Microstructural and Textural Evolution in Hexagonal Close-Packed Metals: The Case of Zirconium, Magnesium, and Titanium

Abstract

Hexagonal close-packed (HCP) metals, particularly Zirconium (Zr), Titanium (Ti), and Magnesium (Mg) alloys, have attracted significant attention due to their unique properties and wide-ranging applications in the aerospace, biomedical, and energy industries. This review paper provides a comprehensive analysis of the microstructural and textural evolution in these HCP materials under various conditions, including rolling, extrusion, drawing, and annealing. The focus of the present work lies on the deformed microstructure and texture development in HCP metals, thus elucidating the fundamental mechanisms that govern their response to mechanical stress. The interaction between dislocation movements, twinning, and slip systems is discussed in detail, illustrating how these factors contribute to the anisotropic behavior characteristic of low-symmetry HCP structures. Unlike high-symmetry metals, deformation in Zr alloys depends on the activation of various slips and twin deformation modes, which are sensitive to crystallographic orientation and strain. Like Zr, Ti alloys present a more complex deformation behavior, heavily influenced by their crystallographic orientation. The most common deformation textures in Ti alloys include split-transverse direction (split-TD), split-rolling direction (split-RD), and normal direction (ND) symmetric basal fiber textures. These textures emerge due to the activation of multiple slip systems and twinning, which are dependent on external factors such as temperature, strain rate, and alloy composition. For Mg alloys, the poor formability and brittleness associated with the dominance of the basal slip system under ambient conditions is a critical material development challenge. The activation of non-basal slip systems introduces complexities in controlling texture and microstructure. However, their activation is crucial for optimizing mechanical properties such as strength and fatigue resistance. The tendency for twinning in Mg alloys further complicates their deformation behavior, leading to challenges in ensuring uniform mechanical performance. Modifying the alloy composition, grain size, and texture can additionally influence the activation of these deformation mechanisms. This review further explores the roles of dynamic recrystallization and grain growth in tailoring mechanical properties, with a particular focus on microstructure and texture evolution during annealing. Through this detailed review, we aim to present a thorough understanding of the microstructural and textural evolution in HCP materials, thereby guiding future research and industrial applications.

1. Introduction

Hexagonal close-packed (HCP) materials and their related alloys exhibit unique material characteristics, including crystallographic anisotropy, restricted deformation behavior due to limited slip systems, and a distinct atomic configuration compared to their body-centered cubic (BCC) or face-centered cubic (FCC) counterparts. These exclusive factors result in unique processing, final properties, and underlying microstructures in HCP materials. Common HCP metals and alloys such as titanium, zirconium, and magnesium are extensively utilized in various industrial and military applications. Despite significant advancements, a deeper understanding of the relationships between processing, microstructures, and material properties remains critical. This work emphasizes the intricate relationships between microstructure and texture evolution as a function of different processing parameters relevant to various HCP materials [1,2,3,4,5,6,7].

Zirconium (Zr) alloys are widely employed as ideal structural materials for thermal nuclear reactors due to their low neutron absorption cross-section combined with excellent mechanical and corrosion properties at reactor operating temperatures [8]. Some grades of Zr are also used widely in the biomedical field [9]. Zr alloys exist in different grades and are typically either predominantly single-phase α HCP or two-phase α+β (HCP+BCC) microstructures. Most commercially used Zr alloys, ranging from Zircaloy-1 to Zircaloy-4, Zr-Nb, are largely HCP single-phase and polycrystalline. The fabrication of Zr component, from cast ingots to final tubes, involves stages of thermo-mechanical processing (TMP) [10,11,12], which is essential not only for shape modification but also for achieving the correct microstructure and, consequently, the desired properties. In service, Zircaloy-4 nuclear fuel claddings are exposed to harsh environments, leading to material degradation under operating conditions. Therefore, stringent TMP control is necessary to achieve desired properties such as low neutron absorption cross-section, radiation damage resistance, superior creep resistance, and high-temperature corrosion performance. TMP involves hot extrusion and a unique fabrication technique called pilgering [7,10,11,13,14,15]. Hot extrusion or hot working relies on the activation of slip-twin systems [6,16,17,18] and the possibilities of dynamic recrystallization (DRx). Pilgering provides triaxiality of stresses, hence higher formability, but involves heterogeneous deformation [19,20], where some grains are fragmented while others remain virtually untouched [19,21]. This heterogeneous microstructure persists even after thermal annealing [22,23]. Consequently, the final microstructure-property relationship is controlled by pilgering-induced microstructural evolution. In Zr alloys, crystallographic texture, microstructure, chemical compositions, residual stresses, and dislocation density effectively control the kinetics of various degradation mechanisms, such as radiation-induced growth [24,25] and total circumferential elongation during simulated burst tests [26,27].

Titanium (Ti) alloys are among the most widely used structural materials due to their superior specific strength, ductility, high-temperature strength, creep, and fatigue properties, making them ideal for applications in the aerospace, biomedical, energy, and petrochemical sectors [4,28,29,30]. Ti undergoes an allotropic phase transformation at 1155 K. Below this temperature, known as the β transus, Ti exists as an HCP structure (α phase) [4,31], and above this temperature, it exists as a BCC structure (β phase) [32]. Alpha-Ti has an HCP crystal structure with a $c/a$ ratio about 2.8% less than the ideal, resulting in the principal slip system being prismatic $〈a〉$ type, $\left(10\overline{1}0\right)〈11\overline{2}0〉$. The secondary slip system is the basal slip system, $\left(0002\right)〈11\overline{2}0〉$, followed by pyramidal $〈c+a〉$ type slip systems, $\left(10\overline{1}1\right)〈11\overline{2}3〉$ [33]. Extension $\left(\left(10\overline{1}2\right)〈\overline{1}011〉,\left(11\overline{2}1\right)〈\overline{11}26〉\right)$ and compression twinning $\left(\left(11\overline{2}2\right)〈\overline{11}23〉\right)$ mechanisms are also frequently observed, especially at low strain levels [34,35]. To accommodate strain along the $c$-axis, the twinning mechanisms often activate before the $〈c+a〉$ slip due to the high critical resolved shear stress (CRSS) of the pyramidal slip systems [4,5]. The inherent anisotropy of the hexagonal crystal and the significant disparity in CRSS values between different slip systems result in the complex interplay of deformation mechanisms [36,37] that dictate the plastic deformation and consequent microstructure and texture evolution in α-Ti. The texture and microstructure evolution during Ti deformation depends on the deformation mode, temperature, initial texture, and grain size, directly affecting the relative activities of various deformation mechanisms.

Magnesium (Mg) and its alloys (AZ31, AZ61, AZ91, WE43, ZE41), known for their exceptionally low weight, are heavily utilized for structural applications in the aerospace, automotive, and biomedical sectors. However, their practicality is limited by their HCP crystal structure, which results in poor formability at room temperature (RT). At RT, the dominant deformation mechanism is the basal slip $\left(0001\right)〈11\overline{2}0〉$, characterized by its minimal CRSS value but offering only two independent slip systems, thus limiting formability [38]. At temperatures exceeding 523 K, other non-basal slip systems, such as prismatic and pyramidal, become active [3,39]. The activity of these non-basal slip systems can also be influenced by alloy composition adjustments, grain size refinement, and modifications to the starting material’s texture. Deformation processes below the recrystallization temperature (cold rolling (CR)) of Mg alloys primarily involve basal slips and the formation of mechanical twins [40,41], which tend to favor pyramidal systems, specifically $\left(10\overline{1}2\right) 〈10\overline{1}1〉$ nd $\left(10\overline{1}1\right) 〈10\overline{12}〉$. However, dynamic recrystallization (DRx) occurs concurrently with deformation mechanisms above the recrystallization temperature, resulting in recrystallized grains alongside twinning and secondary phases [42]. Mechanical twins play a vital role during deformation, impacting the strengthening mechanisms, texture evolution, asymmetric stress-strain behavior, and fracture initiation. The detailed mechanisms related to the effect of deformation on the microstructure and texture of Mg alloys are discussed in the following sections.

Overall, this review discusses the development and deformation mechanisms of structural grades of HCP materials. In this regard, the main theme of the review paper is the material-specific microstructure and crystallographic texture observed during various deformation processing routes. The different material grades and various processing conditions discussed in this review are summarized in

Table 1. Discussions of various deformation and annealing mechanisms for the Zr, Ti, and Mg alloys in the present review work.

S.No.	Grades/Alloys	Characteristics Discussed	Published Year/References
1	Zr-4 Fuel Tube	Pilgering, Texture anisotropy, slip activation	2014 [12], 2015 [10]
2	Zr-4 sheet	Plane strain compression, Twinning, Role of initial texture	2014 [20], 2015 [43]
3	Zr-4 Fuel Tube	Microstructure and texture developments	2008 [13]
4	Zr-1.3Sn-0.2Fe-0.1Cr	Hot extrusion, pilgering	2008 [15]
5	Clock-rolled pure Zr plate	Role of substructure, Selection of deformation modes, Coupling between slip modes, Coupling between slip and twinning modes	2008 [16]
6	Clock-rolled high-purity Zr	Effects of initial texture, Effects of temperature and strain, Secondary twinning within primary twins	2006 [6]
7	Rolled Zircaloy-4 plate	Twin boundary fraction and work-hardening rate, Effect of active deformation modes on the work-hardening rate, Double twinning	2018 [17]
8	CP-Ti	Unidirectional cold rolling and split-TD texture	2017 [44], 2013 [45], 2007 [46], 2014 [47], 2005 [48], 1987 [49], 2008 [50]
9	CP-Ti	Cold cross-rolling and split-RD texture due to varying strain path	2017 [44], 2011 [51]
10	CP-Ti	Elevated temperature and formation of basal—fiber texture	2014 [47], 2016 [52]
11	CP-Ti	Shear strain and formation of Basal fiber texture	2018 [53], 2014 [54]
12	CP-Ti	Split-TD texture in submicron-grained material	2011 [51]
13	CP-Ti	Fiber texture symmetric about extrusion and drawing axis	2010 [55], 2022 [56]
14	CP-Ti	Primary recrystallization texture and microstructure	2008 [50], 2020 [57]
15	CP-Ti	Secondary recrystallization texture and microstructure	2017 [44], 2005 [58], 2020 [57]
16	AZ31	Rolling Microstructure and Texture, Strain hardening behavior, plane slip, and twinning	2019 [59], 2023 [60]
17	AZ61	Deformation mechanism, slip systems	2022 [61]
18	AZ80	Texture evolution	2020 [62]
19	AZ91	Extrusion Texture, strain behavior	2022 [63], 2023 [64]
20	ZK60, Mg-Sn	Texture evolution, deformation mechanism	2022 [65], 2021 [66]
21	Mg-Y-Zn	bimodal microstructure	2023 [67]
22	Mg-Li-Al	Anisothermal aging	2022 [68]
23	Mg-Gd-Nd(-Zn)-Zr alloys	Strain rate and texture	2021 [69]

. Further, issues specific to material development, including the effects of crystal anisotropy, grain fragmentation, and the temperature dependence of CRSS leading to differences in microstructure and texture, along with various deformation mechanisms such as twinning, shear bands (SBs), and strain localizations (SLs), are thoroughly examined and discussed for Zr, Ti, and Mg alloys. The impact of temperature, strain path, and grain size on the crystallographic texture has also been addressed, alongside the softening behavior. Critical issues such as the role of static and dynamic recrystallization, primary and secondary recrystallization, and continuous and discontinuous recrystallization mechanisms in material texture evolution are explored in detail and illustrated with figures. By providing a structured analysis of the existing literature and highlighting key material-specific issues, this review aims to serve as a valuable resource for researchers, engineers, and material scientists, offering a comprehensive and accessible guide to the critical aspects of microstructure and texture evolution in Zr, Ti, and Mg alloys.

2. Deformed Microstructure and Texture in Zirconium

As discussed in the introduction section, several mechanisms contribute to the degradation of Zr alloy structures in reactors, including irradiation growth, oxidation, wear, creep, and hydride formation. During irradiation growth, a high flux of neutrons passing through the Zr alloy cladding induces material degradation by introducing point defects, line defects, interstitial and void clusters, precipitates, and microstructural alteration [25]. This degradation can further promote creep deformation processes in Zr alloy components under favorable stress-temperature regimes present during reactor operation, influenced by dislocation glide, dislocation climb, point defect diffusion, and grain boundary sliding (GBS) [25]. The irradiation growth, suboptimal mechanical characteristics under hydride formation, and the rapid creep rate of Zr alloys at elevated temperatures restrict the selection of Zr microstructures and associated processing [70]. Consequently, it is imperative to understand the microstructural and crystallographic texture developments during various TMPs to enhance the versatility of Zr alloys.

2.1. Role of Plastic Anisotropy during Deformation

The origin of plastic anisotropy in Zr alloys lies in their HCP crystal structure, referred to as the $\alpha$ phase. In Miller-Bravais indices, the hexagonal structure, planes, and orientations are depicted in Figure 1a,b. The $c/a$ ratio of the HCP structure is 1.593 at RT, but increases to 1.597 at 773 K [71,72]. This change in the $c/a$ ratio causes variations in thermal expansion coefficients in different crystallographic directions. For a single crystal of Zircaloy-2, these coefficients are 11.4 × 10⁻⁶ K⁻¹ in the $〈a〉$ direction and 5.7 × 10⁻⁶ K⁻¹ in the $〈c〉$ direction. This disparity in thermal expansion coefficients significantly affects slip activation at different temperatures by influencing lattice slip resistance [72,73] and the hierarchy of close-packed planes. It also results in the formation of thermal residual strains/stresses in addition to deformation-induced ones. The magnitude of these residual stresses in the basal and prismatic planes is considerable (+10⁻³ for $\left(0002\right)$ and −10⁻³ for $\left(10\overline{1}0\right)$) [74]. These residual stresses [12,75] significantly impact the alloy’s deformation behavior and in-service performance [26,76].

2.2. Effect of Temperature and Orientation on Microstructure Development

For Zr alloy components, fabrication (from cast ingots to final tubes and rolled sheets) involves stages of TMP designed to achieve the necessary dimensions. Typical Zr alloy component fabrication includes hot, warm, and cold working. Unlike high symmetry metals, deformation in HCP Zr alloys is highly dependent on the activation of different slip and twin deformation modes, as shown in Figure 1a,b, which are sensitive to crystallographic orientation and strain. Crystallographic orientation becomes a dominant factor \ in slip activation and, more dominantly, in twin activation when the loading direction is considered. Generally, deformation along the $c$-axis is challenging, whereas deformation along the $〈a〉$ direction is less difficult at and above ambient temperatures. Deformation along the $c$-axis requires the activation of pyramidal $〈c+a〉$ slip, which inherently has a high CRSS compared to deformation along non $c$-axes, which only requires the activation of prismatic slip. It is noteworthy that slip and twin activation also depend on the deformation temperature, and the CRSS for slip varies significantly, as discussed in the literature and shown in Figure 1c [16,17,18,77,78,79]. However, the type of twin formation, whether primary tensile $\left(10\overline{1}2\right)〈10\overline{1}\overline{1}〉$ or compressive, depends on the deformation loading direction at both RT and sub-zero liquid nitrogen (LN) temperatures, showing little sensitivity to deformation temperature.

Figure 1. Illustrations showing (a) common slip planes and (b) twin deformation modes in hexagonal Zr, data from [6,72], and (c) combined plot showing the activation CRSS for different slip and twin mechanism as a function of working temperature, data from [16,17,18,80,81,82,83].

Figure 1. Illustrations showing (a) common slip planes and (b) twin deformation modes in hexagonal Zr, data from [6,72], and (c) combined plot showing the activation CRSS for different slip and twin mechanism as a function of working temperature, data from [16,17,18,80,81,82,83].

In case of deformation along non $c$-axes, i.e., in-plane (IP) compression of material with basal texture, tensile twinning, and prismatic slip consistently occurs at RT and LN temperatures. At elevated temperatures, a combination of basal and prismatic slip mechanisms accommodates the deformation. Upon twin formation, subsequent deformation of the twin domains predominantly occurs by pyramidal and $\left(11\overline{2}2\right)〈11\overline{2}\overline{3}〉$ twinning at lower temperatures, and basal slip and $\left(10\overline{1}1\right)〈10\overline{1}\overline{2}〉$ twinning at higher temperatures. Compressive twins do not form at moderate strains but appear within the primary tensile twins at higher strains, contributing substantially to plastic deformation, as shown in Figure 2g–i. The formation of twins is also evidenced by a higher work hardening rate shortly after yielding, as shown in Figure 2j, although it does not significantly contribute to plastic deformation.

In grains with $c$-axes aligned along the loading direction, tensile twinning during IP compression reorients the crystal $c$-axes by 85.2° so that they align with the compression axis near the equator. In this case, slip mechanisms facilitate the migration and spreading of pole intensities along the compression axis towards the equator. In through-thickness (TT) compression, prismatic slip and $\left(11\overline{2}2\right)〈11\overline{2}\overline{3}〉$ dominate at sub-zero temperatures, transitioning to a combination of prismatic $〈a〉$ and pyramidal $〈c+a〉$ slip at ambient and higher temperatures. It is noteworthy that for TT compression at higher temperatures, basal $〈a〉$ slip begins to contribute alongside $\left(10\overline{1}1\right)〈10\overline{1}\overline{2}〉$ twinning [6,18]. As shown in Figure 2j, a sharp yield and a gradually increasing work hardening rate are observed for TT compression, typically characteristic of deformation twinning. Unlike IP compression, during TT compression at sub-zero conditions, the compression axes are oriented close to the $c$-axes containing $\left(11\overline{2}2\right)$ compression twins, while $\left(10\overline{1}2\right)$ tensile twins are found in grains with compression axes oriented far from the $c$-axes, as depicted in Figure 2d–f. The compressive twinning reorients the $c$-axes from near the pole (compression axis) to near the equator [6,18,84]. The loading directions (TT and IP), deformation temperature, and deformation modes contribute to distinct heterogeneous microstructural developments, including slip-induced internal misorientations and SLs features observed in the deformed samples [6,85].

2.3. Effect of Temperature and Orientation on Texture Development

The deformation temperature and the starting crystallographic orientation, along with the deformation mode, profoundly impact the texture development of Zr. Rolling reductions of up to 70% at room temperature (RT) and liquid nitrogen temperature (LN) demonstrate significant differences in texture evolution, as analyzed by electron backscatter diffraction (EBSD), as shown in Figure 3a [86]. At RT, rolling primarily activates dislocation slip, leading to the presence of non-deforming grains with their $c$-axes oriented near the normal direction ($ND$) of the Zr sheet, rendering them unfavorable for slip. However, at LN temperatures, both slip and twinning are activated, with compressive twinning deforming these non-deforming grains and promoting more uniform microstructures. This difference in deformation behavior leads to varied texture intensity development. In RT-rolled specimens, the angle between basal pole peaks and the $ND$ decreases slightly due to the activity of $\left(10\overline{1}1\right)〈11\overline{2}3〉$ pyramidal slip, resulting in the strengthening of the basal texture as compared to LN-rolled specimen, see Figure 3(a-i) [86]. However, compared to as-received, the overall texture intensity significantly drops with progressive deformation. A similar texture development is observed in commercially pure Zr and Zr-2 when uniaxially compressed along the $ND$ [84]. The RT condition primarily activates dislocation slip, maintaining certain grains undeformed due to their unfavorable orientations for slip. In contrast, LN rolling not only activates slip but also induces twinning. The early initiation of twinning in LN-rolled specimens leads to crystal reorientations that help mitigate the centralization of the bimodal basal texture. Twinning-induced reorientations contribute to the strengthening of the $\left(10\overline{1}0\right)$ texture since twinning reorients the basal pole by 85° away from the $ND$ [84,87], see Figure 3(a-ii). This results in a more homogeneous microstructure and improved texture uniformity compared to RT-rolled specimens. The influence of initial orientation is also critical in determining the subsequent annealing behavior, as seen in Zr-4 alloy sheets compressed along $ND$ and rolling direction ($RD$) [88]. As already discussed, $ND$ deformation involving extensive pyramidal $〈c+a〉$ slip and minimal prismatic slip doesn’t lead to significant evolution of texture, see Figure 3(b-i,b-ii), which is also confirmed by Visco-plastic self-consistent (VPSC) simulations [18,88]. On the other hand, deformation along the $RD$ involves a significant amount of twining, identified to be of type $\left(10\overline{1}2\right)$ tensile twin. Since during $RD$ compression the $ND$ axis experiences elongation, tensile twin activation is favored over compressive twinning. The tensile twinning thus leads to enhancement of $〈11\overline{2}0〉$|| $RD$ component during $RD$ deformation, see Figure 3(b-iii,b-iv). However, higher work-hardening rates and stored dislocation density in $ND$ compression lead to differing annealing behaviors at higher temperatures [88].

2.4. Microstructure and Texture Development during Pilgering

Hot working of Zr involves hot extrusion and specialized methods such as pilgering, a deformation technique that involves the simultaneous reduction of the outside diameter, inside diameter, and wall thickness of the tubes over the working length under a pair of dies. The dies have semi-circular tapered grooves cut on them, while a tapered mandrel, with a contour matching that of the dies, controls the wall thickness during deformation [10,15]. Pilgering depends on the activation of slip-twin systems [6,7,16], providing triaxiality of stresses, thereby achieving higher formability [15]. However, the process also involves heterogeneous deformation, where some grains get fragmented while others do not [19]. Pilgering deformation in Zr alloys results in gradual texture development from an initially non-random texture with well-defined texture fibers. Pilgering enhances the $〈1\overline{1}00〉$ and $〈\overline{1}100〉$ fiber texture intensities with an increase in the effective strain ($\overline{\epsilon }$), as shown in Figure 4. The Kearns factors are often used to measure the texture developments in the HCP materials. The Kearns factor $\left(f\right)$ [89,90] represents the fraction of basal poles in one of the three principal directions. In the case of pilgering, the radial Kearns factors (reference direction: $ND$) exhibit an increasing trend with effective strain, as evidenced by the increase in basal pole texture shown in Figure 4c. Conversely, axial and circumferential Kearns factors display a decreasing trend. This indicates that during pilgering, grains undergo rotation and align their $c$-axes closer to the $ND$ direction, as depicted in Figure 4d [7,10]. It is also worth noting that pilgering induces texture asymmetry between the $〈1\overline{1}00〉$ and $〈\overline{1}100〉$ fibers depending on the tube location with respect to the pilgering mandrel [10].

2.5. Grain Fragmentation during Deformation

Zr undergoes heterogeneous deformation, leading to notable features such as the generation and decay of deformation twins and orientation-dependent fragmentation of grains. Grain fragmentation behavior has been reported for cold-rolled (CR) Zr sheet material undergoing plane strain deformation [19], unidirectional rolling [19], simple uniaxial deformation [6,91], and pilgering [10,12]. This heterogeneous microstructure, which develops during deformation, persists after thermal annealing [23] and significantly influences the microstructure-property relationships. The deformed microstructures are often multi-scale, as microstructural heterogeneities occur over a length scale from macro to meso and finally micro. Even a small imposed strain (only a few percent under plane strain compression (PSC)) can induce a significantly higher near-boundary mesoscopic shear strain, approximately an order of magnitude higher [20]. Strikingly, significant differences in plastic strain are locally more observable at specific microscopic features such as GBs and the second phase. These lead to SLs [92], which are essential contributors to grain fragmentation. Direct observations on plane strain-deformed microstructure show that mesoscopic strain distributions are responsible for residual stress (see Figure 5a) and orientation gradient development (see Figure 5b). Significant differences in mesoscopic strain further create local regions of high dislocation density near GBs, acting as precursors to grain fragmentation. Since grain fragmentation is orientation-sensitive, samples deformed along the rolling direction ($RD$) exhibit a different grain fragmentation behavior compared to samples deformed along the $ND$. The origin of the orientation-dependent deformation associated with grain fragmentation is linked to the activation of prismatic and pyramidal $〈c+a〉$ slip [93]. With increasing temperature, the anisotropy between the CRSS of pyramidal $〈c+a〉$ and prismatic $〈a〉$ slip increases, similarly affecting grain fragmentation behavior.

2.6. Crystallographic Texture Evolution during Rolling and Annealing

Another intriguing aspect of the multi-scale heterogeneous deformed microstructure evolution is crystallographic texture development. Most texture measurements focus on the basal pole distribution, which is significant in terms of the anisotropy of HCP metals [70,84,94]. Little attention has been paid to the distribution of prism or pyramidal plane poles, as they are not as crucial for the mechanical behavior of the material as the basal pole distribution. However, they are strong indicators for the degree of annealing and should be quantified to determine the TMP effects on grain reorientation. The definitive orientation of the basal plane $\left(0002\right)$ in all HCP metals under PSC deformation, such as cold-rolled semi-finished commodities (e.g., wire, sheet, or tubing), is parallel to the direction of elongation. Depending on individual properties, deviations from this desired orientation, i.e., tilts of the basal plane and their rotation around its pole, indicate distinctive variances in material deformation.

Figure 5. (a) Residual strain measurements on Zr-4 sample deformed in an interrupted manner using a tensile loading setup for a final strain of 8%. Specific grains with basal and non-basal crystallographic orientations are tracked during interrupted testing, and their residual strains are identified using laboratory scale micro-Laue technique, which shows a hierarchical development [95]. (b) Progressive meso-structure evolution during PSC. Changes in grain shape (or mesoscopic strain) are visible [20] with grain fragmentation after (i) 4% and (ii) 10% PSC. (c) Developments in near-boundary mesoscopic shear (left) and in-grain misorientations (right) shown after 4% PSC. (Reprinted with permission from refs. [20,95]. Copyrights 2014 and 2020, Elsevier).

Figure 5. (a) Residual strain measurements on Zr-4 sample deformed in an interrupted manner using a tensile loading setup for a final strain of 8%. Specific grains with basal and non-basal crystallographic orientations are tracked during interrupted testing, and their residual strains are identified using laboratory scale micro-Laue technique, which shows a hierarchical development [95]. (b) Progressive meso-structure evolution during PSC. Changes in grain shape (or mesoscopic strain) are visible [20] with grain fragmentation after (i) 4% and (ii) 10% PSC. (c) Developments in near-boundary mesoscopic shear (left) and in-grain misorientations (right) shown after 4% PSC. (Reprinted with permission from refs. [20,95]. Copyrights 2014 and 2020, Elsevier).

Variation in the deformation process (applied strain, deformation temperature) also produces a characteristic texture component in both deformed and annealed material for the same starting texture configuration [96]. These are summarized in

Table 2. Ideal orientations in Euler Plots for CWSR and Rex Zircaloy-4 [70].

	CWSR	Recrystallized
$\phi$	$\mathrm{Ideal} \mathrm{Orientations} \left(\right\{hkil\left\}\right[hkil]$)	$\mathrm{Ideal} \mathrm{orientations} \left(\right\{hkil\left\}\right[hkil]$)
$0^{\mathrm{o}}$	$\left\{0002\right\}$	$\left\{\overline{1}016\right\}\left[5\overline{4}11\right]$
	$\left\{\overline{1}011\right\}\left[1\overline{2}10\right]$	$\left\{\overline{1}012\right\}\left[2\overline{3}10\right]$
	$\left\{1011\right\}\left[1\overline{2}10\right]$	$\left\{\overline{1}012\right\}\left[2\overline{3}10\right]$
		$\left\{\overline{1}010\right\}\left[1\overline{2}12\right]$
$10^{\mathrm{o}}$	$\left\{0002\right\}\left[1\overline{3}20\right]$ $\left\{1012\right\}\left[1\overline{2}10\right]$	$\left\{\overline{5}149\right\}\left[1\overline{2}10\right]$
$20^{\mathrm{o}}$	$\left\{\overline{1}011\right\}\left[1\overline{3}10\right]$ $\left\{\overline{3}125\right\}\left[1\overline{4}30\right]$	$\left\{\overline{3}128\right\}\left[1\overline{5}40\right]$
$30^{\mathrm{o}}$	$\left\{\overline{2}118\right\}\left[0\overline{1}10\right]$ $\left\{\overline{2}112\right\}\left[0\overline{1}10\right]$	$\left\{\overline{2}117\right\}\left[0\overline{1}10\right]$
$40^{\mathrm{o}}$	$\left\{\overline{1}1011\right\}\left[0\overline{1}10\right]$ $\left\{\overline{3}218\right\}\left[0\overline{1}10\right]$	$\left\{\overline{3}219\right\}\left[0\overline{1}10\right]$
$50^{\mathrm{o}}$	$\left\{1\overline{1}04\right\}\left[\overline{14}50\right]$	($\overline{1}120) \left[1560\right]$

for cold-work stress-relieved (CWSR) and recrystallized (Rex) specimens of typical Zircaloy-4. A schematic showing the typical annealing and deformation textures for various deformation processes and different product types, such as tube, wire, and sheet specimens, is also illustrated in Figure 6a. For tube specimens, depending on the ratio of $R_w$ (reduction in wall thickness) and $R_D$ (reduction in tube diameter), significant mechanical anisotropy in HCP Zr alloys is observed during deformation. Understanding the textural changes that occur during TMP, particularly during DRx and static recrystallization (SRx), is of critical importance. Most reviews of hot deformation related to DRx focus on flow softening and the corresponding appearance of an inflection point in strain hardening behavior [14]. However, the origin of DRx grains in hot deformed microstructures is related to mechanisms such as continuous DRx (CDRx), geometric DRx, and flow softening leading to standard discontinuous DRx (DDRx). The DRx can be associated with flow saturation in specific orientations; no indication of work softening is noted. This can be evident from the variation in deformation flow behavior in Zr systems and its effect on grain recrystallization [88,97], as shown in Figure 6b. Since initial orientation is critical for deformed microstructure development, it naturally leads to orientation-dependent DRx behavior. As the angle between the deformation axis and $c$-axes increases, the DRx effect is weakened, thus reducing the fraction of recrystallized grains. It is suggested that with $c$-axes moving away from the deformation direction, the easier-to-activate prismatic slip dominates. Hence, the practical stacking faults and stored energy of grains during deformation are ultimately reduced, unlike the case of pyramidal $〈c+a〉$ slip deformation. Regarding the operating mode of DRx, microstructural and misorientation characteristics show a variety of possible mechanisms, including CDRx [97,98], geometric DRx [99], and DDRx [91,100].

We further discuss the stability of deformation components as a function of deformation strain during typical rolling operations involving ‘simple rolling’ (SR) (with rolling along the $RD$), transverse rolling (TR) (rolling along the transverse direction ($TD$)) and cross-rolling (CR) (with alternate passes along the $RD$ and $TD$), as shown in Figure 6c. After significant deformation of 80% SR, the final texture remains unchanged after recrystallization, with just a slight reduction in the texture index throughout primary recrystallization [101]. The recrystallization texture in the case of 50% TR material remains substantially weaker than the deformation texture, with a shift in maxima towards orientations with $〈10\overline{1}0〉$|| $RD$, culminating in a weak maximum of about $\left\{0°,0°-20°,0°\right\}$. During primary recrystallization, the 40% CR specimen also undergoes a considerable textural change: the maximum of the orientation distribution function (ODF) shifts from $\left\{0°,20°,30°\right\}$ to $\left\{0°,20°,0°\right\}$, representing a reoriented volume percentage of around 45% [101]. Thus, the deformation direction and the loading mode significantly affect the nature of SRx.

3. Deformed Microstructure and Texture in Titanium

3.1. Microstructure and Texture Evolution during Rolling

Several authors have investigated the microstructure and texture evolution during the CR of Ti [44,45,46,47,102]. Gurao et al. [45] investigated the microstructure and texture evolution during unidirectional rolling (UDR) of commercially pure titanium (CP-Ti) with a starting hot-rolled sheet as starting material as characterized by a basal radial texture, i.e., $\left(0001\right)$ nearly parallel to ND, as shown in Figure 7a. The microstructure formed after UDR is characterized by elongated grains with a high aspect ratio with the longer axis along the rolling direction. Chun et al. [48] investigated the evolution of microstructure and texture during rolling, observing high twinning activity during the initial stages of deformation (up to about 40%). The evolution of twins is clearly illustrated using EBSD, as shown in Figure 7a–c. The higher fraction of compression twinning and a lower fraction of extension twinning in the early stages of deformation and their absence at higher rolling reductions are apparent from Figure 7d,e.

Though this initial profuse twinning and subsequent suppression is demonstrated by Nourbakhsh and O’Brien [49] using transmission electron microscopy (TEM) (Figure 7f,g), the characteristics of these twinning mechanisms have been understood much later. Rolling of Ti at ambient temperature generally results in a characteristic split-transverse direction (split-TD) type of texture [37,44,46,47,50,103]. This well-known split-TD texture in Ti is characterized by several essential texture components, listed in

Table 3. Important texture components in the rolling texture of Ti [44].

Texture Components	$\left\{{\mathit{\phi }}_1,\mathit{\phi },{\mathit{\phi }}_2\right\}$ Degrees	Description
$E$	$\{0°,40°,30°\}$	$\left\{0001\right\}〈11\overline{2}0〉$ tilted from ND toward TD
$B$	$\{0°,40°,0°\}$	$\left\{0001\right\}〈10\overline{1}0〉$ tilted from ND toward TD
$M$	$\{50°,90°,30°\}$	$\left\{01\overline{1}0\right\}〈2\overline{1}\overline{1}2〉$
$D$	$\{30°,0°,0°\}$	$\left\{0001\right\}〈11\overline{2}0〉$
A	$\{0°,0°,0°\}$	$\left\{0001\right\}〈10\overline{1}0〉$
C	$\{0°,90°,0°\}$	$\left\{11\overline{2}\overline{2}\right\}〈10\overline{1}0〉$

, that can be present in varying proportions in the deformed material. However, it should be noted that this type of texture is often characterized by predominantly two components (i.e., E and B), with other components in minor fractions. On the pole figure, several of these components share the same position. Hence, the texture evolution should be examined using the ODF sections to highlight the major changes.

Gurao et al. [45] reported that a starting basal radial texture evolved into the well-known split-TD type texture with a higher fraction of the E component, as shown in Figure 8a, which displays important texture components in titanium. Conversely, a strong recrystallization texture with high intensity near the E component also developed into a split-TD type texture with a pronounced B component [46]. This characteristic split-TD texture with a strong B component was similarly observed by Ghosh [104], Atasi et al. [44], and Zhong et al. [50] (see Figure 8b,c). However, despite the similar starting texture, Chun et al. [48] noted E component strengthening (Figure 8d,e). Additionally, a weak basal fiber texture and infrequent weak $〈10\overline{1}0〉$ and $〈11\overline{2}0〉$ fibers were also observed during the rolling of α-Ti [44,49,51,53,54,103]. In summary, regardless of the starting texture, a split-TD type texture is the most commonly observed cold rolling texture in Ti. The mechanism of the formation of this texture will be explained in the following section.

3.1.1. Mechanism of Split-TD Texture Formation

Nourbakhsh and O’Brien [49] observed that at 20% deformation, the material exhibited a split rolling direction (SRD-basal poles deviated from $ND$ by $\pm$0–30° towards $RD$) type of texture. This texture undergoes a rapid transition to the commonly observed split-TD texture (STD-basal poles concentrated at 20° from $ND$ towards $TD$) before the deformation reaches 40%. It is also observed that twinning was active only during the initial stages of deformation, i.e., up to 40%. These observations are explained by the following sequence of events. Initially, primary twinning occurs in favorably oriented grains, resulting in a strong SRD texture. Secondary twinning in these primary twins converts the SRD type of texture to an STD type. The presence of primary twins at 20% deformation and secondary twins at 40% is demonstrated using optical and TEM micrographs, see Figure 7f. The sudden orientation transition observed between 20% and 40% could not be attributed to slip, as such rapid orientation change cannot be generated by slip. Short-term annealing of 40% deformed specimens reveals that the secondary twins completely disappear due to partial recrystallization (see Figure 7g), and the texture measurement of this annealed specimen reveals SRD texture. This corroborates the earlier proposition that secondary twins are responsible for the STD texture development from SRD texture.

Twinning is suppressed at higher strains due to the extreme grain refinement caused by initial twining. Further deformation above 40% is carried by slip deformation and only results in slow rotation of individual grains around the basal pole and a rotation towards the $TD$ till about 30–40° from $ND$, where the well-known split-TD texture stabilizes. Using EBSD, Zhong et al. [50] elaborate that primary compression twinning $\left(11\overline{2}2\right)〈11\overline{2}\overline{3}〉$ followed by secondary extension twinning $\left(10\overline{1}2\right)〈10\overline{1}\overline{1}〉$ results in the split-TD type texture formation with the metastable split RD texture at 20% strain [44,48,50]. This sequence of primary compression twinning (CT) followed by secondary extension twinning (ET) is also observed to be active in cryo-rolled titanium, as illustrated in Figure 9 [105]. It is further understood that grains not favorably oriented for twinning are termed ‘white grains’ (i.e., grains with $\left(0002\right)$ making an angle of 30–70° with $\mathrm{N}\mathrm{D}$ in $\mathrm{N}\mathrm{D}-\mathrm{T}\mathrm{D}$ plane). Under the combined action of basal and prismatic slip, these grains slowly reorient towards the [0, 40, 0] position (B component) [44,103]. A more detailed sequence of events has also been proposed to explain the texture evolution. Primary compression twinning takes the B component to the M component, which undergoes secondary extension twinning, taking it to the D component [50].

Similarly, twinning events take the E component to the M’ and then to the A component. However, it is observed that the E component twinning occurs with a much lower probability. The gradual strengthening of the B component occurs due to the rotation of E towards B due to dislocation slip. A reverse mechanism of B reorienting towards E could strengthen the E component, as observed by several others [45,48]. This could be due to a higher probability of E component grains twinning than B due to local incompatibility or grain size effects [36]. Nevertheless, in either case, the characteristic split-TD texture evolves. Hence, the deformation texture evolution in Ti can be categorized into two distinct regimes: (i) the low to intermediate strain level, where texture evolution is predominantly due to compression and extension twinning, and (ii) the high strain regime, where texture evolution is relatively sluggish and is caused solely by slip.

3.1.2. Influence of Strain Path

Two-step cross-rolling (TSCR), multi-step cross-rolling (MSCR), and reverse rolling (RR) are other types of commonly studied strain paths in rolling [44,45]. It is observed that Kernel Average Misorientation (KAM) is low for the cross-rolled specimens. Also, viscoplastic self-consistent simulations (VPSC) show that the average number of active slip systems in the cross-rolled specimens is higher than in the UDR and RR specimens [51,53]. This observation has been used to substantiate microstructural observations. When more slip systems are active, it is well known that the lattice rotation caused would be lower, resulting in lower KAM as seen in cross-rolling. The lower KAM in the cross-rolled specimens is also attributed to the stacking fault energy (SFE) difference between the basal and prismatic planes. Higher basal slip system activity in the cross-rolled specimens can result in a higher amount of cross slip from the high SFE basal plane to the low SFE prism plane, resulting in a lower KAM in cross-rolled samples. Furthermore, the texture post-deformation is also different between the UDR and MSCR samples (see Figure 10a,b, respectively). While the intensity of the E component is higher for the UDR samples, the fraction of the M and C components is higher for the cross-rolled samples. A very strong $〈10\overline{1}0〉$ and $〈11\overline{2}0〉$ fiber is also present in the cross-rolled samples. The strength of these fibers is relatively lower for the UDR samples. The difference in texture between the UDR and MSCR samples is attributed to the difference in slip activities.

3.1.3. Mechanism of Texture Formation during Cross Rolling

Due to the 90° alternation in the rolling direction, the activity of deformation mechanisms is altered during MSCR [44,51]. The slip or twin systems that are not active while rolling along one direction can get activated while rolling along the orthogonal direction. Due to the activation of these systems, latent hardening of the prismatic slip system would be higher. Hence, it would result in the reduction of prismatic slip and a simultaneous increase in basal slip activity [50]. A sequence of events can also be envisaged to explain the texture formation. Initially, grains favorable for twinning undergo compression twinning, resulting in a split-RD type of texture. However, due to the change in rolling direction, secondary extension twinning will not get activated, and hence, the transition to split TD texture will not happen in these grains. This is corroborated by the relative intensities of the contraction twin component (M) and extension twin component (D) in the UDR and MSCR samples [44]. Hence, the split-RD texture stabilizes at higher strains. Additionally, the ‘white grains’ undergo contraction twinning due to rolling along $TD$ and form the split-TD type of texture, which is further stabilized when rolling along $RD$ by activating basal slip. Due to the simultaneous development of split-TD and split-RD components, an overall weak texture with a split along $TD$ and $RD$ is developed. Twinning in white grains is also responsible for the overall weakening and the difference in texture from UDR [44].

3.1.4. Influence of Temperature

At high rolling temperatures around 873 K or 1073 K, a strong basal fiber texture ($〈0001〉$ || $ND$) is commonly observed, see Figure 10c,d [47,52]. To understand the temperature effect, CP-Ti with an initial random texture is hot rolled until 90% under three different strain paths: UDR, MSCR, and RR. The microstructure remained essentially equiaxed for all the deformation paths and did not elongate like in the CR condition. A higher fraction of twins is observed in the MSCR sample, which can be attributed to the change in rolling direction during every alternate pass. Decreased low-angle GB (LAGB) fraction at higher deformation levels indicates DRx. The texture post-deformation is a homogeneous basal fiber ($\left(0001\right)$|| $ND$), independent of the strain paths. The volume fraction of all components except D and A, which are essentially part of the basal fiber, is very low. This kind of texture is also observed by Bahl et al. [47] in CP-Ti after hot rolling at 873 K and 1073 K. This texture differs entirely from the split-TD type texture that it develops after cold rolling. This difference is often rationalized by the higher activity of basal slip at elevated temperatures. It is well known that the CRSS for basal slip is considerably lowered at elevated temperatures [106,107]. Once the basal slip gets activated, rolling deformation, which essentially involves compression along $ND$, rotates the basal planes to align perpendicular to $ND$, i.e., $\left(0001\right)$|| $ND$ [108].

3.1.5. Influence of Shear

Rolling is generally a plane strain deformation process. However, under certain conditions, shear strain components can also be induced during the rolling process. Milner et al. [54] observed a sheared microstructure in the regions near the surface of a CR sheet due to higher shear strain components near the surface. This deformation state is also observed in conditions where friction between the rolls and the sheet is not negligible or in processes like asymmetric rolling where the roll speeds are different. The microstructure and texture have also been distinct between the low shear zone (central regions) and the high shear zones (near the surface); see Figure 10e,f. The grains appear elongated, highly deformed, and inclined by approximately 50° from the normal axis due to intense shearing. A strong basal fiber texture is observed in the high shear zone, while a characteristic split-TD texture prevails in the no-shear zone. Yang et al. [53] studied the influence of shear components of strain on the texture evolution in rolling. It is shown that during pure plane strain deformation, the E component and a heterogeneous $〈10\overline{1}0〉$ || $RD$ are formed. However, with the increase in the shear component, a strong basal fiber, $〈0001〉$ || $ND$, and a partial $〈11\overline{2}0〉$ || $RD$ formed. This variation is attributed to a higher basal and pyramidal slip activity, which has been confirmed by VPSC simulations. This also corroborated the observations made by Milner et al. [54].

3.1.6. Influence of Grain Size

As discussed in the previous section, the role of twinning in the deformation texture and microstructure evolution is very pronounced in Ti. To understand the evolution when twin mechanisms are inactive, Gurao and Suwas [51] performed unidirectional rolling of submicron grain (SMG) size material generated using equal channel angular extrusion (ECAE) and cryo-rolling. The annealed specimen after these operations had a grain size of 500 nm. This SMG material was subjected to unidirectional rolling at RT to a 90% reduction in thickness. The starting texture was a weak shear-type texture generally observed in ECAE-processed Ti [109]. The characteristic texture formed was a split-TD type texture like microcrystalline Ti. However, a close inspection of the ODF revealed that the fraction of the B component was relatively lower compared to the microcrystalline sample. However, a high fraction of the E component was also observed. Furthermore, the overall texture intensity was low for the SMG sample. An interesting observation was the low fraction of M and D components in the deformation texture, pointing towards a lower activity of twins, unlike microcrystalline material. The absence of twins was confirmed using TEM, which also provided evidence of slip activity at very high strain levels. The suppression of twinning with a decrease in grain size is a well-known phenomenon attributed to the increase in twin nucleation stress [110,111]. This increase in twin nucleation stress is attributed to the hindrance of the coordinated movement of $〈10\overline{1}0〉$ and $〈11\overline{2}3〉$ zonal partial dislocations. At the sub-micron length scale, the adjacent slip planes are weakly coupled by threading partial dislocations, which hinders the movement of partials on the adjacent planes, thus hindering twinning. Consequently, a sluggish texture evolution, which is solely due to the activity of basal, prismatic, and pyramidal $〈c+a〉$ slip systems, occurs.

3.2. Microstructure and Texture Evolution during Extrusion and Drawing

Extrusion of CP-Ti produces a fiber texture symmetric about the extrusion axis [55]. Here, the fiber is characterized by basal poles deviated by ~90° from the extrusion axis and spread along the TD line. The extrusion texture does not change significantly, even up to about 623 K or 723 K extrusion temperatures. The microstructure revealed the beginning of recrystallization at 623 K and 723 K. The RT extruded samples showed a large scatter. However, the samples extruded at high temperatures showed a fiber texture symmetric about the extrusion axis. During extrusion, the deformation state is indirect compression, where the specimen experiences a compressive load normal to the extrusion axis. Due to this, the slip planes tend to rotate until they are normal to the compression axis. Since the active deformation mode is basal slip at high temperatures, the basal planes tend to align normally to the compression axis. In axisymmetric products like extruded rods, this manifests as a fiber texture symmetric about the extrusion axis. Sabat et al. [56] investigated the cold drawing of CP-Ti wires and reported a fiber texture symmetric about the drawing axis. The deformation state in the drawing is also an indirect compression normal to the drawing axis, and the fiber-like texture would only develop if basal slip is activated. However, with the prismatic active slip system at RT, the rationale used for hot extrusion may not apply. However, since the reduction per step and the strain rate are high, the difference in strain rate sensitivity between the basal and prismatic slip systems might cause a difference in their relative activities, resulting in the fiber texture [56].

3.3. Microstructure and Texture during Annealing

CP-Ti is found to have the widest application in heat exchangers and storage tanks, where the starting material is always a rolled and recrystallized sheet. The most commonly used annealing treatment is performed at 973 K for 2 h. Several reports discuss the so-called “recrystallization texture” of Ti after annealing in this temperature range. Wagner et al. [103] conducted a systematic study to understand the microstructure and texture evolution mechanism. The evolution of recrystallization texture and microstructure in low alloyed Ti was studied during the annealing of 80% CR sheets. The primary intention was to understand the primary recrystallization stage.

3.3.1. Microstructure and Texture Evolution during Primary Recrystallization

Primary recrystallization in CP-Ti (T40) was divided into two stages. The first stage corresponds to a bimodal microstructure with the appearance of new grains in about 80% of the material volume, with about 25% changing their orientation. The second stage was sluggish and characterized by the disappearance of the so-called white grains, which correspond to [0, 45, 0] orientation, which did not twin during deformation. Most of the recrystallization experiments carried out in the study were done at 773 K for various durations. The samples annealed at 773 K for 1 min showed the beginning of dislocation rearrangement into cell structures. Annealing for a slightly longer time evidenced the polygonization process due to recovery processes; see Figure 11a. Squared and hexagonal dislocation networks forming low-angle boundaries were observed even after longer annealing. The cells formed were depleted of dislocations in the interior, and the recovery process was found to be active homogeneously throughout the material. The recrystallization process was highly heterogeneous as certain deformed grains resisted recrystallization even after long-term annealing (Region 1 in Figure 11b). EBSD analysis confirmed that these grains had an orientation very close to the white grains, see Figure 11b. The transition of cells and sub-grains into recrystallized grains separated by high-angle GBs was also vividly demonstrated using TEM [103].

Microbands and elongated lamellar boundaries characterized the microstructure before annealing. As observed by several authors, twinning dominates in Ti up to about 30–40% strain. However, twinning was not observed in orientations close to that of the white grains, which also agrees with Bozzolo et al. [46] observations. The deformation texture was characterized by a main peak at {0°, 45°, 0°}, i.e., $\left(\overline{1}2\overline{1}3\right)〈10\overline{1}0〉$ with a large spread around it, and a weak peak around {0°, 35°, 30°}, i.e., $\left(10\overline{1}3\right)〈12\overline{1}0〉$, which are close to the B and E components common in Ti rolling texture. The texture post-annealing at 973 K for one hour was characterized by the {0°, 32°, 30°}, i.e., $\left(10\overline{1}3\right)〈12\overline{1}0〉$, and {0°, 30°, 0°}, i.e., $\left(\overline{1}2\overline{1}5\right)〈\overline{1}0\overline{1}0〉$ and was very similar to the so-called “recrystallization texture” in Ti. These components were also present in the deformed material, but a large spread around these ideal orientations is often seen, which has vanished. By comparing the ODF sections of fully recrystallized, i.e., at 973 K annealed and 773 K annealed samples that correspond to the end of primary crystallization, it was concluded that there was only a moderate variation in the texture during primary recrystallization.

Only minor changes were observed by comparing the ODF sections of the CR primary recrystallized samples; see Figure 11c,d. It was observed that the orientation with low and high ϕ angles disappeared, and more orientations appeared around {0°, 32°, 30°}. Additionally, only 25% of the grains changed orientation, with most of this occurring within the first 60 min of annealing at 773 K. The first stage of primary recrystallization is completed fairly rapidly, with about 80% of the material recrystallizing within the first 40 to 80 min at 773 K. Similar trends of recrystallization kinetics were also reported by Shankar et al. [57]. The second stage, which involves consuming the remaining material that resists recrystallization, is sluggish and completed in about 300 min. It was observed that the grains that changed their orientation at the end of the first stage (about 25%) were essentially those that underwent twinning during the rolling deformation and changed orientation towards {0°, 30°, 30°} during the first stage of primary recrystallization. Continuous recrystallization was identified as the mechanism of recrystallization in these grains, which was reinforced by the extent of recovery in this material (Figure 11a). However, unlike cubic materials, where the recovery process triggers the nucleation of new grains that subsequently grow with large misorientation with the matrix, Ti behaves differently as the texture change is observed to be very moderate [57]. A mechanism leading to recrystallized grains by forming sub-grains through dislocation rearrangement and their coarsening was proposed. The remaining material, other than the white grains, also undergoes early continuous recrystallization and a texture change due to the competition during the growth of these grains occurs. Additionally, the observation of new grains near HAGBs, though very scarce, was attributed to DDRx involving classical nucleation and growth.

The white grains were observed to be deformed with a much more homogeneous dislocation structure, resisting discontinuous recrystallization and not giving rise to significant nucleation. The stability of this particular orientation was attributed to the zero-rotation field around this orientation and the absence of twinning. These grains, which primarily deform by a combination of prism and pyramidal slip activity, recrystallize only in the second stage of primary recrystallization. The mechanism by which these grains recrystallize was understood to be a continuous recrystallization process or extended recovery. In the second stage of primary recrystallization, no significant change in texture occurred. The fact that primary recrystallization did not cause any significant changes to the deformation texture emphasizes that the so-called ‘recrystallization textures’ generally reported in Ti annealed above 773 K are not exactly recrystallization textures. They are textures that evolve during the secondary recrystallization process or grain growth.

3.3.2. Microstructure and Texture Evolution during Secondary Recrystallization

Bozzolo et al. [58] investigated the secondary recrystallization process by keeping the primary recrystallized material as the initial material. During secondary recrystallization, significant grain growth occurs, following the common trend concerning time and temperature (Figure 12a). When primary recrystallization was complete, the maximum was near {0°, 35°, 0°}. During secondary recrystallization or grain growth, a broad peak centered around {0°, 35°, 30°} developed. It was also observed that the orientations that disappeared during grain growth were highly misoriented concerning the {0°, 35°, 30°} component and had the smallest grain size. The starting microstructure consisted of regions with small grain sizes and regions with larger grain sizes, likely due to differences in local primary recrystallization kinetics. It was observed that all the small-grained regions disappeared during grain coarsening due to their higher growth rates. The starting material had a texture very close to the deformed state, with a major volume fraction of the {0°, 35°, 0°} component (Figure 12b). The texture after grain growth was characterized by orientations located around {0°, 35°, 30°} with a large spread (Figure 12c). The intermediate stages of grain growth showed these components in varying proportions. Analyzing the differences in the ODF between the starting material and the material after the secondary recrystallization process, the major difference was that {0°, 35°, 30°} increased in volume fraction, whereas the initially major {0°, 35°, 0°} component did not change significantly (Figure 12d). The disappearing orientations were closely located at ${\mathsf{\varphi }}_2$ near 0°/60°, and ϕ below 20° or above 40°, (Figure 12d). The {0°, 35°, 0°} component also increased, but to a much lesser extent compared to the {0°, 35°, 30°} component. The analysis of the ODF of the smallest and the largest grains separately showed that the global texture obtained after extended grain growth was very similar to that of the largest grains. The texture of the smallest grains was close to that of the initial global texture.

The development of certain orientations and the disappearance of others was explained using the correlation between grain size, orientation, and the nature of the GBs according to the energy and mobility criteria. It is well known that mobility and energy are high for highly misoriented GBs. The disappearing grains were observed to have a misorientation greater than 30° with the ideal orientation {0°, 35°, 30°}. Hence, these boundaries were considered to have high mobility. The mechanism responsible for texture evolution predominantly involves boundaries with misorientations greater than 30° with higher mobility. Figure 12e shows grains of A, B, and C types, where A and B correspond to {0°, 35°, 0°} and {0°, 35°, 30°}, respectively.

The C-type grains are widely dispersed in the orientation space and have much smaller grain sizes than the A and B grains. The C-type grains also have a misorientation of more than 30° with the growing {0°, 35°, 30°} component. Their disappearance is due to a combined effect of their small grain size and highly misoriented GBs. The initial major texture component, the {0°, 35°, 0°} (A type) grain, grows much less than the grains close to {0°, 35°, 30°}. The grain size distribution of the A and B-type grains is quite similar. This lower growth rate of A-type grains was attributed to a higher proportion of them being present in the initial material, which causes lower GB mobility due to the lower misorientation angle. The A-type or B-type grains can grow to consume each other; however, due to the orientation pinning effect, the B-type grains consuming the A-type grains are more favored. Thus, B-type grains continue to grow, and the corresponding texture component {0°, 35°, 30°} keeps increasing until it becomes predominant. A different texture evolution was observed when the starting CR texture was dominated by the {0°, 35°, 30°} component. At annealing temperatures up to 873 K, the mechanism as described earlier holds good to an extent; however, at higher annealing temperatures, the component around {0°, 35°, 0°} became the major component, and the {0°, 35°, 30°} component almost vanished [44]. A reverse mechanism like the previous one can be envisaged to explain this.

Despite all these observations and proposed mechanisms, it is important to note that the recrystallization texture of Ti is largely dependent upon the deformation texture and the recrystallization temperature. The annealing texture that develops between 773 K and 973 K consists of $\left(0001\right)〈1\overline{2}10〉$ and $\left(0001\right)〈10\overline{1}0〉$, $\pm$30° to the $TD$. When the temperature range is above 973 K, substantial grain growth occurs, and the recrystallization texture consists of either $\left(10\overline{1}3\right)〈1\overline{2}10〉$ or $\left(20\overline{2}5\right)〈1\overline{2}10〉$ components, which manifest as $\pm$30° across the $TD$ line on the $\left(0001\right)$ pole figure. At temperatures below 773 K, the recrystallization texture is similar to the cold rolling texture. The cross-rolling textures are also different from the unidirectionally rolled textures, and the textures post-recrystallization are also different [44]. The mechanism of recrystallization is also dependent upon the deformed state. Shankar et al. [57] reported sub-grain coarsening in the deformed lath region and random nucleation in the highly deformed regions. 50% CR specimens upon recrystallization showed substantial occurrence of discontinuous sub-grain coarsening and sub-grain coalescence, i.e., oriented nucleation as the recrystallization mechanism [57]. Hence, a unified theory to explain the evolution of recrystallization texture in α-Ti is still absent.

4. Microstructure and Texture Evolution in Magnesium Alloys

4.1. Microstructure and Texture during Annealing

Mg-based alloys are deformed by various processing routes, such as rolling, extrusion, and equal channel angular processing (ECAP). Various rolling processes are performed over Mg alloys to activate the slip systems and modify the grain orientations [112,113]. After hot extrusion, Mg alloy viz. Mg-Y-Zn alloy displays a bimodal microstructure comprising lamellar 14H and block 18R phases. This dual-phase structure enhances the mechanical strength of the Mg alloy by combining the strength of block phases with the deformability of lamellar phases [67]. Hot rolling leads to refined microstructures with 78% and 22% of LAGBs and HAGBs with equiaxed grains. DRx and deformed grains were 68% and 32%, respectively, see Figure 13 [66]. Similarly, hot-rolling annealed samples have HAGBs and LAGBs of 78% and 22%, respectively, with precipitate distribution along the GBs. In the case of Mg-Sn alloys, complete recrystallization occurs at an annealing temperature of 488 K [66]. In the case of ultralight BCC Mg alloys such as Mg-Li-Al alloys, anisothermal aging results in a phase transformation characterized by spinodal decomposition, forming Al-rich zones followed by the nucleation of rod-like θ phase. Subsequent coarsening of the θ phase (Mg₃Al) leads to its transformation into AlLi with a core-shell structure, thereby affecting hardness [68].

In the case of Mg-Re alloy hot rolling at an initial 10% reduction, the parental grains (PG) exhibit large spreads of off-basal orientations that activate $\left(10\overline{1}2\right)$ twins. Twins occupy significant portions of the PG, and these twins can be identified as extension twins, as shown in Figure 14b,c. They exhibit an elliptical or irregular shape and appear thick. The inherent high mobility of $\left(10\overline{1}2\right)$ twins enable them to swiftly occupy and reorient the surrounding matrix, typically by an angle of approximately 86.3°. This, in turn, promotes the facilitation of dislocation slip within the twinned region. However, dislocation slips do not dominate due to the even distributions of intragranular misorientation (IGM) in PG. Still, basal $〈a〉$ slip is significantly activated in the twins [114,115]. The basal $〈a〉$ slip is notably activated within the twins due to the presence of IGM. Despite a high Schmid factor (SF), prismatic $〈a〉$ slip tends to exhibit low activity within the matrix of these PG. This can be attributed to the relatively high CRSS required for prismatic $〈a〉$ slip, especially when compared to the CRSS values for $\left(10\overline{1}2\right)$ twins and basal $〈a〉$ slip at the rolling temperature of 713 K. At 20% reduction {10$\overline{1}$2} twins activated in the twinned regions and uniform IGM can synergistically activate various dislocation systems within the material. As a result, even though PG with different initial orientations may exhibit a variety of deformation mechanisms and activities, they collectively align the c-axes of most PG parallel to the $ND$ [116].

This alignment contributes to the overall development of the basal texture in the material. At 20% reduction, the prevalence of twins within PG significantly increases, as evident in Figure 14d–f. For instance, twin lamellae within ‘Grain 2-A’ can be observed. In these twin lamellae, twin pairs located at GBs of the PGs are indicated by the dotted arrows in Figure 14d. Moreover, secondary twins can be detected within these twin lamellae, as shown by the solid arrows in Figure 14e,f. Meanwhile, neighboring grains like ‘Grain 2-B’ and ‘Grain 2-C’ appear less favorable for twinning activation [118,119]. This highlights the significant role played by the initial orientations of the PG in influencing the twinning response. In the case of Mg-Y-Zn alloy, CR leads to the uniform distribution of SB composed of fine micro-bands. These micro-bands are interspersed with high fractions of compression twins that contain a high density of dislocations.

In general, the twin shear stress was found to have a close relationship with the axial ratio ($c/a$) of the close-packed hexagonal lattice. In the case of Mg alloys, the $\left(10\overline{1}2\right)$ twin exhibited the lowest shear stress, making it the most likely twin type to occur during rolling, as shown in Figure 15. This could be attributed to the random orientation of grains in the sintered Mg alloy [120]. In the early stages of deformation, grains often need continuous adjustments to facilitate slip occurrence during deformation. Consequently, a substantial quantity of twins tends to form in the Mg matrix during the initial stages of deformation as the microstructure transitions from the sintered state to the deformed state. Furthermore, when a significant rolling reduction is applied, the grains experience intense plastic deformation. Given the limited number of slip systems in Mg alloys, dislocations readily accumulate rapidly, reaching the dislocation density necessary for recrystallization. This situation is more conducive to DRx [121]. While a significant quantity of $\left(10\overline{1}2\right)$ twins was observed in the specimen with a 20% rolling reduction, it’s important to note that Mg alloys can exhibit various types of twins. These typically include $\left(10\overline{1}2\right)$ tensile twins, $\left(10\overline{1}1\right)$ compression twins, and $\left(10\overline{1}1\right)-\left(10\overline{1}2\right)$ secondary twins. In the case of asymmetric rolling $\left(101\overline{1}\right)-\left(101\overline{2}\right)$ double twins, $\left(101\overline{2}\right)$ tensile twins, $\left(101\overline{1}\right)$ compression twins appear, and DRx occurs during rolling.

Asymmetric rolling with a 14% reduction rate induces twinning and CDRx phenomena in Mg alloys. Notably, the CDRx grains are smaller and more abundant than those in the sample subjected to symmetric rolling. Additionally, the twins observed in the asymmetrically rolled sample were primarily of the tensile twin variety [63,123]. The prismatic slip typically requires a higher CRSS than basal slip under uniaxial tension conditions; however, the prismatic slip system exhibits significantly higher activity during shear deformation in processes like ECAP. In ECAP, hydrostatic back pressure is applied to materials with HCP structure, introducing an additional stress component to potential slip planes. This added stress compensates for the necessary stress levels to activate non-basal slip systems. Consequently, the imposition of hydrostatic back pressure leads to a notable reduction in yield anisotropy (the CRSS ratio of non-basal to basal slip) and results in the increased activity of non-basal slip, as opposed to basal slip. Furthermore, when added to Mg alloys, rare earth (RE) elements like yttrium can reduce the SFE by altering the dislocation core structure, facilitating the activation of non-basal slip systems [124].

4.2. Texture Evolution in Plastically Deformed and Heat-Treated Materials

In the case of Mg and its alloys, the common slip systems are (i) Basal Slip System: This system is the most dominant at RT deformation because it has the lowest CRSS. It enables the movement of dislocations along the basal plane. (ii) Prismatic Slip System: The prismatic slip system activates when the deformation temperature surpasses 523 K, allowing dislocations to move in the prismatic plane of the crystal. (iii) Pyramidal-I and Pyramidal-II Slip Systems: These systems become significantly active at deformation temperatures exceeding 623 K, contributing to increased formability [125,126,127]. They facilitate dislocation motion in different pyramidal planes. For hot rolling, the resulting texture is primarily basal (0002), similar to the conventional texture observed in rolled Mg. However, the intensity of the basal pole extends from the $ND$ to the $RD$ due to the activation of non-basal slip systems. The presence of solid solution in alloys plays a key role in this effect [128]. The crystallographic texture remains similar, but there is a reduction in intensity in the case of the hot rolled annealed (HRA) sample; see Figure 16. Furthermore, for the HRA sample, there is a more pronounced spread of the basal texture along the $TD$. This spread is approximately 30° and 35° from $ND$ to $RD$ and $TD$, respectively, for the HRA sample.

In the context of $\left(10\overline{1}1\right)-\left(10\overline{1}2\right)$ double twins, it’s important to note that only the variants corresponding to their primary $\left(10\overline{1}1\right)$ twins were considered for SF calculations. Among the primary $\left(10\overline{1}1\right)$ twin variants, one particular variant (oriented at approximately 37.5° around the $〈10\overline{1}2〉$ axis concerning the matrix) is significantly favored over the others due to its minimal compatibility strain. Both primary $\left(10\overline{1}2\right)$ twins and primary $\left(10\overline{1}1\right)$ twins, adhere well to the SF law under the current rolling conditions. These twins are significantly activated in PG with off-basal orientations, typically in PGs where the $c$-axes are tilted by 60–90° away from the $ND$. Based on SF law, twin variants with higher SF exhibit greater activity compared to those with lower SFs. Similarly, the $\left(10\overline{1}2\right)$ twin variants with the highest SFs for typical PG led to twinned regions tilted by 30° from the $ND$. For PG with off-basal orientations, all these $\left(10\overline{1}2\right)$ twin variants cause the matrix orientations to rotate within 30° away from the $ND$. This rotation significantly contributes to the formation of the primary basal texture component, which aligns with findings in other Mg alloys subjected to uniaxial compression after a 10% deformation [129]. As for the secondary intensities tilted by more than 30° from the $ND$ toward the $TD$, these orientations can be attributed to contributions from either $\left(10\overline{1}2\right)$ twins with different variants. At higher levels of reduction, such as 50% reduction, there will be a noticeable increase and subsequent dramatic decrease in the activity of shear bands and double twins, see Figure 17. As a result, SBs and double twins may have a more prominent role in contributing to the formation of the ‘RD-split’ texture as rolling reduction increases. This ‘RD-split’ texture remains stable even after further rolling with accumulated reductions of 0.6 and 0.85, coupled with intermediate annealing. This stability can primarily be attributed to the contribution of SBs, which exhibit higher activity at larger rolling reductions [130].

In the case of ultrasonic surface rolling processing, Mg alloy reveals double twins (DT) in this region of $\left(10\overline{1}2\right)〈10\overline{1}1〉$ extension twin type. Compression twins and double twins are not formed in this process because the CRSS required to form extension twins is much lower than that needed for other twin types. The $c$-axis of the $\left(10\overline{1}2\right)〈10\overline{1}1〉$ extension twins will be perpendicular to the applied stress direction. The misorientation angle between the matrix and the extension twins is approximately 86°. Due to multiple extension twins, the GB content of 86° $\left(10\overline{1}2\right)〈10\overline{1}1〉$ in this region is significantly higher than that of other HAGB [131]. During ultrasonic surface rolling, there are gradient changes in twin density within the material. As the depth of the deformation layer increases, there is a corresponding decrease in twin density [132]. Concurrently, the grain size of the Mg alloy increases with the depth of the deformation layer. Statistical analysis of the grain sizes at different layer depths indicates that near the treated surface, $\left(101\overline{1}\right)$ and $\left(101\overline{3}\right)$ compression twins are readily generated. This phenomenon is attributed to the high plastic strain experienced by the Mg alloy near the surface, which meets the CRSS requirements for compression twin formation. As the depth of the deformation layer increases, the DTs transition to $\left(101\overline{2}\right)$ extension twins. This change can be explained by varying levels of plastic strain experienced by the Mg alloy during ultrasonic surface rolling processing [133]. When the deformation layer depth is shallow, the Mg alloy undergoes significant plastic strain, providing the necessary CRSS for compression twin formation. However, as the plastic strain decreases with increasing deformation layer depth, compression twins are no longer favored. Instead, $\left(101\overline{2}\right)$ extension twins become prominent because their CRSS requirements are much lower than those of compression twins, leading to the generation of numerous $\left(101\overline{2}\right)$ extension twins in the Mg alloy. After rolling, the texture exhibits enhancement in the presence of $\left(1\overline{1}\overline{2}0\right)$ || $TD$ texture. This texture variation leads to distinct mechanical performance differences between the $TD$ and $RD$. The increased $\left(112\overline{3}\right)$ || $ND$ texture promotes slip possibilities, potentially resulting in increased elongation. The SF of $\left(0001\right)〈11\overline{2}0〉$ in $RD$ for Mg alloy samples was greater than in the $TD$. Additionally, the SF of $\left(0001\right)〈11\overline{2}0〉$ exceeded 0.35. These SF values provide evidence of anisotropy in the sample, indicating that initiating cylindrical slip is challenging. This anisotropy may enhance the material’s strength while reducing its elongation, contributing to its mechanical behavior [134]. The ECAP Mg sample reveals the presence of all three slip systems, and both twinning mechanisms play a role in accommodating the strain generated. The increased intensity of the peaks associated with the prismatic and pyramidal planes, along with the centralized pole figures observed in the ECAP-processed sample compared to the homogenized sample, indicates the activation of non-basal slip systems during the ECAP process. After this process, the dominant basal component disappeared, giving way to weak basal and prismatic fibers [135].

4.3. Influence Strain Rate on Plastic Deformation and Texture Development

Strain rate sensitivity in Mg alloys manifests in various deformation mechanisms such as basal, prismatic, pyramidal, and extension twinning, each exhibiting unique sensitivities to different strain rates [64,136]. Higher strain rates typically increase stress, especially in compression along the ND. Texture development is also influenced by strain rate, with initial textures evolving distinctly under varying strain rates (see Figure 18).

For instance, studies using the elasto-viscoplastic self-consistent model have shown that in-plane compression at different strain rates results in different texture evolutions, which are crucial for understanding the mechanical behavior of Mg alloy [137,138,139]. Additionally, higher strain rates in extruded-annealed AZ91 Mg alloy enhance strength but reduce elongation and promote rapid dislocation accumulation. The strain rate also affects the twinning behavior, which is crucial for yield strength and deformation mechanisms in AZ31 Mg alloys [59,60].

4.4. Effect of Temperature on Plastic Deformation and Texture Development

Deformation mechanisms at lower temperatures, such as 373 K, are less effective than at higher temperatures, like 473 K, leading to more inhomogeneous deformation, increased SBs, and cracking [140]. Temperature influences texture development, with initial textures such as basal or prismatic playing a crucial role in the resulting deformation texture. Likewise, the Kink Band mechanism occurs at 473 K, which is related to microstructural refinement and dislocation pile-up [141]. Higher temperatures generally enhance ductility due to increased thermal activation of dislocations and reduced resistance to slip [137,140]. At 523 K, the slip band mechanism is prominent in Mg alloy, where prismatic slip predominates due to increased activation energy. In cases of plastic deformation in Mg-Gd-Nd(-Zn)-Zr alloys, shear bands form at 673 K, leading to micro-cracks and shear fractures. Additionally, reticular shear bands, which are prevalent at 673 K, cause obstructions that contribute to deformation by accommodating strain through twin propagation and dynamic recrystallization [69]. In Figure 19a, the intensity differences along the perimeter suggest varying amounts of twinning at RT strain rates. Figure 19b shows nearly no change in texture during simple shear at 423 K, especially at low strain rates, indicating possible GBs sliding [142]. During low-strain conditions, a noticeable basal texture occurs with c-axes perpendicular to ND. At moderate strains, basal planes tilt toward transverse directions, activating basal and limited non-basal slip systems. High strains induce significant basal texture rotation, reducing intensity and enhancing non-basal slip and twinning [143,144]. Yield strength and flow stress decrease with increasing temperature, which is attributed to the activation of different slip systems and twinning mechanisms. Studies have shown that textures evolve differently under various temperatures; for example, the basal texture intensity decreases while prismatic texture intensity increases as temperature rises [145]. The temperature sensitivity of deformation mechanisms such as basal slip and twinning significantly impacts the mechanical properties and behavior of Mg alloys [146,147].

5. Summary

Understanding the interplay between microstructure and texture evolution during plastic deformation and recrystallization is pivotal for HCP alloys, tailoring their properties to specific application demands. Factors such as processing routes, temperature, and crystallographic orientation strongly influence the resulting microstructure and textures. These are summarized for Zr, Ti, and Mg as follows:

• In Zr, the anisotropy in plastic deformation leads to significant heterogeneities in strain accommodation. For example, during RT and elevated temperature plastic deformation, Zr undergoes grain fragmentation for specific crystallographic orientations, and a significant difference in imposed shear strain is observed near the GBs. Due to the deformation anisotropy in Zr, which is both orientation and temperature-sensitive, strong crystallographic textures often lead to hierarchical differences in deformation texture evolution and residual stresses. The activation of different slip and twin systems is highly dependent on the starting crystallographic texture and working temperatures. Anomalous behavior of basal slip is also observed at higher working temperatures in some cases, which is currently attributed to the oxygen content in the samples. Stored energy and dislocation development in Zr strongly depend on the crystallographic texture and deformation configuration, i.e., strain path and grain morphology. On the other hand, annealing textures are highly dependent on starting crystallographic orientations.
• In CP-Ti, the most common rolling texture is a split-TD type texture, which forms because of primary compression twinning followed by secondary extension twinning. Activation of basal slip systems changes the final texture to basal fiber texture ($〈0001〉$ || ND) due to activation of basal slip systems. Variation in strain path causes lower deformation heterogeneities and variation in crystallographic texture due to a relatively higher number of active slip systems. The presence of high shear components leads to higher activity of basal and pyramidal slip systems and results in a strong basal fiber and a partial $〈11\overline{2}0〉$ || RD texture. The recrystallization texture of Ti is largely dependent upon the deformation texture and the recrystallization temperature. The annealing texture that develops between 773 K and 973 K consists of $\left(0001\right)〈1\overline{2}10〉$ and $\left(0001\right)〈10\overline{1}0〉$, ±30° to the TD. When the temperature range is above 973 K, substantial grain growth occurs, and the recrystallization texture consists of either $\left(10\overline{1}3\right)〈1\overline{2}10〉$ or $\left(20\overline{2}5\right)〈1\overline{2}10〉$ components manifest as ±30° across the TD line on the (0001) pole figure.
• In Mg alloys, minor variations in the strain path lead to variations in deformation magnitude and have been shown to cause asymmetry in texture evolution. Various types of twins evolve in Mg alloys during deformation, including $\left(10\overline{1}2\right)$ tensile twins, $\left(10\overline{1}1\right)$ compression twins, and $\left(10\overline{1}1\right)-\left(10\overline{1}2\right)$ secondary twins. Deformation mechanisms at lower temperatures lead to inhomogeneous deformation, increased SBs, and cracking. Higher temperatures generally enhance the ductility of Mg alloy due to increased thermal activation of dislocations and reduced resistance to slip. Yield strength and flow stress decrease with increasing temperature, attributed to the activation of different slip systems and twinning mechanisms. The strain rate also affects the twinning behavior, which is crucial for yield strength and deformation mechanisms in AZ31 Mg alloys. Higher strain rates in extruded-annealed AZ91 Mg alloy enhance strength but reduce elongation and promote rapid dislocation accumulation.