Deformation Mode and Plastic Flow in Ultra Fine Grained Metals
Transcript of Deformation Mode and Plastic Flow in Ultra Fine Grained Metals
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Materials Science and Engineering A 406 (2005) 205216
Deformation mode and plastic flow in ultra fine grained metals
V.M. Segal
EPM Co., 2874 Laurel Ridge Ln, Howell, MI 48843, USA
Accepted 24 June 2005
Abstract
Mechanical behavior of ultra fine grained (UFG) metals fabricated by severe plastic deformation (SPD) is considered in the paper. The
mechanisms of a crystallographic glide during a continuous micro flow and shear band (SB) localization/fragment rotation during a discontin-
uous micro flow are analyzed by simple models. It is shown that localized flow and the transition to localization are sensitive to deformationmode and conditions of processing or subsequent loading. Experimental data on texture evolution and tensile properties of ultra fine and fine
grained aluminum alloy Al0.5Cu as well as dynamic recrystallization of high purity aluminum Al5N5 arepresented for pure shear and simple
shear deformation modes. These results comply with theoretical models. Tensile tests of ultra fine grained structures reveal two stages of
localization, into a sample neck and inside a planar material layer. In contrast to ordinary materials, the second stage modifies tensile loading
and leads to different fracture mechanisms.
2005 Elsevier B.V. All rights reserved.
Keywords: Severe plastic deformation; Plastic flow mechanisms; Deformation mode; Shear band localization
1. Introduction
Ultra fine grained (UFG) metals produced by severe plas-tic deformation (SPD) show many unusual properties. Plastic
flow in these materials defines their strength, ductility, tough-
ness, fatigue and other characteristics. Understanding of the
corresponding mechanisms is important to interpret results
of mechanical testing and to evaluate possible applications.
Also, fabrication of useful products from bulk billets after
SPD usually requires secondary forming operations with
large plastic strains, such as forging, rolling and extrusion.
In the more general context, processing and application of
UFG materials at temperatures below the temperature of
static recrystallization provide successive loading histories
with similar deformation mechanisms that should be ade-quately described and analyzed.
Despite the great interest in SPD during last years, these
deformation mechanisms are still unclear. Large body of
work with various SPD techniques and conditions presents
different phenomenological models for development of high
angle boundaries (HABs) and structure refinement. Some of
Tel.: +1 517 548 3417; fax: +1 517 548 3417.
E-mail address: vladimir [email protected].
them extend the continuous evolution of dislocation struc-
tures by the crystallographic glide from low and moderate
strains to very large strains [1,2]. An alternative approachdescribes SPD as discontinuous evolution due to localized
flow inside shear bands (SBs) of non-crystallographic orien-
tations [38]. It was also found that material fragmentation by
rotation mayplay a significant role [911] as well as diffusion
flow, recovery and local boundary migration contributing to
more equilibrium HABs [12,13]. For large plastic strains and
non-monotonic deformation paths, all thesemechanisms may
act in different sequences.
Typically, UFG structures fabricated by methods of SPD
are within the sub-micron scale with the average grain
size of more than 100 nm. During mechanical testing of
such structures, they follow the normal HallPetch rela-tion between flow stress and grain size like their coarse
grained counterparts [14]. Therefore, flow mechanisms in
UFG materials at the meso scale should be similar to mech-
anisms of crystallographic glide, shear band localization,
fragments rotation and diffusion plasticity observed during
SPD processing. Each of these mechanisms will provide dif-
ferent mechanicalbehavior. Clearly, theirrealizationdepends
on conditions of macro loading and mechanisms of micro
deformation.
0921-5093/$ see front matter 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.msea.2005.06.035
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206 V.M. Segal / Materials Science and Engineering A 406 (2005) 205216
Gutkin et al. [15,16] reviewed numerous attempts to
explain mechanical properties of UFG and nano materials
by using physical mechanisms of plastic deformation. They
suggested new dislocation and disclination models for lattice
glide, grain boundary sliding and fragment rotation. How-
ever, there are a few principle problems for such physical
description. As pointed out in Ref. [15], it is almost impos-sible to detect elementary deformation acts by experimental
methods. In most cases, they are introduced as theoretical
models. Statistics of dislocation ensembles are not known
and should be also postulated. Moreover, the operation of
different deformation mechanisms depends itself on con-
ditions of macro loading that is especially difficult to take
into account at the micro scale. The ordinary approach for
these contradictions is comparison of calculated results for
postulated models with experimental results. Hence, this the-
oretical downtop approach is still incapable to predict
mechanical properties of UFG materials for different loading
conditions, except some cases when the main deformation
mechanism may be identified [17,18].Usually, UFG materials are analyzed by TEM and EBSD
techniques. These methods detect the final structures after
very large plastic deformations and cannot reveal the acting
mechanisms during small deformation steps. Vinogradov et
al. [19] applied atomic force microscopy to separate incre-
mental and total strains in UFG metals and demonstrated
that the shear band localization at the fine structural scale
is the characteristic mechanism of plastic flow after SPD.
Huang and Langdon [20] using the same method found that
other flow mechanisms may be also observed at certain con-
ditions. For crystallographic glide in polycrystals, it has been
known since Taylors work [21] that continuum mechanicscan be applied only to sufficiently large grain aggregates, but
not to individual grains. However, for localized micro flow
in UFG materials, shear bands are thin and long in com-
parison with the grain size and they are oriented along the
principle macro shear directions. These peculiarities allow
one to extend the continuum mechanics description to the
meso scale and to establish the correlation between flow
mechanisms and loading characteristics. The corresponding
topdown approach silently includes the microstructural
features of UFG materials manifesting HallPetch strength-
ening and localized flow and provides methodological advan-
tages in analysis of mechanical properties in comparison with
more physical downtop approach. Both approaches are
not contradictory and should conjugate at the meso scale.
Using this basis, the paper presents a theoretical and exper-imental investigation of the effect of deformation mode on
plastic flow in UFGmaterials.A similar approach was applied
earlier to examine structure refinement during SPD [22].
2. Mechanisms of plastic flow in UFG metals
Structural peculiarities of UFG metals are almost
dislocation-free, equiaxed grains from a few microns to
sub-micron size with extensive, non-equilibrium boundaries.
Such structures are within a range between ordinary poly-
crystals and nano materials. In different circumstances, UFGmetals exhibit propertiessimilar to bothof these. In particular,
the mechanisms of plastic flow in UFG metals may manifest
any of corresponding characteristics.
2.1. Crystallographic glide
It is known the main mechanism of plastic flow in poly-
crystalline metals is a crystallographic glide. Taylor devel-
oped an upper-bound approach [21] for averaging of virtual
states in grain aggregates by minimizing the dissipation of
plastic work
dW
dt= min
(svsfs) (1)
here s and vs are the resolved shear stresses and glide veloc-
ities and fs is the area of dislocation glide on all active slip
systems s. For a sufficiently large grain aggregate inside a
small material element (Fig. 1a), minimization (1) should
accommodate macro-stressesstrain rates applied to element
Fig. 1. Material elements for: (a) continuous evolution and (b) localized flow.
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V.M. Segal / Materials Science and Engineering A 406 (2005) 205216 207
boundaries
min
(svsfs) = iiw (2)
where i and i are effective von Mises stress and strain
rates, w is an element volume, bold indexes relate to contin-
uum parameters. Eq. (2) establishes the correlation between
continuum mechanics and crystal plasticity. For large plasticstrains during SPD, elastic deformations are negligible and
the simplest analysis of such rigid plastic materials may be
performed by slip line theory related to the principal shear
directions or macro slip lines [23]. Assuming uniform states
and planar flow, slip lines and correspond to the Cartesian
coordinate system (, ) shown in Fig. 1a. Material elements
along slip lines are subjected to the stress tensor T = {, k}and strain rate tensor T = {, } where is the meanstress component, k is the material yield shear stress, and are shear strain rates along and directions. The
slip line theory was originally developed for ideal plastic
materials with k = const, but it also incorporates plastic inho-mogeneity when the yield stress is determined as a function
of strains (), strain rates () and temperature (T):
k = k(, , T).
This constitutive equation should be determined experimen-
tally. For UFG materials, that includes the HallPetch effect
of grain size on yield stress. When expressed in terms of slip
line directions, Eq. (2) becomes
min
(svsfs) = 2kw (3)
where= ( +)/2 describes the intensity of plastic load-
ing. Its distribution along slip lines defines the special char-acter of straining or deformation mode. A tensor parameter
of deformation mode was introduced in Ref. [22].
c = 2(1+ /)1 (4)
The coefficient c varies inside an interval 0 c 1 and
expressed all possible strain rate states into slip line direc-
tions. Two limiting cases correspond to pure shear with c = 1
andsimple shear with c = 0; for numerous intermediate states,
0 < c < 1. Parameters and c describe the strain rate tensor
T = {, }= {, c} where
= (2 c), = c (5)
For assigned stresses (, k), aggregate structure (s,fs)and
properties (s), Eq. (3) together with , c formulates bound-
ary problems for the distribution of glide speeds vs in all
grains inside the material element (Fig. 1a) at the consid-
ered moment. Although the uniqueness of the corresponding
solutions is not clear, however, in any case, vs should be pro-
portional to . It is necessary to note that the coefficient c is
excluded from Eq. (3) and affects only boundary conditions.
Because of the crystallographic nature, these conditions can
be satisfied along element boundaries in average, but not
locally at any point. Also, these boundaries are not strictly
defined and their shift within a grain diameter may signif-
icantly change local states in adjoining grains, but cannot
alter the behavior of the entire grain aggregate. Such relaxed
conditions result in the primary role of glide accommodation
between all grains in accordance with a total element dis-
tortion rather than accommodation along boundaries. Physi-
cally, that means that during continuous flows, deformationmode may have a small effect on generalized characteristics
of crystallographic glide like dislocation density or effective
stressstrain but a strong effect on orientation characteris-
tics like crystallographic texture. These conclusions comply
with known experimental observations. In accordance with
the general framework of evolution of dislocation structures
[1,2], crystallographic glide in UFG metals manifests itself in
grain subdivision, formation of geometrically necessary and
accidental boundaries, distortion of grains along a flow direc-
tion, microstructural and textural hardening. For UFG metals
fabricated by SPD with extremely high strains, microstruc-
tural hardening may be insignificant in comparison with
textural hardening.
2.2. Localized flow
If the material hardening ability disappears (dk/d 0),
continuous flow becomes unstable and localized flow com-
mences alongshear bands[37]. A transition to localizationis
usually observed during production of UFG materials and the
shear band formation is considered to be the dominant mech-
anism of structure refinement during SPD [6,7,13,22,24]. At
the final stage, SPD should produce the finest stable struc-
ture that exhausts hardening and maximizes the flow stress
at particular processing conditions. It is reasonable to expectthat localization will take place at once during subsequent
loadings of UFG materials. However, this situation may be
changed for a few reasons. There is some natural or anneal-
ing recovery after SPD processing and in most cases, the
loading temperature and strain rate are different from the
prior characteristics during SPD. If these changes led to the
decrease of the flow stress k, additional hardening at the
beginning of loading alters localization to continuous crys-
tallographic glide inside ultra fine grains. The subsequent
flow mechanism depends on the deformation mode which
has a strong effect on textural (geometrical) hardening. Fig. 2
presents a model for evolution of originally near random
texture of UFG material [22] under pure shear (Fig. 2b)
and simple shear (Fig. 2c). In these limiting cases, grains
with stable orientations (dashed lines) [5] do not rotate and
change their shape by crystallographic glide along and
slip lines. Compatibility of strains in grains with unstable ori-
entations 13 requires the reciprocal rotation of glide planes
into the flow direction. Under pure shear, unstable orienta-
tions rotate to the first principal stress direction 1 oriented
at an angle 45 to slip lines. Such rotation is accompanied
by the increase of the Schmid factor and textural hardening
that delays localization. On the contrary, for simple shear,
unstable orientations rotate to the slip line that decreases
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Fig. 2. Stable crystallographic orientations at the: (a) original position; (b) after pure shear; (c) after simple shear.
the Schmid factor and lead to textural softening with early
localization.
Similar to amorphous materials, localization in UFG
metals propagates through shear transformation zones of
the structure. Hahn et al. [25] suggest that vicinities of
grain boundaries are corresponding zones in nano crystals.
Although average angles of grain boundary misorientations
in UFG metals produced by SPD are usually less than 18
,Vinogradov et al. [19] found that the special structure of these
boundaries together with an equiaxed grain shape provide
channels for development of shear bands along macro slip
lines. Therefore, material elements outlined by shear bands
are subjected to continuum stresses and velocities at a very
fine structural scale (Fig. 1b). Assuming the shear bands of
thickness 2 and spacing 2h as a glide system with s = k,
Eqs. (3) and (5) give for strain rates inside SBs:
= h/ = (2 c)h/, = h/ = ch/
(6)
The associated normal velocity components along shearbands are [22]:
v = (2 c)h, v = ch. (7)
The time necessary for material particles to cross correspond-
ing shear bands is
t = 2/hc, t = 2/(2 c)h (8)
During crossing, the material obtains shears of
= t = 2(2 c)/c, = 2c/(2 c) (9)
Eq. (9) demonstrates a strong effect of deformation modeon strains inside SBs. The limiting cases of pure shear and
simple shear present the biggest practical interest. For pure
shear (c =1),
= = 2 (10)
In this case, after crossing of shear bands, material particles
flow through a regular grid of SBsand receive identicalstrains
in intervals of time t= 2h/v = 1/. Accumulated macro
shears during this interval are =t= 2 that complies with
Eq. (10). Therefore, for pure shear, equivalent strains = 2
spread gradually over the material similar to continuum flow.
For simple shear (c = 0), the material particles are fixed
inside SBs and their strains increase in proportion with time
= 2ht/ = h/, = 0 (11)
where is the accumulated macro shear during loading. As
h (Fig.1b), localized strains exceed continuum strains
by many times. It is obvious that angles of misorienta-
tion between SBs and the surrounding material correlate withstrains in Eqs. (10) and (11) irrespective of active slip systems
inside shear bands. Consequently, once started, localization
in UFG metals transforms SBs grain boundaries to high angle
configurations [26] at strains that are smaller as c 0 (sim-
ple shear). Also, a multi-slip activity inside shear bands [27]
promotes texture randomization [5]. At the macro-scale, the
transition to localization may change the general character of
plastic flow.
2.3. Rotation fragmentation
When localization proceeds, the density of dislocations,
vacancies and other defects near grain boundaries increases
greatly. Similar to super plasticity, they result in multiply
enhanced diffusivity. In result, the materials become sensitive
to strain rate. Depending on the deformation mode, different
strain rates inside SBs provide different tangential stresses
acting on material elements outlined by SBs (Fig. 3):
k = k(), k = k()
If =, moments of these strains are not balanced
Mo = 4h
2[k() k()] = 0, (12)
and elements start to rotate with angular speed to restorethe equilibrium.
Consider kinematical conditions along a mutual boundary
AA of two rotating elements 1 and 2 (Fig. 3). For the normal
and tangential velocity components at conjugant points M1and M2, one may find
v1 = r sin = v2,
[v] = v2 v1 = 2r cos = 2h = const
These formulae satisfy necessary conditions of continuity
for normal velocity components and constancy of disconti-
nuity for tangential velocity components at any points of the
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V.M. Segal / Materials Science and Engineering A 406 (2005) 205216 209
Fig. 3. Boundary conditions for element rotation.
boundary [23]. Therefore, such rotations are admissible. The
rotation induces an additional strain rate inside the shear band
AA
=h
The full strain rate in the corresponding -SBs is
=(c+ )h
(13)
A similar consideration gives the full strain rate inside-SBs.
=(c )h
(14)
Eqs. (13) and (14) together with Eq. (12) provide the balanceof moments when
= (1 c) (15)
This angular speed equalizes full strain rates in both families
of SBs and reduces the local deformation mode to pure shear.
During a time interval t, the rotation induces an additional
angle of misorientation along shear bands
= (1 c) (16)
where is the increase of continuum effective shear during
the interval t.
Eqs. (15) and (16) show a direct effect of deformationmode on rotation fragmentation during localization. In the
limiting cases, angular speeds and misorientation angles are:
= = 0 for pureshear,
= , = for simple shear.
This analysis has an obvious graphical interpretation. A typ-
ical S-shape diagram k= k() is shown in Fig. 4 for simple
shear (A), an intermediate state (B) and pure shear (C) where
indexes , relate to corresponding SBs. The rotation shifts
points A, A and B, B to the point Cfor pure shear. Such
consistent rotation of material elements does not change the
crystallographic texture but redistributes strains inside SBs
anddevelops high angle boundaries into both shear directions
[10]. This effect is the strongest for simple shear and disap-
pears for pure shear. Rotation fragmentation coupled with
localization was experimentally observed in Refs. [9,11]. In
addition, the enhanced grain boundary diffusivity in UFG
metals promotes local migration and development of more
stable and balanced grain configurations [12,28]. However,
this small scale diffusion flow is supplementary to the plastic
flow and will not be considered further in the paper.
3. Experimental results
3.1. Experimental procedure
To verify some conclusions of the theory, special exper-
iments were performed on the effect of deformation mode
in UFG materials. Two limit cases of pure shear and sim-
ple shear were realized, correspondingly, in the central area
of rolled samples and during equal channel angular extrusion
(ECAE) with a tool angle 90 under carefully controlled con-
ditions [22]. Equivalent von Mises strains between Npasses
ECAEand rolling reduction were calculated with a formula[22]:
= [1 exp1(1.15N)]100%.
High accumulated strains were applied to two initial mate-
rial conditions. For the UFG condition, the aluminum alloy
Al0.5Cu was subjected to 6 ECAE passes via route D (bil-
let rotation of 90 after each pass into the same direction)
and route A (no rotation) that resulted in near uniform struc-
ture with an average grain size 0.5m and medium texture
strength (OD index 3.9). For the fine grain (FG) condition,
the same ECAE processed material was annealed at 225 C,
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Fig. 4. Strain rate distributions along shear bands during element rotation.
1 h to produce a statically recrystallized structure with the
average grain size 20m and a weak texture (OD index
2.2). Also, dynamic recrystallization was investigated in high
pure aluminum Al5N5 (99.9995%) after rolling and ECAE.
For comparison with results of continuum analysis, exper-
imental data on macro texture, mechanical properties and
microstructure were obtained. Crystallographic texture was
measured using X-ray irradiation at Philip XPert Diffrac-tometer with Beatrex software. Dynamic recrystallization
was observed by optical microscopy. Standard tensile speci-
mens 5 mm diameter and 25 mm length were used for tensile
testing after ECAE. The tensile samples after rolling had the
same length and width but a different thickness in accordance
with rolling reductions. Fracture mechanisms after tensile
tests were observed using SEM for FG and UFG materials in
the as processed conditions and after recovery annealing at
125, 150 and 175 C for 1 h. Further details of experiments
can be found elsewhere [22].
3.2. Texture evolution
During rolling of the FG material, the original texture
(Fig. 5a) evolved to a symmetrical texture with the -fiber
running from the brass orientation to copper or, partly, to
Dillamore orientations. This typical rolling texture is attained
after a reductionof about 90% andremains stable with further
rolling (Fig. 5b). For ECAE of the same material, there are
numerous end orientations depending on number of passes
and routes (Fig. 5c, 4 passes via route A). Similar changes
were also observed for the UFG material. Despite different
original orientations (Fig. 5d), the inverse pole figures of final
texture for the UFG and FG materials are identical both for
rolling (Fig. 5e) and ECAE (Fig. 5f). The OD index of tex-
ture strength (Fig. 6) for rolling of the FG material (diagram
1) shows the sharp increase to very strong texture (37 ran-
dom) at reductions from 90 to 95% followed by the decrease
of strength after reductions more than 97%. However, even at
a reduction of 99.2%, the texture remains strong (11 times of
random). Rolling of the UFG material demonstrates a nearly
identical, but smoother change in texture strength (diagram 4)with the maximum OD index 13. For ECAE of the FG mate-
rial, the texture strength (diagram 2) increases only slightly
after two passes and then decreases gradually to near random
texture. This tendency is even more obvious after ECAE of
the UFG material (diagram 3).
3.3. Tensile properties
Fig. 7 presents experimental data on the ultimate tensile
strength (UTS, solid lines) and relative elongation (, dashed
lines). Rolling of the FG material (diagram 1) with large
reductions provides a significant strengthening effect due to
microstructural and textural hardening. ECAE of this mate-
rial (diagram 2) shows noticeably lowerUTS for accumulated
strains larger than 2. Rolling of the UFG material (diagram
3) detects a low hardening effect for moderate reductions.
For large reductions, hardening increases progressively to
very high UTS for the Al0.5Cu alloy. These peculiarities
reflect specific structural changes that will be considered
later. Characteristic changes were also observed for the rel-
ative elongation . The rolling of the FG material shows the
decrease of at reductions less than 75%, some increase at
reductions from 75 to 95% and finally, the sharp drop to
low for large reductions. Possible reasons for such compli-
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Fig. 5. Inverse pole figures for Al0.5Cu alloy: (a) original FG material; (b) FG material after rolling reduction 90%; (c) FG material after 4 passes ECAE,
route A; (d) original UFG material; (e) UFG material after rolling reduction 90%; (f) UFG material after 4 passes ECAE, route A.
cated behavior are the evolution of texture strength (Fig. 6)
and transition to thin samples for large rolling reductions.
Identical experimental results after rolling of the UFG mate-rial are consistent with this conclusion. In contrast, ECAE
of the FG material demonstrates the restoration of ductility
between two and four passes and near constancy of ductility
for a number of passes more than four. ECAE of the UFG
Fig. 6. Effect of equivalent strains on texture strength (OD index) after
rolling of the FG material (curve 1), rolling of the UFG material (curve
4), ECAE of the FG material (curve 2); ECAE of the UFG material
(curve 3).
material provides about the same relative elongation for any
number of passes.
3.4. Fracture mechanisms
In all cases of recovery annealed UFG samples, the frac-
ture mechanisms are identical. Typical pictures of top and
side views of a sample neck after fracture are shown on
Fig. 8a and b for the UFG material after annealing 175 C,
Fig. 7. Effect of strains on ultimate tensile strength (UTS, solid lines) and
relative elongation (, dashed lines) for the FG material (curve 1), ECAE of
the FG material (curve 2); rolling of the UFG material (curve 3).
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Fig. 8. (a) Top and (b) side views of the sample neck after tensile test of the
UFG Al0.5Cu alloy.
1 h. Fracture takes place inside a thin, planar shear zone at an
angle 45 to the sample axis. There are three specific frac-
ture areas (Fig. 8): (A) a free surface of the shear zone; (B)
a dimpled fracture area; (C) a shear decohesion area. Under
greater magnification, each area has the typical appearance
for the corresponding fracture mechanism in ductile metals
(Fig. 9ac) [29].
3.5. Dynamic recrystallization
It is known, that for the high purity aluminum Al5N5, the
recrystallization temperature after large strains is below room
temperature. That allows one to observe dynamically recrys-
tallized structures and many details of plastic flow directly
after severe deformation by optical microscopy [22]. The
first ECAE pass of the original coarse grained structure of
Al5N5 (Fig. 10a) detects highly non-uniform micro-strains
(Fig. 10b). Crystallographic glide in grain subdivided areas
is the main flow mechanism. The microstructure also shows
some shear bands and newly recrystallized grains reflecting
various stages of loading histories at different locations. Dur-
ing next ECAE passes, recrystallization takes place repeat-
edly refining and homogenizing the structure. After four
Fig. 9. Fracture mechanisms of the UFG Al0.5Cu alloy: (a) free surface of
the planar shear zone; (b) dimpled area; (c) shear decohesion area.
passes, the structure is composed of uniform and equiax-
ial grains of the average diameter 75 m (Fig. 10c). This
stable structure remains further almost unchanged and does
not show any evidence of intra-granular flow complying
with the grain boundary sliding and rotation mechanisms.
However, a remarkable difference was observed during sub-
sequent rolling of the ECAE processed material. Additional
rolling reduction 15% after 6 ECAE passes changes the
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Fig. 10. Structures of aluminum Al5N5: (a) original condition; (b) 1 pass ECAE; (c) 4 passes ECAE, route A.
grain shape and develops slip lines inside grains, subdivided
areas and sub-grains which are characteristics of crystallo-
graphic glide (Fig. 11a). After 30% rolling reduction, the
structure is fully recrystallized to large non-uniform grains
(Fig. 11b) which are quite similar to the original structure
shown in Fig. 10a. Subsequent rolling provides numerous
recrystallization sites with a gradual decrease in the grain
size. Examples of such structures after reductions of 90 and
99.2% are shown in Fig. 11c and d. Although the final struc-
ture is sufficiently fine, only a few recrystallized grains may
be observed in Fig. 11d. In most areas,this is thetypical heavy
deformed structure with diffuse boundaries, a large number
of sub-grains and dislocation configurations inside grains.
Rolling of the original material reveals a similar structure
evolution.
4. Discussion
The present analysis of UFG materials relieson the known
mechanisms of plastic flow including crystallographic glide
in grain subdivided areas, shear band localization and frag-
ment rotation. The new result is the critical role of processing
mechanics, in particular, deformation mode, on the realiza-
tion of these mechanisms and their transitions at different
stages of deformation. Experimental data obtained for the
extreme cases of deformation mode and material microstruc-
tures agree with the main conclusions of the theory and
provide some additional details. There is a large similarity
in the inverse pole figures and final texture orientations after
rolling (Fig. 5b and e) and ECAE (Fig. 5c and f) for FG and
UFG materials despite the diversity in the original textures
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214 V.M. Segal / Materials Science and Engineering A 406 (2005) 205216
Fig. 11. Structure of high pure aluminum Al5N5 after 6 passes, route D and additional rolling with reductions; (a) 15%, (b) 30%, (c) 90%; (d) 99.2%.
(Fig. 5a and d). This similarity shows that systems of crys-
tallographic glide depend on deformation mode irrespective
of the grain size.
The deformation mode shows the same strong effect on
transition to localization even for the FG material. Fig. 6illustrates the dramatic difference in the texture strength (OD
index) for FG Al0.5Cu alloy after deformation by pure shear
(diagram 1 for central area of rolling) and simple shear (dia-
gram 2 for ECAE) with equivalent strains. Such behavior
is difficult to explain by continuous evolution of disloca-
tion structures because simple shear with rotation of unstable
grainorientations into directions of stable orientations should
provide stronger textures than pure shear. However, simple
shear is accompanied by textural softening resulting in early
localization and weak textures. Correspondingly, localized
flow is realized at the beginning of simple shear in the UFG
material (Fig. 6, diagram 3 for ECAE). It is noticeable that an
alteration of deformation mode to pure shear during rolling
of the UFG structure restores the crystallographic glide and
induces sufficiently strong texture (Fig. 6, diagram 4 in the
central area of rolling). Diagram 4 is similar to the corre-sponding diagram 1 for FG material but the texture strength
is lower (maximum OD index 13 versus 37). Probably, dur-
ing rolling of the UFG material mechanisms of shear band
localization and fragment rotation contribute continuously to
plastic flow and finally, provide the same balance with crys-
tallographic glide as rolling of the FG material with large
reductions. Similar observations were reported by Mishin and
Gottstein [30].
Additional information on an affect of deformation mode
is presented in Figs. 10 and 11 from experiments on dynamic
recrystallization of high purity Al5N5. For the first ECAE
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V.M. Segal / Materials Science and Engineering A 406 (2005) 205216 215
pass, the main deformation mechanism is crystallographic
glide (Fig. 10b). The microstructure reveals different slip
systems, grain subdivided areas and sub-grains with many
dislocations, but only a few recrystallized grains and shear
bands. During the second and third passes, the deforma-
tion mechanism changed to flow localization along shear
bands. After the forth pass, the structure was composed ofuniform, fine and equaxed grains (Fig. 10c). These grains
grow near simultaneously at regular sites along slip lines.
At subsequent passes, the structure remains stable, without
noticeable changes in grain size, shape, orientation and with-
out any traces of the intracrystalline flow. That suggests that
grain rotation becomes an important mechanism for strain
accommodationunderseverestraining by simple shear.Alter-
ation of deformation mode to pure shear reveals a totally
different microstructure evolution. Even 15% of additional
rolling reduction after 6 passes of ECAE restores the crys-
tallographic glide with strong strain non-uniformity inside
grains (Fig. 11a). After 30% rolling reduction, a non-regular,
stochastic distribution of recrystallization sites produces acoarse structure (Fig. 11b) that is only slightly finer than
the original structure of Al5N (Fig. 10a). Subsequent rolling
subjects this material to repeated recrystallizations with grad-
ual microstructure refinement (Fig. 11c for rolling reduction
90%). However, the very large rolling reduction of 99.2%
still produces a typical heavy deformed structure with a small
number of fine recrystallized grains (Fig. 11d).
Therefore, in accordance with the theoretical analysis, in
UFG materials pure shear promotes crystallographic glide
whereas simple shear favors localizedflow. Since shear bands
may be considered as non-crystallographic slip systems, it
follows from Eqs. (2) and (3) that the transition to local-ization minimizes the plastic work depending on resolved
shear stresses s on glide planes and the flow stress k along
shear bands. Tensile tests data after rolling and ECAE of
FG and UFG materials (Fig. 7) provides further insight.
At strains < 1.5, the plastic flow in the FG material cor-
responds to crystallographic glide in both cases and dia-
grams 1 and 2 for rolling and ECAE are identical. Dur-
ing rolling, this mechanism remains the same for strains
> 2.5 with the continuous increase of the UTS because
of both microstructural and textural hardening. For ECAE
processed specimens, the flow mechanism transforms to
shear band localization and structure refinement to the sub-
micron scale with an insignificant increase of shear stresses
along SBs. Such tendency also occurs during ECAE of
the UFG material up to large number of passes. In this
case, material strengthening is provided by the HallPetch
effect. However, during rolling of the UFG material when
the deformation mode in the central area is changed to
pure shear, the crystallographic glide again becomes the
main flow mechanism (Fig. 7, diagram 3) providing a
large strengthening effect by both HallPetch and structural
hardening.
Characteristic forms of localization and fracture were
detected duringtensile testing of standard cylindrical samples
Fig. 12. Plastic flow during tensile test of cylindrical samples: (a) uniform
elongation; (b) axisymmetrical macro flow into the neck; (c) the beginning
stage of planar shear micro localization; (d) the finite stage of planar local-
ization; (e) fracture.
for the UFG material. At the beginning, the uniform elonga-
tion takes place along sample length with an axisymmetri-
cal stressstrain state and a pure shear deformation mode(Fig. 12a). Depending on the available amount of hardening,
this stage may be prolonged or very short with transition to
plastic localization. For the UFG Al0.5Cu alloy processed
by ECAE at room temperature and annealed at 175 C, 1h,
two stages of flow localization were observed. When the flow
became unstable, deformation first localizes in the sample
neck(Fig.12b). Ina small neckarea, the macro flow remained
axisymmetrical and continuous. At some point, there was a
second transition to micro localization inside a thin material
layer at an angle 45 to the tensile direction (Fig. 12c). This
planar layer was composed of a large number of micro-shear
bands and the deformation mode changed to simple shear.Extended shear in the layer shifts the sample ends and causes
eccentric loading by tensile forcesand bending moments with
the maximum tensile stresses at the left side of a shear zone in
Fig. 12d. Ductile fracture initiated in this area by nucleation
of voids at hard particles, followed by their growth and coa-
lescence (area B, Fig. 12e). At the right side of the shear zone
with significantly lower tensile stresses, the fracture mech-
anism included void coalescence and material decohesion
along shear planes (area C, Fig. 12e). These mechanisms are
in full agreement with the experimental observation of cor-
responding areas A, B and C on Fig. 8. However, there is a
distinctive difference from the fracture mechanism in ductile
FG metals during tensile testing. In the FG metals, material
separation at the sample neck developed by a dimpled crack
propagatedfrom outside the sample center in accordance with
axisymmetrical flow [29].
The models considered and experimental results explain
some contradiction in previous reports [19,20] on plastic flow
mechanisms in UFG structures. In Ref. [19], UFG Cu and Ni
were prepared by ECAE at room temperature. Subsequent
tensile tests were also performed at room temperature with
sufficient strain to develop flow localization at the neck. This
specimen exhibited planar shear along SBs in the material
layer with a simple shear deformation mode. Similar results
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216 V.M. Segal / Materials Science and Engineering A 406 (2005) 205216
were observed in [20] for the aluminum also fabricated and
tested at room temperature beyond the limit of plastic sta-
bility. However, the Zn22%Al alloy fabricated by ECAE
at temperature 200 C but tested at room temperature did
not cause micro localization along SBs and showed the typi-
cal structure of crystallographic glide [20]. Despite the large
incremental strain = 0.37, these conditions provided a suffi-ciently strong hardening effect and stable flow under pure
shear deformation mode without micro localization. It is
interesting to note that the control of localization in UFG
materials by reducing the testing temperature was recently
suggested in Ref. [17].
5. Conclusions
The present analysis shows that mechanical behavior of
UFG metals may be explained by well known mechanisms
of plastic flow rather than some special mechanism. These
mechanisms suppose continuous or discontinuous strain dis-tributions at the micro scale. The first mechanism is a crys-
tallographic glide in grain subdivided areas. The second
mechanism is shear band localization and fragment rotation.
The essential detail is the transition between continuous and
localized flows. The suggested models show that the local-
ized flow and transition to localization are very sensitive to
deformation mode definedby a strainrate ratio along theprin-
cipal shear directions. This effect is strongest for the simple
shear deformation mode and infinitesimal for the pure shear
deformation mode. The transition to localization depends on
shear stress stability duringloading whenmicrostructural and
textural hardening disappears and dk/d 0. This transitionis reversible if the deformation mode or hardening abil-
ity during the processing/loading path is changed. Dynamic
recrystallization of Al5N5 during SPD complies with these
observations as recrystallization sites relate to shear band
localization.
Tensile testing of UFG metals also exhibits specific prop-
erties. There are two stages of plastic localization: (i) macro
localization in the sample neck and (ii) micro localization
insidea thin planar layer. Thetransition to the planar localiza-
tion modifies thedeformationmode from pure shear to simple
shear and develops a stressstrain non-uniformity along a
fracture surface. This causes different fracture mechanisms
ranging from geometrical sample separation to dimpled frac-
ture area and shear decohesion area.
Acknowledgements
The author thanks S. Ferrasse and F. Alford for the help
in performing experiments at Honeywell Electronic Materi-
als. A special appreciation goes to Prof. T. Beiler (MSU) for
useful discussion.
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