Microstructure evolution and strain localization during shear deformation of an aluminium alloy

Vol. 44. No. 10. pp. 4195-4208. 1996 Copyright (' 1996 Acta Metallurgica Inc. Published by Elsevier Science ktd Primed in Great Britain. All rights reserved 1359-645496 $15.00 + 0.00

Acta mater.

Pergamon Pil S 1359-6454(96)00046-8

M I C R O S T R U C T U R E EVOLUTION AND STRAIN LOCALIZATION D U R I N G SHEAR D E F O R M A T I O N OF AN A L U M I N I U M ALLOY M. GASPi~RINP, C. PINNAI"~ and W. S W I A T N I C K I 2 ~institut Galilee. LPMTM. LP CNRS 9001, Av. J. B. Clement. 93430 Villetaneuse, France and -'Warsaw University of Technology, ul. Narbutta 85. 02-524 Warszawa. Poland (Rec'eit'ed 3 April 1995~ in rerised /brnl I1 December 1995)

Abstract--Strain localization by shear banding during shear tests of a commercial aluminium alloy is described at different scales using optical microscopy, SEM and TEM. The evolution of the dislocation microstructure is correlated to the global mechanical behaviour. Two initial states of the material--heavily cold-rolled and recovered after cold-rolling--having the same crystallographical texture are compared. The localization occurs only for the as-rolled samples, and its consequence on damage and fracture depends on the angle between the initial rolling direction and the shearing direction. The discussion focuses on the predominant role of the microstructure, rather than the crystallographic texture, in the localization phenomena. Macroscopic arguments for localization are also evoked. Copyright ~ 1996 Acta Metallurgica hlc.

R6sumg--La Iocalisation en bandes de cisaillement au cours d'essais de cisaillement sur un alliage commercial d'aluminium est ddcrite fi diffdrentes echelles, par microscopie optique. MEB et MET. L'dvolution de la microstructure de dislocations est corrdl~e au comportement mdcanique global. Deux etats initiaux--fortement lamind a froid, et restaur6 apr~s laminage--, de m6me texture cristallographique. ont dtd compards. La localisation n'apparait que pour 1'6tat lamind, et sa consequence sur l'endommagement et la rupture ddpend de l'angle entre la direction de laminage initiale et la direction de cisaillement. La discussion met en dvidence le r61e pr6dominant de la microstructure, par rapport la texture, dans le phdnomene de Iocalisation. Des arguments macroscopiques pour la localisation sont egalement ~voqu6s.

1. INTRODUCTION Microstructural heterogeneities are inherent to the plastic deformation and. even when the macroscopic deformation is homogeneous, the dislocation organization may be spatially inhomogeneous. Starting from a well-annealed state, the dislocation microstructure of f.c.c, polycrystals evolves with increasing strain, as described in several recent studies [1-5]. The c o m m o n feature of this evolution is the creation of low-energy dislocations structures (LEDS) such as dense dislocation walls (DDW). microbands (MBs) or dislocation sheets subdividing the material in small volumes deformed by fewer slip systems than required by the Taylor condition [1]. At large strains, shear banding may appear, especially during cold rolling, after the formation of a lamellar substructure parallel to the rolling plane [6, 7]. The nature and formation of these shear bands have been largely discussed [8-13] and a new theory for shear banding has been proposed very recently [14]. However, up to now this problem is far from being well understood. Moreover, the studies on shear bands focused mainly tPresent address: LMS. Ecole Polytechnique, 91128 Palaiseau cedex, France.

on m o n o t o n o u s strain paths (rolling, channel die, tension . . . . ), although strain localization phenomena may drastically limit the formability when complex strain paths are involved. The presence of a well-organized dislocations structure is expected to modify the subsequent mechanical behaviour. The dislocations structures present in deformed metals can induce flow stress anisotropy [15]. Experimental studies on mild steel emphasized the effect of a strain-path change on the reloading behaviour: the occurrence of transient localization phenomena was shown to depend on the direction of testing in the plane of the sheet, and was associated with microband formation [16-19]. Other studies focused on the effect of strain-path change in a strong textured aluminium sheet [20]. It appears then that both the initial texture and the dislocation microstructure are important parameters governing the behaviour after strain-path changes, but, due to the limited number of available studies, their relative influence is not yet clear. In this paper, the microstructural evolution and the localization phenomena during shear tests of a commercial aluminium alloy with two different initial dislocation microstructures (cold rolled and recovered after cold-rolling) and the same initial

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GASPI~RINI et al.: SHEAR DEFORMATION OF A1

crystallographic texture are investigated. The tests of simple shear permit one to obtain large plastic strains before fracture on thin sheets [16, 21]. To the authors" knowledge, no extensive study has been published on the microstructural aspects in aluminium alloys for these tests. Microstructural and textural evolutions during the shear tests are reported and the localization phenomena observed are described at different levels using optical microscopy, scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The heterogeneity of the strain field and the occurrence of shear bands are analysed as functions of the initial microstructure and the shearing direction with respect to the initial rolling direction. Special attention is paid to the microstructural factors that a r e responsible for strain localization in the alloy, and the relations between crystallographic texture and morphology of the dislocation substructure are discussed. Macroscopic conditions for strain localization are also considered, and the consequences of shear banding on damage and fracture are pointed out. 2. E X P E R I M E N T A L

PROCEDURES

2. I. The material The material o f the present study is a commercial 3004 aluminium alloy used for can making. The composition of the material is given in Table 1. The Mg atoms are in solid solution, whereas the Mn atoms form coarse intermetallic precipitates with Fe (essentially A16MnFe) and small dispersoids (essentially AI3Mn). The sheets are 300/Lm thick, and provided in a extra-hard state obtained by 90% cold rolling reduction. The grains are elongated in the rolling direction (more than 100 #m long) and are less than 10tim thick. Some sheets were then recovered by annealing at 1 9 0 C for 90 h.

2.2. The simple shear test Parallelepipedic samples were cut off from the sheets, with the shearing direction (SD) of the samples making an angle 7 = 0 , 1 5 , 30 , 45'-, 60 ~, 75 c, 90: with the rolling direction (RD) of the sheet (Fig. 1). The dimensions of the samples were: length L = 4 0 , width w = 18, thickness e = 0.3mm. The gauge dimensions were L × b x e, with b = 2 mm in most cases, but 3 or 4 mm in some cases. This choice was consistent, for that thickness, with the geometrical conditions defined in previous studies for minimizing buckling effects and strain inhomogeneity [16, 22]. Actually, because the length of the specimen is finite and its ends are stress free, the resultant

Elements Si % weight 0.18

Fe 0.38

C SD

I.

l Fig. 1. Geometry of the samples for the shear tests. The dashed lines starting near A and B symbolize the initiating shear bands. The normal stresses concentrated towards the corners are indicated by arrows. couple of the shearing forces is equilibrated by normal stresses concentrated towards the corners of the specimen. These stresses are compressive on two opposite corners (A and B) and tensile on the other two (C and D), as indicated in Fig. 1. The shear device, similar to the one used in other studies [16], was mounted on an electromechanical tension testing machine. The average shear stress r was deduced from the load cell z = F/(Le). The displacement u of the moving part of the shear device was measured by an inductive transducer and the average shear strain ~ was computed by 7 = u/b. The strain rate was 1.6 x 10 -3 s -~. F a n d u were digitally recorded, providing r versus 7' curves automatically. The shear tests were conducted on the two states of the sheets: as-received (cold rolled) and recovered after cold-rolling. For the as-received samples, two sets of shear tests were performed for the seven values. In the first one, the tests were interrupted as soon as a localization band was visible to the naked eye; in the second one, the tests were conducted until the initiation of fracture, corresponding to a decrease of the shear stress higher than 10%. For the recovered samples the conditions of testing were chosen for comparison with the as-rolled samples. As the global behaviour o f the recovered samples was similar for all the directions (see below), only the cases • = 0 ° and 60 ° were considered for the microstructural investigations. In all the cases, at least two samples were used in order to verify the results.

2.3. The different levels o f analysis 2.3.1. Mierostructure. Microstructural observations were made at different levels, using optical microscopy, SEM and T E M . All samples were mechanically polished before testing, using only

Table 1. Composition of the alloy Cu Mn Mg Cr Ni Zn 0.14 0.99 0.99 0.01 0.05 0.02

Ti 0.01

Zr 0.05

al. 0.1

GASPI~RINI et al.: SHEAR DEFORMATION OF A1 abrasive paste of thin grain size (from 6 to 1/~m) in order to minimize the thickness reduction. Some samples were furthermore electrochemically polished in a 3.5% HBF~ solution to permit optical microscopy under polarized light. Thin foils for TEM were prepared by double jet electropolishing of 3 mm dia discs punched from sheets previously ground by mechanical polishing to approximately 0.2ram thickness. Because of the thinness of the sheet, observations were limited to foils parallel to the sheet plane. The foils were observed at 100 kV tension. 2.3.2. Measurement of the displacement field. In order to determine the local heterogeneities of the deformation field at a micro level, square micro-grids of 2 mm side with a 40 l~m mesh were deposited on the surface of some samples by a micro-lithography technique using the SEM. SEM pictures of the centres of the mesh crossings were digitized before and after the shear test, then the displacement field and the subsequent deformation gradient F were determined in a semi-automatic manner, assuming plane strain. 2.3.3. Crystallographic texture. Experimental pole figures were measured on the initial sheet and on the deformed samples corresponding to • = 0 ° and 60 °, using the K, ray of a Cu anti-cathod. Then the Orientation Distribution Function (ODF) was calculated using the vector method [23]. 3. R E S U L T S

3.1. Mechanical behaviour during shear tests The shear stress (:)-shear strain (7) curves are shown in Fig. 2. The following points have to be emphasized.

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Fig. 2. Experimental shear stress (r)-shear strain (7) curves for the as-rolled samples and for the recovered samples.

(i) All curves present a rapid hardening followed by a decreasing hardening rate leading to saturation of the flow stress, then a final decrease corresponding to the initiation of failure. (ii) The shear stress r~,, for saturation and the shear strain 7¢ at the beginning of the plateau do not depend significantly on ~. They are. respectively, :~, = 180MPa and 7p, = 0.1 for the as-rolled samples and :sa, = 160MPa and 7p~= 0.17 for the recovered samples. (iii) The failure initiation appears after large strains (y > 1) for the recovered samples whatever the value, whereas for the as-rolled samples the length of the plateau depends significantly on ~, and very large strains have been reached only for = 0 °.

Fig. 3. Optical micrograph of the band. Note the distortion of the granular structure.

4198

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(a)

(b)

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Fig. 4. D e f o r m e d micro-grids: (a) r e c o v e r e d s a m p l e , a = 0 c, 3' = 1; (b) a s - r o l l e d s a m p l e , • = 0 , ? = 1: (c) a s - r o l l e d s a m p l e , ~ = 60 °, ~ = 0.25.

GASPI~RINI et al.: SHEAR DEFORMATION OF AI This is linked to the development of macroscopic shear bands which are described in the following.

3.2. The characteristics of localization 3,2.1. Macroscopic features. Macroscopic shear bands are seen on the as-rolled samples immediately after the beginning of the plateau (y about 0.1-0.15). Their formation is similar for all ~ values: two narrow bands appear at the sample ends, along the grip marks, on the opposite sides undergoing compression----close to the corner zones A and B in Fig. l - - t h e n rapidly progress along the whole length o f the specimen, and eventually come together for the 2 mm-width specimens. If the shearing direction is reversed the bands develop in the same way with respect to the shearing direction, that means from the corners C and D. The bands produce an intense shear locally. Their average orientation becomes close to the macroscopic shearing direction. For y > 0.2, the deformation pattern depends strongly on 7, as explained below. (i) F o r ~ = O , new shear bands are formed, parallel to the first, and develop along the shearing direction, so that the whole specimen is filled

F,, F,.~ F.,, F:: A

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Table 2. Mean values of the grids measurements = 60 (as-rolled) 7= 25% ~=0 "/= I00% Outside Inside Recovered As-rolled the band the band 0.98 0.97 0.95 1.04 0.90 0.81 o. 16 1.92 0.00 0.02 0.01 0.02 1.01 0.97 0.97 0.90 0.02 0.05 0.06 o. 11

with bands. The macroscopic shear may reach up to 1.5 before fracture, which begins by ductile cracks initiated at the corners of the specimen that are subjected to tensile normal stresses, and hence opposite to those corresponding to the shear band initiation. (ii) For :~ :~ 0 , the previously formed bands slightly widen, but the bands do not invade the whole sample. Macroscopic cracks develop in the band for y = 0.25-0.5 and are responsible for the final fracture. In the recovered samples, there is no band localization, and the strain seems homogeneous in the whole specimen even after large deformation. This behaviour does not depend upon ~.

(b)

Fig. 5. Microstructure of the as-rolled sheet before the shear tests: (a) aspects of the DDWls and DDW2s; (b) schematic geometry of the DDWs.

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GASPI~RINI et al.: SHEAR DEFORMATION OF A1

3.2.2. Surface observations. The shear bands were observed on the as-rolled samples by optical microscopy and SEM at the beginning of the plateau of the r-7 curves and at the ultimate stage before failure initiation. The main features are as follows. (i) At the first stage, the initial macroscopic shear bands are 10-30 #m wide, and are composed of several roughly parallel bands. They cause distortion of the granular structure, especially for ~ :~ 0 (Fig. 3). Some of the intermetallic precipitates are fragmented. The bands are seen through the whole thickness of the sheet. (ii) At the final stage the band aspect depends strongly on ~. The narrower the macroband, the more severe the marks of damage: see the differences between ~ = 0: and 60 ~ in Fig. 4. All the cracks are linked to coarse particles for = 60 °, which are often fragmented.

deformation imposed by the test is very close to a simple shear. For ~ = 60- in the as-rolled samples, the shear strain measured inside the band is very high (1.9) [Fig. 4(c)]. this represents an average value for the whole macro-band, outside of which the shear value corresponds approximately to the macroscopic threshold of shear band initiation. This suggests that once the bands appear, they accommodate the whole deformation, although their volume fraction is as small as 0.05. For ~ = 0% as the shear bands are regularly spread [Fig. 4(b)], the grid cannot be directly used to measure the strain distribution and it can be only noticed that the shear strain within each band is very intense (about 2). 3.3. Microstructural evolution 3.3.1. Initial mierostructure.

3.2.3. Deformation field heterogeneities. The presence of shear bands leads to strain heterogeneities, which are well shown by local grid measurements (Fig. 4). Table 2 gives the components of the deformation gradient F deduced from the digitized SEM pictures of the grids in the middle of the samples, each value being an average value of about 100 measurements. Here, 1 refers to the shearing direction and 2 to the normal to the shearing direction in the sheet plane. A = x/(F~, -- 1): +(F22 -- 1)2 + (F2,)2 gives a measure of the deviation from a simple shear. It can be seen from the table that A is relatively small, especially for the recovered samples. Thus the

3.3. I. 1. As-rolled Specimens The observed microstructure [Fig. 5(a)] consists mainly of dense dislocation walls (DDW) which may schematically [Fig. 5(b)] be classified into two types. (i) Dense dislocation walls parallel to the transverse direction and inclined 300-35 ° with respect to the rolling plane, hereafter named DDW1. Their average spacing is 0.25/lm. (ii) Dense dislocation walls nearly parallel to the (RD, ND) plane, hereafter named DDW2, which are found mainly in some grains of "brass" orientation.

Fig. 6. Microstructure of the recovered sheet before the shear tests.

GASPI2RINI et al.: SHEAR DEFORMATION OF AI There are then some deviations from this general pattern, depending on the crystallographic orientation of the grains, and cells may be found in some grains with orientations far from the main components of the crystallographic texture. It can be underlined that the formation of these types of D D W is frequently observed in cell forming metals after cold-working [1, 4].

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3.3.1.2. Recovered Specimens The microstructure is composed of equiaxed cells of about 1 Ftm size, characteristic of the recovery treatment (Fig. 6). In some areas the sub-boundary pattern is similar to the initial D D W l , showing the high stability of these configurations. Thus, the recovery treatment produces a decrease

(b)

Fig. 7. Microstructure of the as-rolled samples after shearing for a = 0°: (a) y = 0.2. Formation of new walls (SW) parallel to the shearing direction (SD); (b) ? = 1. Band area separating low deformed areas.

GASPI~R1NI et al.:

4202

SHEAR DEFORMATION OF Al

in the dislocation density, the dislocations being mainly arranged into sub-boundaries, whereas the precipitates and the grain size remain unchanged.

3.3.2. Microstructures after shearing. 3.3.2. I. As-rolled Specimens. • Shearing along :t = 0 . For ,' = 0.2, new walls parallel to the shearing direction are observed [Fig. 7(a)], eventually deforming the D D W I . This tendency increases with the a m o u n t of shear and results in the formation of bands producing a local

shear. They are composed of highly elongated cells delimited by dense dislocation walls parallel to the shearing direction. For 7 = 1, the microstructure consists of band areas alternating with relatively low deformed areas [Fig. 7(b)]. For , ' = 1.5. the band structure has spread into the whole specimen width and the initial rolling structure has completely disappeared. • Shearing along ~ ~ 0 . The microstructure is strongly heterogeneous: outside the shear band. the initial microstructure is only slightly disturbed,

(b)

Fig. 8. Microstructure of the recovered samples after shearing for = = 0 : (a) y = 0.25. Formation of a dislocation wall (SW) parallel to the shearing direction (SD) through several cells; (b) 7 = 1. Regular array of DDW.

GASPI~RINI et al.: SHEAR DEFORMATION OF AI whereas inside the shear band it mainly consists of narrow cells elongated in the shearing direction, as for ~ = 0 - . 3.3.2.2. Recovered Specimens • Shearing along ~ - - - 0 . For 7 = 0 . 2 5 , the formation of dislocation walls parallel to the shearing direction is seen through several cells [Fig. 8(a)]. With increasing shear, the dislocation walls are progressively transformed into DDW parallel to the shearing direction. The initial cell microstructure is replaced by a regular array of DDW and subgrain boundaries [Fig. 8(b)]. • Shearing along z~ ¢ 0 . Dense dislocation walls parallel to the shearing direction are the main feature. However, for 7 = 1, dislocation walls parallel to RD are also found (Fig. 9). 3.3.3. Comparison between the microstructures. The shear deformation tends to form elongated cells in the shearing direction. The cell size is smaller in the as-rolled specimens (from 0.15 to 0.25 l~m wide) than in the recovered ones (from 0.4 to 0.6 gm wide). In the as-rolled specimens, the microstructure is "composite", with localized bands and almost unchanged microstructure outside the bands. The spatial distribution of bands depends strongly on the shearing direction: it is regularly spread into the matrix for ~ = 0: whereas it is highly concentrated into a macroband for other directions, especially for between 3 0 and 75. In the recovered specimens, the microstructure is homogeneous irrespective of ~ and no banding is observed.

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3.4. Texture analysis The initial crystallographical texture and its evolution with shearing for both the as-rolled and the recovered samples has been analysed considering the main components of the ODF. 3.4. I. hTitial texture. It was verified that the initial texture was identical for the as-rolled sheet and the recovered sheet. This texture [Fig. 10(a)] is characteristic of cold-rolled aluminium alloys [24]. with high values of the ODF for orientations close to the "brass" orientation ~110}(1125, the "'copper" orientation ~112}(111 ~ and an "'S'" orientation close to 11231(6345, 3.4.2. Et'olution of the texture with shearing. Texture measurements were performed on the as-rolled samples before (7 = 0.15) and after ( 7 = 0.25 for ~ = 6 0 , 7 = 1 for a = 0 ) the shear band propagation, and on the recovered samples after large strains ( 7 = 0.45 for ~ = 0 , 7 = 1 for = 60). The most significant I 111] pole figures are presented in Figs 10(b)-(d). For moderate strains the textures are only slightly modified. The main pole reinforcements of the initial pole figures are still present after the shear tests, with a larger dispersion [compare Fig. 10(c) with Fig. 10(a) rotated by 6 0 around the normal direction]. After larger strains [Figs 10(b) and (d)] some initial components are still present (especially the "'brass component" which appears stable with shear) but the initial orthotropy with respect to the rolling and transverse directions has disappeared and is replaced by a centrosymmetry reflecting the new deformation.

Fig. 9. Microstructure of the recovered sample after shearing for a = 60 (7 = 1).

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GASPI~-RINI et al.:

SHEAR DEFORMATION OF AI

SD

SD

a)

b)

--- N=3

N--4

SD

c)

d)

Fig. 10. {111} pole figures: (a) initial sheet: (b) as-rolled samples and recovered samples, :~ = if, 7 = 1; (c) as-rolled sample, x = 6 0 , 7 = 0.25, (d) recovered sample, ~ = 60 ~, ;, = 0.4.

Two i m p o r t a n t points should be noticed. (i) F o r ~ = 60 ° after 7---0.25 the textures are exactly the same if the shear b a n d zone is taken into a c c o u n t or not in the m e a s u r e m e n t s (using different collimators). Thus, the shear b a n d s do not modify the overall texture, p r o b a b l y because o f the weak volume fraction occupied by the bands. (ii) F o r ~ = 0 ° the texture evolution is exactly the

same for the as-rolled a n d the recovered samples, even after large strains [Fig. 10(b)]. F o r ~ = 60', the texture evolution o f the recovered specimens is more dispersed t h a n in the as-rolled specimens, but is qualitatively similar.

4. DISCUSSION In the following discussion, we analyse the material

GASPI~RINI et al.: SHEAR DEFORMATION OF AI behaviour during the shear tests going from the macroscopic aspects to the microscopic ones, and trying to exhibit the main important factors for strain localization. First, the global aspects are considered: sample end effects and strain-path changes. Then the role of the anisotropy due to the crystallographic texture is examined. Finally, the differences in microstructural mechanisms between the as-rolled and the recovered samples and their consequence on the hardening curves are pointed out.

4.1. Macroscopic mechanical behat'iour 4.1.1. Shear band initiation. As already mentioned in Section 3.2.1, the macroscopic shear bands initiate always from the corners of the specimen that are subjected to compressive normal stresses. This peculiarity can be understood by examining a simple finite-element analysis of the stress distribution close to the ends of the specimen. Such calculations--using standard plasticity, a Hill yield function and an isotropic hardening--show that the shear stress starts with a zero value at the very corner of the specimen (for large amounts of shear this is only approximately true since the stress-free end of the specimen turns with respect to the shearing direction) and then rapidly increases to the average value given by the ratio between the shearing force and the area of the longitudinal section of the specimen. On the contrary, the normal stress starts from a maximum value at the corner, and then decreases rapidly with distance from the end of the specimen (Fig. I 1). The resulting stress state leads to a maximum value of the shear stress at a point which is rather close to the corner and on a direction which is close to the shearing direction, i.e. close to the initial direction of the macroband. This analysis shows that the maximum shear stress may be

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considered responsible, at least for some orientations of the shearing, for the initiation of the macrobands. It appears then that the boundary effects, already evoked for local inhomogeneities in a sheared steel [16], are not negligible for strain localization initiation, even if an optimized geometry is used. 4.1.2. Macroscopic strain-path change. The sequence cold-rolling followed by shear involves a strain-path change which depends on the direction of shearing. It can be characterized by the parameter ®, the cosine of the angle between the two successive strain rate tensors, as initially proposed by some authors [25]. In previous studies [16, 17, 19], the occurrence of an earlier flow localization after reloading was correlated with the "'orthogonality'" of the path change (® = 0). If we consider here that the rolling may be represented by a simple shear in the (RD, ND) plane and the shear test by a simple shear into axis rotated by :t in the plane of the sheet (RD, TD), the 19 parameter is proportional to sin(2:0 and vanishes for shearing along RD or TD, which are not the direction of most severe localization in our experimental results. Then this analysis is too macroscopic to permit an explanation of the differences in localization with ~ and suggests that the microstructural mechanisms have to be taken into account.

4.2. Crystallographic aspects Texture instability and geometrical softening are known to promote strain localization [10, 12.20]. Geometrical softening caused by the texture evolution may promote instability if the decrease in local stress due to the lattice rotations is not balanced by sufficient hardening. As a first approximation, the tendency for the experimental textures to promote or

MPa . . ~ - - .~ - 4 2 0 --.~ - 3 4 0 •~ - -

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140

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GASPt~RINI et al.: SHEAR DEFORMATION OF AI

not geometrical softening was examined using mean orientation factors m and M, relating global and local stresses, and corresponding to a Sachs-type model and to a Taylor model, respectively: • for a homogeneous stress tensor with only a non-zero shear component z, ill is defined here as m = YF(g)r(g)/YF(g)z, where r(g) is the maximal resolved shear stress among the octahedral slip systems for the orientation g, with the sum running over all the maxima of the ODF of the measured texture; • M is the Taylor factor for the polycrystal submitted to a homogeneous shear strain increment AT. It is defined as M = A W/ATrc and was calculated with a low strain-rate sensitivity viscoplastic model [26]. AW is the plastic work increment and z, the critical resolved shear stress. The variations of m and 1/M with z are given in Fig. 12, for the initial and the deformed textures. The trends are similar for the two models: the lower values correspond to angles with intense localization and do not increase with strain. Whatever the hypothesis concerning the slip activity--single slip in the Sachs model, multiple slip in the Taylor model--the mean orientation appears then "harder" when the material is sheared out of the initial orthotropy axis. Actually for z~= 3 0 - 6 0 the flow stress of the as-rolled samples is slightly higher than for the other angles (Fig. 2), but this is not true for the recovered samples. Moreover, the occurrence of intense localization is not correlated with a global geometrical softening. Besides, for all angles, the variation of the orientation factors is very low before the shear bands propagation (7 = 0.15). For ~ = 0 ,

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.

60

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Fig. 12. Mean orientation factors m and I~M for shear in the c¢direction.

where large strains can be reached, the m and 1 M decrease with strain is clearer. In this case the initial and final texture are exactly the same for the as-rolled and the recovered samples, but the shear bands occur only in the as-rolled samples. These results suggest that the plateau in the (r,7) curves and the strain localization would rather result from competition between microstructural hardening and softening than from competition between textural softening and microstructural hardening. That means that the role of the crystallographic texture has to be examined for the method in which the local lattice rotations influence the local deformation mechanisms, which require further investigation. 4.3. Microstructural mechanisms 4.3.1. Relation between stoface relief and bulk microstructure. The observations reported above at different scales allow for a good description of the spatial distribution of the deformation during the shear tests, from the very microscopic to the macroscopic level. In particular it can be noticed that the heterogeneities of the dislocation substructure are well correlated with the observations at lower magnifications [compare, for example, Figs 4(a) and 8(b) for the recovered samples, and Figs 4(b) and 7(b) for the as-rolled samples]. Moreover, the grids show unambiguously that the shear bands correspond to highly deformed zones outside of which the strain evolution is Very small. 4.3.2. Ez,olution of the microstructure with shearhlg. The TEM observations permit the understanding of the transformation of the initial microstructure, especially when the shearing direction coincides with the rolling direction. (i) For the recovered samples, the deformation is homogeneous, thanks to the relatively low initial dislocation density organized into a regular array of sub-boundaries. During shearing two concomitant processes occur: formation of dislocation walls parallel to the shear plane causing hardening, and refinement of the walls into subgrain boundaries causing dynamic recovery. Then the saturation stage observed on the macroscopical T vs 7 curves is explained by a balance between hardening (decrease of the cell size by new wall formation) and dynamic recovery (incorporation and/or annihilation of dislocations into the walls) which can develop everywhere simultaneously. In this case, roughly speaking, no specific direction is preferred in the initial microstructure, so that its evolution may be independent of the ~t angle. (ii) For the as-rolled samples, a well-organized dislocation microstructure is initially present. It contains in particular the so-called DDWI walls which are typical of the shear-banding during cold-rolling, similar to previous descriptions

GASPI~RINI et al.: SHEAR DEFORMATION OF AI [6.27] of this alloy. This initial substructure constitutes obstacles for the new strain path. The shearing creates dislocation walls parallel to the shear plane and highly elongated cells in the shearing direction, and the build-up of this structure destroys the DDWl walls progressively. The mechanism seems to be as follows: initiation of shear band destroying the initial DDWs by intense dislocation glide, which in turn produce the dislocation avalanche at constant stress, saturation of the shear-banding and initiation of a new shear band. This is consistent with the modelling of shear bands for copper single crystals in tension [28]. Then the saturation stage in this case would be due to the successive action of shear bands under constant stress. For the samples tested at angles :~ to the rolling direction the mechanism is similar--widening of the macroband due to shear band saturation--but more complex since both the DDWI and DDW2 walls can be strong barriers to subsequent dislocation glide and reduce the mean free path. The saturation stage is very short because of the rapid strain localization into macrobands which results in damage and fracture. We can suggest that in this case, the primary destruction of the initial microstructure causes local softening and then the localization is spatially favoured by an avalanche mechanism, as proposed in previous studies [29, 30]. For :~ = 90 . the DDW1 are expected to be less efficient obstacles (but not the DDW2), and actually the macroband is larger than for the other angles :~ ~ 0 . That means that the DDWI and DDW2 act differently in the local softening mechanism. The specific effect of the DDW2 is not clear from the present study since the observations inside the macroband are similar for all cases. However, the initial microstructure appears clearly to form more efficient obstacles to dislocation glide when the shearing direction is out of the initial orthotropy axis. In this discussion, only the geometrical features of the dislocation configurations have been considered, because the particles do not seem to have a great influence on the substructure formation, it has already been noticed on this alloy [6, 27] that fine particles were associated with cell walls at lower strains, but the cell size was quickly refined to less than the interparticle spacing for large strains. However, as detailed below, the coarse particles" morphology may be very important in damage development. 4.4. Damage mechanisms

The development of macrobands is accompanied by damage, and this is particularly true for the shearing of the as-rolled samples out of the rolling direction, where numerous cracks linked to coarse

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particles are visible. This is due to the incompatibility conditions at the precipitate-matrix interfaces since the particles are brittle. Under macroscopic homogeneous shear, the rotation of a material segment is zero only if it is along the shearing direction: as the coarse particles are initially roughly aligned along the rolling direction, damage development is then naturally favoured when shearing at direction ~ ~ 0 . For the recovered specimens, the damage events are less pronounced, because of the easier plastic accommodation of the incompatibility strains near the particle-matrix interfaces. The macroscopic cracks form preferentially inside the band and at the interface between the macroband and the low deformed material: this can also be viewed as incompatibility accommodation. Moreover, their mean direction is not far from the macroscopical maximum shear stress direction, and we can notice that fracture along the characteristic surface had been already observed [31] in plastic instability during torsion tests of a high strength steel.

5. CONCLUSION In this work, we have described the strain localization at different levels, the microstructure and the texture evolution during shear tests of a hardly cold-rolled sheet of a commercial aluminium alloy. The first conclusions from these investigations are as follows. • Macroscopically, the initiation of the strain Iocalizations occurs in stress concentration areas where the maximum shear stress is important. • The occurrence of the localization strongly depends on the initial microstructure. There is no localization during the shear tests of the recovered material. This is linked to the relative homogeneity of the substructure and the absence of strong barriers to the dislocation glide for the second path. • The initial and induced crystallographic textures are similar for the recovered and the as-rolled samples. Mean orientation factors deduced from the measured textures do not suggest a geometrical softening. • For the as-rolled specimens, the shear band initiation does not depend on the angle ~ between the initial rolling direction and the shearing direction, but the shear band growth depends strongly on ~. However, the microstructural features are similar-formation of DDW parallel to the shear plane and elongated cells in the shearing direction--but not the spatial distribution of the shear bands: for ~ = 0, the shear bands are narrow and regularly separated by low-deformed material: for ~ 4:0 the shear bands are highly concentrated into one macroband. These differences are mainly attributed to the way the dislocations overcome the different DDW formed during rolling, and are increased by the damage

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initiation m e c h a n i s m s p r o m o t e d by testing out of the symmetry axis o f the initial morphological texture. F u r t h e r work is needed to model these p h e n o m ena, in order to predict the response to strainp a t h changes based o n the interactions at the microstructure scale. Acknowledgements--The authors wish to acknowledge the partial support of Pechiney for this work and are grateful to B. Bacroix for her help in the Taylor factor calculations.

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