Grain-subdivision-dominated microstructure evolution in shear bands at high rates

ABSTRACT Shear banding is an important deformation and failure mechanism in metallic systems, especially at high-rate straining. Dynamic recrystallization was often reported to account for the refined microstructure of shear bands but rarely confirmed using direct quantitative measurement. Here, we employ quantitative precession electron diffraction analysis to uncover shear band microstructure in pure titanium. The results reveal that the microstructure is dominated by early stages of grain subdivision process. Dynamic recrystallization is not as prevalent as perceived conventionally. Our results offer key insights into understanding shear banding and highlight the need for quantitative analyses of shear band microstructure. GRAPHICAL ABSTRACT IMPACT STATEMENT A critical quantitative assessment of shear band microstructures is made using precession beam diffraction imaging. Specifically, grain subdivision, as opposed to dynamic recrystallization, drives the shear band microstructure evolution.


Introduction
Shear banding, a type of inhomogeneous plastic flow mode, is considered as one of the most important failure mechanisms in high strain rate deformation of polycrystalline metals [1][2][3]. Shear banding represents localization of large plastic strains (shear strains up to 10 2 ) in thin microscopic bands even when the imposed (macroscopic) deformation state is homogeneous [4]. Shear banding is typically promoted by low thermal conductivity of the material and high strain rates ( > 10 3 s −1 ), factors that promote adiabatic deformation conditions [5]. At a continuum level, the onset of plastic instability, causing the transition from homogeneous to shear band flow, is associated with the maximum on the stress-strain reevaluate the shear band microstructure in early investigations, particularly to quantify the level of DRX and other characteristics in the microstructure.
The basic premise of DRX, either continuous or discontinuous, is the formation of new grains that are strain/dislocation free and bounded by high-angle grain boundaries (HAGBs) driven by the stored energy of deformation [25,26]. Traditionally, the occurrence of DRX has been often reported by post-mortem observations of ultrafine or nanoscale grains within the shear band using conventional transmission electron microscopy (TEM) techniques [12,16,18,22,23]. It is important to note that these grains have been often described as having low dislocation density and high angle grain boundaries (indicators of recrystallization), purely based on the diffraction contrast. DRX has been rarely confirmed using direct quantitative measurements of grain boundary misorientations and their overall statistics. It is well known that the diffraction contrast in TEM is highly sensitive to the misorientation: a few degrees of crystal misorientation could result in dramatic changes in contrast [27]. Therefore, conventional brightfield and dark-field imaging techniques by themselves cannot distinguish between the subgrains separated by low angle grain boundaries (LAGBs) from newly recrystallized grains that are typically characterized by HAGBs.
In light of the above challenge, we employed precession electron diffraction (PED) in TEM to quantitatively map the shear band microstructure in commercially pure Ti in terms of crystal orientation and grain boundary misorientation. PED, while similar to electron backscatter diffraction (EBSD), offers higher spatial resolution ( ∼ 1 nm) needed for shear band analysis [28]. We show that microstructure evolution within a band is characterized by an early stage of the grain subdivision process, where LAGBs dominate the microstructure. In particular, we show that DRX is not as prevalent as generally perceived based on conventional TEM analyses. The overall microstructure bears a strong resemblance to those resulting from severe plastic deformation at ambient temperatures. Our results provide key quantitative information pertaining to microstructure evolution within shear bands. The direct observations from this work are also of value to computational models aimed at predicting the initiation and propagation of shear bands.

Materials and methods
Commercially pure (CP) Ti (grade 2) was used in this study. The material was received in a plate form with an annealed condition (215 HV) and an average grain size of ∼ 100μm (see Figure S1). Two-dimensional plane strain cutting was used as an experimental framework to impose controlled simple shear, which allows the study of single shear bands without interfering effects from other bands [29]. A thin layer of material (t 0 = 125μm) was removed from a workpiece surface in the form of a 'chip' via simple shear imposed by a sharp wedge-shaped tool at a velocity (V 0 ) of 10 m/s ( Figure S2) [4,29]. The chip thus produced was characterized by periodic shear band structures ( Figure S2). Details of this technique can be found in our earlier reports [4,30].
The material microstructural characteristics in and around shear bands were studied using EBSD and TEM. The specimens were firstly mechanically ground and then electrochemically polished to perforation using an electrolyte of 5% perchloric acid, 35% butanol, and 60% methanol at −40°C. A Tescan FERA-3 scanning electron microscope (SEM) was used to obtain EBSD inverse pole figure (IPF) maps (0.5μm step size). Conventional bright-field micrographs and diffraction patterns were obtained using an FEI Tecnai G2 F20 TEM operated at 200 kV. The PED experiments were carried out in a Titan TEM operated at 300 kV equipped with a NanoMEGAS ASTAR system [31]. The orientation mapping was done at a procession-beam angle of 0.6°and a step size of 4 nm.  (1)(2)(3)(4) illustrate the large and uniform shear displacement ( ∼ 100 μm) along the shear band. Note that the displacements across the band result purely from highly localized shear over a thin interface (shear band), and not from fracture, as clearly seen from the chip microstructure in Figure 1(b). Quantitative strain calculations by tracking local changes in the curvature of markers have revealed large shear strains of ∼ 40 at shear band center [4]. The local strain rate experienced by the band is expected to be in the 10 6 s −1 range [29].

Results and discussion
The global microstructural details around the band, resolved using EBSD IPF maps (taken from the flowtransverse plane in Figure 1, i.e., top-view of the chip), are shown in Figure 2(a). Regions outside shear bands are comprised of large grains with an average size of ∼ 10μm and seem to have been only slightly deformed. Some {10-12} extension twins were also observed in these regions. In contrast, microstructure within shear bands could not be resolved using EBSD and appeared as two non-indexed vertical bands in Figure 2(a). This  is a consequence of the high strains and highly refined microstructure within the band. Local microstructural information at a higher resolution was obtained using bright-field TEM, as shown in Figure 2(b-d). Figure 2(b) shows a representative shear band and its neighboring less-deformed regions. The shear band boundaries are highlighted by dotted lines for reference. The shear band width was about 3-4 μm, consistent with our previous estimates of the width based on strain measurements [4].
The coarse-grained regions outside the band exhibit local bending contours, typical of grains with some straining (Figure 2(c)). In comparison, within the shear band (Figure 2(d)), the microstructure is highly refined, further substantiated by a ring-like diffraction pattern (see inset). The fine-grained shear band microstructure seen here bears a strong resemblance to other reports of shear band microstructures in Ti and its alloys, many of which have been interpreted in terms of DRX [10,12,16]. To achieve a more quantitative analysis of shear band beyond the limits of conventional TEM imaging, we collected PED data in the band center, as summarized in Figure 3. Figure 3(a) shows a PED bright-field image from the shear band center. This image resembles the conventional bright-field image in Figure 2(d). A conventional interpretation of the random bright/dark contrasts with feature sizes of tens or hundreds of nanometers would have been to assume that the region of interest has been 'recrystallized' into ultrafine grains. However, the IPF maps in Figures 3(b,c) show that these ultrafine grains with distinct diffraction contrast actually exhibit very similar crystal orientation, with most of them separated by the LAGBs (2-15°). This suggests that these features are likely a result of the parent grain being refined/partitioned into numerous subgrains under the influence of severe mechanical deformation. For example, a relatively large blue grain in the lower-right corner in Figure 3(c) contains considerable subgrains separated mainly by LAGBs. Subgrains, such as the numbered grains 1-4, could be potentially, and have been in the past, incorrectly identified as the recrystallized grains based on conventional bright-or dark-field images. A brief remark regarding how LAGBs can give rise to arcs or rings in the diffraction pattern (Figure 2(d)), which are usually used as indicators for DRX, is perhaps in order. Although the misorientations across each LAGB are small, their accumulation over a distance can result in considerably large misorientation values. This is illustrated in Figure 3(d), where the misorientation data along a line scan spanning multiple subgrain boundaries (top white arrow in Figure 3(c)) is shown. The point-to-point misorientation (represented by blue curve, Figure 3(d)) is small, but the point-to-origin plot (red curve) shows an accumulative misorientation up to ∼ 20°. Moreover, Figure 3(e) presents a visual representation of subgrains and their boundaries in the form of a correlation-coefficient map generated by weighting the similarities between the neighboring PED diffraction patterns. Here, darker lines or regions highlight the areas where neighboring diffraction patterns are most dissimilar, while brighter regions correspond to those with similar diffraction patterns. This representation enables the mapping of misorientations even less than 2°, and thus offers a powerful tool to visualize subgrain boundaries and dislocations arrays/bundles within. As an example, a zoomed-in view of a subgrain is shown in Figure 3(f), where gray lines within the subgrain interior (marked with red arrows) likely correspond to dislocations. This is further illustrated in Figure 3(g and h) which show the diffraction patterns from two locations (I and II) lying on either side of the dislocation line. The relative difference in the diffraction spot intensities at these locations (yellow arrows) is indicative of slight misorientation across the dislocation line in between. As seen from Figure 3(e), the correlation coefficient map reveals substantial levels of dislocation structures within almost every single subgrain, even though these subgrains may appear 'pristine' or 'dislocation-free' in regular bright-field images. The fact that the subgrains are not defect-free lends further support that microstructure refinement within the band is not a result of DRX, but due to progressive breaking down of original grains into subgrains. That is, the underlying mechanism of microstructure evolution is that of grain subdivision, as is typical of severe plastic deformation processes [32,33].
Although LAGBs constitute the majority of observed boundaries, the PED scans over a shear band region also revealed some existence of HAGBs. Figure 4(a) is a ∼ 700 nm x 700 nm view of a local region inside the band. The misorientation line profile in Figure 4(b) shows periodic grain boundaries with misorientation angles of 65 ± 3°, which coincidentally is the {1-212} contraction twin boundary character in Ti. The overall misorientation angle statistics across the entire shear band region (3 um x 3 um), shown in Figure 4(c), also reveals a prominent peak at ∼ 65°corresponding to the contraction twins. However, note that the LAGBs (less than 15°) still constitute the majority, ∼ 2/3rds. Contraction twins are not observed in the counterpart analysis of the regions outside the band ( Figure S3). It is quite likely that contraction twinning has occurred during the initial stages of band formation, leaving debris of a number of HAGBs, since the planar characteristics of the twin boundaries were no longer preserved within the band (due to intense straining). It should be clear that without the quantitative misorientation data, as in conventional bright-field TEM [11,34], it would be challenging to delineate the high-angle twin boundaries from other LAGBs.
Taken as a whole, the quantitative PED results provide new insights into shear band microstructure evolution. As noted earlier, the shear band microstructure has been conventionally interpreted in terms of uniformlydistributed ultrafine grains resulting from DRX, often based on conventional bright-field TEM analysis. Here, using quantitative grain boundary misorientation statistics, we show that shear band microstructure is predominantly ( ∼ 2/3rd) characterized by LAGBs with a misorientation angle less than 15°. DRX does not prevail the microstructure. The limited DRX here is of continuous type from a kinetics standpoint (briefly discussed in the Supplementary Material). More importantly, this together with other secondary observations pertaining to dislocation activity within subgrains (Figure 3(f-h)) and traces of deformation twinning (Figure 4) suggests that the mechanism underlying microstructural changes within the band can be represented as a grain subdivision process, as well documented in the past from the standpoint of severe plastic deformation processing [32,33]. In this process, initial (original) crystals are subdivided by the geometrically necessary boundaries (e.g. twin boundaries or part of dislocation slips) and incidental dislocation boundaries (dislocation cells and bundles) [34], where the misorientation angle across the geometrically necessary boundaries monotonically increases with the plastic strain later. The ultrafine LAGB structure seen inside the band therefore represents the early phase of the grain subdivision process, where HAGBs are not well developed yet in general. It is important to note that this grain subdivision process can take place even at ambient temperatures purely due to mechanical deformation [33,35], without thermal contributions. This further suggests that conventional thermally-driven DRX is not a prerequisite for shear banding.
Before proceeding to the conclusion, it should be noted that the final shear band microstructure critically depends on the local thermomechanical history experienced by the band during its initiation and growth. While the shear band microstructure studied here is representative of bands formed under high strain/strain rate conditions, it is certainly not universal. The focus here has been on highlighting the unique advantages of quantitative PED method in shear band studies and in avoiding certain pitfalls associated with inferring microstructure evolution or softening mechanisms based on conventional TEM observations.

Conclusion
In summary, advanced precession electron diffraction TEM technique is used to quantitatively study the microstructure of shear bands produced in CP Ti under high rate deformation. These results reveal that a mechanically-driven grain subdivision process governs the microstructure evolution. DRX is clearly not as prevalent as perceived by conventional TEM. This work also highlights the need for quantitative high-resolution imaging techniques to reexamine shear band microstructures and associated softening mechanisms.