deformation mode and plastic flow in ultra fine grained metals

8/3/2019 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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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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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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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


12/12


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.

References

[1] N. Hansen, Mater. Sci. Technol. 6 (1990) 1039.

[2] D.A. Hughes, N. Hansen, Acta Mater. 45 (1997) 3874.

[3] A.S. Malin, M. Hatherly, Mater. Sci. 8 (1979) 463.

[4] J. Gil Sevillano, P. Van Houtte, E. Aernoudt, Prog. Mater. Sci. 25

(1981) 69.

[5] J. Hirsch, K. Lucke, M. Hatherly, Acta Metall. 36 (1988) 2905.

[6] A. Korbel, M. Richert, Acta Metall. 33 (1985) 1971.

[7] T.R. MacNalley, D.L. Swisher, M.T. Perez-Prado, Met. Mater. Trans.

33A (2002) 279.

[8] J.R. Bowen, P.B. Pragnel, F.J. Humphreys, Mater. Sci. Technol. 16

(2000) 1246.

[9] V.V. Rybin, Large plastic deformation and fracture of metals, Met-

allurgy (1986) (in Russian).

[10] J.A. Hines, K.S. Vecchio, S. Ahzi, Met. Mater. Trans. 29AS (1998)

191.

[11] M.Yu. Gutkin, A.L. Kolesnikova, I.A. Ovidko, N.V. Skiba, J.

Metastab. Nanocryst. Mater. 12 (2002) 47.

[12] A. Belyakov, R. Kaibyshev, T. Sakai, Met. Mater. Trans. 29A (1998)

161.

[13] P.C. Wu, C.P. Chang, P.W. Kao, Mater. Sci. Eng. A374 (2004) 196.

[14] R.A. Masamura, P.M. Hazzledine, C.S. Pande, Acta Mater. 46 (1998)

4527.

[15] M.Yu. Gutkin, I.A. Ovidko, C.S. Pande, Rev. Adv. Mater. Sci. 2

(2001) 80.

[16] M. Yu Gutkin, I.A. Ovidko, Rev. Adv. Mater. Sci. 4 (2003) 79.

[17] Y.M. Wang, E. Ma, Acta Mater. 52 (2004) 1699.

[18] K.A. Palmandahan, H. Gleiter, Mater. Sci. Eng. A381 (2004) 28.

[19] A. Vinogradov, S. Hashimito, V. Patlan, K. Kitagawa, Mater. Sci.

Eng. A319A321 (2001) 862.

[20] Y. Huang, T.G. Langdon, Mater. Sci. Eng. A358 (2003) 114.

[21] G.I. Taylor, J. Inst. Met. 62 (1938) 307.

[22] V. Segal, Mater. Sci. Eng. A338 (2002) 331.

[23] R. Hill, The Mathematical Theory of Plasticity, Oxford, 1950.

[24] A.N. Tyamentsev, M.V. Tretyak, Yu.P. Pinzhin, A.D. Korotaev, R.Z.

Valiev, R.K. Islamgaliev, A.V. Korznikov, Phys. Met. Metalograph.

90 (2000) 461.

[25] H. Hahn, P. Mondal, K.A. Padmanabhan, Nanostruct. Mater. 9 (1997)

603.

[26] J.K. Mackenzie, Biometrica 45 (1958) 229.

[27] S.N. Haven, H.E. Deve, R.J. Asaro, Acta Metall. 36 (1988) 2435.

[28] P.L. Sun, P.W. Cao, C.P. Chang, Mater. Sci. Eng. A238 (2000) 82.[29] W.A. Backofen, Deformation Processing, Addison-Wesley, 1972.

[30] O.V. Mishin, G. Gottstein, Philos. Mag. A78 (1998) 373.

deformation mode and plastic flow in ultra fine grained metals

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