- Email: [email protected]
Micropillar and macropillar compression responses of magnesium single crystals oriented for single slip or extension twinning
Available online at www.sciencedirect.com
ScienceDirect Acta Materialia 65 (2014) 316–325 www.elsevier.com/locate/actamat
Micropillar and macropillar compression responses of magnesium single crystals oriented for single slip or extension twinning K. Eswar Prasad a,⇑, K. Rajesh a, U. Ramamurty a,b b
a Department of Materials Engineering, Indian Institute of Science, Bangalore 560012, India Center of Excellence for Advanced Materials Research, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Received 6 July 2013; received in revised form 30 October 2013; accepted 31 October 2013 Available online 27 November 2013
Abstract Uniaxial compression experiments were conducted on two magnesium (Mg) single crystals whose crystallographic orientations facilitate the deformation either by basal slip or by extension twinning. Specimen size effects were examined by conducting experiments on lm- and mm-sized samples. A marked specimen size effect was noticed, with micropillars exhibiting significantly higher flow stress than bulk samples. Further, it is observed that the twin nucleation stress exerts strong size dependence, with micropillars requiring substantially higher stress than the bulk samples. The flow curves obtained on the bulk samples are smooth whereas those obtained from micropillars exhibit intermittent and precipitous stress drops. Electron backscattered diffraction and microstructural analyses of the deformed samples reveal that the plastic deformation in basal slip oriented crystals occurs only by slip while twin oriented crystals deform by both slip and twinning modes. The twin oriented crystals exhibit a higher strain hardening during plastic deformation when compared to the single slip oriented crystals. The strain hardening rate, h, of twin oriented crystals is considerably greater in micropillars compared to the bulk single crystals, suggesting the prevalence of different work hardening mechanisms at these different sample sizes. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Magnesium; Deformation twinning; Strain hardening rate; Size-effect; Electron backscattered diffraction (EBSD)
1. Introduction The mechanical behavior of magnesium (Mg) and its alloys has attracted considerable attention from researchers in recent years due to the growing demand for lightweight structural materials, especially for the automobile and aerospace industries. Mg and its alloys have low density (1.79 g cm–3) and high specific strength compared to the materials currently used for automobile applications such as aluminum alloys [1–3]. However, Mg alloys suffer from poor room temperature ductility and formability, which is attributed to their low-symmetry hexagonal close-packed (hcp) crystal structure. Unlike face-centered cubic (fcc) and body-centered cubic (bcc) metals, metals with hcp crystal structure do not possess a high enough number of slip ⇑ Corresponding author.
E-mail address: [email protected] (K.E. Prasad).
systems at room temperature to undergo plastic deformation by slip alone. Hence, twinning has a major role to play during the plastic deformation of hcp metals and makes the deformation far more complex [4]. To develop new Mg alloys with good formability, a detailed understanding of the deformation mechanisms that are operative at different temperatures, strain rates and across multiple length scales is essential. Such an understanding can be employed to modify the existing plasticity models, which do not explicitly contain the length-scale-dependent deformation behavior in their formulation, for improved predictability [5–7]. As the lattice parameterp ratio, ffiffiffiffiffiffiffiffi c/a, of Mg is equal to that of an ideal hcp lattice ð 8=3Þ; basal slip {0 0 0 1}, is the easiest slip system to be activated owing to its low critical resolved shear stress (CRSS) [8,9]. The other slip systems that can potentially play a role in the plastic deformation, are prismatic f1 0 1 0g and pyramidal f1 0 1 1g slip systems. The Burgers vector in all these is along the hai direction
1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.10.073
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
and hence strain accommodation in the hci direction is not possible. This necessitates the activation of deformation modes (either twinning or pyramidal slip) that can accommodate the plastic deformation along the c direction. Due to the high CRSS it is difficult to activate the pyramidal hc + ai slip at room temperature [7] which means that deformation has to occur by twinning. Twinning results in either contraction or extension of the c-axis, known as contraction or extension twinning, respectively. Extension twinning occurs along the f1 0 1 2g planes and is easy to activate due to its low nucleation stress [10]. Experimental studies over the past five decades or so have attempted to understand the deformation mechanisms in single-crystal Mg [11–22]. Many of these studies indicate that stress state, strain rate, temperature and loading orientation (with respect to the crystallographic c-axis) have a significant influence on the principal deformation mode. However, the effect of specimen size on the deformation behavior of Mg has not been examined extensively, although a few studies have recently been reported on lm and sub-lm size single-crystal Mg specimens [23–27]. None of these studies attempted to compare the measured mechanical performance of the lm-scale specimens with that of the bulk single crystals (samples with mm or larger dimensions) to examine any differences in deformation mechanisms. In this context it is worth noting that several studies that were performed in the recent past on both crystalline and amorphous materials have shown that the plastic deformation of lm-sized samples differs significantly when compared to the bulk samples [28–35]. Here, a couple of fundamental differences that exist between micro- and macrosamples are noteworthy. First, the surface-area-tovolume ratio in the microsamples is significantly larger than that in the macro-sized specimens. If the deformation mechanisms are surface-sensitive, i.e. if the stress required for the nucleation of dislocations and/or twins is much lower at a free surface, for example, the measured mechanical responses of micro- and macrospecimens could be significantly different. Second, the necessity to maintain the uniaxiality of the sheared and unsheared parts of the specimens is generally violated in microcompression specimens, leading to unconstrained shear-sliding of one part (typically the top part) with respect to the undeformed part. This is because of the relatively low frictional resistance between the pillar top surface and the surface of the punch indenter. In the case of a macrospecimen, this friction is sufficiently large and hence the specimen has to deform in such a way that uniaxiality is maintained. This, in turn, necessitates slip plane rotation, etc., and hence alters the flow response in a significant manner. Also, most of the microcompression experiments performed on Mg single crystals were limited to c-axis compression. In order to gain better understanding of the deformation mechanisms at different length scales, it is important to conduct deformation experiments on single crystals obtained from the same bulk sample and for orientations that can activate easy deformation modes, i.e. basal
317
slip or extension twinning. In this way, one can rule out the possibilities of composition heterogeneities and misorientations that can arise during processing of the base material. Hence, in the present study we have conducted experiments on both mm- and lm-sized samples whose orientations were chosen in such a way that the predominant deformation occurs either by single slip or by extension twinning. 2. Background The early single-crystal deformation experiments on Mg were performed by Reed-Hill and Robertson [11,12] with tensile loading along the ½1 0 1 0 direction (i.e. parallel to basal planes). On the basis of the results obtained, they suggested that twinning along the f3 0 3 4g and f1 0 1 3g planes is the predominant deformation mode because of the low resolved shear stress (RSS) on basal and non-basal slip systems. Wonsiewicz [13] and Wonsiewicz and Backofen [13,14] have conducted plane strain compression experiments on single-crystal Mg and concluded that significant c-axis strains are accommodated by double twinning along the f1 0 1 1g–f1 0 1 2g planes followed by basal slip within the twinned regions. Kelly and Hosford [15] also performed plane strain compression experiments on single and textured polycrystalline Mg with constraint imposed along either the basal or prismatic direction. They observed large anisotropy in the stress vs. strain behavior and asymmetric yield loci, especially at low plastic strains, which was attributed to the f1 0 1 2g twinning. Obara et al. [16] and Yoshinaga et al. [17] compressed Mg single crystals along the c-axis and made contrasting observations in two different papers. In one study [16] they report slip on the f1 1 2 2gh1 1 2 3i system as the dominant deformation mode while in the other [17], twinning along f3 0 3 4g and f1 0 1 3g followed by basal slip ahead of the twin front and in the parent matrix material were reported. Kitahara et al. [18] and Syed et al. [19] have performed experiments on single-crystal Mg with compression along the c-axis and found that predominant deformation occurs via the second order pyramidal slip. In both these studies, the presence of compression twins in the post-deformed samples was recorded. However, Syed et al. [19], through post-mortem transmission electron microscopy (TEM) investigation of the deformed samples, suggested that twinning could not be a major deformation mode as the total density of twins in the deformed samples is small compared to the slip. Bhattacharya and Niewczas [22] have carried out uniaxial tensile experiments on single-crystal Mg oriented for basal slip at room and sub-zero temperatures. They reported extensive elongation of the samples (engineering strain of 200%) at room temperatures and attributed it to the deformation by slip. Further, the post-deformation microstructures of the samples deformed at sub-zero temperatures reveal the presence of a large number of deformation twins, suggesting that twinning could be one of the major deformation modes at sub-zero temperatures, even in the single slip oriented samples.
318
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
Recent studies [23–27] on the microcompression of Mg single crystals can be summarized as follows. During c-axis compression, Lilleodden [23] has noticed a significant increase in strength with decreasing pillar size, while Byer et al. [24] did not observe any specimen size effect. Moreover, in both the studies the post-mortem analysis of the deformed pillars, either by TEM or by electron backscattered diffraction (EBSD), suggested that deformation occurs by pyramidal slip, and no evidence of deformation twins was to be found. For similar orientations, the in situ compression experiments (on the pillar sizes of 200 nm) in TEM by Yu et al. [25] indicate compression twinning along f1 0 1 1g to be the dominant deformation mode. The source(s) for the differences in the deformation mechanisms despite the similarity of the loading orientations, is (are) not yet clear. In another study, Ye et al. [26] have carried out microcompression on Mg and Mg– 0.2% Ce single crystals with the loading axis slightly off from the c-axis and observed basal glide to be the dominant deformation mode. This could be due to the low CRSS required to activate basal slip. Further, their results revealed that the flow stress decreases with increasing pillar diameter, indicating flow stress dependence on specimen size. A recent study by Byer and Ramesh [27] concludes that the size effect is intimately connected to the initial dislocation density in the pillars. Crystals with high initial dislocation densities offer a large number of potential dislocation nucleation sources and hence the flow stress is independent of specimen size. Although there are several publications describing the micro- and macro-compression deformation response of single-crystal Mg, most of the studies were for c-axis compression and limited to either lm- or mm-sized specimens. Hence, there is a clear need for systematic investigation of deformation behavior by conducting experiments on the samples at two different length scales and with crystallographic orientations which facilitate the easiest deformation modes, i.e. basal slip or tensile twinning. In the present study, we have conducted compression experiments on single crystals of Mg with two crystallographic orientations that favor the basal slip or extension twinning and at two different specimen length scales, with an interest to seek the answers to the following questions: (a) What is effect of orientation on the stress– strain response when the specimen sizes reduced from mm to lm? (b) What is the role of orientation in the deformation behavior? (c) How does the specimen size influence the plastic deformation in different crystallographic orientations? 3. Materials and experiments Mg bicrystal containing two large grains, whose sizes are in the order of several mm, was chosen in the present study; these crystals were produced using the Bridgman technique. Each grain of the bicrystal can be considered as a single crystal and the orientation of the individual grains is determined by EBSD. Rectangular blocks with
3 mm 3 mm cross-section and 4.5 mm height were cut from the large block of bicrystal using electrodischarge machining (EDM). A low power and water pressure were used during EDM to minimize the deformation due to machining. The two ends of samples are gently polished so as to maintain parallelism with respect to the platens. The samples were first polished using successively finer diamond-particle-containing paste and final polishing was performed using colloidal silica. Samples were then etched with a solution of 10 ml HNO3 + 3 ml CH3COOH + 40 ml H2O + 120 ml C2H5OH and EBSD was performed. Uniaxial compression experiments were carried out in an Instron screw-driven machine at a nominal strain rate of 103 s1. A small amount of lubricant was applied at both ends of the sample surfaces to reduce the friction between the platens and the sample surface. Three samples for each orientation were tested and the load–displacement response was found to be highly reproducible. The samples thus tested were directly taken for microstructural characterization as the intermediate polishing may eliminate some important features of deformation. Cylindrical 3 lm diameter micropillars with a height/ diameter aspect ratio of 2 were fabricated via focused ion beam machining using a Tescan Lyra 3GM (Brno, Czech Republic). The aspect ratio was chosen following the protocol proposed by Zhang et al. [36]. Pillars with high aspect ratio tend to buckle during compression whereas a smaller aspect ratio results in non-uniform stress along the length of the sample. The micropillars were produced in two steps: first, rough pillars were made using high beam currents (2– 4 nA) followed by a fine milling at low currents (200 pA) so that the pillars have low taper and a good surface finish. However, a taper of 2° is witnessed, which is commonly noticed in focused ion beam milled pillars and this does not significantly affect the plastic deformation [36]. Five such pillars were made on each grain and the compression tests were carried out in-situ using a custom-made testing system that resides inside a scanning electron microscope (SEM) setup [37]. Tests were conducted at a nominal strain rate of 103 s1 under displacement controlled mode. A diamond indenter with a flat base of 6 lm in diameter was used for compression. 4. Results A part of the EBSD image of the bicrystal is shown in Fig. 1. The original crystals are several mm in size and separated by a high angle grain boundary. The as-grown crystals have typical initial dislocation densities, qin, of 108 m2 and such low qin is attributed to the processing route adapted [38]. As mentioned earlier, qin in particular has a significant effect on the deformation behavior in miniaturized specimens [27]. The orientations of the grains (as represented by their unit cells in Fig. 1) are identified as ½2 1 1 2 and ½2 1 1 0. Hereafter, these are referred to as Grains A and B, respectively. The included angle between the compression axis and c-axis is found to be 56 and 90° for
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325 Grain-A
319
Grain-B
Fig. 1. EBSD image of part of the bicrystal examined in this work. Grains A and B are represented by indices ½2 1 1 2 and ½2 1 1 0, respectively.
Grains A and B, respectively. Schmid factor, m, calculations for Grain A indicate that basal slip system ð0 0 0 1Þ½2 1 1 0 has the highest m (= 0.49), suggesting that plastic deformation for this orientation is favored by single slip. In the case of Grain B, the m values for prismatic slip ð1 0 1 0Þ½1 2 1 0 and tensile twinning through ð1 0 1 2Þ½1 0 1 1 systems are found to be 0.44 and 0.38, respectively. Though the former has a higher m, it is difficult to activate because of the high CRSS and hence the deformation of Grain B should be mediated by tensile twinning. Chapuis and Driver [20] have carried out plane strain compression experiments on Mg single crystals with an orientation similar to Grain B and found that the crystal indeed deforms predominantly by tensile twinning. Representative compression stress, r, vs. strain, e, plots for micropillars of Grains A and B are shown in Fig. 2a and b, respectively. Respective post-deformation images of the pillars are shown as insets in these figures. The measured responses as well as the profiles of the deformed specimens suggest that the active plastic deformation mechanisms in these two orientations are distinctly different. In Fig. 3a and b, both the micro- and macrocompression stress vs. strain curves for Grains A and B are plotted together for comparison. Important differences are highlighted below and will be described in detail in the subsequent section. (1) The microcompression r vs. e curves of Grain A are characterized by several stress drops after the initial elastic deformation and no work hardening is noticed. In-situ visualization of pillars during deformation suggests that these stress drops coincide with the gliding of the material along a parallel set of basal planes. The flow stress at a strain of 2% is observed to be 60 ± 10 MPa and the corresponding CRSS values for the basal slip is computed to be 30 ± 5 MPa. Ye et al. [26] and Byer and Ramesh [27] have conducted microcompression experiments on the orientations that favor basal slip and reported a strong size effect on flow stress. Ye et al. [26] have reported the CRSS values for basal slip in 1.6 lm diameter pillars to be
Fig. 2. Microcompression stress vs. strain curves obtained on grains (a) A and (b) B. Insets show representative post-deformation images of the pillars from each grain.
50 MPa. Byer and Ramesh [27] have found a higher CRSS value (for 3 lm diameter pillars) as compared to the current work, and the reason could due to the slight variation in crystal orientations, leading to different resolved shear stress on the basal planes. The microcompression curves of Grain B exhibit a completely contrasting constitutive behavior when compared to Grain A. A marked drop in the stress is noticed immediately after the elastic deformation, followed by a steady and enhanced strain hardening rate. While a few load drops are still noticed in the stress vs. strain curves of Grain B, their magnitude is considerably higher than those seen in Grain A. The peak flow stress corresponding to the initial plastic deformation is in the range of 175 ± 25 MPa and reaches a maximum value of 675 ± 35 MPa at 15% strain. (2) The flow curves of bulk samples differ completely from those of the micropillars for Grain A orientation. No intermediate stress drops were noticed; however, a significant size effect in strength was observed. The flow stress at a strain of 2% is 10 MPa and from this the CRSS for basal slip was estimated to be 5 MPa. Surprisingly, Grain A, which does not exhibit any strain hardening at large plastic strains
320
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
deformation by twinning. Moreover, Barnett et al. [43] suggested that in a polycrystalline Mg, a higher j is associated with a greater number of grains undergoing deformation twinning. In the present study a higher j is noticed in the case of micropillars of Grain B, compared to the large samples indicating predominance of deformation twinning in micropillars. Further, the post-deformation EBSD images of the bulk samples indicate that the deformation twinning is localized into a few regions while the parent orientation is still prevalent in some regions of the crystal. (4) The variation of strain hardening rate, h (= dr/de), is plotted as a function of e for Grains A and B in Fig. 4a and b, respectively. The strain hardening rate of Grain A decreases with increasing strain. Grain A, which does not exhibit any strain hardening during microcompression, shows a negligible amount of strain hardening during macrocompression. For Grain B, in contrast, both the micro- and macrocompression samples exhibit significant strain hardening. Several spikes in the h are noticed for micropillars and these are associated with the stress drops occurring during deformation. An interrupted compression test, wherein the sample was strained only up to 5%, was conducted on the Grain
Fig. 3. A comparison of the macro- and microcompression responses of grains (a) A and (b) B.
during microcompression, exhibits strain hardening – albeit only a small one – during macrocompression. Bhattacharya and Niewczas [22] have performed tensile experiments on Mg single crystals with orientations similar to that of Grain A and reported a CRSS of 1.1 MPa at a true strain of 0.2%, which are similar to the present study. Chapuis and Driver [20] have reported a CRSS of 5 MPa at a plastic strain of 1%, considerably higher than the uniaxial compression values, and the differences are attributed to the differences in stress state. The macrocompression curves of Grain B are similar to the micropillars; however, no stress drops are witnessed during deformation. (3) The stress vs. strain curves of Grain B during both micro- and macrocompression are characterized by three stages of hardening. Following initial elastic deformation, a plateau and high strain hardening regions are noticed. A significant concavity, j ( = d2r/de2) is observed after the plateau region, which is evaluated by fitting a quadratic equation to the r vs. e curve. Similar r vs. e behavior was reported by several researchers during the uniaxial and plane strain compression testing of single- [13–15,20] and highly textured poly-crystalline Mg and its alloys [39–43]. The concave behavior is attributed to
Fig. 4. Strain hardening rate, h, plotted as a function of strain for (a) single slip and (b) twin oriented crystals.
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
B and the r vs. e response with the corresponding SEM image of the pillar is shown in Fig. 5. The objective of this test is to ascertain whether load drop following elastic deformation produces any slip offset in the micropillars. The image of the deformed pillar indicates that there are no slip steps until 5% strain. Such stress drops in the r vs. e curves are reported previously during the deformation of nanopillars of Mg [25] and Ag [44] and are associated with the twin nucleation. The post-deformation optical micrographs of the mmsized samples are shown in Fig. 6a and b for Grain A and B, respectively. Note that the microstructures are obtained on the as-deformed surfaces without any intermediate polishing as this may obliterate some of the important deformation features (e.g. presence of slip bands) from the surface. Optical micrographs of Grain A indicate the presence of slip traces with no evidence of deformation twinning while high twin densities are noticed in Grain B and these twins are wide and long, resembling tensile twins [43]. It can also be seen from the optical micrographs of Grain B (Fig. 6b) that large a number of slip bands are present within and at the intersection of twins. The coexistence of slip and twins was previously observed by Vaidya and Mahajan [46] on shock-loaded hcp cobalt (Co) single crystals. TEM analyses of the post-deformed Co samples reveal basal and non-basal slip dislocations ahead of the terminating twins and at twin intersections. They have argued that high stress concentrations ahead of the twin tip are relaxed by the emission of the dislocations. The present observations are consistent with their reports. Post-deformation EBSD images of Grain A and B samples compressed to a strain of 15% are presented in Fig. 7a and b. These images further suggest that the orientation of Grain A retains its initial orientation while large fraction of Grain B undergoes deformation twinning. Inverse pole figure maps indicate that the twinned lattice reorients by 86°, confirming that these twins are tensile in nature occurring along f1 0 1 2g planes.
321
(a)
10 µm
(b) Slip bands Slip bands
20 µm
Fig. 6. Representative post-deformation optical micrographs of the macrocompression samples of grains (a) A and (b) B. Slip bands are noticed in grain A with no evidence of twinning. Microstructures of grain B comprise both twin and slip bands (the encircled regions show the slip bands).
5. Discussion The experimental results presented in the preceding section show that the specimen size and orientation exert a significant influence on the deformation behavior of Mg crystals, with micropillars exhibiting a higher strength. There are significant differences in the strain hardening behavior in both Grains A and B and are described below in detail. 5.1. Deformation behavior of single slip oriented crystal: specimen size effect
Fig. 5. Engineering stress–strain curve of a micropillar that was compressed to a total strain of 5%. The corresponding image of the pillar is also shown. Notice the absence of slip steps at this strain.
Post-deformation images of the micropillars of Grain A indicate the deformation along the single set of planes (Fig. 2a) while SEM micrographs of bulk samples show extensive slip bands (Fig. 6a) on the surface. The angle between the compression axis and these slip planes or bands was found to be 45°, suggesting deformation along the basal planes. The behavior of bulk samples is consistent with the observations of Bhattacharya and Niewczas [22], who also have observed extensive slip bands on the sample surfaces during the tensile experiments on basal slip
322
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
[28–33]. However, recent compression experiments on bcc [49] and hcp [27] micropillars reveal that qin has a considerable influence on the size effect observed in flow stress. Bei et al. [49] have indicated that pillars made from perfect crystals (whiskers) and pillars with a large density of dislocations do not show the size effect whereas the pillars with low qin exhibit strong size dependence of the flow stress. Byer and Ramesh [27] also have made similar observations in Mg micropillars with low qin and attribute it to the dislocation source controlled behavior. In lm-sized samples, the number of potential dislocation nucleation sources is small due to the low volume, and hence a higher stress is needed to initiate plastic deformation. In contrast, bulk samples contain a large number of dislocation sources and hence the plastic flow occurs at relatively lower stress [50–52]. In this context, it is worth noting that Parthasarathy et al. [53] have proposed a “source-truncation hardening” mechanism to rationalize the size effect in single-crystal micropillars. This mechanism is intimately connected to the initial dislocation density, the number of dislocation sources and their distribution within the pillars. The variation of h with e in micropillars is characterized by several spikes whereas it is smooth in bulk samples. The spikes in h correspond to the stress drops during plastic deformation (Fig. 1a) due to the basal glide of the micropillars. The smooth hardening behavior in bulk samples is attributed to the large number of dislocation nucleation sources (due to the higher sample volume). These large numbers of sources provide an increase in the mobile dislocation density during deformation and their interaction leads to forest hardening. A comparison of the EBSD images of the crystals before and after deformation leads to the following interesting observation. Orientation of the Grain A after deformation is similar to the initial orientation, indicating that deformation is predominantly by basal slip with no evidence of twinning.
Fig. 7. Post-deformation EBSD images of grains (a) A and (b) B, illustrating that grain A, which deforms by single slip, does not undergo any crystallographic reorientation (compare it with Fig. 1a). For grain B, the parent orientation is in blue whereas the twinned regions are in red. Orientations corresponding to different colored regions of EBSD image are indicated by numbers and the unit cells representing each number are also shown. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
oriented Mg single crystals. Moreover, the plastic deformation of micropillars is characterized by several load drops and these discrete events during plastic deformation are associated with plastic flow localization into a single set of planes. Such events are previously reported in micropillar compression experiments of bcc and fcc single crystals oriented for single slip [33,47,48]. The estimated CRSS of micropillars ( 30 MPa) is considerably higher than the bulk samples ( 5 MPa), indicating the strong dependence of flow stress on the specimen size. The specimen size dependence of flow stress is widely studied in literature
5.2. Deformation behavior of twin oriented crystal: specimen size effect The stress vs. strain curves of Grain B show a plateau region after yielding, where a small increase in stress results in a significant increase in strain, and such behavior is associated with twin propagation during deformation [15,20]. The maximum plastic strain in the plateau region is ~ 0.05-0.08 and this corresponds to the strain associated with twinning shear (0.129). A key observation of the current study is the difference in yield behavior of the micropillars and bulk samples. It is evident from Fig. 3b that yield in micropillars is followed by a significant stress drop whereas the flow curves are smooth in bulk samples. Sedlmayr et al. [44] have also observed such abrupt drop in stress (immediately following yield stress) during the tensile deformation of gold nanowhiskers and subsequent TEM and EBSD analyses of these whiskers reveal that these events are associated with twin nucleation, preferentially at the pillar surface. In another study, Yu et al. [25] have carried out in situ tensile
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
experiments on Mg nanopillars and noticed significant stress drops immediately after yield stress. The TEM images suggest that these stress bursts correlate with the nucleation of f1 0 1 2g twins (tension twins) from the pillar surface. Given the low initial dislocation density (108 m–2) in the initial crystals and size of the micropillars, it is reasonable to assume that the pillars do not contain enough dislocation sources within them and hence twins have to nucleate from the pillar surface. The twin nucleation stress, stw, is 150– 200 MPa (Fig. 2b), which is considerably lower than the values reported by Yu et al. [25] for Mg nanopillars. Such large differences (as high as 600 MPa) in stw are even observed in Au nanowhiskers [44] within the pillars of similar size (diameters 65 nm). Further, the molecular dynamics (MD) simulations of pillars having different initial surface roughness suggests that the observed variations in stw are due to the differences in surface roughness values. The stw drops precipitously with increasing surface roughness. Hence, the variability in stw observed between the micro- and nano-pillars could be attributed to the differences in surface roughness. However, a detailed understanding of twin nucleation mechanisms is far from complete and needs further investigation. The stress bursts are not noticed during the compression of bulk samples, suggesting that stw exhibits a strong dependence on specimen size. The differences in twin nucleation between the micropillars and bulk samples can be explained as follows: deformation twinning (DT), mediated by shear assisted co-operative movement of a finite number of atoms, occurs by nucleation and propagation [10]. Heterogeneous twin nucleation models [10,54] suggest that twins are more likely to nucleate at grain boundaries and sessile dislocation poles due to the presence of high stress concentration associated with those defects [10,54,55]. Wang et al. [55] have performed atomistic simulations on hcp crystals to understand the mechanisms of ð1 0 1 2Þ twin nucleation. Their observations suggest that a stable twin nucleus formed by zonal twinning mechanism (simultaneous glide of zonal dislocations consisting of a partial dislocation and multiple twinning dislocations) is preferred because of the lower elastic energy. The probability of finding such potential nucleation sites is higher in bulk single crystals and polycrystalline samples because the twin nucleation occurs at relatively low stresses. In Fig. 4b, variation of h with e is compared for both the sample sizes. Three stages of hardening are noted: (1) a constant h regime, (2) an increasing h followed by (3) a decreasing h. The peak strain hardening rates during stage I (hI) and II (hII) for both the sample sizes are listed in Table 1. While the differences in hI for the two sample sizes is negligible, the maximum value of h in stage II, hII,max, is much higher in micropillars compared to the bulk samples. These observations indicate that sample size has a negligible influence on h in the plateau region, suggesting the operation of similar deformation mechanisms at both the sample sizes. A possible reason for this behavior may be
323
the constant twinning shear, ctw, caused by the extension twinning. The area Hunder the stress vs. strain curves in the plateau region, n ¼ rde, which represents an indirect measure of energy expended in twin propagation, is listed in Table 1. A low n in the case of micropillars suggests that twins can propagate easily in micropillars, although their nucleation is difficult. As already indicated, the nucleation stress in the current pillars is attributed to the low initial dislocation density. But as the plastic deformation proceeds, the dislocation density increases substantially, resulting in a concomitant increase in the density of the mobile dislocations. In consideration of the fact that twin propagation occurs by the movement of twin partial dislocations [55], it is obvious to note that a lower stress is needed for twin propagation. Another important observation from Fig. 3b is that the plateau strain in micropillars is lower than that observed in the bulk samples. Assuming that this strain is associated with the twin propagation within the crystal, it is reasonable to argue that twin propagation is difficult in bulk samples due to the large volume of the material. A systematic experimental investigation with varying sample sizes is desirable for improved understanding of the fundamental mechanisms responsible for this atypical behavior. The concavity, j, in the strain ranges between 0.04 and 0.08 for micropillars and 0.04 and 0.12 for bulk samples is listed in Table 1. Barnett et al. [43] have plotted the magnitude of j against the percentage of twinned grains for different grain size samples of a polycrystalline Mg alloy subjected to uniaxial compression (Fig. 5 in Ref. [43]). Their results indicate that a higher j results when the majority of the grains deform by twinning. The j value estimated for micropillars of Grain B is an order of magnitude greater than the bulk samples, suggesting that the deformation twinning is more predominant in micropillars. Post-mortem optical and EBSD images (Figs. 6b and 7b) of the bulk samples suggest that the entire crystal does not undergo deformation by twinning as the inverse pole figure maps show regions of crystal with parent and other intermediate configurations. This indicates that in bulk single crystals, besides twinning, a significant amount of deformation is still mediated by slip (slip bands are even evident in optical micrographs). Both the micropillars and bulk samples exhibit a substantial increase in work hardening after the plateau region. Such observations are reported in the literature for the plane strain compression experiments on singlecrystal Mg when the deformation proceeds by twinning [14,15,20]. As a result of extension twinning, the parent lattice undergoes a crystallographic re-orientation which in turn increases the resistance to basal slip [7] as the reoriented crystal will have its hci axis normal to the principal stress axis. Hence, subsequent deformation has to proceed through either pyramidal slip or compression twinning; both of which lead to substantial work hardening [20,41,42]. Recent uniaxial compression experiments by Hong et al. [41] and Knezevic et al. [42] on a highly
324
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
Table 1 Strain hardening rate, h, during stages I and II and work done, n, in stage I and concavity j during compression of Grain B.
Microcompression Macrocompression
j (GPa)
hI (GPa)
hII,max (GPa)
eII,max (%)
nI (J)
0.6 ± 0.1 0.08 ± 0.02
0.8 ± 0.03 0.7 ± 0.01
18 ± 2 5±1
6.65 ± 0.5 11.2 ± 1
0.45 0.80
textured polycrystalline Mg also report a maximum strain hardening rate, hII,max, of 5 GPa at a strain, eII,max, of 8%. They attribute the increase in h during stage II to the (i) reduction in the effective grain size (due to the formation of contraction twins) and (ii) resistance offered by the twin boundaries to the pyramidal dislocations. Moreover, the uniaxial tensile experiments of polycrystalline Mg indicate lower strain hardening levels [41]. The difference in strain hardening between tension and compression experiments are attributed to the active twin variants that are present under these loading conditions. In the present study, though the loading path is the same for both micropillars and bulk samples, a significant difference in hII,max and eII,max (Table 1) was noticed. This observation highlights the fact that sample size also exerts a considerable influence on the measured strain hardening behavior. In the case of micropillars it is possible that the total twin volume fraction is higher than the bulk samples. Yu et al. [25] have also noticed that twin thickness increases with sample size; bulk samples often contain thicker twins compared to the micro- and nano-sized pillars. The EBSD maps (Fig. 7b) of the bulk samples indicate thick twins with a typical twin area fraction of 10–15% of the total area. This suggests a possible explanation for the increase in strain hardening in micropillars. It is widely discussed in Mg literature that (1) the twin boundaries act as barriers for dislocation motion and promote the strain hardening (see for example Refs. [8,56]) and (2) the twinned lattice (as a result of re-orientation) favors slip on hard crystallographic slip systems, thereby offering large resistance dislocation motion [57]. It is also argued that the dislocations that are mobile in the parent lattice can become immobile in the twinned lattice due to the crystallographic reorientation [57]. In samples with high twin density and small twin thickness, the above-mentioned mechanisms have a pronounced effect on the deformation behavior and could result in an increased strain hardening rate. However, a detailed experimental investigation is warranted in this direction. 5.3. Morphology of the post-deformed pillars The post-deformation images of the pillars, shown in Fig. 2, indicate that the plane on which deformation localizes is largely influenced by the orientation of the crystals with loading axis. In micropillars of Grain A, which deform predominantly by single slip, the glide plane is at an angle of 45 ± 3° to the compression axis whereas in Grain B it is almost normal to the compression axis. In bcc and fcc micropillars that are oriented for single slip,
the glide plane is 45° to the compression axis [45,46]. Dimiduk et al. [47] have shown that apart from the orientation, specimen size has a strong influence on the glide plane. It is generally observed that for pillars less than 1 lm in size the glide planes are found to be oriented at an angle that is greater than 45° to the loading axis [32,45].The reason for this behavior could be due to large taper that is generally present in the sub-micron sized pillars. A specific angle between the deformation plane and loading axis could not be assigned for micropillars of Grain B. A close examination of the deformed pillars suggests that their overall appearance is similar to that of the Mg micropillars compressed along the c-axis reported in the literature [23,24]. In those cases, pyramidal slip is found to be the dominant deformation during c-axis compression. As discussed in Section 5.2, tensile twinning results in reorientation of Grain B to 86°. The twinned lattice is oriented in such a way that the c-axis is in line with the compression axis, which is similar to the initial orientation of the crystals tested by Lilleodden [23] and Byer et al. [24]. These results indicate that the failure morphology of the pillars is sensitive not only to the initial orientation of the crystal but also to the changes that occur during plastic deformation. 6. Conclusions Two Mg single crystals with orientations favorable for deformation by basal slip and extension twinning were studied on two sample sizes ranging from mm to lm. Crystals in both the orientations exhibit significant size effects in strength and strain hardening behavior. Micropillars which deform by basal slip exhibit several load drops during plastic deformation and each of these events correspond to glide of the pillar on a single set of planes. In contrast, the load drops are not noticed in bulk samples and they show negligible strain hardening. Another important conclusion of the present study is the effect of specimen size on twin nucleation and propagation in the crystals favorable for deformation by extension twinning. A higher stress is required to nucleate the twins in micropillars than the bulk crystals but their propagation is difficult in bulk samples. The initial dislocation density in the samples appears to have significant effect on the twin nucleation stress, particularly in lm-sized pillars. Microstructural and EBSD analyses of the bulk samples suggest that the plastic deformation of basal slip oriented crystals occurs only by single slip while in twin oriented crystals it occurs both by slip and by twinning. The interaction between the slip
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
dislocations and twins could be a possible reason for a higher strain hardening behavior in twin oriented crystals. Further, our observations also suggests that the specimen size has a marked influence on the strain hardening rate, h, with h increasing with decreasing specimen size. Acknowledgments We are grateful to Dr. Rejin Raghavan of EMPA, Thun for his assistance in the conduct of micropillar compression experiments reported in this work and Dr. Johann Michler for his permission to use the facilities in his lab. We would like to thank Profs. T. Watanabe and A.H. Chokshi for providing the bicrystals. We also would like to express our gratitude to the anonymous reviewer for his/her constructive comments on the manuscript. References [1] Easton M, Beer A, Barnett M, Davies C, Dunlop G, Durandet Y, et al. J Met 2008;11:57. [2] Caceres CH. Metall Mater Trans A 2007;38:1649. [3] Kulekci MK, Int J. Adv Manuf Technol 2008;39:851. [4] Groves GW, Kelly A. Philos Mag 1963;8:877. [5] Graff S, Brocks W, Steglich D. Int J Plast 2007;23:1957. [6] Kalidindi SR. J Mech Phys Solids 1998;46:267. [7] Zhang J, Joshi SP. J Mech Phys Solids 2012;60:945. [8] Yoo MH. Metall Trans A 1981;12:409. [9] Munroe N, Tan X, Gu H. Scripta Mater 1997;36:1383. [10] Christian JW, Mahajan S. Prog Mater Sci 1995;39:1. [11] Reed-Hill RE, Robertson WD. Trans AIME 1957;209:496. [12] Reed-Hill RE, Robertson WD. Acta Metall 1957;5:717. [13] Wonsiewicz BC. PhD thesis, Massachusetts Institute of Technology; 1966. [14] Wonsiewicz BC, Backofen WA. Trans Metall Soc AIME 1967;239:1422. [15] Kelly EW, Hosford WF. Trans Metall Soc AIME 1968;242:5. [16] Obara T, Yoshinga H, Morozumi S. Acta Metall 1973;21:845. [17] Yoshinaga H, Obara T, Morozumi S. Mater Sci Eng 1973;12:255. [18] Kitahara T, Ando S, Tsushida M, Kitahara H, Tonda H. Key Eng Mater 2007;345:129. [19] Syed B, Geng J, Mishra RK, Kumar KS. Scripta Mater 2012;67:700. [20] Chapuis A, Driver JH. Acta Mater 2011;59:1986. [21] Li Q. Mater Sci Eng A 2013;568:96. [22] Bhattacharya B, Niewczas M. Philos Mag 2011;91:2227. [23] Lilleodden E. Scripta Mater 2010;62:532. [24] Byer CM, Li B, Cao B, Ramesh KT. Scripta Mater 2010;62:536.
325
[25] Yu Q, Qi L, Chen K, Mishra RK, Li J, Minor AM. Nano Lett 2012;12:887. [26] Ye J, Mishra RK, Sachdev AK, Minor AM. Scripta Mater 2011;64:292. [27] Byer CM, Ramesh KT. Acta Mater 2013;61:3808. [28] Uchic MD, Dimiduk DM, Florando JN, Nix WD. Science 2004;305:986. [29] Dehm G. Prog Mater Sci 2009;54:664. [30] Greer JR, DeHosson JM. Prog Mater Sci 2011;56:654. [31] Uchic MD, Shade PA, Dimiduk DM. Annu Rev Mater Sci 2009;39:361. [32] Volkert CA, Donohue A, Spaepen F. J Appl Phys 2008;103:083539. [33] Volkert CA, Lilleodden ET. Philos Mag 2006;86:5567. [34] Schuster BE, Wei Q, Hufnagel TC, Ramesh KT. Acta Mater 2008;56:5091. [35] Dubach A, Prasad KE, Raghavan R, Lo¨ffler JF, Michler J, Ramamurty U. J Mater Res 2009;24:2697. [36] Zhang H, Schuster BE, Wei Q, Ramesh KT. Scripta Mater 2006;54:181. [37] Rabe R, Breguet JM, Schwaller P, Stauss S, Haug FJ, Patscheider J, et al. Thin Solid Films 2004;469:206. [38] Tsivinsky SV. Kris Tech 1975;10:5. [39] Barnett MR. Mater Sci Eng A 2007;464:1. [40] Proust G, Tome´ CN, Jain A, Agnew SR. Int J Plast 2009;25:861. [41] Hong S, Park SH, Lee CS. Acta Mater 2010;58:5873. [42] Knezevic M, Levinson A, Harris R, Mishra RK, Doherty RD, Kalidindi SR. Acta Mater 2010;58:6230. [43] Barnett MR, Keshavarz Z, Beer AG, Atwell D. Acta Mater 2004;52:5093. [44] Sedlmayr A, Bitzek E, Gianola DS, Richter G, Monig R, Kraft O. Acta Mater 2012;60:3985. [45] Koike J. Metall Mater Trans A 2005;36A:1689. [46] Vaidya S, Mahajan S. Acta Mater 1980;28:1123. [47] Dimiduk DM, Uchic MD, Parthasarathy TA. Acta Mater 2005;53:4065. [48] Schneider AS, Kaufmann D, Clark BG, Frick CP, Gruber PA, Monig R, et al. Phys Rev Lett 2009:105501. [49] Bei H, Shim S, Pharr GM, George EP. Acta Mater 2008;56:4762. [50] Benzerga AA. Int J Plast 2008;24:1128. [51] Rao SI, Dimiduk DM, Parthasarathy TA, Uchic MD, Tang M, Woodward C. Acta Mater 2008;56:3245. [52] Senger J, Weygand D, Gumbsch P, Kraft O. Scripta Mater 2008;58:587. [53] Parthasarathy TA, Rao SI, Dimiduk DM, Uchic MD, Trinkle DR. Scripta Mater 2007;56:313. [54] Mahajan S. Scripta Mater 2013;68:95. [55] Wang J, Hirth JP, Tome CN. Acta Mater 2007;57:5521. [56] Serra A, Bacon DJ. Acta Metall Mater 1995;43:4465. [57] Niewczas M. Acta Mater 2010;58:5848.
ScienceDirect Acta Materialia 65 (2014) 316–325 www.elsevier.com/locate/actamat
Micropillar and macropillar compression responses of magnesium single crystals oriented for single slip or extension twinning K. Eswar Prasad a,⇑, K. Rajesh a, U. Ramamurty a,b b
a Department of Materials Engineering, Indian Institute of Science, Bangalore 560012, India Center of Excellence for Advanced Materials Research, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Received 6 July 2013; received in revised form 30 October 2013; accepted 31 October 2013 Available online 27 November 2013
Abstract Uniaxial compression experiments were conducted on two magnesium (Mg) single crystals whose crystallographic orientations facilitate the deformation either by basal slip or by extension twinning. Specimen size effects were examined by conducting experiments on lm- and mm-sized samples. A marked specimen size effect was noticed, with micropillars exhibiting significantly higher flow stress than bulk samples. Further, it is observed that the twin nucleation stress exerts strong size dependence, with micropillars requiring substantially higher stress than the bulk samples. The flow curves obtained on the bulk samples are smooth whereas those obtained from micropillars exhibit intermittent and precipitous stress drops. Electron backscattered diffraction and microstructural analyses of the deformed samples reveal that the plastic deformation in basal slip oriented crystals occurs only by slip while twin oriented crystals deform by both slip and twinning modes. The twin oriented crystals exhibit a higher strain hardening during plastic deformation when compared to the single slip oriented crystals. The strain hardening rate, h, of twin oriented crystals is considerably greater in micropillars compared to the bulk single crystals, suggesting the prevalence of different work hardening mechanisms at these different sample sizes. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Magnesium; Deformation twinning; Strain hardening rate; Size-effect; Electron backscattered diffraction (EBSD)
1. Introduction The mechanical behavior of magnesium (Mg) and its alloys has attracted considerable attention from researchers in recent years due to the growing demand for lightweight structural materials, especially for the automobile and aerospace industries. Mg and its alloys have low density (1.79 g cm–3) and high specific strength compared to the materials currently used for automobile applications such as aluminum alloys [1–3]. However, Mg alloys suffer from poor room temperature ductility and formability, which is attributed to their low-symmetry hexagonal close-packed (hcp) crystal structure. Unlike face-centered cubic (fcc) and body-centered cubic (bcc) metals, metals with hcp crystal structure do not possess a high enough number of slip ⇑ Corresponding author.
E-mail address: [email protected] (K.E. Prasad).
systems at room temperature to undergo plastic deformation by slip alone. Hence, twinning has a major role to play during the plastic deformation of hcp metals and makes the deformation far more complex [4]. To develop new Mg alloys with good formability, a detailed understanding of the deformation mechanisms that are operative at different temperatures, strain rates and across multiple length scales is essential. Such an understanding can be employed to modify the existing plasticity models, which do not explicitly contain the length-scale-dependent deformation behavior in their formulation, for improved predictability [5–7]. As the lattice parameterp ratio, ffiffiffiffiffiffiffiffi c/a, of Mg is equal to that of an ideal hcp lattice ð 8=3Þ; basal slip {0 0 0 1}, is the easiest slip system to be activated owing to its low critical resolved shear stress (CRSS) [8,9]. The other slip systems that can potentially play a role in the plastic deformation, are prismatic f1 0 1 0g and pyramidal f1 0 1 1g slip systems. The Burgers vector in all these is along the hai direction
1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.10.073
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
and hence strain accommodation in the hci direction is not possible. This necessitates the activation of deformation modes (either twinning or pyramidal slip) that can accommodate the plastic deformation along the c direction. Due to the high CRSS it is difficult to activate the pyramidal hc + ai slip at room temperature [7] which means that deformation has to occur by twinning. Twinning results in either contraction or extension of the c-axis, known as contraction or extension twinning, respectively. Extension twinning occurs along the f1 0 1 2g planes and is easy to activate due to its low nucleation stress [10]. Experimental studies over the past five decades or so have attempted to understand the deformation mechanisms in single-crystal Mg [11–22]. Many of these studies indicate that stress state, strain rate, temperature and loading orientation (with respect to the crystallographic c-axis) have a significant influence on the principal deformation mode. However, the effect of specimen size on the deformation behavior of Mg has not been examined extensively, although a few studies have recently been reported on lm and sub-lm size single-crystal Mg specimens [23–27]. None of these studies attempted to compare the measured mechanical performance of the lm-scale specimens with that of the bulk single crystals (samples with mm or larger dimensions) to examine any differences in deformation mechanisms. In this context it is worth noting that several studies that were performed in the recent past on both crystalline and amorphous materials have shown that the plastic deformation of lm-sized samples differs significantly when compared to the bulk samples [28–35]. Here, a couple of fundamental differences that exist between micro- and macrosamples are noteworthy. First, the surface-area-tovolume ratio in the microsamples is significantly larger than that in the macro-sized specimens. If the deformation mechanisms are surface-sensitive, i.e. if the stress required for the nucleation of dislocations and/or twins is much lower at a free surface, for example, the measured mechanical responses of micro- and macrospecimens could be significantly different. Second, the necessity to maintain the uniaxiality of the sheared and unsheared parts of the specimens is generally violated in microcompression specimens, leading to unconstrained shear-sliding of one part (typically the top part) with respect to the undeformed part. This is because of the relatively low frictional resistance between the pillar top surface and the surface of the punch indenter. In the case of a macrospecimen, this friction is sufficiently large and hence the specimen has to deform in such a way that uniaxiality is maintained. This, in turn, necessitates slip plane rotation, etc., and hence alters the flow response in a significant manner. Also, most of the microcompression experiments performed on Mg single crystals were limited to c-axis compression. In order to gain better understanding of the deformation mechanisms at different length scales, it is important to conduct deformation experiments on single crystals obtained from the same bulk sample and for orientations that can activate easy deformation modes, i.e. basal
317
slip or extension twinning. In this way, one can rule out the possibilities of composition heterogeneities and misorientations that can arise during processing of the base material. Hence, in the present study we have conducted experiments on both mm- and lm-sized samples whose orientations were chosen in such a way that the predominant deformation occurs either by single slip or by extension twinning. 2. Background The early single-crystal deformation experiments on Mg were performed by Reed-Hill and Robertson [11,12] with tensile loading along the ½1 0 1 0 direction (i.e. parallel to basal planes). On the basis of the results obtained, they suggested that twinning along the f3 0 3 4g and f1 0 1 3g planes is the predominant deformation mode because of the low resolved shear stress (RSS) on basal and non-basal slip systems. Wonsiewicz [13] and Wonsiewicz and Backofen [13,14] have conducted plane strain compression experiments on single-crystal Mg and concluded that significant c-axis strains are accommodated by double twinning along the f1 0 1 1g–f1 0 1 2g planes followed by basal slip within the twinned regions. Kelly and Hosford [15] also performed plane strain compression experiments on single and textured polycrystalline Mg with constraint imposed along either the basal or prismatic direction. They observed large anisotropy in the stress vs. strain behavior and asymmetric yield loci, especially at low plastic strains, which was attributed to the f1 0 1 2g twinning. Obara et al. [16] and Yoshinaga et al. [17] compressed Mg single crystals along the c-axis and made contrasting observations in two different papers. In one study [16] they report slip on the f1 1 2 2gh1 1 2 3i system as the dominant deformation mode while in the other [17], twinning along f3 0 3 4g and f1 0 1 3g followed by basal slip ahead of the twin front and in the parent matrix material were reported. Kitahara et al. [18] and Syed et al. [19] have performed experiments on single-crystal Mg with compression along the c-axis and found that predominant deformation occurs via the second order pyramidal slip. In both these studies, the presence of compression twins in the post-deformed samples was recorded. However, Syed et al. [19], through post-mortem transmission electron microscopy (TEM) investigation of the deformed samples, suggested that twinning could not be a major deformation mode as the total density of twins in the deformed samples is small compared to the slip. Bhattacharya and Niewczas [22] have carried out uniaxial tensile experiments on single-crystal Mg oriented for basal slip at room and sub-zero temperatures. They reported extensive elongation of the samples (engineering strain of 200%) at room temperatures and attributed it to the deformation by slip. Further, the post-deformation microstructures of the samples deformed at sub-zero temperatures reveal the presence of a large number of deformation twins, suggesting that twinning could be one of the major deformation modes at sub-zero temperatures, even in the single slip oriented samples.
318
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
Recent studies [23–27] on the microcompression of Mg single crystals can be summarized as follows. During c-axis compression, Lilleodden [23] has noticed a significant increase in strength with decreasing pillar size, while Byer et al. [24] did not observe any specimen size effect. Moreover, in both the studies the post-mortem analysis of the deformed pillars, either by TEM or by electron backscattered diffraction (EBSD), suggested that deformation occurs by pyramidal slip, and no evidence of deformation twins was to be found. For similar orientations, the in situ compression experiments (on the pillar sizes of 200 nm) in TEM by Yu et al. [25] indicate compression twinning along f1 0 1 1g to be the dominant deformation mode. The source(s) for the differences in the deformation mechanisms despite the similarity of the loading orientations, is (are) not yet clear. In another study, Ye et al. [26] have carried out microcompression on Mg and Mg– 0.2% Ce single crystals with the loading axis slightly off from the c-axis and observed basal glide to be the dominant deformation mode. This could be due to the low CRSS required to activate basal slip. Further, their results revealed that the flow stress decreases with increasing pillar diameter, indicating flow stress dependence on specimen size. A recent study by Byer and Ramesh [27] concludes that the size effect is intimately connected to the initial dislocation density in the pillars. Crystals with high initial dislocation densities offer a large number of potential dislocation nucleation sources and hence the flow stress is independent of specimen size. Although there are several publications describing the micro- and macro-compression deformation response of single-crystal Mg, most of the studies were for c-axis compression and limited to either lm- or mm-sized specimens. Hence, there is a clear need for systematic investigation of deformation behavior by conducting experiments on the samples at two different length scales and with crystallographic orientations which facilitate the easiest deformation modes, i.e. basal slip or tensile twinning. In the present study, we have conducted compression experiments on single crystals of Mg with two crystallographic orientations that favor the basal slip or extension twinning and at two different specimen length scales, with an interest to seek the answers to the following questions: (a) What is effect of orientation on the stress– strain response when the specimen sizes reduced from mm to lm? (b) What is the role of orientation in the deformation behavior? (c) How does the specimen size influence the plastic deformation in different crystallographic orientations? 3. Materials and experiments Mg bicrystal containing two large grains, whose sizes are in the order of several mm, was chosen in the present study; these crystals were produced using the Bridgman technique. Each grain of the bicrystal can be considered as a single crystal and the orientation of the individual grains is determined by EBSD. Rectangular blocks with
3 mm 3 mm cross-section and 4.5 mm height were cut from the large block of bicrystal using electrodischarge machining (EDM). A low power and water pressure were used during EDM to minimize the deformation due to machining. The two ends of samples are gently polished so as to maintain parallelism with respect to the platens. The samples were first polished using successively finer diamond-particle-containing paste and final polishing was performed using colloidal silica. Samples were then etched with a solution of 10 ml HNO3 + 3 ml CH3COOH + 40 ml H2O + 120 ml C2H5OH and EBSD was performed. Uniaxial compression experiments were carried out in an Instron screw-driven machine at a nominal strain rate of 103 s1. A small amount of lubricant was applied at both ends of the sample surfaces to reduce the friction between the platens and the sample surface. Three samples for each orientation were tested and the load–displacement response was found to be highly reproducible. The samples thus tested were directly taken for microstructural characterization as the intermediate polishing may eliminate some important features of deformation. Cylindrical 3 lm diameter micropillars with a height/ diameter aspect ratio of 2 were fabricated via focused ion beam machining using a Tescan Lyra 3GM (Brno, Czech Republic). The aspect ratio was chosen following the protocol proposed by Zhang et al. [36]. Pillars with high aspect ratio tend to buckle during compression whereas a smaller aspect ratio results in non-uniform stress along the length of the sample. The micropillars were produced in two steps: first, rough pillars were made using high beam currents (2– 4 nA) followed by a fine milling at low currents (200 pA) so that the pillars have low taper and a good surface finish. However, a taper of 2° is witnessed, which is commonly noticed in focused ion beam milled pillars and this does not significantly affect the plastic deformation [36]. Five such pillars were made on each grain and the compression tests were carried out in-situ using a custom-made testing system that resides inside a scanning electron microscope (SEM) setup [37]. Tests were conducted at a nominal strain rate of 103 s1 under displacement controlled mode. A diamond indenter with a flat base of 6 lm in diameter was used for compression. 4. Results A part of the EBSD image of the bicrystal is shown in Fig. 1. The original crystals are several mm in size and separated by a high angle grain boundary. The as-grown crystals have typical initial dislocation densities, qin, of 108 m2 and such low qin is attributed to the processing route adapted [38]. As mentioned earlier, qin in particular has a significant effect on the deformation behavior in miniaturized specimens [27]. The orientations of the grains (as represented by their unit cells in Fig. 1) are identified as ½2 1 1 2 and ½2 1 1 0. Hereafter, these are referred to as Grains A and B, respectively. The included angle between the compression axis and c-axis is found to be 56 and 90° for
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325 Grain-A
319
Grain-B
Fig. 1. EBSD image of part of the bicrystal examined in this work. Grains A and B are represented by indices ½2 1 1 2 and ½2 1 1 0, respectively.
Grains A and B, respectively. Schmid factor, m, calculations for Grain A indicate that basal slip system ð0 0 0 1Þ½2 1 1 0 has the highest m (= 0.49), suggesting that plastic deformation for this orientation is favored by single slip. In the case of Grain B, the m values for prismatic slip ð1 0 1 0Þ½1 2 1 0 and tensile twinning through ð1 0 1 2Þ½1 0 1 1 systems are found to be 0.44 and 0.38, respectively. Though the former has a higher m, it is difficult to activate because of the high CRSS and hence the deformation of Grain B should be mediated by tensile twinning. Chapuis and Driver [20] have carried out plane strain compression experiments on Mg single crystals with an orientation similar to Grain B and found that the crystal indeed deforms predominantly by tensile twinning. Representative compression stress, r, vs. strain, e, plots for micropillars of Grains A and B are shown in Fig. 2a and b, respectively. Respective post-deformation images of the pillars are shown as insets in these figures. The measured responses as well as the profiles of the deformed specimens suggest that the active plastic deformation mechanisms in these two orientations are distinctly different. In Fig. 3a and b, both the micro- and macrocompression stress vs. strain curves for Grains A and B are plotted together for comparison. Important differences are highlighted below and will be described in detail in the subsequent section. (1) The microcompression r vs. e curves of Grain A are characterized by several stress drops after the initial elastic deformation and no work hardening is noticed. In-situ visualization of pillars during deformation suggests that these stress drops coincide with the gliding of the material along a parallel set of basal planes. The flow stress at a strain of 2% is observed to be 60 ± 10 MPa and the corresponding CRSS values for the basal slip is computed to be 30 ± 5 MPa. Ye et al. [26] and Byer and Ramesh [27] have conducted microcompression experiments on the orientations that favor basal slip and reported a strong size effect on flow stress. Ye et al. [26] have reported the CRSS values for basal slip in 1.6 lm diameter pillars to be
Fig. 2. Microcompression stress vs. strain curves obtained on grains (a) A and (b) B. Insets show representative post-deformation images of the pillars from each grain.
50 MPa. Byer and Ramesh [27] have found a higher CRSS value (for 3 lm diameter pillars) as compared to the current work, and the reason could due to the slight variation in crystal orientations, leading to different resolved shear stress on the basal planes. The microcompression curves of Grain B exhibit a completely contrasting constitutive behavior when compared to Grain A. A marked drop in the stress is noticed immediately after the elastic deformation, followed by a steady and enhanced strain hardening rate. While a few load drops are still noticed in the stress vs. strain curves of Grain B, their magnitude is considerably higher than those seen in Grain A. The peak flow stress corresponding to the initial plastic deformation is in the range of 175 ± 25 MPa and reaches a maximum value of 675 ± 35 MPa at 15% strain. (2) The flow curves of bulk samples differ completely from those of the micropillars for Grain A orientation. No intermediate stress drops were noticed; however, a significant size effect in strength was observed. The flow stress at a strain of 2% is 10 MPa and from this the CRSS for basal slip was estimated to be 5 MPa. Surprisingly, Grain A, which does not exhibit any strain hardening at large plastic strains
320
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
deformation by twinning. Moreover, Barnett et al. [43] suggested that in a polycrystalline Mg, a higher j is associated with a greater number of grains undergoing deformation twinning. In the present study a higher j is noticed in the case of micropillars of Grain B, compared to the large samples indicating predominance of deformation twinning in micropillars. Further, the post-deformation EBSD images of the bulk samples indicate that the deformation twinning is localized into a few regions while the parent orientation is still prevalent in some regions of the crystal. (4) The variation of strain hardening rate, h (= dr/de), is plotted as a function of e for Grains A and B in Fig. 4a and b, respectively. The strain hardening rate of Grain A decreases with increasing strain. Grain A, which does not exhibit any strain hardening during microcompression, shows a negligible amount of strain hardening during macrocompression. For Grain B, in contrast, both the micro- and macrocompression samples exhibit significant strain hardening. Several spikes in the h are noticed for micropillars and these are associated with the stress drops occurring during deformation. An interrupted compression test, wherein the sample was strained only up to 5%, was conducted on the Grain
Fig. 3. A comparison of the macro- and microcompression responses of grains (a) A and (b) B.
during microcompression, exhibits strain hardening – albeit only a small one – during macrocompression. Bhattacharya and Niewczas [22] have performed tensile experiments on Mg single crystals with orientations similar to that of Grain A and reported a CRSS of 1.1 MPa at a true strain of 0.2%, which are similar to the present study. Chapuis and Driver [20] have reported a CRSS of 5 MPa at a plastic strain of 1%, considerably higher than the uniaxial compression values, and the differences are attributed to the differences in stress state. The macrocompression curves of Grain B are similar to the micropillars; however, no stress drops are witnessed during deformation. (3) The stress vs. strain curves of Grain B during both micro- and macrocompression are characterized by three stages of hardening. Following initial elastic deformation, a plateau and high strain hardening regions are noticed. A significant concavity, j ( = d2r/de2) is observed after the plateau region, which is evaluated by fitting a quadratic equation to the r vs. e curve. Similar r vs. e behavior was reported by several researchers during the uniaxial and plane strain compression testing of single- [13–15,20] and highly textured poly-crystalline Mg and its alloys [39–43]. The concave behavior is attributed to
Fig. 4. Strain hardening rate, h, plotted as a function of strain for (a) single slip and (b) twin oriented crystals.
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
B and the r vs. e response with the corresponding SEM image of the pillar is shown in Fig. 5. The objective of this test is to ascertain whether load drop following elastic deformation produces any slip offset in the micropillars. The image of the deformed pillar indicates that there are no slip steps until 5% strain. Such stress drops in the r vs. e curves are reported previously during the deformation of nanopillars of Mg [25] and Ag [44] and are associated with the twin nucleation. The post-deformation optical micrographs of the mmsized samples are shown in Fig. 6a and b for Grain A and B, respectively. Note that the microstructures are obtained on the as-deformed surfaces without any intermediate polishing as this may obliterate some of the important deformation features (e.g. presence of slip bands) from the surface. Optical micrographs of Grain A indicate the presence of slip traces with no evidence of deformation twinning while high twin densities are noticed in Grain B and these twins are wide and long, resembling tensile twins [43]. It can also be seen from the optical micrographs of Grain B (Fig. 6b) that large a number of slip bands are present within and at the intersection of twins. The coexistence of slip and twins was previously observed by Vaidya and Mahajan [46] on shock-loaded hcp cobalt (Co) single crystals. TEM analyses of the post-deformed Co samples reveal basal and non-basal slip dislocations ahead of the terminating twins and at twin intersections. They have argued that high stress concentrations ahead of the twin tip are relaxed by the emission of the dislocations. The present observations are consistent with their reports. Post-deformation EBSD images of Grain A and B samples compressed to a strain of 15% are presented in Fig. 7a and b. These images further suggest that the orientation of Grain A retains its initial orientation while large fraction of Grain B undergoes deformation twinning. Inverse pole figure maps indicate that the twinned lattice reorients by 86°, confirming that these twins are tensile in nature occurring along f1 0 1 2g planes.
321
(a)
10 µm
(b) Slip bands Slip bands
20 µm
Fig. 6. Representative post-deformation optical micrographs of the macrocompression samples of grains (a) A and (b) B. Slip bands are noticed in grain A with no evidence of twinning. Microstructures of grain B comprise both twin and slip bands (the encircled regions show the slip bands).
5. Discussion The experimental results presented in the preceding section show that the specimen size and orientation exert a significant influence on the deformation behavior of Mg crystals, with micropillars exhibiting a higher strength. There are significant differences in the strain hardening behavior in both Grains A and B and are described below in detail. 5.1. Deformation behavior of single slip oriented crystal: specimen size effect
Fig. 5. Engineering stress–strain curve of a micropillar that was compressed to a total strain of 5%. The corresponding image of the pillar is also shown. Notice the absence of slip steps at this strain.
Post-deformation images of the micropillars of Grain A indicate the deformation along the single set of planes (Fig. 2a) while SEM micrographs of bulk samples show extensive slip bands (Fig. 6a) on the surface. The angle between the compression axis and these slip planes or bands was found to be 45°, suggesting deformation along the basal planes. The behavior of bulk samples is consistent with the observations of Bhattacharya and Niewczas [22], who also have observed extensive slip bands on the sample surfaces during the tensile experiments on basal slip
322
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
[28–33]. However, recent compression experiments on bcc [49] and hcp [27] micropillars reveal that qin has a considerable influence on the size effect observed in flow stress. Bei et al. [49] have indicated that pillars made from perfect crystals (whiskers) and pillars with a large density of dislocations do not show the size effect whereas the pillars with low qin exhibit strong size dependence of the flow stress. Byer and Ramesh [27] also have made similar observations in Mg micropillars with low qin and attribute it to the dislocation source controlled behavior. In lm-sized samples, the number of potential dislocation nucleation sources is small due to the low volume, and hence a higher stress is needed to initiate plastic deformation. In contrast, bulk samples contain a large number of dislocation sources and hence the plastic flow occurs at relatively lower stress [50–52]. In this context, it is worth noting that Parthasarathy et al. [53] have proposed a “source-truncation hardening” mechanism to rationalize the size effect in single-crystal micropillars. This mechanism is intimately connected to the initial dislocation density, the number of dislocation sources and their distribution within the pillars. The variation of h with e in micropillars is characterized by several spikes whereas it is smooth in bulk samples. The spikes in h correspond to the stress drops during plastic deformation (Fig. 1a) due to the basal glide of the micropillars. The smooth hardening behavior in bulk samples is attributed to the large number of dislocation nucleation sources (due to the higher sample volume). These large numbers of sources provide an increase in the mobile dislocation density during deformation and their interaction leads to forest hardening. A comparison of the EBSD images of the crystals before and after deformation leads to the following interesting observation. Orientation of the Grain A after deformation is similar to the initial orientation, indicating that deformation is predominantly by basal slip with no evidence of twinning.
Fig. 7. Post-deformation EBSD images of grains (a) A and (b) B, illustrating that grain A, which deforms by single slip, does not undergo any crystallographic reorientation (compare it with Fig. 1a). For grain B, the parent orientation is in blue whereas the twinned regions are in red. Orientations corresponding to different colored regions of EBSD image are indicated by numbers and the unit cells representing each number are also shown. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
oriented Mg single crystals. Moreover, the plastic deformation of micropillars is characterized by several load drops and these discrete events during plastic deformation are associated with plastic flow localization into a single set of planes. Such events are previously reported in micropillar compression experiments of bcc and fcc single crystals oriented for single slip [33,47,48]. The estimated CRSS of micropillars ( 30 MPa) is considerably higher than the bulk samples ( 5 MPa), indicating the strong dependence of flow stress on the specimen size. The specimen size dependence of flow stress is widely studied in literature
5.2. Deformation behavior of twin oriented crystal: specimen size effect The stress vs. strain curves of Grain B show a plateau region after yielding, where a small increase in stress results in a significant increase in strain, and such behavior is associated with twin propagation during deformation [15,20]. The maximum plastic strain in the plateau region is ~ 0.05-0.08 and this corresponds to the strain associated with twinning shear (0.129). A key observation of the current study is the difference in yield behavior of the micropillars and bulk samples. It is evident from Fig. 3b that yield in micropillars is followed by a significant stress drop whereas the flow curves are smooth in bulk samples. Sedlmayr et al. [44] have also observed such abrupt drop in stress (immediately following yield stress) during the tensile deformation of gold nanowhiskers and subsequent TEM and EBSD analyses of these whiskers reveal that these events are associated with twin nucleation, preferentially at the pillar surface. In another study, Yu et al. [25] have carried out in situ tensile
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
experiments on Mg nanopillars and noticed significant stress drops immediately after yield stress. The TEM images suggest that these stress bursts correlate with the nucleation of f1 0 1 2g twins (tension twins) from the pillar surface. Given the low initial dislocation density (108 m–2) in the initial crystals and size of the micropillars, it is reasonable to assume that the pillars do not contain enough dislocation sources within them and hence twins have to nucleate from the pillar surface. The twin nucleation stress, stw, is 150– 200 MPa (Fig. 2b), which is considerably lower than the values reported by Yu et al. [25] for Mg nanopillars. Such large differences (as high as 600 MPa) in stw are even observed in Au nanowhiskers [44] within the pillars of similar size (diameters 65 nm). Further, the molecular dynamics (MD) simulations of pillars having different initial surface roughness suggests that the observed variations in stw are due to the differences in surface roughness values. The stw drops precipitously with increasing surface roughness. Hence, the variability in stw observed between the micro- and nano-pillars could be attributed to the differences in surface roughness. However, a detailed understanding of twin nucleation mechanisms is far from complete and needs further investigation. The stress bursts are not noticed during the compression of bulk samples, suggesting that stw exhibits a strong dependence on specimen size. The differences in twin nucleation between the micropillars and bulk samples can be explained as follows: deformation twinning (DT), mediated by shear assisted co-operative movement of a finite number of atoms, occurs by nucleation and propagation [10]. Heterogeneous twin nucleation models [10,54] suggest that twins are more likely to nucleate at grain boundaries and sessile dislocation poles due to the presence of high stress concentration associated with those defects [10,54,55]. Wang et al. [55] have performed atomistic simulations on hcp crystals to understand the mechanisms of ð1 0 1 2Þ twin nucleation. Their observations suggest that a stable twin nucleus formed by zonal twinning mechanism (simultaneous glide of zonal dislocations consisting of a partial dislocation and multiple twinning dislocations) is preferred because of the lower elastic energy. The probability of finding such potential nucleation sites is higher in bulk single crystals and polycrystalline samples because the twin nucleation occurs at relatively low stresses. In Fig. 4b, variation of h with e is compared for both the sample sizes. Three stages of hardening are noted: (1) a constant h regime, (2) an increasing h followed by (3) a decreasing h. The peak strain hardening rates during stage I (hI) and II (hII) for both the sample sizes are listed in Table 1. While the differences in hI for the two sample sizes is negligible, the maximum value of h in stage II, hII,max, is much higher in micropillars compared to the bulk samples. These observations indicate that sample size has a negligible influence on h in the plateau region, suggesting the operation of similar deformation mechanisms at both the sample sizes. A possible reason for this behavior may be
323
the constant twinning shear, ctw, caused by the extension twinning. The area Hunder the stress vs. strain curves in the plateau region, n ¼ rde, which represents an indirect measure of energy expended in twin propagation, is listed in Table 1. A low n in the case of micropillars suggests that twins can propagate easily in micropillars, although their nucleation is difficult. As already indicated, the nucleation stress in the current pillars is attributed to the low initial dislocation density. But as the plastic deformation proceeds, the dislocation density increases substantially, resulting in a concomitant increase in the density of the mobile dislocations. In consideration of the fact that twin propagation occurs by the movement of twin partial dislocations [55], it is obvious to note that a lower stress is needed for twin propagation. Another important observation from Fig. 3b is that the plateau strain in micropillars is lower than that observed in the bulk samples. Assuming that this strain is associated with the twin propagation within the crystal, it is reasonable to argue that twin propagation is difficult in bulk samples due to the large volume of the material. A systematic experimental investigation with varying sample sizes is desirable for improved understanding of the fundamental mechanisms responsible for this atypical behavior. The concavity, j, in the strain ranges between 0.04 and 0.08 for micropillars and 0.04 and 0.12 for bulk samples is listed in Table 1. Barnett et al. [43] have plotted the magnitude of j against the percentage of twinned grains for different grain size samples of a polycrystalline Mg alloy subjected to uniaxial compression (Fig. 5 in Ref. [43]). Their results indicate that a higher j results when the majority of the grains deform by twinning. The j value estimated for micropillars of Grain B is an order of magnitude greater than the bulk samples, suggesting that the deformation twinning is more predominant in micropillars. Post-mortem optical and EBSD images (Figs. 6b and 7b) of the bulk samples suggest that the entire crystal does not undergo deformation by twinning as the inverse pole figure maps show regions of crystal with parent and other intermediate configurations. This indicates that in bulk single crystals, besides twinning, a significant amount of deformation is still mediated by slip (slip bands are even evident in optical micrographs). Both the micropillars and bulk samples exhibit a substantial increase in work hardening after the plateau region. Such observations are reported in the literature for the plane strain compression experiments on singlecrystal Mg when the deformation proceeds by twinning [14,15,20]. As a result of extension twinning, the parent lattice undergoes a crystallographic re-orientation which in turn increases the resistance to basal slip [7] as the reoriented crystal will have its hci axis normal to the principal stress axis. Hence, subsequent deformation has to proceed through either pyramidal slip or compression twinning; both of which lead to substantial work hardening [20,41,42]. Recent uniaxial compression experiments by Hong et al. [41] and Knezevic et al. [42] on a highly
324
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
Table 1 Strain hardening rate, h, during stages I and II and work done, n, in stage I and concavity j during compression of Grain B.
Microcompression Macrocompression
j (GPa)
hI (GPa)
hII,max (GPa)
eII,max (%)
nI (J)
0.6 ± 0.1 0.08 ± 0.02
0.8 ± 0.03 0.7 ± 0.01
18 ± 2 5±1
6.65 ± 0.5 11.2 ± 1
0.45 0.80
textured polycrystalline Mg also report a maximum strain hardening rate, hII,max, of 5 GPa at a strain, eII,max, of 8%. They attribute the increase in h during stage II to the (i) reduction in the effective grain size (due to the formation of contraction twins) and (ii) resistance offered by the twin boundaries to the pyramidal dislocations. Moreover, the uniaxial tensile experiments of polycrystalline Mg indicate lower strain hardening levels [41]. The difference in strain hardening between tension and compression experiments are attributed to the active twin variants that are present under these loading conditions. In the present study, though the loading path is the same for both micropillars and bulk samples, a significant difference in hII,max and eII,max (Table 1) was noticed. This observation highlights the fact that sample size also exerts a considerable influence on the measured strain hardening behavior. In the case of micropillars it is possible that the total twin volume fraction is higher than the bulk samples. Yu et al. [25] have also noticed that twin thickness increases with sample size; bulk samples often contain thicker twins compared to the micro- and nano-sized pillars. The EBSD maps (Fig. 7b) of the bulk samples indicate thick twins with a typical twin area fraction of 10–15% of the total area. This suggests a possible explanation for the increase in strain hardening in micropillars. It is widely discussed in Mg literature that (1) the twin boundaries act as barriers for dislocation motion and promote the strain hardening (see for example Refs. [8,56]) and (2) the twinned lattice (as a result of re-orientation) favors slip on hard crystallographic slip systems, thereby offering large resistance dislocation motion [57]. It is also argued that the dislocations that are mobile in the parent lattice can become immobile in the twinned lattice due to the crystallographic reorientation [57]. In samples with high twin density and small twin thickness, the above-mentioned mechanisms have a pronounced effect on the deformation behavior and could result in an increased strain hardening rate. However, a detailed experimental investigation is warranted in this direction. 5.3. Morphology of the post-deformed pillars The post-deformation images of the pillars, shown in Fig. 2, indicate that the plane on which deformation localizes is largely influenced by the orientation of the crystals with loading axis. In micropillars of Grain A, which deform predominantly by single slip, the glide plane is at an angle of 45 ± 3° to the compression axis whereas in Grain B it is almost normal to the compression axis. In bcc and fcc micropillars that are oriented for single slip,
the glide plane is 45° to the compression axis [45,46]. Dimiduk et al. [47] have shown that apart from the orientation, specimen size has a strong influence on the glide plane. It is generally observed that for pillars less than 1 lm in size the glide planes are found to be oriented at an angle that is greater than 45° to the loading axis [32,45].The reason for this behavior could be due to large taper that is generally present in the sub-micron sized pillars. A specific angle between the deformation plane and loading axis could not be assigned for micropillars of Grain B. A close examination of the deformed pillars suggests that their overall appearance is similar to that of the Mg micropillars compressed along the c-axis reported in the literature [23,24]. In those cases, pyramidal slip is found to be the dominant deformation during c-axis compression. As discussed in Section 5.2, tensile twinning results in reorientation of Grain B to 86°. The twinned lattice is oriented in such a way that the c-axis is in line with the compression axis, which is similar to the initial orientation of the crystals tested by Lilleodden [23] and Byer et al. [24]. These results indicate that the failure morphology of the pillars is sensitive not only to the initial orientation of the crystal but also to the changes that occur during plastic deformation. 6. Conclusions Two Mg single crystals with orientations favorable for deformation by basal slip and extension twinning were studied on two sample sizes ranging from mm to lm. Crystals in both the orientations exhibit significant size effects in strength and strain hardening behavior. Micropillars which deform by basal slip exhibit several load drops during plastic deformation and each of these events correspond to glide of the pillar on a single set of planes. In contrast, the load drops are not noticed in bulk samples and they show negligible strain hardening. Another important conclusion of the present study is the effect of specimen size on twin nucleation and propagation in the crystals favorable for deformation by extension twinning. A higher stress is required to nucleate the twins in micropillars than the bulk crystals but their propagation is difficult in bulk samples. The initial dislocation density in the samples appears to have significant effect on the twin nucleation stress, particularly in lm-sized pillars. Microstructural and EBSD analyses of the bulk samples suggest that the plastic deformation of basal slip oriented crystals occurs only by single slip while in twin oriented crystals it occurs both by slip and by twinning. The interaction between the slip
K.E. Prasad et al. / Acta Materialia 65 (2014) 316–325
dislocations and twins could be a possible reason for a higher strain hardening behavior in twin oriented crystals. Further, our observations also suggests that the specimen size has a marked influence on the strain hardening rate, h, with h increasing with decreasing specimen size. Acknowledgments We are grateful to Dr. Rejin Raghavan of EMPA, Thun for his assistance in the conduct of micropillar compression experiments reported in this work and Dr. Johann Michler for his permission to use the facilities in his lab. We would like to thank Profs. T. Watanabe and A.H. Chokshi for providing the bicrystals. We also would like to express our gratitude to the anonymous reviewer for his/her constructive comments on the manuscript. References [1] Easton M, Beer A, Barnett M, Davies C, Dunlop G, Durandet Y, et al. J Met 2008;11:57. [2] Caceres CH. Metall Mater Trans A 2007;38:1649. [3] Kulekci MK, Int J. Adv Manuf Technol 2008;39:851. [4] Groves GW, Kelly A. Philos Mag 1963;8:877. [5] Graff S, Brocks W, Steglich D. Int J Plast 2007;23:1957. [6] Kalidindi SR. J Mech Phys Solids 1998;46:267. [7] Zhang J, Joshi SP. J Mech Phys Solids 2012;60:945. [8] Yoo MH. Metall Trans A 1981;12:409. [9] Munroe N, Tan X, Gu H. Scripta Mater 1997;36:1383. [10] Christian JW, Mahajan S. Prog Mater Sci 1995;39:1. [11] Reed-Hill RE, Robertson WD. Trans AIME 1957;209:496. [12] Reed-Hill RE, Robertson WD. Acta Metall 1957;5:717. [13] Wonsiewicz BC. PhD thesis, Massachusetts Institute of Technology; 1966. [14] Wonsiewicz BC, Backofen WA. Trans Metall Soc AIME 1967;239:1422. [15] Kelly EW, Hosford WF. Trans Metall Soc AIME 1968;242:5. [16] Obara T, Yoshinga H, Morozumi S. Acta Metall 1973;21:845. [17] Yoshinaga H, Obara T, Morozumi S. Mater Sci Eng 1973;12:255. [18] Kitahara T, Ando S, Tsushida M, Kitahara H, Tonda H. Key Eng Mater 2007;345:129. [19] Syed B, Geng J, Mishra RK, Kumar KS. Scripta Mater 2012;67:700. [20] Chapuis A, Driver JH. Acta Mater 2011;59:1986. [21] Li Q. Mater Sci Eng A 2013;568:96. [22] Bhattacharya B, Niewczas M. Philos Mag 2011;91:2227. [23] Lilleodden E. Scripta Mater 2010;62:532. [24] Byer CM, Li B, Cao B, Ramesh KT. Scripta Mater 2010;62:536.
325
[25] Yu Q, Qi L, Chen K, Mishra RK, Li J, Minor AM. Nano Lett 2012;12:887. [26] Ye J, Mishra RK, Sachdev AK, Minor AM. Scripta Mater 2011;64:292. [27] Byer CM, Ramesh KT. Acta Mater 2013;61:3808. [28] Uchic MD, Dimiduk DM, Florando JN, Nix WD. Science 2004;305:986. [29] Dehm G. Prog Mater Sci 2009;54:664. [30] Greer JR, DeHosson JM. Prog Mater Sci 2011;56:654. [31] Uchic MD, Shade PA, Dimiduk DM. Annu Rev Mater Sci 2009;39:361. [32] Volkert CA, Donohue A, Spaepen F. J Appl Phys 2008;103:083539. [33] Volkert CA, Lilleodden ET. Philos Mag 2006;86:5567. [34] Schuster BE, Wei Q, Hufnagel TC, Ramesh KT. Acta Mater 2008;56:5091. [35] Dubach A, Prasad KE, Raghavan R, Lo¨ffler JF, Michler J, Ramamurty U. J Mater Res 2009;24:2697. [36] Zhang H, Schuster BE, Wei Q, Ramesh KT. Scripta Mater 2006;54:181. [37] Rabe R, Breguet JM, Schwaller P, Stauss S, Haug FJ, Patscheider J, et al. Thin Solid Films 2004;469:206. [38] Tsivinsky SV. Kris Tech 1975;10:5. [39] Barnett MR. Mater Sci Eng A 2007;464:1. [40] Proust G, Tome´ CN, Jain A, Agnew SR. Int J Plast 2009;25:861. [41] Hong S, Park SH, Lee CS. Acta Mater 2010;58:5873. [42] Knezevic M, Levinson A, Harris R, Mishra RK, Doherty RD, Kalidindi SR. Acta Mater 2010;58:6230. [43] Barnett MR, Keshavarz Z, Beer AG, Atwell D. Acta Mater 2004;52:5093. [44] Sedlmayr A, Bitzek E, Gianola DS, Richter G, Monig R, Kraft O. Acta Mater 2012;60:3985. [45] Koike J. Metall Mater Trans A 2005;36A:1689. [46] Vaidya S, Mahajan S. Acta Mater 1980;28:1123. [47] Dimiduk DM, Uchic MD, Parthasarathy TA. Acta Mater 2005;53:4065. [48] Schneider AS, Kaufmann D, Clark BG, Frick CP, Gruber PA, Monig R, et al. Phys Rev Lett 2009:105501. [49] Bei H, Shim S, Pharr GM, George EP. Acta Mater 2008;56:4762. [50] Benzerga AA. Int J Plast 2008;24:1128. [51] Rao SI, Dimiduk DM, Parthasarathy TA, Uchic MD, Tang M, Woodward C. Acta Mater 2008;56:3245. [52] Senger J, Weygand D, Gumbsch P, Kraft O. Scripta Mater 2008;58:587. [53] Parthasarathy TA, Rao SI, Dimiduk DM, Uchic MD, Trinkle DR. Scripta Mater 2007;56:313. [54] Mahajan S. Scripta Mater 2013;68:95. [55] Wang J, Hirth JP, Tome CN. Acta Mater 2007;57:5521. [56] Serra A, Bacon DJ. Acta Metall Mater 1995;43:4465. [57] Niewczas M. Acta Mater 2010;58:5848.