temperatures
before reaching the final recrystallization temperature. It
should be pointed out that the grain sizes shown in Table
1 are not the equilibrium grain sizes for the temperatures
given, only the grain sizes at the completion, or near completion, of recrystallization. Grain sizes of similar copper
Fig. 5. Boundary image sequence showing the development of a ‘‘new’’ grain nucleated from a twin that emanated from a grain whose growth had
stagnated. The large arrow indicates the first apparent position of the twin nucleus that grows into a new grain. The A with the small arrow indicates the
position of a twin boundary with the same crystallite lattice orientation as the new grain indicated.
D.P. Field et al. / Acta Materialia 55 (2007) 4233–4241
specimens after annealing at various temperatures are
reported elsewhere [28,29].
During recrystallization it was often observed that when
the growth of grains became stagnant, annealing twins
would form so that growth could resume. When growth
stagnation occurred, the boundary between the recrystallizing grain and the deformed matrix was often in a region of
low dislocation density and/or low misorientation angle.
Twinning would alter the misorientation and apparently
offer the additional boundary energy required to continue
growth. An example of this is shown in Fig. 5 that contains
a story board presentation of consecutive EBSD images
similar to that shown in Fig. 3. The arrow shows the position where the nucleus of a new twin grain was first
observed. This nucleus has the same orientation as the twin
grain labeled A on the image. As recrystallization occurs,
the twin continues to grow – and appears to be completely
independent of the parent grain whose growth had previously stagnated. This type of behavior was observed
directly for several boundaries during in situ annealing at
various temperatures. Such analysis would be impossible
using optical metallography techniques or even ex situ orientation mapping techniques. This observation emanates
solely from in situ analysis of the evolving structure.
When the grain boundary growth rate was high, fewer
twins developed, but when the growth rate was low, more
twins were generally found. Fig. 6 shows a plot of boundary velocity vs. twin density for the specimen annealed at
165 C. The boundary velocity was calculated from the
increase in average grain radius as a function of time.
The number of twins per grain was obtained by first determining the number of grains by considering twin boundaries as regular grain boundaries and again by ignoring
twin variants as boundaries. The ratio of these values gives
the number of twins per grain plotted on the horizontal
axis. These data are in direct contradiction to data presented by various authors that show a general increase in
twin density as the growth rate increases [25–27]. The
growth accident model is generally used to explain that
higher boundary velocities result in a higher probability
Fig. 6. The comparison of twin density (average number of twins per
grain) with the average grain boundary velocity for the sample annealed at
165 C. The average boundary velocity was measured as the change in
grain radius over the annealing time.
4239
of growth accidents and thus an increase in twin density.
In the present experiments, the driving force for recrystallization was necessarily very small to ensure that there
was sufficient time to obtain several orientation maps during the recrystallization process. With this constraint, even
the more rapidly moving boundaries in this study migrated
at a relatively low rate. The range of boundary velocities
was perhaps slow enough that a difference in the rate of
growth accidents as a function of boundary velocity was
insignificant.
The mechanism for more twin grains appearing at
slower growth rates appears to be that of the twin misorientation with the deformed matrix offering an advantage to
growth over that of the parent grain. Since the driving
force for growth is directly affected by temperature, twinning may have been necessary for the growth of grains to
continue to complete recrystallization at the lower temperatures. At higher temperatures, the growth of grains may
have had less of a dependence on twinning, since adequate
driving force was supplied by thermal energy. This is analogous to the lower driving force applied during strain
annealing that is used to create special boundaries in grain
boundary engineered structures; namely, that of small plastic deformations. If larger deformations are imposed, the
driving force for recrystallization overwhelms any boundary effects that might contribute to the process and special
boundaries fail to be created to the same extent [16].
In the each of the recrystallized structures, many neighboring grains that appeared completely unrelated by morphology were twin related, or higher order twin related
(R3n). Fig. 7 contains a representative image of a structure
annealed at 200 C that shades grains only according to the
grain definition. Fig. 7a defines grains simply as a set of
contiguous points whose misorientation with neighboring
measurements is <5. Fig. 7b shows the same image but
those boundaries having a twin related misorientation to
within 5 are not considered to separate different grains.
This same effect is apparent in all recrystallized structures,
but is more pronounced when the fraction of twin boundaries is highest. This observation tends to support the concept first proposed by Haasen [1], that twinning is an
important mechanism in determining the recrystallization
structure for such materials and that twin boundaries
develop to further the recrystallization process. It was further observed in various locations that the first nuclei to
appear had either an orientation that was similar to that
of the deformed matrix or that was twin related with
respect to the deformed matrix. It is proposed that those
nuclei that had a twin relation to the deformed matrix first
nucleated with the orientation of the matrix. Because of the
low angle relationship the nuclei necessarily had with the
matrix, stacking faults developed forming twins to the original nuclei that provided new grains with high angle relationships to the deformed matrix. These grains grew
rapidly and were the first apparent nuclei to be observed
at the specimen surface, even though the original nucleation events were perhaps not observed.
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D.P. Field et al. / Acta Materialia 55 (2007) 4233–4241
Fig. 7. Unique grain shading maps for the copper sample fully recrystallized at 200 C for (a) individual grains defined as having a minimum grain size of
10 with a tolerance of 5 and (b) the same grains but shaded as groups of grains that are twin related (first and second order twin boundaries excluded with
a 5 tolerance).
4. Discussion
Since the formation and growth of twins is an increasingly important topic in the arena of GBE, the mechanisms
for twin formation should be better understood. A model
proposed by Gleiter in 1969 [25] considers twins to be a
result of growth accidents leading to stacking faults. These
growth accidents are presumed to increase in frequency as
boundary velocity during recrystallization increases. A
recent study [27] follows up with these ideas and suggests
the utility of the model in certain circumstances and using
properly defined constants. This model lacks a mechanistic
description of twin formation. Two independent investigations observed that annealing twins may form at irregularities on grain boundaries where a packet of stacking faults
is formed, resulting in a twin boundary [30,31]. Again,
mechanistic details are lacking in this description. A more
mechanistic model was proposed and later developed by
Mahajan and co-workers [26,32–34]. This model envelopes
the idea of growth accidents as suggested by Gleiter and
describes the mechanism by which various twin geometries
are likely to occur. The model is capable of describing twin
boundary formation either parallel or normal to the
growth front, as is observed experimentally. The large
amount of deformation initially present in the copper samples from this study will increase the probability of stacking
faults and therefore contribute to the development of
twins, according to this model. Another consideration from
a recent paper suggests the possibility that large shear
deformation present in the specimens also increases the
likelihood of stacking faults on certain planes and leads
to an increase in twin boundary density [35]. The ECAE
process, by which the specimens from the present study
were deformed, certainly provides a strong shearing component and may contribute to the twin densities observed.
The average grain diameters of the specimens from this
study generally decreased with increasing temperature, as
shown in Table 1. Although the data vary from temperature to temperature, the grain size appears to be related
to the twin density, supporting the proposal made by
Mahajan et al. [32]. This mechanistic growth accidents
model is satisfactory in explaining twin density (twins per
grain) with relation to grain size. When exploring this relationship, Mahajan made the conclusion that twinning is
only influenced by temperature through its effects on grain
size. In this model, twinning is controlled by the existence
of stacking faults and the behavior of the migrating grain
boundaries. Although temperature is thought to have a
weak influence on twinning, lower twin densities were
sometimes found to develop at higher temperatures (observation noted in Ref. [30]). This was again observed recently
by a group analyzing recrystallization of cold-rolled Cu
[36]. This corresponds to the same results found in the present study. Table 1 presented the trend that suggests higher
twin densities developed at lower annealing temperatures.
The main contribution of the present work is to describe
the effects of twin boundary formation for very low driving
forces such as with the low temperature anneals of the
heavily deformed copper of the present study or the small
deformations employed in strain annealing. A mechanistic
D.P. Field et al. / Acta Materialia 55 (2007) 4233–4241
description for this phenomenon was proposed by Kumar
et al. [37] as an explanation for structure evolution during
the strain annealing process. A unified model for annealing
twin formation should be developed to include both
growth accidents and the observed phenomena prevalent
with low driving forces. This is beyond the scope of the
present work.
5. Summary
Analysis of recrystallization in most polycrystalline
materials is convenient and seemingly accurate using
in situ EBSD analysis. In the case of analyzing heavily
deformed copper at temperatures between 170 and
400 C, 3 min scans were inadequate to capture all of the
recrystallization kinetics, so more rapid scanning techniques must be employed. Recent speed enhancements in
EBSD detectors have increased the possible scanning rates
by a factor of three over that used in the present study, but
this is still too slow to capture recrystallization kinetics
under most circumstances. Nucleation was observed to
typically occur below the specimen surface, which disabled
the measurement of exact nuclei/matrix orientation relationships. It was apparent in some cases that the nucleus
was near the same orientation as the deformed matrix
and also often occurred in a twin relationship with the surrounding structure.
Annealing twins played an important role during the
recrystallization process. When a grain appeared to stagnate in growth, it would often twin and rapid growth
would resume. In the final structure, there are many neighboring grains that appear to be independent from one
another by morphology, but are twin related according
to the misorientation relationship. This supports the notion
that growth is dependent upon twinning in these structures
– a theory first advanced by Haasen [1] nearly two decades
ago. It must be emphasized that this mechanism likely
occurs only under conditions of low driving force for
recrystallization. The growth accidents mechanism for twin
formation is probably prevalent at higher temperatures.
Acknowledgements
The authors acknowledge the experimental and analytical support provided by P. Trivedi of WSU and S.I. Wright
of TSL/EDAX. This work was partially performed using
an instrument purchased under the NSF IMR program
(Award No. DMR-0414294). A portion of this work was
also supported by the US Department of Energy, Office
4241
of Energy Efficiency and Renewable Energy, FreedomCAR and Vehicle Technologies Program Office, under
DOE Idaho Operations Office Contract DE-AC0705ID14517.
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