Quantifying the mesoscopic shear strains in plane strain compressed polycrystalline zirconium
Introduction
Deformation in polycrystalline metallic materials can be viewed from the tenets of classical plasticity and/or microstructural developments. In Taylor theory [1], [2], the local deformation/strain is assumed to match the global values. The assumption of strain homogeneity is, however, questionable from the observations on microstructural developments [3], [4], [5], [6], [7], [8], [9]. Microstructural observations have always revealed the presence of heterogeneities: both between different grains and within the same grain [4], [5], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. The continuity across grain boundaries is thought to be maintained through relative activation of slip systems in different regions [5]. The actual physics can be approximated through numerically intensive solutions, like the crystal plasticity finite element method [19], [20], [21], [22], [23], [24]. For experimental comparison, however, the model requires knowledge of the local 3-D grain arrangements and orientations – knowledge that is almost never available. Another alternative is to capture mechanics of grain interactions through suitable model assumptions. This may include two- or multi-grain models [25], [26], [27], or models attempting to address creation of geometrically necessary dislocations [28], [29], [30]. It is best to complete this discussion by referring to a recently published article [29] that highlights the differences between model predictions and experimental observations in polycrystalline aluminum. It was reported that deviations between the models happen under complex strain mode: classical Taylor-type models ignore the aspects of near-boundary shear.
During plastic deformation in polycrystalline material, near-boundary gradients of orientation/misorientation have been reported [31], [32], [33], [34], [35], [36]. Such zones, generalized as near boundary gradient zone (NBGZ), appear to depend on the strain mode [31] and on the plasticity of the neighboring grain [32]. Though the phenomenon of NBGZ appears to be potentially very important in crystal plasticity, there has not been a direct experimental attempt to relate NBGZ with mesoscopic or in-grain strains. Such strains can be quantified through digital image correlation (DIC). For example, images before and after plastic deformation can be compared digitally, based on the displacement of identifiable markers, and displacement fields or strains estimated.
Starting from the initial days [37], where laser speckles were used to identify displacement and/or deformation, the subject of DIC has evolved [38], [39], [40], [41], [42], [43], [44], [45] remarkably. Efforts were/are made to measure microscale strains, even employing elegant corrections [38] for drift and distortion associated with scanning electron microscope (SEM) imaging. It is, however, important to note that there are certain intrinsic ‘limitations’. DIC-based strain calculations depend on the pixel subset size and step size. The subset size needs to be carefully chosen to obtain continuity of deformation and hence must approximate distinguishable microstructural features or externally imposed markers. For in-grain strain measurements, the challenge is to put numerous, small, permanent and passive markers around the grain boundary [43], [45]. A high number of measurements is important to resolve local strains, while grain interior measurements demand smaller sizes. The marker also needs to be permanent and passive, so that it does not get altered or affect the deformation-induced microstructure developments. For the latter, using electron backscattered diffraction (EBSD) is a natural development [41], [42], [43]. However, placing appropriate markers and measuring local strains and subsequent EBSD of the same region are non-trivial [41], [42], [43], [44], [45]. Furthermore, the commercial packages usually do not have the ability to consider appropriate/flexible user-defined inputs (UDI), thus restricting the use of microstructural features as markers for strain estimation. In this study a new DIC model/algorithm was developed. The algorithm, described in the Appendix, estimates near boundary in-plane strains: both the expected/imposed normal strains and any additional or redundant local shear strains. These are estimated from displacements of identifiable grain boundary segments. Estimated mesoscopic shear strain values were then correlated with different aspects of the deformed microstructures.
Section snippets
Experimental details
To explore the use of the proposed algorithm (see Appendix), predominantly single-phase fully recrystallized Zircaloy-4 (chemical composition listed in Table 1) was selected. The selected material was then precision machined to provide split channel die samples (see Fig. 1). In this technique, described in greater detail elsewhere [46], [47], [48], [49], effectively internal regions of a material were subjected to plane strain compression (PSC) and the same grains were observed before and after
Results
Fig. 2 shows the EBSD measurements from progressive PSC reductions. EBSD scans were made at respective step sizes of 0.3 and 0.1 μm. As discussed later, this was needed to establish measurement uncertainties at various EBSD resolutions. As shown in Fig. 3, the so-called non-indexed points (or points below 0.1 confidence index (CI)) were insignificant (and were primarily on the grain boundaries) up to 4% PSC reduction. Though this changed at 8% and 10% PSC, a clear visualization of grain
Discussion
Polycrystalline plasticity can be viewed [2] from isostress or isostrain: the basis of the Sachs [52] and Taylor [1] models. The former falters as isostress automatically demands differences in strains between the crystallites, resulting in serious compatibility issues across grain boundaries. The Taylor model, irrespective of microstructural criticisms [2], [9], remains the working model even today. The basic assumption of strain homogeneity is, however, questioned by a number of
Conclusions
An algorithm was proposed to measure local/mesoscopic near-boundary shear strain in a lightly deformed polycrystalline material. This was then used in split-channel-die study of lightly PSC polycrystalline zirconium.
- 1.
Although plastic deformation did not impose macroscopic shear, very strong localized near boundary shear strains were found. These were much larger than the imposed PSC strains and the estimated measurement uncertainties. Clear observations on opposing shear strains were noted on
Acknowledgements
The authors acknowledge support from DST (Department of Science and Technology, India) and BRNS (Board of Research in Nuclear Sciences, India). R.D. acknowledges support from IIT Bombay as a visiting professor.
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