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Volume 59, Issue 9, May 2011, Pages 3431-3446 e r ap n In esea m 3 The evolution of microstructure and texture during room temperature compression of commercially pure Ti with four different initial �4 �1 materials that are extensively used in mechanical and struc- and zirconium [12–19], due to the...

Volume 59, Issue 9, May 2011, Pages 3431-3446
e r ap n In esea m 3 The evolution of microstructure and texture during room temperature compression of commercially pure Ti with four different initial �4 �1 materials that are extensively used in mechanical and struc- and zirconium [12–19], due to their technological impor- tance. In particular, titanium and its alloys find extensive use in aerospace and biomedical applications due to their investigation from the fundamental as well as engineering sively for different deformation modes [3–7]. A good num- ber of studies have focussed on the strain hardening characteristics of titanium during deformation [8–10]. Modelling texture evolution in hcp metals has been an intriguing problem due to a propensity for twinning during deformation. Tome´ and co-workers [12,13] employed the ⇑ Corresponding author. Tel.: +91 80 22933245; fax: +91 80 23600472. E-mail address: satyamsuwas@materials.iisc.ernet.in (S. Suwas). Available online at www.sciencedirect.com Acta Materialia 59 (2011) 3431–34 tural applications. The deformation response of hexagonal close-packed (hcp) metals and alloys is generally guided by their axial (c/a) ratio [1]. The deformation behaviour of hcp materials is, however, very complex, due to activation of different type of slip as well as twinning systems under dif- ferent conditions. The onset of twinning during the initial stages of deformation leads to a unique hardening response of these materials. Crystallographic texture also plays an important role in deciding the mechanical behaviour of hcp metals and alloys. Amongst the hcp metals, the major- ity of investigations have been directed at titanium [2–11] points of view. Various characterization techniques, such as electron backscatter diffraction (EBSD) [20] and X-ray [21] and neutron diffraction [22], have been employed to fully understand the evolution of microstructure and texture during different deformation processes. Attempts have been made to simulate the experimental stress–strain curves and texture evolution using various crystal plasticity mod- els ranging from the simple Taylor model to the advanced crystal plasticity finite element (CPFEM) model. The mechanical response of titanium has been studied exten- orientations were studied under quasi-static and dynamic loading conditions. At a low strain rate _e = 3 � 10 s all the different initial textures yielded the same end texture, despite different microstructural evolution in terms of twin boundaries. High strain rate deforma- tion at _e = 1.5 � 103 s�1 was characterized by extensive twinning and evolution of a texture that was similar to that at low strain rate with minor differences. However, there was a significant difference in the strength of the texture for different orientations that was absent for low strain rate deformed samples at high strain rate. A viscoplastic self-consistent model with a secant approach was used to corroborate the experimental results by simulation. � 2011 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. Keywords: Titanium; Texture; Twinning; Electron backscatter diffraction 1. Introduction Hexagonal materials form a class of low symmetry excellent mechanical and physical properties, like high spe- cific strength, good ductility and excellent corrosion resis- tance [2]. Hence, it has been the subject of detailed Deformation behaviour of comm strain N.P. Gurao a, Rajeev K aDepartment of Materials Engineering, India bMaterials Group, Bhabha Atomic R Received 21 June 2010; received in revised for Abstract 1359-6454/$36.00 � 2011 Published by Elsevier Ltd. on behalf of Acta Mater doi:10.1016/j.actamat.2011.02.018 rcially pure titanium at extreme ates oor b, Satyam Suwas a,⇑ stitute of Science, Bangalore 560 012, India rch Centre, Mumbai 400 085, India 0 December 2010; accepted 14 February 2011 www.elsevier.com/locate/actamat 46 ialia Inc. ter volume fraction transfer (VFT) scheme of Van Houtte [23] and proposed the predominant twin reorientation (PTR) scheme to model the deformation behaviour of zirconium. Kalidindi and co-workers [10,11], on the other hand, employed a Taylor-type rate sensitive crystal plasticity model to simulate the deformation behaviour of Ti. The effect of initial orientation has been investigated exten- sively, with most studies being carried out on two different orientations, namely the through thickness orientation with strong basal texture and the in-plane orientation with pris- matic texture [11,19]. It has been observed that the two extremely different initial textures lead to different mechan- ical responses. The basal orientation shows a higher yield strength but a lower strain hardening rate, while the pris- matic orientation shows lower yield strength and a higher strain hardening rate. Crystal plasticity models have been able to predict different mechanical responses with respect to the initial orientation. The mechanical response of differ- ent initial orientations can be indirectly influenced by the value of stacking fault energy (SFE), which is different for different planes in hcp metals like titanium (300 mJ m�2 in the basal plane and 150 mJ m�2 in the prismatic plane) [24]. The deformation of titanium by virtue of its less than ideal c/a ratio (1.588) is contributed by prismatic slip. However, since the basal and the prismatic slip systems provide only four independent slip systems, plastic defor- mation in Ti has to be accommodated by hc + ai slip or twinning. The major twinning systems that can operate in compression of a single crystal Ti are {1 0 �1 2}h1 0 �1�1i, {1 1 �2 2}h1 1 �2�3i and {1 1 �2 1}h�1�1 2 6i. The choice of the twinning system depends on the initial orientation [5]. Twinning, being a polar transformation, is sensitive not only to the magnitude of shear but also to the direction of shear [25]. Depending on the loading direction, different twin systems become active and alter the deformation response, as well as the texture evolution, in Ti. A detailed study of the strain hardening behaviour of polycrystalline titanium under compression, plane strain compression and torsion has been carried out by Salem et al. [8–10]. The authors [8] categorized three distinct stages in the stress–strain curve, labelled A, B and C. The first regime, stage A, was characterized by a decreasing strain hardening rate, similar to the dynamic recovery regime observed in high stacking fault energy (SFE) metals. This was followed by stage B, a region with increasing strain hardening rate in both plane strain and uniaxial compression. Stage C exhib- ited a decreasing strain hardening rate. During stage A, deformation was accommodated only by slip. The activa- tion of cross slip between the basal and prism planes with a common slip direction leads to easy dynamic recovery and, hence, a lower strain hardening rate. The pyramidal hc + ai slip system, being considerably harder than the prism or basal slip systems, could be activated to make up the five independent slip systems. In stage B, twinning 3432 N.P. Gurao et al. / Acta Ma led to an increase in strain hardening rate as twin activity increased with increasing strain. As the twin systems oper- ative in hcp materials are non-coplanar with the slip sys- tems, a considerable amount of hardening occurred during stage B. The decreasing strain hardening rate in stage C was explained due to increasing difficulty in pro- ducing deformation twins with further straining. This the- ory proposed by the authors [8] was further supported by simulations obtained from a Taylor-type crystal plasticity model by Wu et al. [11]. However, most of these studies did not consider the effect of strain rate on the strain hard- ening response and texture evolution. Such studies are of paramount importance, as twinning and additional mecha- nisms such as shear banding are expected to play a very important role in the deformation behaviour of hexagonal materials at high strain rates. The present work is an attempt to complement the findings of Salem et al. [8] for the quasi-static deformation of titanium and to explore the validity of these concepts in a dynamic strain rate regime. 2. Experimental Cylindrical samples of 6 mm diameter and 9 mm height were obtained from a rolled block of commercially pure (CP) Ti plate with a strong basal texture. Samples were machined in four different orientations (Fig. 1a), namely I–IV, to ensure different starting textures. Samples I–III were machined along the RD, ND and TD directions of the rolled block while sample IV was machined at a 45� angle to the RD–ND plane. Each of these samples was sub- jected to compression testing at a strain rate of 3 � 10�4 s�1 in a servo-hydraulic DARTEC mechanical testing set-up to a true strain of e = 0.36. The high strain rate tests at 1500 s�1 were carried out using a split Hopkinson pressure bar (SHPB) with incident and transmission bars of 13 mm diameter and 1300 mm length. Cylindrical specimens of all four orientations with diameters and heights of 6 mm were used for the test. A MoS2 lubricant was used between the sample and the bar interfaces. For a general discussion see the relevant ASM Handbook [26]. The samples were then sectioned along the compression direction and sub- jected to metallographic preparation with electropolishing in a solution of 60 ml of perchloric acid in 600 ml of meth- anol and 400 ml of butycellosolve. The samples were etched with Krolls reagent for optical microscopy, while EBSD studies were carried out by field emission gun scanning elec- tron microscopy (FEG-SEM) (SIRION). A step size of 1 lm was used to capture large area scans for the starting and deformed samples. High resolution EBSD measure- ments were done using a step size of 50 nm for the samples deformed at high strain rate. Data acquisition and analysis were carried out using TSL software version 5.2. 3. Viscoplastic self-consistent simulations In the present investigation viscoplastic self-consistent ialia 59 (2011) 3431–3446 simulation code VPSC-6 was used to simulate the experi- mental texture. The VPSC model is described in detail in ater RD (x) TD (y) ND (z) I III 0110 0110 01122000 N.P. Gurao et al. / Acta M Tome´ et al. [27] and the PTR scheme in Lebensohn and Tome´ [13]. The texture measured by EBSD was discretized to obtain 2000 single orientations, that were used as input to the model. The critical resolved shear stress (CRSS) and hardening parameters for Voce type hardening were obtained by fitting the stress–strain curve for sample II, for which minimum twin activity is observed. Wu et al. [11] obtained these values from shear tests on titanium, wherein twinning is minimal, from the hardening curves, as against stress–strain curves in the present case. In addi- tion to extended Voce hardening (for statistical disloca- tions), hardening due to the presence of twin barriers is superimposed [13]. We have adopted the uncoupled approach as against the coupled grain approach used by Proust et al. [18]. In this approach the increase in twin activity and subsequent sat- uration with the amount of deformation in Zr was mod- elled by using negative hardening parameters for twinning. However, they followed this strategy to model up to a strain of 0.3. As a consequence, with the increase in amount of strain there was an increase in twinning activ- ity. This is not the case for titanium, where it has been shown experimentally that twinning is replaced by pyrami- dal slip at higher strains. In the present work the minimum volume fraction of twins in a grain is assumed to be 0.1, while a saturation value of 0.5 has been used in the simula- 01122000 Fig. 1. (a) Geometry of samples obtained from a Ti plate with initial strong ba figures for samples with different orientations. (a) IIIII I IV II IV 0110 0110 01122000 ialia 59 (2011) 3431–3446 3433 tions. The activation of any particular slip system as well as twin system is a strong function of initial orientation and, hence, different samples with different orientations show dissimilar stress–strain and strain hardening responses. In the present investigation, microstructural evidence of twin boundaries was used to fine tune the model. The fraction of the twin boundaries obtained from orientation imaging microscopy (OIM) by EBSD was used as an indication of the activity of that particular twin system. A higher frac- tion of a particular type of twin boundary indicates a higher activity of that particular twin system. 4. Results 4.1. Initial texture Inverse pole figures corresponding to the compression direction (CD) representing the initial texture of the start- ing samples as measured from large area EBSD scans are shown in Fig. 1b. The differently oriented Ti samples extracted from the rolled plate ensured that the initial tex- ture was significantly different for each sample. Sample I, cut along RD, showed a majority of orientations along the h1 0 �1 0i and h2 �1�1 0i lines, with maximum intensity at h3 �1�2 0i, while sample II, cut along ND, had a strong near basal texture with a maxima for the h2 �1�1 4i compo- (b) 01122000 sal texture and (b) corresponding compression direction (CD) inverse pole nent. Sample III, cut along TD, was characterized by a spread of orientations along the h1 0 �1 0i–h2 �1�1 0i line. The texture was relatively weaker and showed higher inten- sities for the h6 �3�3 2i and h1 0 �1 0i orientations. For sample IV, cut at 45� to the ND–RD plane, most of the crystallites were oriented towards the h2 �1�1 0i–h1 0 �1 0i region of the inverse pole figure with a maximum intensity at h1 0 �1 0i. 4.2. Mechanical behaviour The plastic region of the true stress–strains curve obtained from the compression tests at low strain rate, shown in Fig. 2a, indicates that the differently oriented samples have distinctly different responses. The yield strength of sample II was higher than that of the other three samples and also showed a low strain hardening rate. In the case of sample I the true stress increased steadily with strain up to e = 0.15 and then increased steeply to reach a maximum value amongst all the studied samples at e = 0.36. The stress in the case of sample II increased gently to reach a value slightly less than that for sample I. Samples III and IV showed almost the same true stress at e = 0.36, which was lower than that for sample II. The stress–strain curve of sample IV coincided with the stress–strain curve of sample I up to e = 0.15 and then devi- ated to coincide with the sample III curve, giving the same stress at e = 0.36. The samples tested at high strain rate pared with the low strain rate deformed samples. The increase in yield strength was lower for samples I and II, while a substantial increase was observed for samples III and IV. However, the nature of the stress–strain curve remained similar for sample II at low and high strain rates, showing minimum strain hardening compared with the other three samples. In order to study the dependence of orientation on the strain hardening behaviour of titanium the strain hardening curves were calculated numerically. The strain hardening rate and stress were normalized with respect to the shear modulus of titanium (44 GPa) and the normalized strain hardening rate dðr�r0Þ=deG � � versus normal- ized stress ðr�r0ÞG � � for the low and high strain rate deformed samples are plotted in Fig. 2b. As expected, the hardening curves showed the three regimes of strain hard- ening observed by Salem et al. [8]. Samples I, III and IV deformed at low strain rate showed the three stages of strain hardening quite distinctly, while sample II showed dominant stages A and C. The onset of stages B and C was different for these samples. Amongst these samples sample III showed the onset of stage B at higher values of strain, indicating late onset of twinning for this texture. Sample II with a strong basal texture was markedly dis- tinct, with stage A dominant to large strains, indicating an absence of twinning. Also, the slope of the hardening (a (b 3434 N.P. Gurao et al. / Acta Materialia 59 (2011) 3431–3446 showed an increase in stress level at a given strain com- 0 200 400 600 800 1000 0 0.1 0.2 0.3 0.4 Strain St re ss (M Pa ) I II III IV RSL 0 0.01 0.02 0.03 0.04 0.05 0.06 0 0.005 0.01 0.015 0.02 Normalized Stress N or m al iz ed S tra in H ar de ni ng R at e I II III IV RSL Fig. 2. (a) True stress–strain curves and (b) hardening curves for curve showed the minimum strain hardening rate for sample II. Another important observation is that the hard- 0 200 400 600 800 1000 Strain St re ss (M Pa ) I II III IV 0 0.1 0.2 0.3 0.4 RSH 0 0.02 0.04 0.06 0.08 0.1 0.12 0 0.005 0.01 0.015 0.02 0.025 Normalized Stress N or m al iz ed S tr ai n H ar de ni ng R at e I II III IV RSH ) ) samples I–IV tested at low and high strain rates, respectively. ening curve for sample II was shifted to the right, as it had got a higher yield point but a lower strain hardening rate due to the absence of twinning. The hardening curves for the samples tested at the high strain rate were similar to those at the low strain rate, how- ever, there were some important distinctions. A higher hardening rate was observed at the high strain rate, in addi- tion to a higher stress level. However, the difference between various samples disappeared and the hardening curves of samples I, III and IV almost coincided. The strain harden- ing curves for all four orientations were similar, unlike at the low strain rate, where stage B is absent in sample II. 4.3. Evolution of texture Despite a marked difference in the initial texture of the four samples, the overall texture evolution in all the cases was near basal at low strain rate (Fig. 3a). In addition, there was a clustering of orientations near h2 �1�1 4i for all four samples. Some crystallites were oriented near the h2 �1�1 0i corner of the inverse pole figure. A spread of ori- entations from h2 �1�1 4i to h1 0 �1 4i was observed in sam- ples I, II and IV, while sample III shows a spread of orientations along the h0 0 0 1i–h2 �1�1 0i line. The reorien- tation of crystallites towards the basal orientation was dominant in samples I and IV, while there was little change in texture of sample II, which had a strong basal texture. Although the texture in sample II was different from the remaining three samples, it is believed that with increasing strain it will also form the near basal h2 �1�1 4i orientation, which is a stable end orientation. At a high strain rate, there was a slight weakening of texture and an additional, however weak, h1 0�1 0i component appeared that was absent from the samples deformed at a low strain rate (Fig. 3b). All the samples showed a texture characterized by the presence of orientations near the h2 �1�1 0i and h2 �1�1 4i components. There was a spread of orientations from these components towards the line joining the lines h2 �1�1 0i–h1 0 �1 0i and h0 0 0 1i–h1 0 �1 0i. It can be observed that the high strain rate deformed samples mani- fest a higher strength of the h2 �1�1 0i component compared with the h2 �1�1 4i component, which is dominant at the low I II IIIIV 01100110 0110 0110 0112 01120002 0002 4112 002 N.P. Gurao et al. / Acta Materialia 59 (2011) 3431–3446 3435 01120002 0002 I III 0002 0002 00002 0112 0112 0110 0110 (a) (b) Fig. 3. Compression direction (CD) inverse pole figure showing final texture a strain rate (HSR). 0112 II IV 0112 0112 0110 0110 fter deformation of samples I–IV at (a) low strain rate (LSR) and (b) high strain rate. Another important observation was the spread of orientations towards h1 0 �1 0i from h2 �1�1 0i in the high strain rate deformed samples. The texture was stronger for samples I and II while a weaker texture evolves in sam- ples III and IV. 4.4. Evolution of microstructure Optical microscopy as well as scanning ele
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