- Email: [email protected]
Microstructure and microtexture evolution during strain path changes of an initially stable Cu single crystal
Available online at www.sciencedirect.com
Acta Materialia 58 (2010) 2799–2813 www.elsevier.com/locate/actamat
Microstructure and microtexture evolution during strain path changes of an initially stable Cu single crystal H. Paul a,b,*, C. Maurice c, J.H. Driver c a
Polish Academy of Sciences, Institute of Metallurgy and Materials Science, 25 Reymonta St., 30-059 Krakow, Poland b Opole University of Technology, Mechanical Department, 5 Mikolajczyka St., 45-271 Opole, Poland c ´ Ecole des Mines de Saint-E´tienne, Centre SMS, Laboratoire PECM CNRS UMR 5146, 158 Cours Fauriel, 42023 Saint-E´tienne, Cedex 2, France Received 3 August 2009; received in revised form 16 November 2009; accepted 31 December 2009 Available online 15 February 2010
Abstract The microstructure and microtexture evolution in a deformed Goss oriented crystal were characterized after a sample rotation and consequent change in strain path, over a range of scales by optical microscopy, high resolution scanning electron microscopy equipped with field emission gun and electron packscattered diffraction facilities and transmission electron microscopy orientation mapping. High purity copper single crystals with initial Goss{1 1 0}h0 0 1i orientation were channel-die compressed 59% to develop a homogeneous structure composed of two sets of symmetrical primary microbands. New samples with ND rotated orientations of Goss{1 1 0}h0 0 1i, brass{1 1 0}h1 1 2i, M{1 1 0}h1 1 1i and H{1 1 0}h0 0 1i, were then cut out and further compressed in channel-die by a few per cent. The change in flow stress could be correlated with the change in dislocation substructure and microtexture, particularly along shear bands initiated by the strain path change. In the H{1 1 0}h0 1 1i and M{1 1 0}h1 1 1i orientations, the flow stress increased by Taylor factor hardening then decreased by intense macroscopic shear band (MSB) formation. In the softer brass orientation and in the absence of Taylor factor hardening, more diffuse MSB formation occurred. The local rotations in the band were used to deduce the possible local slip systems initiated during the strain path change. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Shear bands; Changing strain path; Orientation mapping; Texture; Copper
1. Introduction Many industrial processes typically involve multi-axial strain paths. A change in the strain path may lead to significant transitions in microstructure, deformation texture and mechanical behavior. From transmission electron microscopy (TEM) investigations, it is well known that the dislocation microstructure is sensitive to the applied deformation mode, and this “sensibility” increases with applied deformation [1,2]. During a strain path change, the reorientation of the pre-existing dislocation barriers is typically accompanied by transients in softening or harden* Corresponding author. Address: Polish Academy of Sciences, Institute of Metallurgy and Materials Science, 25 Reymonta St., 30-059 Krako´w, Poland. Tel.: +48 126374200. E-mail address: [email protected] (H. Paul).
ing behavior resulting from the plastic anisotropy induced during the previous deformation [3–5]. These transients have been the object of several recent theoretical papers, which model their behavior on the basis of abrupt deformation microstructure evolution [6–10]. Experimental results, e.g., Refs. [11–14], have shown that a change in plastic flow direction can promote a transition from a homogeneous to a heterogeneous mode of deformation. This can be temporary (a transient stage) or in some cases leads to localized shear banding and eventually failure. The mechanical response during a change in strain path should therefore be examined with regard to both the general and local changes in microstructure and texture. This is not easy in polycrystals, since dislocation arrangements develop which are characteristic of specific grain orientations [15,16] and lead to mechanical anisotropy with quite different behavior after a strain path change [14,17].
1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2009.12.055
2800
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Microscopic observations of many channel-die compressed metals indicate that shear banding is preceded by the formation of obstacles to homogeneous dislocation glide in individual crystallites. The formation of barriers is strongly influenced by the crystallography and stacking fault energy (SFE). If the obstacles are fine twin-matrix lamellae typical of low SFE metals, the shear bands (SB) are classified as brass type [5,18,19]. If the precursory obstacles are the elongated dislocation walls of a cell block structure, the SB are of the copper type; they are typically observed in materials with high or medium SFE [12,20]. The present work investigates the latter case of copper-type shear bands. A fundamental contribution to understanding slip in prestrained crystals and slip organization into shear bands has been provided by Basin´ski and Jackson [21]. They concluded that, in general, dislocation structures are unstable with respect to slip on one system, with a single exception, when slip takes place on the same plane during pre- and re-straining. The obstacles formed along active slip planes have a finite strength and, under some conditions, may be broken. In most previous work, the strain path change was such that the second deformation activated significantly different slip systems from the pre-strain. The question then arises as to whether the resulting plastic instabilities are due to changes in slip activity, in deformation microstructure or both. It is quite difficult to separate these effects, but a guide to this can be obtained by looking at samples where the slip systems do not change dramatically. This is the situation of a set of {1 1 0}hu v wi orientations in channel-die. For a wide range of hu v wi directions, two common slip systems are predominant, and other minor systems can be activated according to the hu v wi direction [22]. In this study, the pre-strain was performed on the well-known Goss{1 1 0}h0 0 1i orientation, which deforms homogeneously in plane strain compression up to strains of 1–1.5 [23–25]. The influence of this substructure on microstructure evolution, particularly SB formation, was analyzed after strain path changes by compression along new directions (obtained by cutting the pre-strained sample) corresponding to the brass{1 1 0}h1 1 2i, M{1 1 0}h1 1 1i and hard{1 1 0}h0 1 1i orientations. These structures after small re-strains were then compared with those of
(a)
monotonically deformed Goss samples. The investigations were performed on single crystals of pure copper, which represent many medium–high SFE face-centered cubic metals. In most cases, the study of slip localization requires examination of relatively large areas containing small shear bands; high resolution electron backscatter diffraction (EBSD) is particularly suited for this type of problem, since shear bands leave a clearly defined microtexture signature. 2. Experimental procedures High purity (99.998%) copper single crystals with Goss{1 1 0}h0 0 1i (or G) initial orientation, were grown from the melt by the Bridgman method. Samples with dimensions 10 10 10 mm3 were carefully machined using a wire saw from the as-grown ingots and deformed in a mechanical Instron machine at a nominal strain rate of 104 s1. The initial orientation of the samples was within 2° of the ideal Goss orientation. All samples were deformed in plane strain compression using a channel-die device. The experiment was carried out in two stages. In the first stage, the Teflone lubricated samples were deformed up to true (logarithmic) strains of 0.9 (thickness reduction of 59%) at room temperature. In order to reduce the frictional constraints between the specimen and the compression die walls, the Teflone films were regularly changed at strain intervals of 0.15. The final deformations were such that two symmetrical sets of clearly defined microbands could be observed. This pre-deformed sample was then sectioned (wire saw cutting of new samples with dimensions 4 4 10 mm (height length width) to provide deformed crystals of Goss{1 1 0}h0 0 1i, brass{1 1 0}h1 1 2i, M{1 1 0}h1 1 1 i and hard{1 1 0}h0 0 1i (or H) orientations. Fig. 1 gives the sectioning scheme and the sample reference notations. The first three samples were then compressed a further 10%, whereas the hard{1 1 0}h0 1 1i orientation was only compressed 3% (since the intense shear banding in this crystal promoted early shear failure). In each case, the sample geometry was maintained constant (the sample height to length ratio of the new test piece was equal to 1 at the beginning of the second stage). New orientations are
(b)
(c)
TD2
TD2
TD2
ED2 ED2
ED1 35o TD1
(d)
55o
90o ED2
ND1=ND
Fig. 1. Schematic presentation of the sample cut from pre-deformed Goss single crystal: (a) no rotation, Goss–Goss; (b) rotation 35° around ND, Goss– brass; (c) rotation 55° around ND, Goss–M{1 1 0}h1 1 1i; (d) rotation 90° around ND, Goss–hard{1 1 0}h0 0 1i. ED1–TD1 coordinate system refers to the pre-deformed sample, ED2–TD2 coordinate system refers to the sample deformed after the strain path change.
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
(a)
ED
1
ND1=2
2801
(b)
ED1=2
ND1=2
ED2
(c) o
35
TD1=2
TD2
2 11 1
111
3 11 1
TD
ND1=2 TD2
1 11
111
(d)
ED2 o
55
ND1=2
ED2
(e)
TD2
111 4
Fig. 2. Stereographic projections (in (1 1 0) plane) of analyzed orientations. Schematic presentation of the slip planes in samples prepared from predeformed Goss crystal: (a) Goss{1 1 0}h0 0 1i – 1; (b) brass{1 1 0}h1 1 2i – 2; (c) M{1 1 0}h1 1 1i – 3; (d) hard{1 1 0}h0 0 1i – 4.
shown in Fig. 2a on a stereographic projection, while the locations of the important slip planes are shown schematically in Fig. 2b–e. The microtextures and microstructures were investigated by a combination of local orientation measurements in TEM and scanning electron microscopy (SEM) using a 200 kV Philips CM20 with semi automated Kikuchi (or spot) pattern analysis and a high resolution JEOL JSM 6500F with automatic EBSD software. Specimens for detailed microscopic investigations were cut from the deformed crystals with edges parallel to ND and ED2 (longitudinal section of the re-strained samples), where: ND and ED are the normal and extension directions, respectively. They were mechanically ground with SiC papers. The TEM thin foils were prepared by a twinjet technique using TenuPol-5 in a standard Struers D2 solution (10 V/5 °C). The microstructure/microtexture evolution during deformation was analyzed by systematic local orientation measurements (orientation mapping) in TEM using a step size within the range 10–35 nm. Post-processing analysis of the orientation maps was performed using HKL Technology Channel 5 software. Systematic local orientation measurements on larger areas were performed by high resolution scanning electron microscopy equipped with field emission gun and electron packscattered diffraction facilities (FEG–SEM–EBSD) using backscattered electrons at 20 kV to reveal crystallographic contrast. In that case, microscope control, pattern acquisition and solution were also carried out with the HKL Channel 5 system. In all cases, a step size of 0.1 lm or 0.2 lm was applied. The surfaces of the specimens taken from the longitudinal section (perpendicular to TD2), where TD is the transverse direction, were also mechanically ground with SiC paper followed by a paste containing diamond particles of 3 lm. The last preparation step was electropolishing with Struers D2 electrolyte (10 V/10 °C). For more global observations on the sample scale, optical microscopy was used on mechanically and chemically polished/etched samples. Local orientation data, obtained
by TEM and SEM/EBSD techniques in the longitudinal plane (ND–ED2) were transformed to the standard (ED2–TD2) reference system, and presented in the form of {1 1 1} pole figures. 3. Results 3.1. Stress–strain curve The experimentally measured true stress–strain curves, presented in Fig. 3a, were calculated using standard definitions, r = F/S and e = ln (to/t), where F, S, to and t are the current compression load, compression surface and specimen thickness (initial and actual), respectively. They clearly indicate changes in true stress as a function of true strain due to the changing strain path. The first part of the stress–strain curve, up to 0.9 strain, is due to monotonic straining of the stable Goss{1 1 0}h0 0 1i orientation. In accordance with earlier investigations, e.g., Ref. [25], this part of the curve can be divided into three work-hardening stages (II, III and IV) described by different work-hardening coefficients. After the change in strain path, the subsequent part of the true stress–strain curve reveals quite different behavior, due to the “soft” or the “hard” behavior of the new crystal orientations deformed in plane strain compression. The samples exhibited significant differences in flow stress levels in the general order: hard > M > Goss > brass. The relationship between flow stress and crystal orientation may be correlated, to first order, with the average Taylor factor for channel-die compression [22]. The hard{1 1 0}h0 1p1i ffiffiffi orientation with the highest Taylor factor MT of 2 6 (4.9) is always substantially harder and represents the highest value of the flow stress peak just after the strain path change. The M{1 1 0}h1 1 1i orientation possesses a lower Taylor factor of 3.67. After the peak stress, both orientations reveal a clear softening, which will be shown pffiffiffi to be due to shear banding. p The brass{1 1 0}h1 1 2i ð 6Þ and ffiffiffi the Goss{1 1 0}h0 0 1i ð 6Þ orientations are “softer” and
2802
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Continuous straining
Straining after changing deformation path
Taylor (H)
1.0
M{110}<111> H{110}<011> Brass{110}<112>
Δσ/σGoss
True stress (MPa)
600
400
H Taylor (M)
0.5
M
200 {110}<001> (1) pr6 - 1 Goss initial {110}<001> pr7 - 2 Goss (2) {110}<111> (3) pr6 - 3 {110}<111> {110}<011> pr6 - 4 Hard (4) {110}<112> pr7 - 5 Brass (5)
0 0
0.4
0.8
0.0
brass 1.2
True strain
(a)
0
0.1
0.2
True strain
(b)
Fig. 3. (a) True stress–true strain curves for pre-strained samples and deformed after strain path change; (b) stress–strain curves of crystals during restraining relative to Goss crystal.
represent significantly lower flow stresses, without any visible stress peaks. Note that the re-shaped Goss crystal becomes slightly softer, possibly by relaxation, but on further straining does not harden. The stress–strain curves after the strain path change are given in more detail in Fig. 3b as values relative to those of the “monotonic Goss”, i.e., (rcrystal rGoss)/rGoss. In all cases, they fall below the value expected of the Taylor factor, indicating softening of the active slip planes. 3.2. Microstructure and texture characteristics in monotonically deformed Goss oriented single crystal Optical micrographs of the Goss sample deformed to 0.9 reveal an almost homogeneous distribution of slips (Fig. 4a) without any significant tendency to strain localization. The orientation maps in Fig. 4b and c were made at true strains of 0.2 and 0.9, i.e., at the beginning and the end of pre-straining just before the strain path changes. For the lower deformation, the misoriented dislocation walls strictly coincide with the traces of the {1 1 1} planes on the longitudinal plane (Fig. 4d). At higher deformations, the microstructure progressively appears more “wavy”. Owing to significant spatial variations in the dislocation walls a strong scattering of the h1 1 1i poles was observed (Fig. 4e). This relatively homogeneous substructure constitutes the basic material microstructure for the subsequent strain path changes. The microband structures observed at the meso-scale by the FEG–SEM–EBSD system were very similar to the dislocation microstructures observed by TEM. The TEM observations and local orientation measurements of continuously deformed in Goss-position samples were carried out on longitudinal sections at deformations of 0.12, 0.62 and 1.12 (logarithmic strains). In accordance with previous
investigations, homogeneously deformed crystals of Goss orientation remained stable up to large strains and did not reveal the formation of band-like strain inhomogeneities; only a uniform dislocation cell substructure was formed (Fig. 5a), as observed for example by Bauer et al. [23], Ferry and Humphreys [24] and Borbe´ly et al. [25] on similarly oriented Cu crystals. Up to strains of 1.12, the microstructures consisted of two complementary sets of elongated bands, initially inclined at ±35° to ED (Fig. 5a–c). Both sets of dislocation walls marking the bands were inclined very close to the expected traces of the active {1 1 1} slip planes. As a result of their intersection, rectangular cells with dimensions of 1–2 lm, were formed. Each set of dislocation bands occupied nearly the same volume of the crystal, but usually one set of the walls was more pronounced locally. For higher strains, the microstructure appeared to be progressively more “wavy” (Fig. 5c), and the traces of the active slip systems were not as regular as those observed at lower deformations, indicating significant cross-slip in this stage IV deformation. The orientations of areas corresponding to the above microstructures were analyzed by TEM orientation maps and displayed in Fig. 5d–f, as {1 1 1} pole figures. They confirm the stability of the initial orientation at low deformations and clearly visible scattering of the h1 1 1i poles around ND and ED at higher deformations. 3.3. Microstructure and texture evolution during a strain path change The following four types of changing strain path were applied to the initially pre-deformed samples: Goss{1 1 0}h0 0 1i ? Goss{1 1 0}h0 0 1i deformed 0.11), no rotation.
(additionally
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
2803
Fig. 4. Microstructure and texture development in continuously deformed sample of Goss orientation. (a) Sample scale: optical image of the longitudinal section after deformation of 0.9; (b and c) orientation maps presented as a “function” of Euler 2 angle, showing microstructure development for samples deformed: (b) 0.15; (c) 0.9; (d and e) {1 1 1} pole figures corresponding to (b) and (c), respectively. FEG–SEM–EBSD local orientation measurements in longitudinal plane.
Goss{1 1 0}h0 0 1i ? brass{1 1 0}h1 1 2i (0.10), rotation 35° around ND. Goss{1 1 0}h0 0 1i ? M{1 1 0}h1 1 1i (0.08), rotation 55° around ND. Goss{1 1 0}h001 i ?hard{1 1 0}h001i (0.03), rotation 90° around ND. The description of all 12 slip systems using the Bishop and Hill notation is given in Table 1. The principal slip systems expected to operate in the new configuration can be determined by a classical relaxed Taylor model for
channel-die compression of {1 1 0}hu v wi crystals (e.g., Ref. [22]). On the assumption of homogeneous deformation and equal critical resolved shear stress, they are listed in Table 2. Apart from the exact Goss and hard orientations, slip is expected (in equal quantities) on the +a2 and b1 systems, but which of course make different traces with the sample surfaces. In the Goss orientation, slip occurs on the same two planes, but each slips in two directions (co-planar or CP slip). For the hard orientation, an additional slip plane (with two directions) should be activated.
2804
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Fig. 5. Microstructure and texture development in continuously deformed sample of Goss orientation: (a) early and (b) advanced stages of cell substructure formation; (c) microstructure with dominating family of microbands; (d–f) corresponding {1 1 1} pole figures. Deformations of: (a and d) 0.12; (b) and (e) 0.56; (c) and (f) 1.12. TEM local orientation measurements in ND–ED2 plane.
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
2805
Table 1 Description of the slip systems in Bishop and Hill notation. Slip plane
111
Slip direction Bishop and Hill notation
011 a1
111 101 a2
110 a3
011 b1
111 101 b2
Table 2 Active slip systems operating in all analyzed orientations (classical relaxed Taylor model for channel-die compression). Crystal orientation
Active slip systems (Bishop and Hill notation)
Goss(1 1 0)½0 0 1 Brass(1 1 0)½1 1 2 M(1 1 0)½1 1 1 Hard(1 1 0)½1 1 0
a1,+a2, b1,+b2 +a2, b1 +a2, b1 (+ minor slip on –a3,+b3,+d1 and –d2) a1, a2, b1,+b2,+c1, c2,+d1, d2
3.3.1. Microstructure evolution, optical microscopy Detailed optical microscopy observations were carried out on longitudinal sections characteristic of the re-strain,
110 b3
011 c1
111 101 c2
110 c3
011 d1
101 d2
110 d3
i.e., ND–ED2 section. The microstructures observed after a change in deformation path showed a strong tendency to strain localization, but the apparent shear planes were clearly orientation dependent. 3.3.1.1. Goss{1 1 0}h0 0 1i ) Goss{1 1 0}h0 0 1i, no rotation. Although the crystal orientation is unchanged, the sample is now much shorter and tends to undergo a macroscopic flow along two arms at 45° to ED. This flow pattern is typical of large strain compression of “equiaxed” samples and appears to be accommodated by two sets of macroscopic shear band (MSB), as shown in Fig. 6a. The bands penetrated the whole sample along planes parallel to TD.
Fig. 6. Macroscopic shear band formation in: (a) continuously deformed Goss {1 1 0}h0 0 1i (true strain: 0.9 + 0.1) oriented samples then after changing strain path; (b) brass{1 1 0}h1 1 2i (0.9 + 0.1); (c) M{1 1 0}h1 1 1i (0.9 + 0.08); (d) hard{1 1 0}h0 0 1i (0.9 + 0.03) orientations. Optical images in longitudinal ND–ED2 planes (of 2nd deformation). Macroscopic shear bands in (e) M{1 1 0}h1 1 1i and (f) hard{1 1 0}h0 11 i orientations observed in the plane perpendicular to ED2. Areas marked in (a–d) show locations of more detailed investigated by TEM and FEG–SEM–EBSD.
2806
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
3.3.1.2. Goss {1 1 0}h0 0 1i ) brass{1 1 0}h1 1 2i type rotation (Fig. 6b). The pre-deformed Goss sample was rotated 35° around ND towards brass{1 1 0}h1 1 2i and then further deformed to a strain of 0.1. After the final reduction, the sample had shape distortions in both ND–ED2 and ED2–TD2 sections with clearly marked traces of two intersecting and almost symmetrical families of MSB (as observed in the ND–ED2 plane). A detailed inspection on three perpendicular sections showed that the band planes of both families were not parallel to TD. 3.3.1.3. Goss {1 1 0}h0 0 1i ) M{1 1 0}h1 1 1i type rotation (Fig. 6c and e). In this case, the additional deformation was 0.08. Optical microscopy revealed significant changes in the sample shape in both the ND–ED2 and ED2–TD2 sections with clearly marked traces of two MSB families, visible in the ND–TD2 plane. Further inspection of the as-deformed sample on all sections showed that both families of the bands were situated nearly symmetrically and formed a characteristic “zig-zag” shape in the ND–TD2 plane (Fig. 6e). 3.3.1.4. Goss {1 1 0}h0 0 1i ) hard{1 1 0}h0 0 1i type rotation (Fig. 6d and f). This change in strain path promoted the most radical changes. The pre-deformed Goss sample was rotated 90° around ND and then slightly deformed 0.03. On the sample scale, the traces of two intersecting families of highly localized MSB were clearly observed in the ND–ED2 section (Fig. 6d). At the surface they form pronounced intrusions. Inspection of three orthogonal sections showed that the shear band planes were not regular, i.e., the MSB (of each family) did not lie in one plane as was clearly visible on the ND–TD2 (Fig. 6f) and ED2– TD2 sections. 3.3.2. Texture/microstructure evolution at the meso-scale: local orientation measurements by FEG–SEM–EBSD More detailed analyses of the texture and microstructure development in the MSB areas after the strain path change were performed by high resolution FEG–SEM–EBSD measurements with a step size of 200 nm and nano-scale TEM observations of the dislocation microstructure. Fig. 7a shows an orientation map measured in the ND– ED2 section within a diffuse MSB area for the sample further compressed as Goss. The map shows that the distribution of low angle boundaries (<15°) is similar to that observed at lower deformations in continuously deformed samples. The traces of one set of dislocation boundaries are inclined 15° to ED, whereas the second family has an inclination up to 45–50° to coincidence with macroscopically visible traces of SB. The initial orientation scattering is clearly visible in the {1 1 1} pole figure (Fig. 7b), and the maximum density deviates only slightly from the initial Goss position. In the case of the Goss–brass-type rotation, the orientation map (from an area of the band) in the ND–ED2 section (Fig. 7c and d) showed clusters of single bands
inclined at 40° to ED2. The walls of elongated sub-cells were situated nearly parallel to ED2. The activity of the dominant bands was responsible for a characteristic Sshaped distortion of the background microstructure. As a result the microband clusters, initially situated along ED2, changed their inclination. This led to a strong dispersion of the h1 1 1i poles (Fig. 7d), mostly due to rotations around axes near TD2. For the Goss–M-type sample rotation (Fig. 7e and f), the orientation map of the MSB area showed clusters of new generation bands inclined at 30° to ED, revealing the strong instability of this microstructure. The newly active set of microbands formed a characteristic S-shaped distortion of the background structure of elongated subcells. The corresponding {1 1 1} pole figure exhibited strong and relatively complex tendencies of orientation scattering (Fig. 7f). The maximum misorientation angle could be directly correlated with the areas within the band. In both cases (brass and M orientations), the boundaries of the background structure of elongated cells periodically change inclination with respect to the external axes when crossed by micro shear bands. The last case of strain path change is pre-deformation of Goss and secondary straining as the hard orientation. An orientation map on the longitudinal section from the area of the MSB showed a broad, highly localized band inclined at 30° to ED2 with a very sharp boundary between the band and the slightly deformed matrix (Fig. 8a and b). The corresponding {1 1 1} pole figures in Fig. 8c–e illustrate quite different textural behavior within the stable matrix and strongly rotated MSB areas. The different rotations within SB led to a wide scatter of the h1 1 1i poles so that identification of the rotation axes and hence the mechanisms responsible for crystal decomposition is difficult to obtain. Fig. 9 compares typical misorientation line scans for the five different strain paths. The monotonically deformed Goss sample revealed a relatively small orientation spread. The misorientation angles only rarely attained 10° (Fig. 9a), and the misorientation axes were close to ND. In samples further strained in Goss position after sample cutting (no rotation), a misorientation line scan along ND showed a small increase in the orientation spread occasionally up to 12° (Fig. 9b). The misorientation distribution was relatively homogeneous, and the adjacent sub-cells displayed opposite rotation senses, as reported earlier, e.g., by Ferry and Humphreys [24] and Borbe´ly et al. [25]. When the strain path is of Goss–brass type, the misorientations across the bands (line scan in Fig. 9c) show significantly higher rotations (30–40°). The same type of misorientations between neighboring elongated sub-cells reach only 15–20°. The line scan for the Goss–M sample (Fig. 9d) showed that the orientation scattering attained 30–35° when the bands crossed. Misorientations between neighboring elongated sub-cells outside the band were lower and only very rarely exceeded 10–12°.
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
2807
Fig. 7. Orientation maps displayed as a “function of Euler 2” in grayscale showing shear band formation in samples deformed: (a) continuously in Goss orientation, and after changing strain path: (c) brass, (e) M orientations, and (b, d, f) corresponding {1 1 1} pole figures. FEG–SEM–EBSD orientation measurements with step size 200 nm.
In the case of Goss–hard-type strain path change (Fig. 9e), a line scan along ND across the boundary between the band and neighboring matrix showed misori-
entations of 40–45°. The quality of the band contrast in this case was the lowest of all the samples, indicating strong strain localization within the band.
2808
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Fig. 8. Shear band formation in 3% compressed hard orientation sample after Goss pre-strain: (a) optical microstructure; (b) Kikuchi band contrast map from the area of shear band marked in (a) and {1 1 1} pole figures; (c) summary of the whole map; (d) deformed matrix; (e) shear band area. FEG–SEM– EBSD orientation measurements with step size 200 nm.
3.3.3. Evolution of the dislocation microstructure after changing deformation path: TEM observations and local orientation measurements The dislocation microstructure observed in samples deformed as Goss followed by sample cutting and further straining of 10% was similar to that observed in continuous straining after comparable reductions (Fig. 10a). The activation of secondary microbands inclined at 40–50° to ED2 was clearly visible and led to a characteristic S-shaped distortion of the primary microband family (inactive). The corresponding {1 1 1} pole figure showed a slight rotation of the crystal lattice from Goss (Fig. 10b). A line scan across both sets of microbands showed periodic lattice rotation, associated with an increase in misorientation angle up to 8–10° across the secondary microbands (Fig. 10c). In the case of the sample rotated 35° around ND towards brass, the observed dislocation microstructure was finer. The newly formed set of microbands, inclined
at 35–40° to ED2 (Fig. 11a) cut the microstructure of elongated sub-cells from the previous Goss orientation. The {1 1 1} pole figure calculated on the basis of TEM local orientation measurements corresponding to the bright field image showed a clear, broad scattering of poles (Fig. 11b). The misorientation profile across the newly activated set of microbands revealed differences in orientations which were 22–25° (Fig. 11c). The microstructure observed in the sample rotated 55° around ND, from Goss towards M, was similar to that described above, i.e., Goss–brass. The newly activated microbands were inclined at 50° to ED and penetrated the microstructure of elongated sub-cells without any significant changes in shear direction (Fig. 12a). The {1 1 1} pole figure (Fig. 12b) showed much stronger orientation scattering of orientations than before, with misorientation profiles across the new set of microbands rotated 35–40° with respect to the neighboring background microstructure (Fig. 12c).
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
2809
At a macroscopic scale, all the deformation path changes induced more or less drastic changes in softening/hardening behavior and led to macroscopic inhomogeneities of plastic flow. Since the strain path changes did not involve major changes in active slip systems (usually the same set of major systems with variations in the minor ones), it is clear that plastic instabilities induced by variations in strain path are not just due to the activation of new systems; more subtle effects of deformation microstructure play a significant role. The stress–strain behavior of the crystallites after a strain path change can be correlated, to first order, with the relative strength parameter, i.e., Taylor factor. As could be expected the initially “soft” Goss orientation became very “hard” in the H{1 1 0}h0 1 1i and M{1 1 0}h1 1 1i orientations and remained relatively “soft” in the brass{1 1 0}h1 1 2i orientation. However, the Taylor factor is insufficient to explain the detailed hardening/softening behavior; in particular, after reorienting, all the crystals immediately become softer (in relative terms) than Taylor factor hardening would indicate and then do not resume hardening during continued straining (they usually soften further). This large softening during secondary straining on the hard H and M orientations is associated with a massive concentration of slip into shear bands. Fig. 9. Misorientation line scans along ED, with respect to the first measured point for: (a) continuously deformed 59% Goss oriented sample; (b) Goss oriented sample after 69% deformation, and the change in strain path; (c) Goss–brass, (d) Goss–M; (e) Goss–hard type, respectively. FEG– SEM–EBSD orientation measurements with step size 200 nm.
In the case of the reorientation to the hard orientation, strong shear bands divided the crystal into large blocks, with a sharp boundary between the matrix and shear band. The freshly formed shear bands were composed of very fine, nearly equiaxed sub-cells (Fig. 13a). Their morphology was quite different in comparison with the background microstructure of elongated microbands. The orientation of the matrix was practically unchanged, whereas within shear bands very strong orientation scattering was observed (Fig. 13b and c) as shown by the misorientation line scan across the boundary (shear band)/matrix, where misorientations were 40–50° (Fig. 13d).
4.1. Strain path changes inducing very unstable plastic flow and intense shear banding This occurs in both the hard H and medium hard M orientations after pre-straining as Goss. The flow stress initially increases, since the resolved shear stress on the active systems immediately decreases (by a factor of 2 in the H orientation), but then strain very rapidly becomes localized into a few shear bands. By shear on these narrow bands of width 10–100 lm, the orientations within the bands undergo major changes (typical rotations of 30° for M and 40° for H), so that they tend towards single slip configurations. In the case of the M orientation, this mechanism reorients the crystal lattice about the h1 1 2i axes orthogonal to the slip plane normal and direction towards two groups of orientations near (1 5 5)½5 0 1 and ð5 4 3Þ½1 2 1. The rotations can be described as follows: ð1 1 0Þ½1 1 1 rotation of ðþÞ30 ½2 1 1 and ðÞ30 ½1 2 1 ! ð1 5 5Þ½5 0 1
4. Discussion The observations of the microstructure and microtexture changes provide a basis for discussion on the origin and nature of micro- and macro-scale strain localizations and their influence on stress–strain behavior. The most important features of plane strain compressed Goss-oriented copper single crystals after a changing deformation path may be summarized as follows:
ð1 1 0Þ½1 1 1 rotation of ðÞ10 ½2 1 1 þ ðÞ10 ½1 2 1 ! ð5 4 3Þ½1 2 1 The decomposition of the “hard” orientation, i.e., (1 1 0)½1 1 0, is difficult to describe in a simple way, mainly because of the very wide orientation scattering identified inside the band. However, two apparently successive lattice rotation tendencies towards (2 5 4)½3 2 1 and then
2810
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Fig. 10. (a) TEM microstructure showing early stage of strain localization in Goss sample continuously deformed up to 69%. (b) Misorientations with respect to the first measured point along line scan presented in (a), and corresponding line scan (c) {1 1 1} pole figure. TEM local orientation measurements in ND–ED2 plane.
(5 2 0)½1 3 1 can be detected and interpreted as due to single slip. Both cases suggest a very sharp geometric softening term dMT/de, often invoked as a criterion for plastic instability and shear banding. Note that, when the H and M crystal orientations are deformed monotonically, their behavior is very material dependent: Cu crystals of the H orientation develop shear bands after 20% strain, whereas Al crystals of the same orientation at high strains gradually break up by deformation banding into a wide set of orientations [22]. The dramatic transformation by a strain path change to localized single slip and intense shear banding raises the question of whether this particular single crystal behavior could occur in similarly oriented grains of a polycrystal. Of course in the channel-die compression experiment, the free surface along ED2 facilitates the formation of major surface relief effects due to the large slip steps of the bands at the free surface. This should not be so easy for a more constrained grain in a polycrystal, but nevertheless the softening tendency induced by localized shearing appears to be so strong that there is a very good chance of this occurring, first in some individual grains and then extending to groups of grains.
mation microstructure (Fig. 7c) are strongly perturbed by the strain path change over large areas of the crystal. The corresponding TEM micrograph in Fig. 11 showing new microbands shearing the previous cell structure suggests an instability of the previous deformation microstructure. The reorientations induced by the secondary deformation occur, to first order, about axes close to TD1 or ½1 1 0 (Figs. 7d and 11b). A more detailed analysis (Fig. 14) shows that the matrix decomposes by rotations towards two nearly symmetrically situated groups of orientations close to (1 1 1)½4 1 3 (“A”) and ð3 2 1Þ½1 4 5 (“B”), respectively, as identified within the bands. For both orientation groups, the rotation can be correlated with previous co-planar slip systems operating on the (1 1 1) and ð1 1 1Þ planes. It can be described schematically as follows:
4.2. Strain path changes followed by relatively stable plastic flow
The orientation scattering leading to the “A” and “B” groups of orientations must be based on local operating slip systems. Since the rotation axes lie close to the ½1 1 0 direction, the rotation leading to the “A” group of orientation could be regarded as a “sum” of rotations about ½2 1 1
This is the case of the Goss to brass orientation change. The microband alignments which characterize the defor-
\A"
ð1 1 0Þ½1 1 2 rotations of ðþÞ20 ½2 1 1 and
ðÞ20 ½1 2 1 ! ð1 1 1Þ½4 1 3 \B"
ð1 1 0Þ½1 1 2 rotation of ðÞ10 ½2 1 1 and
ðþÞ10 ½1 2 1 ! ð3 2 1Þ½1 4 5
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
2811
Fig. 11. (a) TEM microstructure showing strain localization in Goss to brass sample finally deformed 70%. (b) Misorientations with respect to the first measured point along line scan presented in (a), and corresponding line scan (c) {1 1 1} pole figure. TEM local orientation measurements in ND–ED2 plane.
Fig. 12. (a) TEM microstructure showing strain localization in Goss to M sample deformed finally 67%. (b) {1 1 1} Pole figure. (c) Misorientations with respect to the first measured point along line scan presented in (a). TEM local orientation measurements in ND–ED2 plane.
2812
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Fig. 13. (a) TEM microstructure showing strain localization in Goss to hard sample deformed 62%; (b) and (c) {1 1 1} pole figures for shear bands and deformed matrix; (d) misorientations with respect to the first measured point along line scan presented in (a). TEM local orientation measurements in ND– ED2 plane.
and ½1 2 1 axes, resulting from the operation of two CP1, i.e., ð1 1 1Þ½0 1 1 (b1) and ð1 1 1Þ½1 0 1 (b2) slip systems, respectively. The first slip system is expected from standard crystal plasticity for the brass orientation, whereas the second is a system that slips in the Goss orientation but should not slip in the brass (unexpected). Similarly, in the “B” group of orientations, two CP2 slip systems are
required; the expected (1 1 1)½1 0 1 (a2) and unexpected (1 1 1)½0 1 1 (a1) which was active in the previous Goss orientation. In other words, although the brass orientation should only slip on two systems during monotonic straining in channel-die compression (as confirmed by many previous studies), after this type of strain path change it slips on all four systems previously active in the Goss
Fig. 14. The two rotation tendencies observed in Goss to brass sample finally deformed by 70%: (a) {1 1 1} pole figures showing orientation of highly misoriented areas within the (“A” and “B”) bands; (b) neighboring deformed matrix with marked slip systems and rotation axes responsible for observed rotation tendencies. Red points in (a) mark the “average” matrix orientation. FEG–SEM–EBSD local orientation measurements in ND–ED2 plane. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
orientation. This could be described as a form of overshooting, but now tends to spread out the slip distribution (instead of severely restricting it as in the M and H cases). It also implies that, during the strain path change, these two previous systems (in principle now latent systems for the brass orientation) must have softened relative to the two expected active systems. This is opposite to standard latent hardening and has been termed “slow” latent hardening (as described in more detail by Beyerlein and Tome´ [6]). However, in the present case, it occurs for co-planar slip as opposed to cross-slip, which is more standard for this behavior. This brass crystal appears to be initially softer than Goss (Fig. 3) but, also in contrast to the above examples, then starts hardening up to the level of the Goss orientation. This is what is usually expected of strain path changes in polycrystals, which create transient softening stages before hardening up to the previous rates. As a final, more general, point it appears that this type of systematic single crystal study of strain path changes via orientation changes can provide significant information on the evolution of slip system hardening for non-monotonic straining conditions at large strains—a major theoretical problem. It would be interesting to extend this work to the case of hard)soft orientations and also to cases which favor (or disfavor) cross-slip onto new slip systems. 5. Conclusions Copper single crystals of the stable Goss{1 1 0}h0 0 1i orientation were deformed in a channel-die to reductions of 59% to form a well-defined structure of microbands, then ND rotated at different angles to {1 1 0}hu v wi samples which were then further deformed 3–10%. In principle, this orientation change does not require major changes in slip activity, but has the potential to change the current deformation microstructure. The evolution of deformation microstructures and microtextures during these strain path changes was then characterized by FEG–SEM–EBSD and TEM. The analysis addresses the relation between slip activity, microstructure (and microtexture) and stress– strain behavior due to the crystal anisotropy after a strain path change. The most important features may be summarized as follows. 1. The secondary straining of all deformed crystals showed different softening/hardening behavior, which could be correlated to first order with the change in Taylor factors. However, this was insufficient to describe the exact hardening and softening evolution. 2. The most radical changes were observed in the case of the sample rotated from Goss towards the “hard”
2813
H{1 1 0}h0 1 1i orientation. Even small additional strains developed intense shear bands composed of equiaxed sub-cells. The intermediate M{1 1 0}h1 1 1i orientation also formed very pronounced shear bands but at a slightly lower rate. In both cases, the microtextures suggested a rapid evolution to localized deformation by near single slip along the shear bands and consequent significant softening. 3. The brass {1 1 0}h1 1 2i orientations developed diffuse shear bands and revealed characteristic S-shaped, cyclic disturbances of the pre-existing microband structure. A detailed analysis of the local rotations associated with this substructure change leads to the conclusion that the “new” brass crystal deforms on all four systems active in the previous orientation, i.e., in contrast to standard latent hardening theory. This crystal, after an initial softening, work hardens up to the previous flow stress levels. References [1] Franciosi P, Stout MG, O’Rourke J, Erskine B, Kocks UF. Acta Metall 1987;35:2115. [2] Korbel A, Martin P. Acta Metall 1988;36:2575. [3] Peters B, Kalidindi SR, Van Houtte P, Aernoudt E. Acta Mater 2000;48:2123. [4] Peters B, Bacroix B, Teodosiu C, Van Houtte P, Aernoudt E. Acta Mater 2001;49:1621. [5] Paul H, Driver JH, Jasien´ski Z. Acta Mater 2002;50:815. [6] Beyerlein IJ, Tome´ CN. Int J Plast 2007;23:640. [7] Rauch EF, Gracio JJ, Barlat F. Acta Mater 2007;55:2939. [8] Holmedal B, Van Houtte P, An Y. Int J Plast 2008;24:1360. [9] Viatkina ME, Brekelman WAM, Geers MGD. J Mater Process Technol 2009;209:186. [10] Yapici GG, Beyerlein IJ, Karaman I, Tome´ CN. Acta Mater 2007;55:4603. [11] El-Danaf E, Kalidindi SR, Doherty RD, Necker C. Acta Mater 2000;48:2665. [12] Wro´bel M, Dymek S, Blicharski M. Scripta Metall Mater 1996;35:417. [13] Luft A. Prog Mater Sci 1991;35:97. [14] Thuillier S, Rauch EF. Acta Metall Mater 1994;42:1973. [15] Driver JH, Jensen DJuul, Hansen N. Acta Metall Mater 1994;42:3105. [16] Li BL, Godfrey A, Meng QC, Liu Q, Hansen N. Acta Mater 2004;52:1069. [17] Schmitt JH, Fernandes JV, Gracio JJ, Vieira MF. Mater Sci Eng 1991;A147:143. [18] Paul H, Morawiec A, Driver JH, Bouzy E. Int J Plast 2009;25:1588. [19] Paul H, Driver JH, Maurice C, Pia˛tkowski A. Acta Mater 2007;55:833. [20] Wagner P, Engler O, Lu¨cke K. Acta Metall Mater 1995;43:3799. [21] Basin´ski ZS, Jackson PJ. Phys Status Solidi 1965;10:45. [22] Skalli A, Driver JH, Wintenberger M. Rev Metall 1983;6:293. [23] Bauer RE, Mecking H, Lu¨cke K. Mater Sci Eng 1977;27:163. [24] Ferry M, Humphreys FJ. Mater Sci Eng 2006;A435–436:447. [25] Borbe´ly A, Maurice Cl, Piot D, Driver JH. Acta Mater 2007;55:487.
Acta Materialia 58 (2010) 2799–2813 www.elsevier.com/locate/actamat
Microstructure and microtexture evolution during strain path changes of an initially stable Cu single crystal H. Paul a,b,*, C. Maurice c, J.H. Driver c a
Polish Academy of Sciences, Institute of Metallurgy and Materials Science, 25 Reymonta St., 30-059 Krakow, Poland b Opole University of Technology, Mechanical Department, 5 Mikolajczyka St., 45-271 Opole, Poland c ´ Ecole des Mines de Saint-E´tienne, Centre SMS, Laboratoire PECM CNRS UMR 5146, 158 Cours Fauriel, 42023 Saint-E´tienne, Cedex 2, France Received 3 August 2009; received in revised form 16 November 2009; accepted 31 December 2009 Available online 15 February 2010
Abstract The microstructure and microtexture evolution in a deformed Goss oriented crystal were characterized after a sample rotation and consequent change in strain path, over a range of scales by optical microscopy, high resolution scanning electron microscopy equipped with field emission gun and electron packscattered diffraction facilities and transmission electron microscopy orientation mapping. High purity copper single crystals with initial Goss{1 1 0}h0 0 1i orientation were channel-die compressed 59% to develop a homogeneous structure composed of two sets of symmetrical primary microbands. New samples with ND rotated orientations of Goss{1 1 0}h0 0 1i, brass{1 1 0}h1 1 2i, M{1 1 0}h1 1 1i and H{1 1 0}h0 0 1i, were then cut out and further compressed in channel-die by a few per cent. The change in flow stress could be correlated with the change in dislocation substructure and microtexture, particularly along shear bands initiated by the strain path change. In the H{1 1 0}h0 1 1i and M{1 1 0}h1 1 1i orientations, the flow stress increased by Taylor factor hardening then decreased by intense macroscopic shear band (MSB) formation. In the softer brass orientation and in the absence of Taylor factor hardening, more diffuse MSB formation occurred. The local rotations in the band were used to deduce the possible local slip systems initiated during the strain path change. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Shear bands; Changing strain path; Orientation mapping; Texture; Copper
1. Introduction Many industrial processes typically involve multi-axial strain paths. A change in the strain path may lead to significant transitions in microstructure, deformation texture and mechanical behavior. From transmission electron microscopy (TEM) investigations, it is well known that the dislocation microstructure is sensitive to the applied deformation mode, and this “sensibility” increases with applied deformation [1,2]. During a strain path change, the reorientation of the pre-existing dislocation barriers is typically accompanied by transients in softening or harden* Corresponding author. Address: Polish Academy of Sciences, Institute of Metallurgy and Materials Science, 25 Reymonta St., 30-059 Krako´w, Poland. Tel.: +48 126374200. E-mail address: [email protected] (H. Paul).
ing behavior resulting from the plastic anisotropy induced during the previous deformation [3–5]. These transients have been the object of several recent theoretical papers, which model their behavior on the basis of abrupt deformation microstructure evolution [6–10]. Experimental results, e.g., Refs. [11–14], have shown that a change in plastic flow direction can promote a transition from a homogeneous to a heterogeneous mode of deformation. This can be temporary (a transient stage) or in some cases leads to localized shear banding and eventually failure. The mechanical response during a change in strain path should therefore be examined with regard to both the general and local changes in microstructure and texture. This is not easy in polycrystals, since dislocation arrangements develop which are characteristic of specific grain orientations [15,16] and lead to mechanical anisotropy with quite different behavior after a strain path change [14,17].
1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2009.12.055
2800
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Microscopic observations of many channel-die compressed metals indicate that shear banding is preceded by the formation of obstacles to homogeneous dislocation glide in individual crystallites. The formation of barriers is strongly influenced by the crystallography and stacking fault energy (SFE). If the obstacles are fine twin-matrix lamellae typical of low SFE metals, the shear bands (SB) are classified as brass type [5,18,19]. If the precursory obstacles are the elongated dislocation walls of a cell block structure, the SB are of the copper type; they are typically observed in materials with high or medium SFE [12,20]. The present work investigates the latter case of copper-type shear bands. A fundamental contribution to understanding slip in prestrained crystals and slip organization into shear bands has been provided by Basin´ski and Jackson [21]. They concluded that, in general, dislocation structures are unstable with respect to slip on one system, with a single exception, when slip takes place on the same plane during pre- and re-straining. The obstacles formed along active slip planes have a finite strength and, under some conditions, may be broken. In most previous work, the strain path change was such that the second deformation activated significantly different slip systems from the pre-strain. The question then arises as to whether the resulting plastic instabilities are due to changes in slip activity, in deformation microstructure or both. It is quite difficult to separate these effects, but a guide to this can be obtained by looking at samples where the slip systems do not change dramatically. This is the situation of a set of {1 1 0}hu v wi orientations in channel-die. For a wide range of hu v wi directions, two common slip systems are predominant, and other minor systems can be activated according to the hu v wi direction [22]. In this study, the pre-strain was performed on the well-known Goss{1 1 0}h0 0 1i orientation, which deforms homogeneously in plane strain compression up to strains of 1–1.5 [23–25]. The influence of this substructure on microstructure evolution, particularly SB formation, was analyzed after strain path changes by compression along new directions (obtained by cutting the pre-strained sample) corresponding to the brass{1 1 0}h1 1 2i, M{1 1 0}h1 1 1i and hard{1 1 0}h0 1 1i orientations. These structures after small re-strains were then compared with those of
(a)
monotonically deformed Goss samples. The investigations were performed on single crystals of pure copper, which represent many medium–high SFE face-centered cubic metals. In most cases, the study of slip localization requires examination of relatively large areas containing small shear bands; high resolution electron backscatter diffraction (EBSD) is particularly suited for this type of problem, since shear bands leave a clearly defined microtexture signature. 2. Experimental procedures High purity (99.998%) copper single crystals with Goss{1 1 0}h0 0 1i (or G) initial orientation, were grown from the melt by the Bridgman method. Samples with dimensions 10 10 10 mm3 were carefully machined using a wire saw from the as-grown ingots and deformed in a mechanical Instron machine at a nominal strain rate of 104 s1. The initial orientation of the samples was within 2° of the ideal Goss orientation. All samples were deformed in plane strain compression using a channel-die device. The experiment was carried out in two stages. In the first stage, the Teflone lubricated samples were deformed up to true (logarithmic) strains of 0.9 (thickness reduction of 59%) at room temperature. In order to reduce the frictional constraints between the specimen and the compression die walls, the Teflone films were regularly changed at strain intervals of 0.15. The final deformations were such that two symmetrical sets of clearly defined microbands could be observed. This pre-deformed sample was then sectioned (wire saw cutting of new samples with dimensions 4 4 10 mm (height length width) to provide deformed crystals of Goss{1 1 0}h0 0 1i, brass{1 1 0}h1 1 2i, M{1 1 0}h1 1 1 i and hard{1 1 0}h0 0 1i (or H) orientations. Fig. 1 gives the sectioning scheme and the sample reference notations. The first three samples were then compressed a further 10%, whereas the hard{1 1 0}h0 1 1i orientation was only compressed 3% (since the intense shear banding in this crystal promoted early shear failure). In each case, the sample geometry was maintained constant (the sample height to length ratio of the new test piece was equal to 1 at the beginning of the second stage). New orientations are
(b)
(c)
TD2
TD2
TD2
ED2 ED2
ED1 35o TD1
(d)
55o
90o ED2
ND1=ND
Fig. 1. Schematic presentation of the sample cut from pre-deformed Goss single crystal: (a) no rotation, Goss–Goss; (b) rotation 35° around ND, Goss– brass; (c) rotation 55° around ND, Goss–M{1 1 0}h1 1 1i; (d) rotation 90° around ND, Goss–hard{1 1 0}h0 0 1i. ED1–TD1 coordinate system refers to the pre-deformed sample, ED2–TD2 coordinate system refers to the sample deformed after the strain path change.
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
(a)
ED
1
ND1=2
2801
(b)
ED1=2
ND1=2
ED2
(c) o
35
TD1=2
TD2
2 11 1
111
3 11 1
TD
ND1=2 TD2
1 11
111
(d)
ED2 o
55
ND1=2
ED2
(e)
TD2
111 4
Fig. 2. Stereographic projections (in (1 1 0) plane) of analyzed orientations. Schematic presentation of the slip planes in samples prepared from predeformed Goss crystal: (a) Goss{1 1 0}h0 0 1i – 1; (b) brass{1 1 0}h1 1 2i – 2; (c) M{1 1 0}h1 1 1i – 3; (d) hard{1 1 0}h0 0 1i – 4.
shown in Fig. 2a on a stereographic projection, while the locations of the important slip planes are shown schematically in Fig. 2b–e. The microtextures and microstructures were investigated by a combination of local orientation measurements in TEM and scanning electron microscopy (SEM) using a 200 kV Philips CM20 with semi automated Kikuchi (or spot) pattern analysis and a high resolution JEOL JSM 6500F with automatic EBSD software. Specimens for detailed microscopic investigations were cut from the deformed crystals with edges parallel to ND and ED2 (longitudinal section of the re-strained samples), where: ND and ED are the normal and extension directions, respectively. They were mechanically ground with SiC papers. The TEM thin foils were prepared by a twinjet technique using TenuPol-5 in a standard Struers D2 solution (10 V/5 °C). The microstructure/microtexture evolution during deformation was analyzed by systematic local orientation measurements (orientation mapping) in TEM using a step size within the range 10–35 nm. Post-processing analysis of the orientation maps was performed using HKL Technology Channel 5 software. Systematic local orientation measurements on larger areas were performed by high resolution scanning electron microscopy equipped with field emission gun and electron packscattered diffraction facilities (FEG–SEM–EBSD) using backscattered electrons at 20 kV to reveal crystallographic contrast. In that case, microscope control, pattern acquisition and solution were also carried out with the HKL Channel 5 system. In all cases, a step size of 0.1 lm or 0.2 lm was applied. The surfaces of the specimens taken from the longitudinal section (perpendicular to TD2), where TD is the transverse direction, were also mechanically ground with SiC paper followed by a paste containing diamond particles of 3 lm. The last preparation step was electropolishing with Struers D2 electrolyte (10 V/10 °C). For more global observations on the sample scale, optical microscopy was used on mechanically and chemically polished/etched samples. Local orientation data, obtained
by TEM and SEM/EBSD techniques in the longitudinal plane (ND–ED2) were transformed to the standard (ED2–TD2) reference system, and presented in the form of {1 1 1} pole figures. 3. Results 3.1. Stress–strain curve The experimentally measured true stress–strain curves, presented in Fig. 3a, were calculated using standard definitions, r = F/S and e = ln (to/t), where F, S, to and t are the current compression load, compression surface and specimen thickness (initial and actual), respectively. They clearly indicate changes in true stress as a function of true strain due to the changing strain path. The first part of the stress–strain curve, up to 0.9 strain, is due to monotonic straining of the stable Goss{1 1 0}h0 0 1i orientation. In accordance with earlier investigations, e.g., Ref. [25], this part of the curve can be divided into three work-hardening stages (II, III and IV) described by different work-hardening coefficients. After the change in strain path, the subsequent part of the true stress–strain curve reveals quite different behavior, due to the “soft” or the “hard” behavior of the new crystal orientations deformed in plane strain compression. The samples exhibited significant differences in flow stress levels in the general order: hard > M > Goss > brass. The relationship between flow stress and crystal orientation may be correlated, to first order, with the average Taylor factor for channel-die compression [22]. The hard{1 1 0}h0 1p1i ffiffiffi orientation with the highest Taylor factor MT of 2 6 (4.9) is always substantially harder and represents the highest value of the flow stress peak just after the strain path change. The M{1 1 0}h1 1 1i orientation possesses a lower Taylor factor of 3.67. After the peak stress, both orientations reveal a clear softening, which will be shown pffiffiffi to be due to shear banding. p The brass{1 1 0}h1 1 2i ð 6Þ and ffiffiffi the Goss{1 1 0}h0 0 1i ð 6Þ orientations are “softer” and
2802
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Continuous straining
Straining after changing deformation path
Taylor (H)
1.0
M{110}<111> H{110}<011> Brass{110}<112>
Δσ/σGoss
True stress (MPa)
600
400
H Taylor (M)
0.5
M
200 {110}<001> (1) pr6 - 1 Goss initial {110}<001> pr7 - 2 Goss (2) {110}<111> (3) pr6 - 3 {110}<111> {110}<011> pr6 - 4 Hard (4) {110}<112> pr7 - 5 Brass (5)
0 0
0.4
0.8
0.0
brass 1.2
True strain
(a)
0
0.1
0.2
True strain
(b)
Fig. 3. (a) True stress–true strain curves for pre-strained samples and deformed after strain path change; (b) stress–strain curves of crystals during restraining relative to Goss crystal.
represent significantly lower flow stresses, without any visible stress peaks. Note that the re-shaped Goss crystal becomes slightly softer, possibly by relaxation, but on further straining does not harden. The stress–strain curves after the strain path change are given in more detail in Fig. 3b as values relative to those of the “monotonic Goss”, i.e., (rcrystal rGoss)/rGoss. In all cases, they fall below the value expected of the Taylor factor, indicating softening of the active slip planes. 3.2. Microstructure and texture characteristics in monotonically deformed Goss oriented single crystal Optical micrographs of the Goss sample deformed to 0.9 reveal an almost homogeneous distribution of slips (Fig. 4a) without any significant tendency to strain localization. The orientation maps in Fig. 4b and c were made at true strains of 0.2 and 0.9, i.e., at the beginning and the end of pre-straining just before the strain path changes. For the lower deformation, the misoriented dislocation walls strictly coincide with the traces of the {1 1 1} planes on the longitudinal plane (Fig. 4d). At higher deformations, the microstructure progressively appears more “wavy”. Owing to significant spatial variations in the dislocation walls a strong scattering of the h1 1 1i poles was observed (Fig. 4e). This relatively homogeneous substructure constitutes the basic material microstructure for the subsequent strain path changes. The microband structures observed at the meso-scale by the FEG–SEM–EBSD system were very similar to the dislocation microstructures observed by TEM. The TEM observations and local orientation measurements of continuously deformed in Goss-position samples were carried out on longitudinal sections at deformations of 0.12, 0.62 and 1.12 (logarithmic strains). In accordance with previous
investigations, homogeneously deformed crystals of Goss orientation remained stable up to large strains and did not reveal the formation of band-like strain inhomogeneities; only a uniform dislocation cell substructure was formed (Fig. 5a), as observed for example by Bauer et al. [23], Ferry and Humphreys [24] and Borbe´ly et al. [25] on similarly oriented Cu crystals. Up to strains of 1.12, the microstructures consisted of two complementary sets of elongated bands, initially inclined at ±35° to ED (Fig. 5a–c). Both sets of dislocation walls marking the bands were inclined very close to the expected traces of the active {1 1 1} slip planes. As a result of their intersection, rectangular cells with dimensions of 1–2 lm, were formed. Each set of dislocation bands occupied nearly the same volume of the crystal, but usually one set of the walls was more pronounced locally. For higher strains, the microstructure appeared to be progressively more “wavy” (Fig. 5c), and the traces of the active slip systems were not as regular as those observed at lower deformations, indicating significant cross-slip in this stage IV deformation. The orientations of areas corresponding to the above microstructures were analyzed by TEM orientation maps and displayed in Fig. 5d–f, as {1 1 1} pole figures. They confirm the stability of the initial orientation at low deformations and clearly visible scattering of the h1 1 1i poles around ND and ED at higher deformations. 3.3. Microstructure and texture evolution during a strain path change The following four types of changing strain path were applied to the initially pre-deformed samples: Goss{1 1 0}h0 0 1i ? Goss{1 1 0}h0 0 1i deformed 0.11), no rotation.
(additionally
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
2803
Fig. 4. Microstructure and texture development in continuously deformed sample of Goss orientation. (a) Sample scale: optical image of the longitudinal section after deformation of 0.9; (b and c) orientation maps presented as a “function” of Euler 2 angle, showing microstructure development for samples deformed: (b) 0.15; (c) 0.9; (d and e) {1 1 1} pole figures corresponding to (b) and (c), respectively. FEG–SEM–EBSD local orientation measurements in longitudinal plane.
Goss{1 1 0}h0 0 1i ? brass{1 1 0}h1 1 2i (0.10), rotation 35° around ND. Goss{1 1 0}h0 0 1i ? M{1 1 0}h1 1 1i (0.08), rotation 55° around ND. Goss{1 1 0}h001 i ?hard{1 1 0}h001i (0.03), rotation 90° around ND. The description of all 12 slip systems using the Bishop and Hill notation is given in Table 1. The principal slip systems expected to operate in the new configuration can be determined by a classical relaxed Taylor model for
channel-die compression of {1 1 0}hu v wi crystals (e.g., Ref. [22]). On the assumption of homogeneous deformation and equal critical resolved shear stress, they are listed in Table 2. Apart from the exact Goss and hard orientations, slip is expected (in equal quantities) on the +a2 and b1 systems, but which of course make different traces with the sample surfaces. In the Goss orientation, slip occurs on the same two planes, but each slips in two directions (co-planar or CP slip). For the hard orientation, an additional slip plane (with two directions) should be activated.
2804
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Fig. 5. Microstructure and texture development in continuously deformed sample of Goss orientation: (a) early and (b) advanced stages of cell substructure formation; (c) microstructure with dominating family of microbands; (d–f) corresponding {1 1 1} pole figures. Deformations of: (a and d) 0.12; (b) and (e) 0.56; (c) and (f) 1.12. TEM local orientation measurements in ND–ED2 plane.
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
2805
Table 1 Description of the slip systems in Bishop and Hill notation. Slip plane
111
Slip direction Bishop and Hill notation
011 a1
111 101 a2
110 a3
011 b1
111 101 b2
Table 2 Active slip systems operating in all analyzed orientations (classical relaxed Taylor model for channel-die compression). Crystal orientation
Active slip systems (Bishop and Hill notation)
Goss(1 1 0)½0 0 1 Brass(1 1 0)½1 1 2 M(1 1 0)½1 1 1 Hard(1 1 0)½1 1 0
a1,+a2, b1,+b2 +a2, b1 +a2, b1 (+ minor slip on –a3,+b3,+d1 and –d2) a1, a2, b1,+b2,+c1, c2,+d1, d2
3.3.1. Microstructure evolution, optical microscopy Detailed optical microscopy observations were carried out on longitudinal sections characteristic of the re-strain,
110 b3
011 c1
111 101 c2
110 c3
011 d1
101 d2
110 d3
i.e., ND–ED2 section. The microstructures observed after a change in deformation path showed a strong tendency to strain localization, but the apparent shear planes were clearly orientation dependent. 3.3.1.1. Goss{1 1 0}h0 0 1i ) Goss{1 1 0}h0 0 1i, no rotation. Although the crystal orientation is unchanged, the sample is now much shorter and tends to undergo a macroscopic flow along two arms at 45° to ED. This flow pattern is typical of large strain compression of “equiaxed” samples and appears to be accommodated by two sets of macroscopic shear band (MSB), as shown in Fig. 6a. The bands penetrated the whole sample along planes parallel to TD.
Fig. 6. Macroscopic shear band formation in: (a) continuously deformed Goss {1 1 0}h0 0 1i (true strain: 0.9 + 0.1) oriented samples then after changing strain path; (b) brass{1 1 0}h1 1 2i (0.9 + 0.1); (c) M{1 1 0}h1 1 1i (0.9 + 0.08); (d) hard{1 1 0}h0 0 1i (0.9 + 0.03) orientations. Optical images in longitudinal ND–ED2 planes (of 2nd deformation). Macroscopic shear bands in (e) M{1 1 0}h1 1 1i and (f) hard{1 1 0}h0 11 i orientations observed in the plane perpendicular to ED2. Areas marked in (a–d) show locations of more detailed investigated by TEM and FEG–SEM–EBSD.
2806
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
3.3.1.2. Goss {1 1 0}h0 0 1i ) brass{1 1 0}h1 1 2i type rotation (Fig. 6b). The pre-deformed Goss sample was rotated 35° around ND towards brass{1 1 0}h1 1 2i and then further deformed to a strain of 0.1. After the final reduction, the sample had shape distortions in both ND–ED2 and ED2–TD2 sections with clearly marked traces of two intersecting and almost symmetrical families of MSB (as observed in the ND–ED2 plane). A detailed inspection on three perpendicular sections showed that the band planes of both families were not parallel to TD. 3.3.1.3. Goss {1 1 0}h0 0 1i ) M{1 1 0}h1 1 1i type rotation (Fig. 6c and e). In this case, the additional deformation was 0.08. Optical microscopy revealed significant changes in the sample shape in both the ND–ED2 and ED2–TD2 sections with clearly marked traces of two MSB families, visible in the ND–TD2 plane. Further inspection of the as-deformed sample on all sections showed that both families of the bands were situated nearly symmetrically and formed a characteristic “zig-zag” shape in the ND–TD2 plane (Fig. 6e). 3.3.1.4. Goss {1 1 0}h0 0 1i ) hard{1 1 0}h0 0 1i type rotation (Fig. 6d and f). This change in strain path promoted the most radical changes. The pre-deformed Goss sample was rotated 90° around ND and then slightly deformed 0.03. On the sample scale, the traces of two intersecting families of highly localized MSB were clearly observed in the ND–ED2 section (Fig. 6d). At the surface they form pronounced intrusions. Inspection of three orthogonal sections showed that the shear band planes were not regular, i.e., the MSB (of each family) did not lie in one plane as was clearly visible on the ND–TD2 (Fig. 6f) and ED2– TD2 sections. 3.3.2. Texture/microstructure evolution at the meso-scale: local orientation measurements by FEG–SEM–EBSD More detailed analyses of the texture and microstructure development in the MSB areas after the strain path change were performed by high resolution FEG–SEM–EBSD measurements with a step size of 200 nm and nano-scale TEM observations of the dislocation microstructure. Fig. 7a shows an orientation map measured in the ND– ED2 section within a diffuse MSB area for the sample further compressed as Goss. The map shows that the distribution of low angle boundaries (<15°) is similar to that observed at lower deformations in continuously deformed samples. The traces of one set of dislocation boundaries are inclined 15° to ED, whereas the second family has an inclination up to 45–50° to coincidence with macroscopically visible traces of SB. The initial orientation scattering is clearly visible in the {1 1 1} pole figure (Fig. 7b), and the maximum density deviates only slightly from the initial Goss position. In the case of the Goss–brass-type rotation, the orientation map (from an area of the band) in the ND–ED2 section (Fig. 7c and d) showed clusters of single bands
inclined at 40° to ED2. The walls of elongated sub-cells were situated nearly parallel to ED2. The activity of the dominant bands was responsible for a characteristic Sshaped distortion of the background microstructure. As a result the microband clusters, initially situated along ED2, changed their inclination. This led to a strong dispersion of the h1 1 1i poles (Fig. 7d), mostly due to rotations around axes near TD2. For the Goss–M-type sample rotation (Fig. 7e and f), the orientation map of the MSB area showed clusters of new generation bands inclined at 30° to ED, revealing the strong instability of this microstructure. The newly active set of microbands formed a characteristic S-shaped distortion of the background structure of elongated subcells. The corresponding {1 1 1} pole figure exhibited strong and relatively complex tendencies of orientation scattering (Fig. 7f). The maximum misorientation angle could be directly correlated with the areas within the band. In both cases (brass and M orientations), the boundaries of the background structure of elongated cells periodically change inclination with respect to the external axes when crossed by micro shear bands. The last case of strain path change is pre-deformation of Goss and secondary straining as the hard orientation. An orientation map on the longitudinal section from the area of the MSB showed a broad, highly localized band inclined at 30° to ED2 with a very sharp boundary between the band and the slightly deformed matrix (Fig. 8a and b). The corresponding {1 1 1} pole figures in Fig. 8c–e illustrate quite different textural behavior within the stable matrix and strongly rotated MSB areas. The different rotations within SB led to a wide scatter of the h1 1 1i poles so that identification of the rotation axes and hence the mechanisms responsible for crystal decomposition is difficult to obtain. Fig. 9 compares typical misorientation line scans for the five different strain paths. The monotonically deformed Goss sample revealed a relatively small orientation spread. The misorientation angles only rarely attained 10° (Fig. 9a), and the misorientation axes were close to ND. In samples further strained in Goss position after sample cutting (no rotation), a misorientation line scan along ND showed a small increase in the orientation spread occasionally up to 12° (Fig. 9b). The misorientation distribution was relatively homogeneous, and the adjacent sub-cells displayed opposite rotation senses, as reported earlier, e.g., by Ferry and Humphreys [24] and Borbe´ly et al. [25]. When the strain path is of Goss–brass type, the misorientations across the bands (line scan in Fig. 9c) show significantly higher rotations (30–40°). The same type of misorientations between neighboring elongated sub-cells reach only 15–20°. The line scan for the Goss–M sample (Fig. 9d) showed that the orientation scattering attained 30–35° when the bands crossed. Misorientations between neighboring elongated sub-cells outside the band were lower and only very rarely exceeded 10–12°.
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
2807
Fig. 7. Orientation maps displayed as a “function of Euler 2” in grayscale showing shear band formation in samples deformed: (a) continuously in Goss orientation, and after changing strain path: (c) brass, (e) M orientations, and (b, d, f) corresponding {1 1 1} pole figures. FEG–SEM–EBSD orientation measurements with step size 200 nm.
In the case of Goss–hard-type strain path change (Fig. 9e), a line scan along ND across the boundary between the band and neighboring matrix showed misori-
entations of 40–45°. The quality of the band contrast in this case was the lowest of all the samples, indicating strong strain localization within the band.
2808
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Fig. 8. Shear band formation in 3% compressed hard orientation sample after Goss pre-strain: (a) optical microstructure; (b) Kikuchi band contrast map from the area of shear band marked in (a) and {1 1 1} pole figures; (c) summary of the whole map; (d) deformed matrix; (e) shear band area. FEG–SEM– EBSD orientation measurements with step size 200 nm.
3.3.3. Evolution of the dislocation microstructure after changing deformation path: TEM observations and local orientation measurements The dislocation microstructure observed in samples deformed as Goss followed by sample cutting and further straining of 10% was similar to that observed in continuous straining after comparable reductions (Fig. 10a). The activation of secondary microbands inclined at 40–50° to ED2 was clearly visible and led to a characteristic S-shaped distortion of the primary microband family (inactive). The corresponding {1 1 1} pole figure showed a slight rotation of the crystal lattice from Goss (Fig. 10b). A line scan across both sets of microbands showed periodic lattice rotation, associated with an increase in misorientation angle up to 8–10° across the secondary microbands (Fig. 10c). In the case of the sample rotated 35° around ND towards brass, the observed dislocation microstructure was finer. The newly formed set of microbands, inclined
at 35–40° to ED2 (Fig. 11a) cut the microstructure of elongated sub-cells from the previous Goss orientation. The {1 1 1} pole figure calculated on the basis of TEM local orientation measurements corresponding to the bright field image showed a clear, broad scattering of poles (Fig. 11b). The misorientation profile across the newly activated set of microbands revealed differences in orientations which were 22–25° (Fig. 11c). The microstructure observed in the sample rotated 55° around ND, from Goss towards M, was similar to that described above, i.e., Goss–brass. The newly activated microbands were inclined at 50° to ED and penetrated the microstructure of elongated sub-cells without any significant changes in shear direction (Fig. 12a). The {1 1 1} pole figure (Fig. 12b) showed much stronger orientation scattering of orientations than before, with misorientation profiles across the new set of microbands rotated 35–40° with respect to the neighboring background microstructure (Fig. 12c).
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
2809
At a macroscopic scale, all the deformation path changes induced more or less drastic changes in softening/hardening behavior and led to macroscopic inhomogeneities of plastic flow. Since the strain path changes did not involve major changes in active slip systems (usually the same set of major systems with variations in the minor ones), it is clear that plastic instabilities induced by variations in strain path are not just due to the activation of new systems; more subtle effects of deformation microstructure play a significant role. The stress–strain behavior of the crystallites after a strain path change can be correlated, to first order, with the relative strength parameter, i.e., Taylor factor. As could be expected the initially “soft” Goss orientation became very “hard” in the H{1 1 0}h0 1 1i and M{1 1 0}h1 1 1i orientations and remained relatively “soft” in the brass{1 1 0}h1 1 2i orientation. However, the Taylor factor is insufficient to explain the detailed hardening/softening behavior; in particular, after reorienting, all the crystals immediately become softer (in relative terms) than Taylor factor hardening would indicate and then do not resume hardening during continued straining (they usually soften further). This large softening during secondary straining on the hard H and M orientations is associated with a massive concentration of slip into shear bands. Fig. 9. Misorientation line scans along ED, with respect to the first measured point for: (a) continuously deformed 59% Goss oriented sample; (b) Goss oriented sample after 69% deformation, and the change in strain path; (c) Goss–brass, (d) Goss–M; (e) Goss–hard type, respectively. FEG– SEM–EBSD orientation measurements with step size 200 nm.
In the case of the reorientation to the hard orientation, strong shear bands divided the crystal into large blocks, with a sharp boundary between the matrix and shear band. The freshly formed shear bands were composed of very fine, nearly equiaxed sub-cells (Fig. 13a). Their morphology was quite different in comparison with the background microstructure of elongated microbands. The orientation of the matrix was practically unchanged, whereas within shear bands very strong orientation scattering was observed (Fig. 13b and c) as shown by the misorientation line scan across the boundary (shear band)/matrix, where misorientations were 40–50° (Fig. 13d).
4.1. Strain path changes inducing very unstable plastic flow and intense shear banding This occurs in both the hard H and medium hard M orientations after pre-straining as Goss. The flow stress initially increases, since the resolved shear stress on the active systems immediately decreases (by a factor of 2 in the H orientation), but then strain very rapidly becomes localized into a few shear bands. By shear on these narrow bands of width 10–100 lm, the orientations within the bands undergo major changes (typical rotations of 30° for M and 40° for H), so that they tend towards single slip configurations. In the case of the M orientation, this mechanism reorients the crystal lattice about the h1 1 2i axes orthogonal to the slip plane normal and direction towards two groups of orientations near (1 5 5)½5 0 1 and ð5 4 3Þ½1 2 1. The rotations can be described as follows: ð1 1 0Þ½1 1 1 rotation of ðþÞ30 ½2 1 1 and ðÞ30 ½1 2 1 ! ð1 5 5Þ½5 0 1
4. Discussion The observations of the microstructure and microtexture changes provide a basis for discussion on the origin and nature of micro- and macro-scale strain localizations and their influence on stress–strain behavior. The most important features of plane strain compressed Goss-oriented copper single crystals after a changing deformation path may be summarized as follows:
ð1 1 0Þ½1 1 1 rotation of ðÞ10 ½2 1 1 þ ðÞ10 ½1 2 1 ! ð5 4 3Þ½1 2 1 The decomposition of the “hard” orientation, i.e., (1 1 0)½1 1 0, is difficult to describe in a simple way, mainly because of the very wide orientation scattering identified inside the band. However, two apparently successive lattice rotation tendencies towards (2 5 4)½3 2 1 and then
2810
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Fig. 10. (a) TEM microstructure showing early stage of strain localization in Goss sample continuously deformed up to 69%. (b) Misorientations with respect to the first measured point along line scan presented in (a), and corresponding line scan (c) {1 1 1} pole figure. TEM local orientation measurements in ND–ED2 plane.
(5 2 0)½1 3 1 can be detected and interpreted as due to single slip. Both cases suggest a very sharp geometric softening term dMT/de, often invoked as a criterion for plastic instability and shear banding. Note that, when the H and M crystal orientations are deformed monotonically, their behavior is very material dependent: Cu crystals of the H orientation develop shear bands after 20% strain, whereas Al crystals of the same orientation at high strains gradually break up by deformation banding into a wide set of orientations [22]. The dramatic transformation by a strain path change to localized single slip and intense shear banding raises the question of whether this particular single crystal behavior could occur in similarly oriented grains of a polycrystal. Of course in the channel-die compression experiment, the free surface along ED2 facilitates the formation of major surface relief effects due to the large slip steps of the bands at the free surface. This should not be so easy for a more constrained grain in a polycrystal, but nevertheless the softening tendency induced by localized shearing appears to be so strong that there is a very good chance of this occurring, first in some individual grains and then extending to groups of grains.
mation microstructure (Fig. 7c) are strongly perturbed by the strain path change over large areas of the crystal. The corresponding TEM micrograph in Fig. 11 showing new microbands shearing the previous cell structure suggests an instability of the previous deformation microstructure. The reorientations induced by the secondary deformation occur, to first order, about axes close to TD1 or ½1 1 0 (Figs. 7d and 11b). A more detailed analysis (Fig. 14) shows that the matrix decomposes by rotations towards two nearly symmetrically situated groups of orientations close to (1 1 1)½4 1 3 (“A”) and ð3 2 1Þ½1 4 5 (“B”), respectively, as identified within the bands. For both orientation groups, the rotation can be correlated with previous co-planar slip systems operating on the (1 1 1) and ð1 1 1Þ planes. It can be described schematically as follows:
4.2. Strain path changes followed by relatively stable plastic flow
The orientation scattering leading to the “A” and “B” groups of orientations must be based on local operating slip systems. Since the rotation axes lie close to the ½1 1 0 direction, the rotation leading to the “A” group of orientation could be regarded as a “sum” of rotations about ½2 1 1
This is the case of the Goss to brass orientation change. The microband alignments which characterize the defor-
\A"
ð1 1 0Þ½1 1 2 rotations of ðþÞ20 ½2 1 1 and
ðÞ20 ½1 2 1 ! ð1 1 1Þ½4 1 3 \B"
ð1 1 0Þ½1 1 2 rotation of ðÞ10 ½2 1 1 and
ðþÞ10 ½1 2 1 ! ð3 2 1Þ½1 4 5
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
2811
Fig. 11. (a) TEM microstructure showing strain localization in Goss to brass sample finally deformed 70%. (b) Misorientations with respect to the first measured point along line scan presented in (a), and corresponding line scan (c) {1 1 1} pole figure. TEM local orientation measurements in ND–ED2 plane.
Fig. 12. (a) TEM microstructure showing strain localization in Goss to M sample deformed finally 67%. (b) {1 1 1} Pole figure. (c) Misorientations with respect to the first measured point along line scan presented in (a). TEM local orientation measurements in ND–ED2 plane.
2812
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
Fig. 13. (a) TEM microstructure showing strain localization in Goss to hard sample deformed 62%; (b) and (c) {1 1 1} pole figures for shear bands and deformed matrix; (d) misorientations with respect to the first measured point along line scan presented in (a). TEM local orientation measurements in ND– ED2 plane.
and ½1 2 1 axes, resulting from the operation of two CP1, i.e., ð1 1 1Þ½0 1 1 (b1) and ð1 1 1Þ½1 0 1 (b2) slip systems, respectively. The first slip system is expected from standard crystal plasticity for the brass orientation, whereas the second is a system that slips in the Goss orientation but should not slip in the brass (unexpected). Similarly, in the “B” group of orientations, two CP2 slip systems are
required; the expected (1 1 1)½1 0 1 (a2) and unexpected (1 1 1)½0 1 1 (a1) which was active in the previous Goss orientation. In other words, although the brass orientation should only slip on two systems during monotonic straining in channel-die compression (as confirmed by many previous studies), after this type of strain path change it slips on all four systems previously active in the Goss
Fig. 14. The two rotation tendencies observed in Goss to brass sample finally deformed by 70%: (a) {1 1 1} pole figures showing orientation of highly misoriented areas within the (“A” and “B”) bands; (b) neighboring deformed matrix with marked slip systems and rotation axes responsible for observed rotation tendencies. Red points in (a) mark the “average” matrix orientation. FEG–SEM–EBSD local orientation measurements in ND–ED2 plane. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H. Paul et al. / Acta Materialia 58 (2010) 2799–2813
orientation. This could be described as a form of overshooting, but now tends to spread out the slip distribution (instead of severely restricting it as in the M and H cases). It also implies that, during the strain path change, these two previous systems (in principle now latent systems for the brass orientation) must have softened relative to the two expected active systems. This is opposite to standard latent hardening and has been termed “slow” latent hardening (as described in more detail by Beyerlein and Tome´ [6]). However, in the present case, it occurs for co-planar slip as opposed to cross-slip, which is more standard for this behavior. This brass crystal appears to be initially softer than Goss (Fig. 3) but, also in contrast to the above examples, then starts hardening up to the level of the Goss orientation. This is what is usually expected of strain path changes in polycrystals, which create transient softening stages before hardening up to the previous rates. As a final, more general, point it appears that this type of systematic single crystal study of strain path changes via orientation changes can provide significant information on the evolution of slip system hardening for non-monotonic straining conditions at large strains—a major theoretical problem. It would be interesting to extend this work to the case of hard)soft orientations and also to cases which favor (or disfavor) cross-slip onto new slip systems. 5. Conclusions Copper single crystals of the stable Goss{1 1 0}h0 0 1i orientation were deformed in a channel-die to reductions of 59% to form a well-defined structure of microbands, then ND rotated at different angles to {1 1 0}hu v wi samples which were then further deformed 3–10%. In principle, this orientation change does not require major changes in slip activity, but has the potential to change the current deformation microstructure. The evolution of deformation microstructures and microtextures during these strain path changes was then characterized by FEG–SEM–EBSD and TEM. The analysis addresses the relation between slip activity, microstructure (and microtexture) and stress– strain behavior due to the crystal anisotropy after a strain path change. The most important features may be summarized as follows. 1. The secondary straining of all deformed crystals showed different softening/hardening behavior, which could be correlated to first order with the change in Taylor factors. However, this was insufficient to describe the exact hardening and softening evolution. 2. The most radical changes were observed in the case of the sample rotated from Goss towards the “hard”
2813
H{1 1 0}h0 1 1i orientation. Even small additional strains developed intense shear bands composed of equiaxed sub-cells. The intermediate M{1 1 0}h1 1 1i orientation also formed very pronounced shear bands but at a slightly lower rate. In both cases, the microtextures suggested a rapid evolution to localized deformation by near single slip along the shear bands and consequent significant softening. 3. The brass {1 1 0}h1 1 2i orientations developed diffuse shear bands and revealed characteristic S-shaped, cyclic disturbances of the pre-existing microband structure. A detailed analysis of the local rotations associated with this substructure change leads to the conclusion that the “new” brass crystal deforms on all four systems active in the previous orientation, i.e., in contrast to standard latent hardening theory. This crystal, after an initial softening, work hardens up to the previous flow stress levels. References [1] Franciosi P, Stout MG, O’Rourke J, Erskine B, Kocks UF. Acta Metall 1987;35:2115. [2] Korbel A, Martin P. Acta Metall 1988;36:2575. [3] Peters B, Kalidindi SR, Van Houtte P, Aernoudt E. Acta Mater 2000;48:2123. [4] Peters B, Bacroix B, Teodosiu C, Van Houtte P, Aernoudt E. Acta Mater 2001;49:1621. [5] Paul H, Driver JH, Jasien´ski Z. Acta Mater 2002;50:815. [6] Beyerlein IJ, Tome´ CN. Int J Plast 2007;23:640. [7] Rauch EF, Gracio JJ, Barlat F. Acta Mater 2007;55:2939. [8] Holmedal B, Van Houtte P, An Y. Int J Plast 2008;24:1360. [9] Viatkina ME, Brekelman WAM, Geers MGD. J Mater Process Technol 2009;209:186. [10] Yapici GG, Beyerlein IJ, Karaman I, Tome´ CN. Acta Mater 2007;55:4603. [11] El-Danaf E, Kalidindi SR, Doherty RD, Necker C. Acta Mater 2000;48:2665. [12] Wro´bel M, Dymek S, Blicharski M. Scripta Metall Mater 1996;35:417. [13] Luft A. Prog Mater Sci 1991;35:97. [14] Thuillier S, Rauch EF. Acta Metall Mater 1994;42:1973. [15] Driver JH, Jensen DJuul, Hansen N. Acta Metall Mater 1994;42:3105. [16] Li BL, Godfrey A, Meng QC, Liu Q, Hansen N. Acta Mater 2004;52:1069. [17] Schmitt JH, Fernandes JV, Gracio JJ, Vieira MF. Mater Sci Eng 1991;A147:143. [18] Paul H, Morawiec A, Driver JH, Bouzy E. Int J Plast 2009;25:1588. [19] Paul H, Driver JH, Maurice C, Pia˛tkowski A. Acta Mater 2007;55:833. [20] Wagner P, Engler O, Lu¨cke K. Acta Metall Mater 1995;43:3799. [21] Basin´ski ZS, Jackson PJ. Phys Status Solidi 1965;10:45. [22] Skalli A, Driver JH, Wintenberger M. Rev Metall 1983;6:293. [23] Bauer RE, Mecking H, Lu¨cke K. Mater Sci Eng 1977;27:163. [24] Ferry M, Humphreys FJ. Mater Sci Eng 2006;A435–436:447. [25] Borbe´ly A, Maurice Cl, Piot D, Driver JH. Acta Mater 2007;55:487.