Over the past two decades, HR-DIC in the SEM has emerged as an important tool for quantitatively capturing deformation processes at the nanometer scale over large fields of view such that the effects of microstructure heterogeneities and the distribution and characteristics of deformation can be elucidated (22). Tatschl et al. (1) demonstrated the ability to capture high-resolution deformation fields by combining optical imaging DIC methods with the SEM for enhanced resolution. Subsequently, efforts to increase the resolution of the technique have led to refinement of the speckle patterning method (23–25) and SEM imaging parameter optimization to minimize spatial and/or drift distortions and to reduce beam scanning defects (25–27). The resulting increases in spatial resolution and strain sensitivity permit the imaging of direct signatures of single deformation processes during plastic deformation, such as slip (2, 22, 28–39), deformation twinning (40, 41), or grain boundary sliding (42). With the development of SEM image acquisition automation and automated strain field stitching procedures (38, 41, 43), these localization events are obtained over millimeter-scaled regions, making HR-DIC measurements statistically relevant at the microstructural scale of most polycrystalline engineering alloys (2, 19, 41). In addition, complex loading conditions such as cyclic, biaxial, or high-temperature loading (36, 44) have been applied, with HR-DIC measurements still able to be performed. The HR-DIC technique has also recently been adapted for data fusion between correlative multimodal measurements (31, 45–48), dynamic measurements (38), and quantitative measurements (33, 49).
在过去的二十年里，SEM 中的 HR-DIC 已成为一种重要的工具，能够在大视场范围内定量捕捉纳米尺度的变形过程，从而阐明微观结构异质性的影响以及变形的分布和特征（22）。Tatschl 等人（1）通过将光学成像 DIC 方法与 SEM 结合，展示了捕捉高分辨率变形场的能力，从而提高了分辨率。随后，为了提高该技术的分辨率，人们改进了散斑图案方法（23-25），并对 SEM 成像参数进行了优化，以最小化空间和/或漂移畸变，并减少束扫描缺陷（25-27）。由此提高的空间分辨率和应变灵敏度，使得能够成像塑性变形过程中单个变形过程的直接特征，如滑移（2, 22, 28-39）、变形孪晶（40, 41）或晶界滑动（42）。 随着 SEM 图像采集自动化和自动应变场拼接程序的发展（38, 41, 43），这些定位事件可以在毫米级区域内获得，使得 HR-DIC 测量在大多数多晶工程合金的微观结构尺度上具有统计意义（2, 19, 41）。此外，还应用了循环、双轴或高温加载等复杂加载条件（36, 44），HR-DIC 测量仍然能够进行。HR-DIC 技术最近也被用于相关多模态测量（31, 45-48）、动态测量（38）和定量测量（33, 49）的数据融合。

HR-DIC measurements performed over 10 mm² during deformation of a magnesium alloy (shown in Figure 1a ) allowed a statistical analysis of the deformation twin variants that form relative to the grain structure (40, 41). A similar study related slip localization to microstructure for a number of materials including titanium, nickel-based superalloys, stainless steels, aluminum, niobium, high-entropy alloys, and alloys processed by additive manufacturing (19). Slip localization measurements by HR-DIC enable identification of operative slip systems (31, 50), slip intensity (49), slip length, and slip morphology (19). The resolution of HR-DIC was further enhanced by treating the deformation induced by slip as discrete discontinuities rather than averaging the deformation across the slip bands using a continuum-type approach. The development of these advanced discontinuity codes (49, 51–54) enabled quantitative measurements of localized slip-induced displacements (see Figure 1b for a nickel-based superalloy and a niobium alloy after plastic deformation). Each slip event and its intensity, given in nanometers, are captured over square-millimeter fields of view, revealing the microstructure features that induce intense slip localization. HR-DIC measurements have also been integrated with transmission electron microscopy (TEM) (31) or 3D grain measurements (TriBeam tomography 3D EBSD or synchrotron X-ray near-field grain mapping) (45, 46, 55) to provide correlative and multimodal data sets that inform the role of the 3D grain structure on surface plastic activity. Using the combination of site-specific TEM and large field of view HR-DIC measurements in a titanium alloy ( Figure 1c ), the active slip systems and dislocation activity were captured (31) to understand the details of the dislocation mechanisms that lead to slip localization. The combination of 3D grain structure and HR-DIC measurements to generate a 3D multimodal data set ( Figure 1d ) extends plasticity observations by HR-DIC beyond surface-only measurements to the first subsurface layer of deforming grains. In addition, HR-DIC data measurements can facilitate the verification of numerical simulations such as crystal plasticity (CP) simulations (56), accelerating the identification of microstructure–mechanical behavior relationships.
在镁合金（如图 1a 所示）变形过程中进行的 HR-DIC 测量，允许对相对于晶粒结构的变形孪晶变体进行统计分析（40, 41）。一项类似的研究将滑移定位与微观结构相关联，涉及钛、镍基高温合金、不锈钢、铝、铌、高熵合金以及增材制造合金（19）。HR-DIC 的滑移定位测量能够识别作用滑移系统（31, 50）、滑移强度（49）、滑移长度和滑移形态（19）。通过将滑移引起的变形处理为离散不连续性，而不是使用连续体方法在整个滑移带中对变形进行平均，HR-DIC 的分辨率得到了进一步提升。这些先进的不连续性代码（49, 51–54）的发展，使得能够对局部滑移引起的位移进行定量测量（镍基高温合金和铌合金在塑性变形后的局部滑移位移如图 1b 所示）。 每个滑移事件及其纳米米量级的强度被捕捉在平方毫米的视场内，揭示了导致强烈滑移局部化的微观结构特征。高分辨率数字图像相关（HR-DIC）测量还与透射电子显微镜（TEM）（31）或三维晶粒测量（TriBeam 断层扫描 3D EBSD 或同步辐射 X 射线近场晶粒映射）（45, 46, 55）相结合，以提供关联和多模式数据集，这些数据集揭示了三维晶粒结构对表面塑性活动的作用。通过在钛合金中结合特定位置的 TEM 和大型视场 HR-DIC 测量（图 1c），捕捉了活跃的滑移系统和位错活动（31），以了解导致滑移局部化的位错机制的细节。三维晶粒结构和 HR-DIC 测量的结合，以生成三维多模式数据集（图 1d），将 HR-DIC 的塑性观察从仅表面测量扩展到变形晶粒的第一亚表面层。 此外，HR-DIC 数据测量可以促进对数值模拟（如晶体塑性模拟）的验证（56），加速微观结构-力学行为关系的识别。

Figure 1  图 1  Representative quantitative and correlative measurements of deformation events by HR-DIC. (a) HR-DIC measurement over a large field of view in a magnesium alloy allowing twin variant identification. Panel adapted from Reference 41 with permission from Springer Nature. (b) Quantitative measurement of deformation slips by the Heaviside-DIC method in (left) a nickel-based superalloy and (right) a niobium alloy. The intensity of each slip event that developed during deformation is provided in nanometers. Panel adapted from Reference 19 with permission from AAAS. (c) Correlative measurement between HR-DIC, EBSD, and TEM to identify dislocation activity that led to slip localization in a titanium alloy. Panel adapted from Reference 31 with permission from Elsevier. (d) Multimodal data between HR-DIC and 3D grain structure measurements merged to capture the subsurface grain structure effect on surface slip activity. Panel adapted from Reference 46 with permission from Elsevier. Abbreviations: EBSD, electron backscatter diffraction; HR-DIC, high-resolution digital image correlation; ND, normal direction; RD, rolling direction; TD, transverse direction; TEM, transmission electron microscopy.
HR-DIC 对变形事件的代表性定量和相关性测量。(a)在镁合金中进行的 HR-DIC 测量，允许识别孪晶变体。面板改编自参考文献 41，经 Springer Nature 授权。(b)使用 Heaviside-DIC 方法对(左)镍基高温合金和(右)铌合金的变形滑移进行定量测量。每个滑移事件在变形过程中发展的强度以纳米为单位提供。面板改编自参考文献 19，经 AAAS 授权。(c)HR-DIC、EBSD 和 TEM 的相关性测量，用于识别钛合金中导致滑移局部化的位错活动。面板改编自参考文献 31，经 Elsevier 授权。(d)HR-DIC 和 3D 晶粒结构测量之间的多模态数据合并，以捕获亚表面晶粒结构对表面滑移活动的影响。面板改编自参考文献 46，经 Elsevier 授权。 缩写：EBSD，电子背散射衍射；HR-DIC，高分辨率数字图像相关；ND，法向；RD，轧向；TD，横向；TEM，透射电子显微镜。

Figure 1 

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Incipient plasticity in nickel-based superalloys (11) and titanium alloys (28) was observed by rarely occurring intense slip localization events at stresses far below the macroscopic yield strength. In a titanium alloy loaded to 65% of the yield strength, only two slip localization events were detected in more than 20,000 grains ( Figure 2a ). Fatigue crack nucleation has been observed at these rare features due to the continued increase in slip amplitude during repeated cycling to the high-cycle fatigue regime in nickel-based superalloys (57) and titanium alloys (28). Interestingly, for all of the investigated titanium and nickel-based alloys, the majority of the incipient slip localization events and associated crack nucleation sites were observed near or at special boundaries (twin or twist boundaries) where slip developed parallel to the boundaries. Such a configuration is referred to as parallel slip configuration (33) and is the preferred mechanism for incipient slip localization and crack nucleation in various engineering alloys with face-centered-cubic (fcc) structures (19).
镍基高温合金（11）和钛合金（28）在远低于宏观屈服强度的应力下，通过罕见且剧烈的滑移局部化事件观察到初始塑性。在加载至屈服强度 65%的钛合金中，超过 20,000 个晶粒中仅检测到两次滑移局部化事件（图 2a）。由于在镍基高温合金（57）和钛合金（28）中反复循环至高周疲劳阶段时滑移幅度的持续增加，疲劳裂纹萌生已在这些罕见特征处观察到。有趣的是，对于所有研究的钛合金和镍基合金，大部分初始滑移局部化事件及相关裂纹萌生位点均出现在特殊边界（孪晶或扭转边界）附近或边界上，滑移平行于边界发展。这种配置被称为平行滑移配置（33），是具有面心立方（fcc）结构的各种工程合金中初始滑移局部化和裂纹萌生的首选机制（19）。

Figure 2  图 2  (a) Incipient slip localization in a titanium alloy loaded at 65% of its yield strength. Only two slip events are observed along twist boundaries over the 2-mm² investigated region. Fatigue crack nucleation is also observed at twist boundaries in the investigated titanium alloy. Panel adapted from Reference 28 with permission from Elsevier. (b) Relationship between fatigue strength and slip localization in metallic materials with bcc, fcc, and hcp crystal structures. The fatigue ratio (left) is observed to be correlated with the intensity of the highest slip localization event after the first fatigue cycle (right). The dots and bars correspond to the average and highest intensity of all detected slip localization events, respectively. Panel adapted from Reference 19 with permission from AAAS. Abbreviations: bcc, body-centered cubic; fcc, face-centered cubic; hcp, hexagonal close-packed; HEA, high-entropy alloy.
(a) 在 65%屈服强度下加载钛合金的初始滑移局部化。在 2 毫米的 ² 研究区域内，仅观察到沿扭转边界发生的两次滑移事件。在所研究的钛合金中，扭转边界处也观察到疲劳裂纹萌生。面板根据参考文献 28 改编，经 Elsevier 许可使用。(b) 具有体心立方(bcc)、面心立方(fcc)和密排六方(hcp)晶体结构的金属材料疲劳强度与滑移局部化的关系。观察到疲劳比（左）与第一次疲劳循环后最高滑移局部化事件的强度（右）相关。点和条分别对应所有检测到的滑移局部化事件的平均值和最高强度。面板根据参考文献 19 改编，经 AAAS 许可使用。缩写：bcc，体心立方；fcc，面心立方；hcp，密排六方；HEA，高熵合金。

Figure 2 

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In fatigue, the amplitude of the most intense slip localization was observed to correlate with the fatigue ratio (fatigue strength divided by yield strength) for a variety of metallic materials (19). The well-known relationship between the yield strength and fatigue ratio is followed on the left side of Figure 2b , with high-yield strength materials displaying low fatigue ratios. The data on the right side of Figure 2b result from a statistical and quantitative investigation of slip localization during the first fatigue cycle for over 10,000 localization events. The slip length normalizes the data to include the grain size effect. Several fundamental aspects of the fatigue behavior were demonstrated: (a) Materials that develop high and irreversible slip localization have low fatigue ratios; (b) body-centered-cubic (bcc) materials generally show a much more homogeneous distribution of plasticity that manifests itself in a high density of localization events with low intensity, resulting in a high fatigue ratio; and, most importantly, (c) the slip localization state after the first cycle controls the fatigue strength of metallic alloys.
在疲劳过程中，最强烈的滑移局部化振幅被发现与疲劳比（疲劳强度与屈服强度的比值）相关，这一现象适用于多种金属材料（19）。图 2b 左侧展示了屈服强度与疲劳比之间众所周知的关联，高屈服强度的材料表现出较低的疲劳比。图 2b 右侧的数据是对首次疲劳循环中超过 10,000 次局部化事件的统计和定量研究结果。滑移长度将数据标准化以包含晶粒尺寸效应。疲劳行为的基本方面得到了证实：(a) 发生高且不可逆滑移局部化的材料具有较低的疲劳比；(b) 体心立方（bcc）材料通常表现出更均匀的塑性分布，这体现在低强度的局部化事件高密度上，从而导致高疲劳比；最重要的是，(c) 首次循环后的滑移局部化状态控制了金属合金的疲劳强度。

HR-DIC measurements also provided insight into the contribution of slip localization to the overall plastic deformation. Slip localization was observed to contribute to more than 90% of the overall plastic deformation at low macroscopic plastic deformation levels in nickel-based superalloys (58), while other forms of nonlocalized plasticity such as geometrically necessary dislocations (GNDs) contributed more significantly at higher levels of deformation. This highlights the importance of slip localization at low levels of plastic deformation.
HR-DIC 测量还提供了关于滑移局部化对整体塑性变形贡献的见解。在镍基高温合金中（58），当宏观塑性变形水平较低时，观察到滑移局部化对整体塑性变形的贡献超过 90%，而其他形式的非局部化塑性，如几何必需位错（GNDs），在更高变形水平下贡献更为显著。这突出了在低塑性变形水平下滑移局部化的重要性。

Another insight provided by the statistical investigation of slip localization is how slip localization events are connected through the microstructure in metallic materials. For instance, regions of grains with low misorientation, such as microtextured regions in titanium alloys, promote the connectivity of slip events and consequently reduce the yield strength (59, 60). These previously described observations demonstrate the necessity of investigating the characteristics of slip such as the slip intensity, slip connectivity, and slip irreversibility to inform the relationship between microstructure and mechanical properties.
滑移局部化的统计分析还提供了另一个见解：滑移局部化事件如何通过金属材料的微观结构相互连接。例如，晶粒取向差较低的区域，如钛合金中的微观纹理区域，会促进滑移事件的连通性，从而降低屈服强度（59, 60）。这些先前描述的观察结果证明了研究滑移特征（如滑移强度、滑移连通性和滑移不可逆性）的必要性，以阐明微观结构与力学性能之间的关系。

Electron channeling contrast imaging (ECCI) enables characterization of dislocations in bulk samples in the SEM environment rather than, for instance, in thin foils in a TEM environment. A detailed discussion of the history of the use and development of ECCI and EBSD is given in a review article by Wilkinson & Hirsch (61). ECCI is a particularly useful method for quickly determining dislocation densities and spatial distributions over large fields of view (62) since it requires only a backscattered electron (BSE) detector in the SEM and can be performed on bulk material, potentially eliminating the need for TEM observations. It also provides a unique opportunity for the direct observation of dislocation glide, as shown in Reference 63. With improvements in SEM imaging automation and image analysis algorithms, ECCI measurements are emerging as a tool for defect (see Figure 3a ) and small-scale microstructure characterization at the nanometer scale over large fields of view (62, 64).
电子通道衬度成像（ECCI）能够在 SEM 环境下表征块状样品中的位错，而不是在 TEM 环境下表征薄箔中的位错。关于 ECCI 和 EBSD 的使用和发展历史的详细讨论，可以在 Wilkinson & Hirsch 的综述文章（61）中找到。ECCI 是一种特别有用的方法，可以快速确定位错密度和在大视野范围内的空间分布（62），因为它只需要 SEM 中的背散射电子（BSE）探测器，并且可以在块状材料上进行，可能无需 TEM 观察。它还提供了一个直接观察位错滑移的独特机会，如参考文献 63 所示。随着 SEM 成像自动化和图像分析算法的改进，ECCI 测量正在成为一种在大视野范围内（62, 64）表征纳米尺度缺陷（见图 3a）和小尺度微观结构特征的工具。

Figure 3  图 3  Automated and correlative measurement of defects by ECCI. (a) Methodology for quantitative and automatic dislocation characterization of a bulk sample in a scanning electron microscope. Panel adapted from Reference 62 with permission from Elsevier. (b) Dislocation arrangements in the bulk of a specimen spatially determined via correlation between electron backscatter diffraction and ECCI measurements. Panel adapted from Reference 67 with permission from Elsevier. Abbreviations: BSE, backscattered electron; ECCI, electron channeling contrast imaging; GND, geometrically necessary dislocation; KAM, kernel average misorientation.
ECCI 自动和相关测量缺陷。(a)在扫描电子显微镜中对块状样品进行定量和自动位错表征的方法。面板经参考文献 62 授权转载，来自 Elsevier。(b)通过电子背散射衍射和 ECCI 测量之间的相关性在样品块中空间确定的位错排列。面板经参考文献 67 授权转载，来自 Elsevier。缩写：BSE，背散射电子；ECCI，电子通道衬度成像；GND，几何必需位错；KAM，核平均取向。

Figure 3 

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In metallic materials, ECCI provides unique opportunities to elucidate the relationships between mechanical behavior and plasticity (65, 66). ECCI resolves some of the confounding issues associated with in situ TEM studies, including the requirement of a thin foil, preventing thin-foil imaging effects, the small and not necessarily representative regions that are able to be studied with TEM, and the straightforward specimen preparation for ECCI. The efficacy of ECCI for capturing plastic deformation has been broadly demonstrated including the systematic study of localization during creep deformation in single crystal Ni-based superalloys (67), shown in Figure 3b . ECCI has also been used to reveal the strain-hardening behavior of twinning-induced plasticity steels (64), dislocation structures leading to slip localization in iron and 304L stainless steel deformed by fatigue (68) and dislocation cells, veins, and persistent slip in Cu and stainless steels (69, 70). Additionally, recent studies show the dislocation structures that develop in Cu during fatigue with increasing strain amplitudes (71) and the effects of phase fraction on deformation behavior in a dual-phase high-entropy alloy (72), and comparisons have been made between model predictions of dislocation structures and direct ECCI observations in 316L steel (73).
在金属材料中，ECCI 为阐明力学行为与塑性之间的关系提供了独特的机会（65，66）。ECCI 解决了原位 TEM 研究的一些混杂问题，包括对薄箔的要求、防止薄箔成像效应、TEM 所能研究的区域小且不一定具有代表性，以及 ECCI 的样品制备过程简单。ECCI 在捕捉塑性变形方面的有效性已得到广泛证实，包括对单晶镍基高温合金蠕变变形过程中局部化的系统研究（67），如图 3b 所示。ECCI 还用于揭示孪晶诱导塑性钢的应变硬化行为（64）、疲劳变形的铁和 304L 不锈钢中导致滑移局部化的位错结构（68），以及铜和不锈钢中的位错胞、位错纹和持续滑移（69，70）。 此外，最近的研究表明，在 Cu 中随着应变幅度的增加而发展的位错结构（71），以及相分数对双相高熵合金变形行为的影响（72），并且已经对 316L 钢中位错结构的模型预测与直接 ECCI 观察结果进行了比较（73）。

The recent availability of solid-state scanning transmission electron microscopy (STEM) detectors for SEMs with high-quality field emission sources allows for the direct imaging of dislocations over volumes much larger than those available in TEM (74). Combined with innovative micromechanical stages and with increased versatility for in situ measurements due to relaxed vacuum chamber constraints, the dynamics of dislocation motion and strain localization can be directly observed (75, 76) ( Figure 4 ). In this approach, referred to as TSEM, imaging can be conducted in bright-field, dark-field, and weak-beam modes. The combination of a lower extinction distance, lower accelerating voltages in the SEM compared with those in TEM, and a reduction of dynamical scattering due to bend contours and thickness fringes results in sharper dislocation contrast (74). Additionally, STEM imaging has improved signal-to-noise ratio compared with conventional TEM imaging due to the convergence of the beam (77). As there are no postspecimen lenses, the camera length used in imaging is constrained; however, with the large SEM chamber, additional detectors such as EBSD, energy dispersive X-ray spectroscopy, BSE, secondary electron, and cathodoluminescence TSEM can provide a wealth of multimodal information.
近年来，配备高质量场发射源的扫描电子显微镜（SEM）出现了固态扫描透射电子显微镜（STEM）探测器，这使得可以直接观察比透射电子显微镜（TEM）更大幅度的位错区域（74）。结合创新的微机械平台以及在真空室约束放宽后对原位测量的多功能性提升，位错运动和应变局部化的动力学可以直接被观察到（75, 76）（图 4）。这种方法被称为 TSEM，可以在明场、暗场和弱束模式下进行成像。与 TEM 相比，SEM 具有更低的消光距离、更低的加速电压，以及由于弯曲轮廓和厚度条纹导致的动态散射减少，这些因素都导致了更清晰的位错对比度（74）。此外，由于束流汇聚，STEM 成像与传统 TEM 成像相比具有更高的信噪比（77）。 因为没有后置标本透镜，成像所使用的相机长度受到限制；然而，由于具有大型扫描电镜室，额外的探测器如 EBSD、能量色散 X 射线光谱、BSE、二次电子和阴极发光 TSEM 可以提供丰富的多模态信息。

Figure 4  图 4  Dislocation dynamics leading to slip localization. (a) Use of transmission scanning electron microscopy to facilitate in situ testing with transmission imaging. Panel adapted from Reference 76 with permission from Elsevier. (b) Dislocation dynamics in a nickel-based superalloy. Panel adapted from Reference 76 with permission from Elsevier. (c) Edge and screw dislocation components in a high-entropy alloy. Panel adapted from Reference 78 with permission from AAAS.
导致滑移局部化的位错动力学。(a) 使用透射扫描电子显微镜通过透射成像促进原位测试。面板经参考文献 76 许可转载自 Elsevier。(b) 镍基高温合金中的位错动力学。面板经参考文献 76 许可转载自 Elsevier。(c) 高熵合金中的刃位错和螺位错分量。面板经参考文献 78 许可转载自 AAAS。

Figure 4 

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Figure 4 shows examples of TSEM imaging of dislocations gliding along slip planes in a nickel-based superalloy and a refractory multiprincipal element alloy (MPE) (76, 78). In the polycrystalline nickel-based alloy (76), TSEM reveals a complex strain localization process, whereby partial dislocations initially residing in the fcc matrix are pushed into the ordered L12 precipitates, creating superlattice intrinsic stacking faults, sometimes across multiple precipitates. The localization process then proceeds as additional dislocations gliding on the same plane push trailing partials through the precipitates, completely erasing the stacking faults. This repeated faulting and defaulting process disrupts the shape of the coherent precipitates on the plane of localization, softening the material locally. The benefits of the dynamical aspects of the TSEM approach are also leveraged during in situ straining of a bcc MoNbTi MPE alloy (78), where gliding dislocations show significant nonscrew character unlike their conventional refractory element counterparts that are dominated by the glide of screw dislocations. Similarly, under cyclic loading, an HfNbTaTiZr MPE alloy displays a distinctly different localization behavior compared with conventional bcc alloys, suggesting that intrinsically different behaviors are possible when no single element dominates the compositional landscape (19).
图 4 展示了镍基高温合金和难熔多主元合金（MPE）中位错沿滑移面滑移的 TSEM 成像示例(76, 78)。在多晶镍基合金(76)中，TSEM 揭示了一个复杂的应变局部化过程，其中初始存在于面心立方基体中的部分位错被推入有序的 L12 析出物，形成超晶格本征层错，有时跨越多个析出物。局部化过程随后继续进行，随着同一平面上的其他位错滑移将拖曳的部分位错推过析出物，完全消除了层错。这种反复的层错形成和默认过程破坏了局部化平面上的相干析出物的形状，使材料局部软化。TSEM 方法的动力学方面的优势在 bcc MoNbTi MPE 合金的原位变形过程中也得到了利用(78)，其中滑移位错表现出显著的非螺位错特征，这与传统的难熔元素对应物以螺位错滑移为主形成鲜明对比。 同样地，在循环加载下，HfNbTaTiZr MPE 合金表现出与传统体心立方合金明显不同的局部化行为，这表明当没有单一元素主导成分特征时，可能存在本质上不同的行为（19）。

Increases in EBSD collection rates and high-quality and high-resolution patterns have been enabled by the development of monolithic active pixel sensors (MAPS) and other direct electron detectors (79–83). Several research topics that will benefit from the continued development of faster, higher-quality EBSD detectors are (a) rapid high-quality data collection due to the fast readout and sparse sampling, (b) more rapid collection of high-angular-resolution EBSD (HR-EBSD) data, (c) higher-spatial-resolution EBSD data at lower accelerating voltage, and (d) more efficient application to a broader spectrum of materials classes. As shown in Figure 5a , sparse sampling can be used to read out a limited number of pixel rows, which are sufficient for EBSD indexation, resulting in a significant increase in data collection speed (79, 80).
单晶主动像素传感器（MAPS）和其他直接电子探测器的开发，实现了电子背散射衍射（EBSD）收集速率的提高以及高质量和高分辨率图样的获取（79-83）。以下是一些将从更快速、更高品质的 EBSD 探测器持续发展中受益的研究课题：（a）由于快速读出和稀疏采样，实现快速高质量数据收集；（b）更快速地收集高角分辨率 EBSD（HR-EBSD）数据；（c）在较低加速电压下获取更高空间分辨率的 EBSD 数据；（d）更高效地应用于更广泛的材料类别。如图 5a 所示，稀疏采样可用于读出有限数量的像素行，这些像素行足以进行 EBSD 标定，从而显著提高数据收集速度（79, 80）。

Figure 5  图 5  Sparse sampling, integrated forward modeling approaches, and 3D tomography using EBSD. (a) Sparse sampling is used on a MAPS direct electron detecting EBSD detector to decrease acquisition time. Panel adapted from Reference 80 with permission from Elsevier. (b) A 3D EBSD data set obtained using Tribeam tomography. Panel adapted from Reference 86 with permission from Elsevier. (c) An integrated forward modeling approach to determine the dislocation density based on Kikuchi band sharpness. Panel adapted from Reference 87 with permission from Elsevier. Abbreviations: AM, additively manufactured; EBSD, electron backscatter diffraction; MAPS, monolithic active pixel sensor.
稀疏采样、集成正向建模方法以及使用 EBSD 进行的三维断层扫描。(a) 在 MAPS 直接电子探测 EBSD 探测器上使用稀疏采样以减少采集时间。面板改编自参考文献 80，经 Elsevier 许可。(b) 使用 Tribeam 断层扫描获得的三维 EBSD 数据集。面板改编自参考文献 86，经 Elsevier 许可。(c) 基于 Kikuchi 带锐度来确定位错密度的集成正向建模方法。面板改编自参考文献 87，经 Elsevier 许可。缩写：AM，增材制造；EBSD，电子背散射衍射；MAPS，单片主动像素传感器。

Figure 5 

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In serial sectioning experiments for 3D data collection, one of the most time-intensive steps is the EBSD data collection at each slice. An increase in data collection speed or quality can significantly reduce the time and cost of collection of a data set (84, 85). EBSD serial sectioning experiments have now become a robust technique for 3D microstructure characterization (86) that is widely used to identify microstructure–mechanical behavior relationships. With the development of software infrastructure, slicing, and cleanup approaches, 3D data sets such as those shown in Figure 5b can be rapidly generated to capture microstructure at the cubic millimeter–scale while having a submicrometer spatial resolution to capture grain shape, twins, and grain boundary networks. Furthermore, rich information beyond the crystallographic orientation is present in the diffraction patterns obtained by EBSD measurements. Integrated forward modeling approaches of electron diffraction use Kikuchi band sharpness (87, 88) to determine statistically stored dislocation densities, as shown in Figure 5c , which can be combined with existing approaches to calculate GND densities (89–91). In parallel, the use of lower accelerating voltages enables researchers to collect data with a smaller interaction volume (87, 92), allowing collection from materials with small grain sizes (93), small features, and multiple phases that have typically necessitated TEM (94) or transmission Kikuchi diffraction (95), as well as materials with significant amounts of misorientation, whether from damage (96, 97), processing (98, 99), or inherent microstructure (85). The enhanced electron detection efficiency and the ability to operate at lower accelerating voltages also present opportunities for beam-sensitive materials and those that are prone to sample charging.
在用于 3D 数据收集的连续切片实验中，最耗时的步骤之一是在每个切片上进行 EBSD 数据采集。提高数据采集速度或质量可以显著减少数据集采集的时间和成本（84, 85）。EBSD 连续切片实验现已成为一种强大的 3D 微观结构表征技术（86），被广泛用于识别微观结构与力学行为之间的关系。随着软件基础设施、切片和清理方法的进步，如图 5b 所示的三维数据集可以快速生成，以在立方毫米尺度上捕捉微观结构，同时具有亚微米空间分辨率来捕捉晶粒形状、孪晶和晶界网络。此外，EBSD 测量获得的衍射图中除了晶体学取向之外还包含丰富的信息。电子衍射的集成正向建模方法利用 Kikuchi 带的锐度（87, 88）来确定统计存储位错密度，如图 5c 所示，这可以与现有方法结合来计算 GND 密度（89–91）。 与此同时，使用较低加速电压使研究人员能够以更小的相互作用体积收集数据（87，92），从而可以从具有小晶粒尺寸（93）、小特征和多种相的材料中收集数据，这些材料通常需要透射电子显微镜（94）或透射 Kikuchi 衍射（95）进行分析，以及具有大量取向差的材料，无论是由于损伤（96，97）、加工（98，99）还是固有微观结构（85）。增强的电子检测效率和能够在较低加速电压下操作也为对电子束敏感的材料和易发生样品充电的材料提供了机会。

The ability to generate and analyze 3D EBSD data has revolutionized the understanding of the role of rare microstructural features and characteristic microstructural neighborhoods in plastic deformation processes. For instance, combining slip localization measurements, numerical simulations, and 3D EBSD measurements, a governing effect of particular bulk triple junction lines on surface plasticity, crack initiation, and therefore material failure has been identified (46). Observations have shown that the full 3D microstructural neighborhood plays an important role in the development of plasticity and have indicated that conventional surface measurements are limited in their potential for determining the influence of microstructure without subsurface information. The contribution of this research is detailed in Section 3. In addition, 3D EBSD has revealed which 3D microstructural features promote damage initiation and propagation in superalloys (100), where the importance of the 3D subsurface grain boundary network and twin relations in predicting surface crack initiation in nickel-based superalloys was observed. Furthermore, 3D measurements validated the coherency of twins with slip planes in these fcc superalloys, enabling the application of crack initiation criteria (101) to large-area 2D measurements to determine the location of early strain localization, which leads to crack initiation (102).
能够生成和分析三维 EBSD 数据彻底改变了人们对稀有微观结构特征和典型微观结构邻域在塑性变形过程中作用的理解。例如，通过结合滑移定位测量、数值模拟和三维 EBSD 测量，发现特定体积三重结线对表面塑性、裂纹萌生以及材料失效具有主导作用（46）。观察表明，完整的 3D 微观结构邻域在塑性发展过程中发挥着重要作用，并指出传统的表面测量在确定微观结构影响方面受到限制，除非具备亚表面信息。这项研究的贡献详见第 3 节。此外，三维 EBSD 揭示了哪些 3D 微观结构特征促进了超合金中的损伤萌生和扩展（100），其中观察到镍基超合金中三维亚表面晶界网络和孪晶关系的 3D 重要性，有助于预测表面裂纹的萌生。 此外，3D 测量验证了这些面心立方高温合金中孪晶与滑移面的相干性，使得可以应用裂纹萌生判据（101）对大面积 2D 测量进行分析，以确定早期应变局部化的位置，该位置会导致裂纹萌生（102）。

Signatures of slip localization in metals can now be identified due to increases in EBSD angular measurement resolution. For instance, the changes in orientation within a grain can be determined with higher resolution by measuring the shifts of subregions in electron backscatter patterns using cross-correlation techniques (103). The HR-EBSD technique has been used extensively to determine the GND content (91) and elastic strains (104). Interestingly, in titanium and nickel-based superalloys, slip localization is observed to produce intense stress concentration and lattice rotation in front of the slip band–grain boundary intersection as shown in Figure 6a,b . These small-scale regions of high stresses and lattice rotation, referred to as microvolumes (105, 106), are important features that promote crack nucleation in nickel-based superalloys. These microvolumes were observed to develop at the surface and in the bulk of the specimen (55) and occur when slip transmission is prevented (low m′ factor) and slip localization is intense ( Figure 6c ). It has also been demonstrated that these slip band–induced stress fields can affect the deformation behavior even at the grain interior in bcc steel (107).
由于 EBSD 角测量分辨率的提高，金属中滑移局部化的特征现在可以被识别。例如，通过使用互相关技术测量电子背散射图案中子区域的位移，可以以更高的分辨率确定晶粒内的取向变化（103）。HR-EBSD 技术已被广泛用于确定 GND 含量（91）和弹性应变（104）。有趣的是，在钛和镍基高温合金中，观察到滑移局部化会在滑移带与晶界交点前产生强烈的应力集中和晶格旋转，如图 6a,b 所示。这些高应力和晶格旋转的小规模区域，被称为微体积（105, 106），是促进镍基高温合金裂纹萌生的关键特征。这些微体积在样品表面和内部均可观察到（55），并在滑移传递被阻止（低 m′因子）且滑移局部化强烈时出现（图 6c）。 它还已被证明，这些滑移带诱导的应力场即使在体心立方钢的晶粒内部也能影响变形行为（107）。

Figure 6  图 6  Blocked slip bands in titanium and nickel-based superalloys. (a) HR-EBSD of a blocked slip band at a grain boundary intersection, producing a localized stress concentration in the adjacent grain in a titanium alloy. Panel adapted from Reference 108 with permission from Elsevier. (b) HR-EBSD of blocked slip bands similar to those in panel a but in a superalloy and resulting in a crack nucleation event. Color images adapted from Reference 105 with permission from Wiley. Grayscale scanning electron microscopy image adapted from Reference 106 with permission from Elsevier. (c) 3D EBSD data set obtained from Tribeam tomography indicating intense lattice rotation due to the presence of a slip localization event. This intense lattice localization occurs when slip transmission of intense slip bands is prevented (low m′ factor). Abbreviations: EBSD, electron backscatter diffraction; GROD, grain reference orientation deviation; HR-EBSD, high-angular-resolution EBSD; IPF, inverse pole figure; LD, loading direction.
钛和镍基高温合金中的受阻滑移带。(a) 在晶界交叉处受阻滑移带的 HR-EBSD 图像，在钛合金的相邻晶粒中产生局部应力集中。面板改编自参考文献 108，经 Elsevier 许可使用。(b) 与面板 a 类似的受阻滑移带的 HR-EBSD 图像，但存在于高温合金中，并导致裂纹形核事件。彩色图像改编自参考文献 105，经 Wiley 许可使用。灰度扫描电子显微镜图像改编自参考文献 106，经 Elsevier 许可使用。(c) 通过 Tribeam 断层扫描获得的 3D EBSD 数据集，表明由于滑移局部化事件的存在而导致的强烈晶格旋转。这种强烈的晶格局部化发生在强烈滑移带的滑移传递被阻止时（低 m′因子）。缩写：EBSD，电子背散射衍射；GROD，晶粒参考取向偏差；HR-EBSD，高角分辨率 EBSD；IPF，反极图；LD，加载方向。

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The penetrating power of hard X-rays has been used for decades to gather information from the bulk of deformed materials. X-ray topography, initially based on laboratory X-ray sources and photographic films or nuclear plates, provided projection images of dislocations and other crystal defects for more than 70 years (for a recent review, see Reference 109). With the constant increase in spatial resolution [thanks in particular to synchrotron light source upgrades (110)] and advances in detector technology, it is now possible to directly image plastic deformation events throughout the interior of cubic millimeter–scaled samples. X-ray TT combines the orientation contrast obtained in topography mode (109), where crystal defects locally alter the Bragg condition (resulting in contrast on the collected image), with tomography acquisition via the rotation of the crystal around the chosen scattering vector (111).
硬 X 射线的穿透力几十年来一直用于获取变形材料的内部信息。X 射线形貌学最初基于实验室 X 射线源和照相底片或核乳胶，为 70 多年提供了位错和其他晶体缺陷的投影图像（最近的综述见参考文献 109）。随着空间分辨率的持续提高[特别感谢同步辐射光源的升级（110）]和探测器技术的进步，现在可以直接成像立方毫米级样品内部的塑性变形事件。X 射线 TT 结合了形貌模式下获得的取向对比度（109），其中晶体缺陷局部改变了布拉格条件（导致在收集的图像上产生对比度），并通过晶体绕所选散射矢量的旋转进行断层扫描采集（111）。

This technique can also be used with extended plate geometry if the scattering vector is normal to the plate in a variant termed diffraction laminography. This has been used to study slip localization in silicon and was able to map dislocation arrays in three dimensions with great accuracy (112). However, this use case is quite restrictive and may not be used other than in selected, well-oriented monocrystals.
这种技术也可以用于扩展板状几何结构，如果散射矢量与板垂直，则称为衍射层状成像。这已被用于研究硅中的滑移定位，并能够以极高的精度（112）在三维空间中绘制位错阵列。然而，这种应用场景非常有限，可能仅在特定的、取向良好的单晶中使用。

The combination of X-ray diffraction contrast tomography (DCT) and TT was first used to image slip events with a polycrystalline Al–Li alloy ( Figure 7a ) during in situ deformation and then relate these events to the 3D grain structure (8). Striking band contrast observed on the topographs could be related to individual slip systems activated and forming slip bands in the bulk of the material. Aside from analyzing the individual topographs, collected X-ray TT data can be further used to reconstruct the 3D orientation field within the crystal (right side of Figure 7a ). The reconstruction can combine data from several reflections and from X-ray DCT and TT (113) to improve the spatial resolution.
X 射线衍射衬度断层扫描（DCT）和 TT 的结合首次用于在原位变形过程中对多晶 Al–Li 合金的滑移事件成像（图 7a），然后将这些事件与三维晶粒结构相关联（8）。在形貌图上观察到的显著带状衬度可以与激活并形成材料主体中的滑移带的单个滑移系统相关联。除了分析单个形貌图外，收集的 X 射线 TT 数据还可以进一步用于重建晶体内部的三维取向场（图 7a 的右侧）。重建可以结合来自多个反射以及 X 射线 DCT 和 TT 的数据（113）来提高空间分辨率。

Figure 7  图 7  Bulk slip localization events probed by X-ray diffraction imaging methods. (a) Slip event identification in a deformed Al–Li alloy. Panel adapted from Reference 114 with permission from Elsevier. (b) Deformed titanium alloy Ti–7Al specimen studied using diffraction contrast tomography. Fifty-five grains were measured using topotomography to uncover the 3D network of activated slip planes. Panel adapted from Reference 9 with permission from Elsevier. (c) Dark-field X-ray microscopy experiment with a grain extracted from a fatigued nickel-based superalloy specimen. The α° and β° indicate the orientation deviation along the principal axis. Panel adapted from Reference 115 with permission from Springer-Nature. Abbreviations: DTC, diffraction contrast tomography; FIB, focused ion beam; GROD, grain reference orientation deviation.
通过 X 射线衍射成像方法探测的体滑定位事件。(a)变形 Al–Li 合金中的滑移事件识别。面板经参考文献 114 许可转载自 Elsevier。(b)使用衍射衬度断层成像研究的变形钛合金 Ti–7Al 样品。通过拓扑断层成像测量了 55 个晶粒，以揭示激活滑移面的三维网络。面板经参考文献 9 许可转载自 Elsevier。(c)从疲劳镍基高温合金样品中提取的晶粒的暗场 X 射线显微镜实验。α°和β°表示沿主轴的方向偏差。面板经参考文献 115 许可转载自 Springer-Nature。缩写：DTC，衍射衬度断层成像；FIB，聚焦离子束；GROD，晶粒参考方向偏差。

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Thanks to progress in automation, a recent study using the X-ray TT technique in a titanium Ti-7Al alloy could more systematically map entire grain neighborhoods and therefore provide a statistical study of slip localization and transmission to the next grain, in grains located both at the surface and within the bulk ( Figure 7b ). For surface grains, a comparison with HR-DIC measurements concluded that X-ray TT is able to capture slip bands exceeding a minimum shear amplitude of 50 nm. Furthermore, the study highlighted important differences between surface and bulk slip transmission regarding the transmission of plasticity to neighboring grains (9). In particular, it was shown that the often-observed network of continuous bands across different grains at the surface does not occur in the bulk, suggesting a strong impact of the free surface on the slip system selection.
得益于自动化技术的进步，一项最近使用 X 射线 TT 技术对钛 Ti-7Al 合金的研究能够更系统地绘制整个晶粒邻域，因此为滑移定位和向下一晶粒的传递提供了统计研究，这些晶粒既位于表面也位于块体内部（图 7b）。对于表面晶粒，与高分辨率数字图像相关（HR-DIC）测量的比较表明，X 射线 TT 能够捕捉到剪切幅度超过 50 纳米的滑移带。此外，该研究强调了表面滑移和块体滑移传递之间在塑性向邻近晶粒传递方面的重要差异（9）。特别是，研究表明，表面不同晶粒之间经常观察到的连续带网络在块体中并不存在，这表明自由表面对滑移系统选择具有强烈影响。

The spatial resolution of full-field X-ray diffraction imaging techniques such as X-ray DCT and TT or near-field high-energy X-ray diffraction microscopy (HEDM) is inherently limited by detector technology. The X-ray-to-visible-light conversion process in the deployed X-ray imaging detectors limits the ultimate spatial resolution to about 1 μm. Moreover, the simultaneous illumination of extended (3D) sample volumes gives rise to highly convoluted signals on the detector, challenging the quantitative analysis and (tomographic) reconstruction of local orientation and elastic strain of the crystal lattice.
全场 X 射线衍射成像技术（如 X 射线 DCT 和 TT）或近场高能 X 射线衍射显微镜（HEDM）的空间分辨率本质上受限于探测器技术。部署的 X 射线成像探测器中的 X 射线到可见光的转换过程将极限空间分辨率限制在约 1 微米。此外，对扩展（三维）样品体积的同时照射会在探测器上产生高度复杂的信号，挑战晶体格子的局部取向和弹性应变的定量分析和（断层）重建。

To alleviate and overcome this limitation, another X-ray diffraction imaging method termed DFXM has been developed (116). With this method an X-ray objective lens is placed in the diffracted beam and used to produce a magnified image on a detector that can be placed several meters away from the sample, achieving spatial resolutions better than 100 nm in the detector plane. Focusing optics are used to produce a line beam (typically 1 μm thick) to illuminate a specific layer of the sample (either a monocrystal or a grain within a polycrystal), and 3D reconstructions can be achieved by stacking several layers. A series of tilt motors allows scanning of the sample and measuring of both local orientations (mosaicity scans) and strain fields (strain scans) within the bulk. In a typical DFXM experiment, only one reflection is usually captured, preventing the measure of all strain components.
为缓解并克服这一限制，研究人员开发了一种名为 DFXM 的 X 射线衍射成像方法（116）。该方法将 X 射线物镜置于衍射光束中，用于在距离样品数米远的探测器上形成放大的图像，在探测器平面上实现优于 100 纳米的空间分辨率。聚焦光学系统用于产生线束（通常 1 微米厚），以照射样品的特定层（单晶或多晶中的晶粒），通过堆叠多个层可以实现三维重建。一系列倾斜电机允许扫描样品，并测量块体内的局部取向（马赛克扫描）和应变场（应变扫描）。在典型的 DFXM 实验中，通常只捕获一个反射，这阻碍了对所有应变分量的测量。

DFXM has been used to visualize individual dislocations and their strain fields, such as in References 117 and 118. Porz et al. (119) were able to study a full dislocations array in a silicon crystal deformed by indentation. Yildirim et al. (120) studied a cold-rolled Fe–Si–Sn alloy that was heated in situ to trigger recrystallization and were able to capture the presence of shear bands in the as-deformed sample. Upon heating at 610°C, higher misorientation zones such as grain boundaries or deformation band junction points were found to be preferential nucleation regions. DFXM can also be used advantageously to magnify specific grains in a deformed sample of known microstructure (typically one that has already been characterized by X-ray DCT or HEDM). However, this may involve extracting a smaller region of interest in order to maintain sufficient transmission at the X-ray energies available at the current implementation of the instrument [at the European Synchrotron Radiation Facility (ESRF), beamline ID06] (121). Using this approach, Gustafson et al. (115) investigated the orientation and strain fields in a specific grain of a fatigued nickel-based superalloy specimen. The gauge section was first mapped using HEDM and then cyclically loaded to develop intragranular deformation localization due to plasticity. A specific location was extracted using focus ion beam milling and characterized via DFXM to access the local orientation and strain fields of the grain of interest (see Figure 7c ). This analysis demonstrated the occurrence of intense slip localization near a bulk twin boundary during fatigue of a nickel-based superalloy.
DFXM 已被用于可视化单个位错及其应变场，例如在参考文献 117 和 118 中。Porz 等人（119）能够研究被压痕变形的硅晶体中的完整位错阵列。Yildirim 等人（120）研究了在原位加热以引发再结晶的冷轧 Fe–Si–Sn 合金，并能够捕捉到变形样品中剪切带的存在。在 610°C 加热时，发现诸如晶界或变形带连接点等高取向差区是优先形核区域。DFXM 也可用于放大已知微观结构的变形样品中的特定晶粒（通常该样品已通过 X 射线 DCT 或 HEDM 进行表征）。然而，这可能需要提取一个较小的感兴趣区域，以在当前仪器实现的 X 射线能量下保持足够的透射率[在欧洲同步辐射设施（ESRF），ID06 光束线]（121）。使用这种方法，Gustafson 等人（115）研究了疲劳镍基高温合金样品中特定晶粒的取向和应变场。 测量段首先使用 HEDM 进行映射，然后循环加载以发展由于塑性导致的晶粒内变形局部化。通过聚焦离子束研磨提取特定位置，并通过 DFXM 表征以获取目标晶粒的局部取向和应变场（见图 7c）。这项分析表明，在镍基高温合金的疲劳过程中，在体积孪晶边界附近发生了强烈的滑移局部化。

Similar to electron microscopy, scanning techniques deploying a focused X-ray probe have been developed over the past two decades. The ultimate spatial resolution is now given by the size of the X-ray probe and the positional stability and precision of the sample positioning system. Values reported from dedicated synchrotron endstations (122, 123) currently range between 100 and 500 nm. One has to further distinguish between polychromatic (Laue) microdiffraction and monochromatic beam variants, which imply sample rotations.
与电子显微镜类似，过去二十年里发展了使用聚焦 X 射线探头的扫描技术。目前的最终空间分辨率由 X 射线探头的尺寸和样品定位系统的定位稳定性和精度决定。来自专用同步辐射端站的报告值（122, 123）目前介于 100 至 500 纳米之间。必须进一步区分多色（劳厄）微衍射和单色束变体，后者涉及样品旋转。

Polychromatic microdiffraction endstations such as 34-ID-E at the Advanced Photon Source (APS) or BM32 at the ESRF deploy achromatic, reflective focusing optics (124) and exploit X-ray energies in the range of 7–25 keV. A wire-scanning technique termed differential aperture X-ray microscopy (DAXM) (125) allows for isolating diffraction information from limited (submicrometer) sample subvolumes and hence the characterizing of 3D sample volumes by means of a 3D scanning procedure [one translational wire scan per sample (X, Y) position]. The tremendous increase in brilliance provided by the ongoing upgrade of all major synchrotron sources worldwide and the availability of fast-readout, highly efficient X-ray detector systems results in acquisition rates of several tens up to hundreds of hertz. From the collected and postprocessed Laue patterns, one can extract the local crystallographic orientation and deviatoric part of the elastic lattice strain tensor. The 34-ID-E endstation furthermore offers optional switching to monochromatic beam and energy scans, enabling accurate peak position and full width at half maximum (FWHM) analysis of the crystal reflection curve. Research by Li et al. (126) shows a cross-sectional view of a grain in a specimen of stainless steel that has undergone fatigue loading in the low-cycle regime. As shown in Figure 8a , the presence of (persistent) slip bands is clearly visible in the FWHM map acquired in a monochromatic beam. Moreover, analysis of the local lattice orientation revealed a subdivision of the grain into weakly misoriented domains, separated by these bands. The analysis of lattice strain before and after an incremental plastic deformation of the same sample reveals the presence of high gradients in lattice strain at the intersection of the primary and secondary slip bands.
多色微衍射端站，如先进光子源（APS）的 34-ID-E 或欧洲同步辐射光源（ESRF）的 BM32，采用色差校正反射聚焦光学系统（124），并利用 7–25 keV 范围内的 X 射线能量。一种称为差分孔径 X 射线显微镜（DAXM）（125）的线扫描技术，能够从有限的（亚微米）样品子体积中分离衍射信息，从而通过三维扫描程序[每个样品（X，Y）位置进行一次平移线扫描]来表征三维样品体积。全球所有主要同步辐射源正在进行的升级提供了巨大的亮度提升，以及快速读出、高效率 X 射线探测系统的可用性，使得采集速率达到每秒几十至几百赫兹。从收集并后处理的劳厄图中，可以提取局部晶体学取向和弹性晶格应变张量的偏部分量。34-ID-E 端站还提供可选的单色束和能量扫描切换功能，能够对晶体反射曲线的峰值位置和半高全宽（FWHM）进行精确分析。 李等人（126）的研究显示了一块经过低周疲劳加载的不锈钢样品中晶粒的横截面图。如图 8a 所示，在单色束下获得的 FWHM 图中可以清楚地看到（持续的）滑移带的存在。此外，局部晶格取向的分析揭示晶粒被这些带分隔成弱取向差的区域。对相同样品在增量塑性变形前后的晶格应变分析表明，在主滑移带和次滑移带的交点处存在晶格应变的高梯度。

Figure 8  图 8  (a) Network of persistent slip bands in stainless steel as revealed by the monochromatic beam energy and wire-scanning method at 34-ID-E. Panel adapted from Reference 126 with permission from PNAS. (b) Principle of scanning 3D X-ray diffraction. Panel adapted from Reference 129 with permission from the International Union of Crystallography. Abbreviation: FWHM, full width at half maximum.
(a) 通过 34-ID-E 的单色束能量和线扫描方法揭示的不锈钢中持续的滑移带网络。面板改编自参考文献 126，经 PNAS 许可使用。（b）扫描 3D X 射线衍射的原理。面板改编自参考文献 129，经国际晶体学联合会许可使用。缩写：FWHM，半高全宽。

Figure 8 

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Whereas depth resolution (along the X-ray beam) in DAXM is achieved by the wire-scanning method (no sample rotation and no mathematical inversion involved), monochromatic beam scanning 3D X-ray diffraction (3DXRD) (127, 128) follows a different strategy: The sample rotation stage is translated in small steps in the direction perpendicular to the rotation axis while the sample is continuously rotated over 180° for each of these lateral positions (see Figure 8b ). This procedure is repeated for a series of vertical sample positions. Scanning 3DXRD can be used at higher X-ray energies and offers more space and flexibility for sample environments (mechanical load, temperature, etc.). Various analysis strategies can now be used to recover the local orientation and (full) elastic strain tensor from such sets of projection data (122, 129). The diffraction signals recorded for a given grain are integrated along the in-depth (beam) direction, and the solution of the inverse problem depends on the magnitude of the orientation and strain gradients inside the material. Henningsson & Hendriks (130) demonstrated successful recovery of the elastic strain components for the case of small intragranular orientation spread and report a strain sensitivity on the order of 10⁻⁴. The solution of the more general problem (i.e., a combination of orientation and strain gradients) is actively being worked on, and the ultimate sensitivity is yet to be determined.
尽管在 DAXM 中，深度分辨率（沿 X 射线束方向）是通过线扫描方法实现的（无需样品旋转和数学反演），单色束扫描三维 X 射线衍射（3DXRD）（127, 128）则采用不同的策略：样品旋转台在垂直于旋转轴的方向上以小步长移动，同时样品在每个横向位置上连续旋转 180°（见图 8b）。该步骤在一系列垂直样品位置上重复进行。扫描 3DXRD 可以在更高的 X 射线能量下使用，并为样品环境（机械负载、温度等）提供更多的空间和灵活性。现在可以使用各种分析策略来从这些投影数据集中恢复局部取向和（完整）弹性应变张量（122, 129）。对于给定晶粒记录的衍射信号沿深度（光束）方向进行积分，反问题的解取决于材料内部取向和应变梯度的幅度。 亨宁森与亨德里克斯（130）展示了在小晶粒内取向扩散情况下弹性应变分量的成功恢复，并报告了约 10^-6 量级的应变敏感性。更普遍的问题（即取向和应变梯度的组合）正在积极研究中，最终敏感性尚未确定。

Differences in beam scanning artifacts, beam drift, sample charging, geometrical scanning distortions, and sample or instrument misalignment will impact multimodal data collection with at least two different detectors. Indeed, each detector comes with its own artifacts and spatial and angular resolution, and the information contained in each pixel may come from interaction volumes that vary between the primary beam and the sample. This results in complex distortions, particularly when different dwell times, voltages, and tilt angles are used for each detector (139). In a SEM, EBSD is usually the most heavily distorted data modality due to the highly tilted sample during data collection. Modality alignment routines use various assumptions regarding the shape of the distortion function (affine, trapeze, barrel, polynomial) and the definition of point sets (e.g., fiducials, microstructural features, sample shape) visible in all detector modes and used to define this function (43, 140–147). Point-set definition and registration are particularly challenging due to differences in feature contrast and imaging resolution between modalities. Attempting to address this challenge, clustering (43, 148) and microstructure digitization routines are being used to preprocess the different data modalities. Currently, this step is generally performed after alignment and is a central part of automated data analysis.
束扫描伪影、束漂移、样品充电、几何扫描失真以及样品或仪器未对准的差异会影响至少使用两个不同探测器的多模态数据采集。实际上，每个探测器都有其自身的伪影和空间及角度分辨率，每个像素包含的信息可能来自主光束与样品相互作用体积的变化。这会导致复杂的失真，尤其是在为每个探测器使用不同的停留时间、电压和倾斜角度时（139）。在扫描电镜中，由于数据采集时样品倾斜度很大，EBSD 通常是失真最严重的数据模式。模式对齐程序使用各种关于失真函数形状（仿射、梯形、桶形、多项式）和点集定义（例如、基准标记、微观结构特征、样品形状）的假设，这些点集在所有探测器模式下可见，并用于定义该函数（43、140-147）。由于模式间特征对比度和成像分辨率的不同，点集定义和配准尤其具有挑战性。 试图应对这一挑战，聚类（43，148）和微观结构数字化程序被用于预处理不同的数据模态。目前，这一步骤通常在对齐之后执行，是自动化数据分析的核心部分。

The purpose of digitization is to create a numerical rendering of the microstructure and features of plasticity, with the aim of studying eventual correlations and conducting statistical analyses. Amid the variety of data modalities collected to probe either the plastic localization or the microstructure, no unified framework currently exists to analyze correlated data sets. Isolated efforts have led to the development of custom frameworks that build upon preexisting software for microstructure feature segmentation (9, 149), such as DREAM.3D (150), pymicro (151), or commercially available EBSD software. These are convenient tools to identify individual grains and boundaries, as well as their respective properties. Two approaches have been used to featurize the plastic strain field: segmentation using conventional image processing tools and computer vision. Using iterative Hough transformations and Bresenham's algorithm, Charpagne et al. (152) were able to vectorize thousands of slip bands in Ti-6Al-4V and Inconel 718 deformed at room temperature. It is worth noting that all slip bands exhibited a planar character, an essential aspect incorporated into the workflow. Clustering techniques overcome this obstacle by allowing minimal assumptions on the shape of the objects of interest. The research efforts of Daly and colleagues have led to the successful identification of both slip bands (43) and deformation twins (40) in correlated DIC-EBSD data sets, which has allowed for the identification of the active twinning systems without conventional trace analyses.
数字化旨在创建塑性微观结构和特征的数值表示，目的是研究最终的相关性并进行统计分析。在收集用于探究塑性局部化或微观结构的各种数据模式中，目前尚无统一的框架来分析相关数据集。零散的努力已导致开发出基于现有软件的定制框架，用于微观结构特征分割（9, 149），例如 DREAM.3D（150）、pymicro（151）或市售的 EBSD 软件。这些是识别单个晶粒和边界及其相应属性的便捷工具。用于塑性应变场特征化的方法有两种：传统图像处理工具分割和计算机视觉。Charpagne 等人（152）利用迭代 Hough 变换和 Bresenham 算法，成功将室温下变形的 Ti-6Al-4V 和 Inconel 718 中的数千条滑移带向量化。值得注意的是，所有滑移带均表现出平面特征，这是工作流程中纳入的关键要素。 聚类技术通过允许对感兴趣对象的形状做出最小假设来克服这一障碍。Daly 及其同事的研究工作成功地在相关 DIC-EBSD 数据集中识别出了滑移带（43）和变形孪晶（40），这使得无需传统跟踪分析即可识别出活跃的孪晶系统。

Slip trace analyses have been carried out manually for decades to identify key mechanisms of plastic localization and slip transmission (153–157), generally with the goal of determining the active slip or twinning system. In large data sets, manual analysis of thousands of slip traces is obviously impractical. When a slip trace is visible, automated assessment of the active slip plane consists of computing the candidate traces from potentially active systems and comparing them with the experimental trace using a deviation tolerance. This tolerance should depend on the lattice structure (number of candidate traces). When several slip directions are active onto the plane, most researchers will follow the assumption that the one with the highest Schmid factor is active, which is one limitation of the sole analysis of the trace. To increase the confidence of the slip system determination, Chen & Daly (50) have proposed a complementary metric, the relative displacement ratio (RDR), calculated from HR-DIC data. When added to the Schmid factor as a constraint, the RDR has proven particularly successful at identifying slip systems in several hexagonal-close-packed (hcp) materials (31) ( Figure 9a ).
滑移迹线分析在过去几十年中一直通过人工方式进行，目的是识别塑性局部化和滑移传递的关键机制（153–157），通常是为了确定活跃的滑移或孪晶系统。在大数据集中，对数千条滑移迹线进行人工分析显然是不切实际的。当滑移迹线可见时，对活跃滑移面的自动评估包括从潜在活跃系统中计算候选迹线，并使用偏差容差将其与实验迹线进行比较。这个容差应该取决于晶格结构（候选迹线的数量）。当多个滑移方向活跃于该平面时，大多数研究人员会遵循 Schmid 因子最高的那个是活跃的这一假设，这是仅分析迹线的一个局限性。为了提高滑移系统确定的置信度，Chen & Daly（50）提出了一种补充指标，即相对位移比（RDR），该指标根据 HR-DIC 数据计算得出。 当作为约束条件添加到 Schmid 因子中时，RDR 已被证明在识别几种密排六方（hcp）材料中的滑移系统方面特别成功（31）（图 9a）。

Figure 9  图 9  Automated slip trace analyses from coupled DIC-EBSD data sets. (a) Coupled Schmid factor and RDR approaches in hcp titanium. Panel adapted from Reference 31 (CC BY 4.0). (b) Slip trace and direction determination from Heaviside-DIC/EBSD data sets. Panel adapted from Reference 152 with permission from Elsevier. (c) Cross-slip identification in the fcc nickel-based alloy RR1000 after 0.02% macroscopic strain, showing the slip system amplitude field and the angle between the horizontal direction and the slip plane orientation, with transparency inversely scaled with the slip amplitude. The red ellipses highlight areas where cross-slip occurs. Panel adapted from Reference 158 (CC BY 4.0). Abbreviations: bcc, body-centered cubic; DIC, digital image correlations; EBSD, electron backscatter diffraction; hcp, hexagonal-close-packed; HR-DIC, high-resolution DIC; IPF, inverse pole figure; ND, normal direction; RD, rolling direction; RDR, relative displacement ratio; TD, transverse direction.
来自耦合 DIC-EBSD 数据集的自动滑移迹线分析。（a）hcp 钛中的耦合 Schmid 因子和 RDR 方法。面板改编自参考文献 31（CC BY 4.0）。（b）从 Heaviside-DIC/EBSD 数据集中确定滑移迹线和方向。面板改编自参考文献 152，经 Elsevier 许可。（c）在经过 0.02%宏观应变后的 fcc 镍基合金 RR1000 中识别交叉滑移，显示了滑移系统振幅场以及水平方向与滑移面方向之间的角度，透明度与滑移振幅成反比缩放。红色椭圆突出了发生交叉滑移的区域。面板改编自参考文献 158（CC BY 4.0）。缩写：bcc，体心立方；DIC，数字图像相关；EBSD，电子背散射衍射；hcp，密排六方；HR-DIC，高分辨率 DIC；IPF，倒极图；ND，法向；RD，轧向；RDR，相对位移比；TD，横向。

Figure 9 

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New techniques such as Heaviside-DIC offer the opportunity to identify both the slip plane and direction on the basis of the analysis of the discontinuity when the crystal orientation is known (49). Charpagne et al. (140) have automated the procedure, leading to the identification of over 80% of the active slip systems in an fcc superalloy in an automated manner ( Figure 9b ). However, classic slip trace analysis, either manual or automatic, is of limited use when the slip band morphology is wavy or when bands appear locally discontinuous as a result of diffuse slip or extensive cross-slip. Alternative postprocessing routines relying on the collection of correlated SEM-DIC and EBSD data are currently emerging in efforts by Hoefnagels and colleagues (158) ( Figure 9c ). They are an attractive alternative in the presence of complex slip activity and particularly relevant in the case of materials with hcp or bcc lattices or fcc materials deformed at high temperature.
当晶体取向已知时，Heaviside-DIC 等新技术能够基于不连续性的分析来识别滑移面和滑移方向（49）。Charpagne 等人（140）已将此过程自动化，从而以自动方式识别了面心立方超合金中超过 80%的活性滑移系统（图 9b）。然而，当滑移带形态呈波浪状或由于扩散滑移或广泛交叉滑移导致带局部不连续时，经典滑移迹线分析，无论是手动还是自动，都有限制作用。Hoefnagels 及其同事（158）正在努力中开发基于收集相关 SEM-DIC 和 EBSD 数据的替代后处理程序（图 9c）。在存在复杂滑移活动的情况下，它们是一种有吸引力的替代方案，尤其与具有密排六方或体心立方晶格的材料或高温变形的面心立方材料相关。

With the advent of nanoscale DIC (34) and 3D characterization techniques, correlative analyses bridge length scales and bring a 3D perspective to 2D measurements collected on free surfaces. Vermeij et al. (35) have recently designed a correlative nanomechanical testing framework that allows the collection of DIC, BSE, and EBSD data on the front and rear sides of specimens with carefully designed geometry, followed by a microstructure-to-strain alignment procedure to couple the different data modalities. Using this framework, the authors were able to link nanoscale and mesoscale deformation processes in the martensite and ferrite phases in steel samples and relate incipient plasticity to cracking phenomena in intricate microstructures. The collection of DIC data on the front and rear sides of a thin specimen also allows for the extrapolation of the subsurface to 3D behavior.
随着纳米级 DIC（34）和三维表征技术的出现，相关性分析能够连接不同的尺度，并为自由表面上收集的二维测量数据提供三维视角。Vermeij 等人（35）最近设计了一种相关性纳米力学测试框架，该框架允许在几何设计精密的样品前后表面收集 DIC、BSE 和 EBSD 数据，随后通过微观结构到应变对齐程序将不同的数据模态耦合起来。利用该框架，作者能够将钢样品中马氏体和铁素体相的纳米级和介观级变形过程联系起来，并将初始塑性现象与复杂微观结构中的开裂现象相关联。在薄样品前后表面收集 DIC 数据还允许将亚表面外推到三维行为。

Indeed, as the traces observed on a specimen's surface are the result of bulk processes, investigation of slip traces in three dimensions gives new perspectives on the origins of slip band formation as a function of the complete, 3D microstructure. Charpagne et al. (159) have led these efforts and proposed the first 2D-to-3D multimodal data merging framework that reconstructs slip bands in 3D EBSD data sets using 2D slip traces (45). Using these analyses, they were able to reconstruct over 1,000 slip bands in 3D EBSD data sets measuring over 500 μm × 500 μm × 500 μm in both Inconel 718 and Ti-7Al after deformation beneath and beyond the macroscopic yield point. The procedure consists of projecting automatically identified slip planes associated with each slip trace into the 3D microstructure, as shown in Figure 10a,b . Statistics depicting how the slip bands relate to the subsurface microstructure features are extracted from these rich data sets. As such, Charpagne et al. (159) have highlighted the role of triple junctions (3D lines joining three individual grains) for slip band formation, as illustrated in Figure 10c . Furthermore, while this technique reconstructs slip bands in only the first layer of grains, it still reveals possible surface effects. In a highly textured Ti-7Al data set, the authors observed long-range slip transmission, revealing its prominent role in the development of the plastic localization network ( Figure 10d ). All transmitted slip bands appeared to be connected via a point located on the free surface, suggesting possible surface effects on the slip transmission behavior, as discussed in Section 2.5.
确实，由于样品表面的痕迹是体相过程的结果，对三维滑移痕迹的调查为滑移带形成的起源提供了新的视角，该起源是完整三维微观结构的函数。Charpagne 等人(159)领导了这些工作，并提出了第一个二维到三维多模态数据融合框架，该框架使用二维滑移痕迹重建三维 EBSD 数据集中的滑移带(45)。通过这些分析，他们能够在 Inconel 718 和 Ti-7Al 的宏观屈服点下方和上方，重建了超过 1000 条滑移带，这些 EBSD 数据集的尺寸超过 500 μm × 500 μm × 500 μm。该过程包括将自动识别的与每个滑移痕迹相关的滑移面投影到三维微观结构中，如图 10a,b 所示。从这些丰富的数据集中提取了描述滑移带如何与亚表面微观结构特征相关的统计数据。因此，Charpagne 等人(159)强调了三重结点（连接三个单个晶粒的三维线）在滑移带形成中的作用，如图 10c 所示。 此外，尽管该技术仅在晶粒的第一层重建了滑移带，但它仍然揭示了可能的表面效应。在一个高度织构化的 Ti-7Al 数据集中，作者观察到长程滑移传输，揭示了其在塑性定位网络发展中的显著作用（图 10d）。所有传输的滑移带似乎通过位于自由表面上的一个点相互连接，这表明了表面效应对滑移传输行为可能产生的影响，正如 2.5 节中讨论的那样。

Figure 10  图 10  3D visualization of slip bands from HR-DIC/3D EBSD correlated data sets. (a) 2D slip traces visible on the surface of the 3D EBSD data set and identified slip plane. (b) Slip trace projected into the 3D microstructure. (c) Slip band emerging from a triple junction in a nickel-based Inconel 718 superalloy. (d) Long-range transmission in Ti-7Al shown spanning across three grains. Figure adapted from Reference 45 with permission from Springer Nature. Abbreviations: EBSD, electron backscatter diffraction; HR-DIC, high-resolution digital image correlation; IPF, inverse pole figure; LD, loading direction.
HR-DIC/3D EBSD 相关数据集的滑移带 3D 可视化。（a）3D EBSD 数据集表面可见的 2D 滑移迹线以及确定的滑移面。（b）滑移迹线投影到 3D 微观结构中。（c）镍基 Inconel 718 高温合金中从三重结点处出现的滑移带。（d）Ti-7Al 中跨越三个晶粒的长程传输。图改编自参考文献 45，经 Springer Nature 许可使用。缩写：EBSD，电子背散射衍射；HR-DIC，高分辨率数字图像相关；IPF，倒极图；LD，加载方向。

Figure 10 

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The experimental techniques and approaches presented in Sections 2 and 3 take advantage of recent improvements in detector technology, hardware, and software to collect high-resolution data over large fields of view. Furthermore, these capabilities also enable data collection over smaller fields of view at higher frame rates. While the possibility of acquiring time-resolved measurements has been demonstrated by Stinville et al. (38), this avenue still remains largely unexplored. The opportunities offered by these time-resolved measurements are detailed in Section 6. Implementing these techniques will certainly rely on the extensive knowledge gained from small-scale mechanical testing, as detailed in the next section.
第 2 节和第 3 节中介绍的实验技术和方法利用了探测器技术、硬件和软件的最新改进，以在宽视场范围内收集高分辨率数据。此外，这些功能还能够在较小的视场范围内以更高的帧率收集数据。虽然 Stinville 等人（38）已经证明了获取时间分辨测量的可能性，但这一途径仍然基本未得到探索。这些时间分辨测量的机遇在第 6 节中详细阐述。实施这些技术无疑将依赖于下一节中详细介绍的从小规模机械测试中获得的大量知识。

Today, automated nanoindentation is standard equipment in environments where mechanical behavior and structure–property relationships are investigated. For details on the method, the reader is referred to References 167 and 169. Instead of focusing on indentation hardness or modulus, we consider nanoindentation as a probe for localized plastic activity, which means we are paying attention to the first deviation from the elastic contact, referred to as a pop-in, which for conospherical indentation tips is captured with a Hertzian contact model. At this point, the corresponding shear yield stress can conveniently be derived according to τ y ≈ A(F p E r ²/(π³ R ²))^1/3, where A is some prefactor, F p the load at the pop-in, E r the reduced modulus, and R the tip radius. Continued penetration of the tip into the material triggers further pop-ins, where the mechanistic origin of the local plastic instability may differ from the first pop-in. It is therefore meaningful to differentiate between the first pop-in (1, i = 1) and higher-order pop-ins (2, 3, 4, etc.; i > 1), as done in Reference 170. Below, we refer to a pop-in displacement magnitude as u i , where i is the order.
如今，自动纳米压痕仪是研究力学行为和结构-性能关系环境中的标准设备。关于该方法的具体细节，读者可参考参考文献 167 和 169。我们不是关注压痕硬度或模量，而是将纳米压痕视为探测局部塑性活动的工具，这意味着我们关注的是从弹性接触开始的第一偏差，称为"触发"，对于圆锥形压头，这可以用赫兹接触模型来捕捉。此时，相应的剪切屈服应力可以方便地根据τy ≈ A(FpErR/(πR))^(1/2)推导出来，其中 A 是某个前因子，Fp 是触发时的载荷，Er 是折减模量，R 是压头半径。压头继续深入材料会引发进一步的触发，其中局部塑性不稳定的机理可能与第一次触发不同。因此，区分第一次触发（1，i=1）和更高阶的触发（2，3，4 等；i>1）是有意义的，正如参考文献 170 中所做的那样。下面，我们将触发位移幅度称为 u，其中 i 是阶数。

Pop-in behavior for shallow indentation is a long-known feature that was predominantly investigated for pop-in 1, and its mechanistic origin has been ascribed to heterogeneous dislocation nucleation (171). An instructive case is Fe-3%Si, first reported by Gerberich et al. (172), who linked the abrupt strain increment to an avalanche of dislocations, the number of which depends on the yield point load F p. Decades later, Zhang & Ohmura (173) revealed the spatial signature of the dislocation network formed at the indent site in response to the first pop-in for the same material. This extended more than a micrometer into the substrate for indents with a penetration depth of 40–50 nm. TEM evidence comparing the formed dislocation structures for only pop-in 1 and for pop-in 1 plus continued loading revealed relatively random debris for pop-in 1 alone and increasingly ordered line defects with pile-up characteristics when adding elastoplastic deformation after the pop-in. There is thus a dramatic transition in the microstructure one probes before and after the first local plastic event (174).
浅层压入的"突然跳变"行为是一个早已为人熟知的现象，主要针对"突然跳变"1 进行了研究，其机理被认为源于非均匀位错形核（171）。一个典型的例子是 Fe-3%Si，该材料首先由 Gerberich 等人（172）报道，他们将突变的应变增量归因于位错雪崩，其数量取决于屈服点载荷 Fp。几十年后，Zhang & Ohmura（173）揭示了相同材料在第一次"突然跳变"时在压入位置形成的位错网络的空间特征。对于压入深度为 40-50 nm 的压入，该网络延伸超过一微米进入基体。透射电子显微镜（TEM）证据对比了仅发生"突然跳变"1 和"突然跳变"1 加持续加载时形成的位错结构，结果显示单独"突然跳变"1 时形成相对随机的碎片，而在"突然跳变"后添加弹塑性变形时则形成具有堆积特征的越来越有序的线缺陷。因此，在第一次局部塑性事件前后探测到的微观结构发生了剧烈转变（174）。

In addition to quantifying spatially fluctuating dislocation-nucleation or source-activation stresses from the first pop-in, appropriate thermal-activation models using statistical methods offer a way of determining the effective barrier energies of the underlying mechanisms, such as dislocation nucleation (175) or shear-band initiation in metallic glasses (176, 177). How to link the average first critical stress from a large number of indentation curves to the deforming volume and how to evaluate the underlying density of discrete plastic events from an extreme value statistics approach have also been demonstrated (178). Furthermore, recent efforts reveal that the maximum stress of the first pop-in may be linked to the material's stacking-fault energy (179). These new developments rely on quantifying spatially varying τ y and have in common that they use statistically robust data sets from incipient and localized plasticity to determine fundamental materials properties.
除了通过首次突现来量化空间波动的位错形核或源激活应力外，采用统计方法的热激活模型为确定基础机制（如位错形核（175）或金属玻璃中的剪切带起始（176，177））的有效势垒能提供了一种途径。如何将大量压痕曲线的平均首次临界应力与变形体积联系起来，以及如何从极值统计方法评估离散塑性事件的基础密度，也得到了证明（178）。此外，近期的研究表明，首次突现的最大应力可能与材料的层错能（179）有关。这些新进展依赖于量化空间变化的τy，并且它们共同的特点是使用初始和局部塑性的统计稳健数据集来确定基本材料特性。

Loading beyond pop-in 1, most materials admit a sequence of higher-order pop-ins, which have been neglected in the literature so far. One reason for this is the lack of an analytical expression that allows determining τ yi where i > 1 and instead only corresponding displacements of higher-order pop-ins can be used to statistically assess how the formed dislocation network under the tip progressively evolves. In the case of the first pop-in, both τ y1 and u 1 are known to follow Weibull statistics (extreme value statistics) when probing a large number of point-to-point fluctuations, therefore adhering to the weakest-link picture that is compatible with heterogeneous dislocation nucleation. Interestingly, this statistical signature changes for u i>1 to a log-normal distribution (indicative of correlated dislocation activity) in a prototypical Cu single crystal (170), demonstrating how sufficiently large data sets can discriminate between different types of localized plasticity, in this case nucleation and network evolution. How much unused potential in characterizing localized plasticity is offered by a statistical treatment of discontinuous nanoindentation data?
超过突现 1 之后，大多数材料会出现一系列高阶突现，而这些现象迄今为止在文献中已被忽视。其原因之一是缺乏能够确定τyi（其中 i>1）的解析表达式，而只能使用相应的高阶突现位移来统计评估在尖端下方形成的位错网络如何逐步演化。对于第一次突现，τy1 和 u1 在探测大量点对点波动时都遵循韦伯统计（极值统计），因此符合与异质位错形核相兼容的最弱链图景。有趣的是，在典型的铜单晶中（170），当 u>1 时，这种统计特征会转变为对数正态分布（表明位错活动相关），这展示了足够大的数据集如何区分不同类型的局部塑性，在此情况下为形核和网络演化。对不连续纳米压痕数据进行统计分析，在表征局部塑性方面提供了多少未充分利用的潜力？

Figure 11a highlights another example of how a specific type of localized plasticity can be identified from the loading portion of a nanoindentation experiment. Instead of a first, very large pop-in followed by much smaller, higher-order pop-ins, typically seen for pure single crystalline metals, a distinct signature of continuously increasing u i can be observed for metallic glasses (180), NiPd solid solutions (181), and intermetallics (182). Specific to such data sets is that F i ∝ u i (see the inset in Figure 11a ), and, at least in the case of metallic glasses, it was shown that the removal of pop-in segments allows for recovering a continuation of the Hertzian elastic contact model, demonstrating essentially elastic behavior in between instabilities. This response was attributed to a geometrical scaling effect, where lines of sufficiently high shear stress around the indentation tip allow the material to deform plastically via shear localization into shear bands (183). Consequently, every newly formed shear band at a new indentation depth has a longer shear path, thereby admitting a larger pop-in size measured as an axial displacement. In fact, in the case of intermetallics, a shear-banding phenomenon could also be revealed, giving rise to the speculation that plastic localization into shear bands generally may be linked to this particular F − u scaling. In direct contrast to the above-quoted, log-normally distributed higher-order pop-in displacements of pure single crystalline Cu, the continuously increasing signature of the pop-in magnitudes of the intermetallic was reported to follow Weibull statistics ( Figure 11b ). If each instability is linked to a newly formed shear instability, this is compatible with the insight from point-to-point probed dislocation nucleation or source activation of pure metal crystals. While the available data are scarce, these results indicate the potential of revealing mechanistic information of the proceeding local plastic processes underneath the indenter from a statistical evaluation.
图 11a 展示了如何从纳米压痕实验的加载部分识别特定类型的局部塑性。与纯单晶金属通常观察到的第一个非常大的突跳随后是许多较小的更高阶突跳不同，金属玻璃（180）、NiPd 固溶体（181）和金属间化合物（182）中可以观察到 u 持续增加的独特特征。这类数据集的特点是 F ∝ u（见图 11a 的插图），并且在金属玻璃的情况下，研究表明移除突跳段允许恢复赫兹弹性接触模型的连续性，这表明在失稳之间基本上表现出弹性行为。这种响应归因于几何缩放效应，其中压痕尖端周围足够高的剪切应力线允许材料通过剪切局部化形成剪切带（183）。因此，在新的压痕深度形成的新剪切带具有更长的剪切路径，从而允许测量到更大的突跳尺寸，以轴向位移表示。 事实上，在金属间化合物的情况下，也可能出现剪切带现象，这引发了这样一种推测：塑性局部化到剪切带通常可能与这种特定的 F − u 标度有关。与上述引用的内容形成鲜明对比的是，纯单晶铜的对数正态分布的高阶爆裂位移，金属间化合物的爆裂幅值不断增加的特征据报道遵循韦伯统计（图 11b）。如果每个不稳定性都与一个新形成的剪切不稳定性相关联，这与纯金属晶体中通过逐点探测位错形核或源激活所获得的见解相一致。虽然现有数据很少，但这些结果表明，通过统计评估有可能揭示压头下方进行局部塑性过程的机理信息。

Figure 11  图 11  Slip localization probed with nanoindentation. (a) Four indentation curves of a CuAl2 intermetallic, exhibiting an unusual continued increase of pop-in magnitude with load (182). Panel adapted from Reference 182 with permission from Elsevier. The inset displays the force–size correlation for the shown indentation curves and a Zr-based metallic glass that follows a similar trend. (b) A statistical analysis of the higher-order pop-in data of pure single crystalline Cu and the data shown in panel a, revealing fundamentally different distributions: log-normal behavior for the dislocation network evolution and Weibull statistics for shear banding.
使用纳米压痕法探测滑移定位。 (a) CuAl2 金属间化合物的四个压痕曲线，显示在载荷下突跳幅度异常持续增加（182）。面板经参考文献 182 授权转载自 Elsevier。插图显示了所示压痕曲线和一种具有类似趋势的 Zr 基金属玻璃的力-尺寸相关性。(b) 纯单晶铜的高阶突跳数据的统计分析以及(a)面板中所示数据，揭示出根本不同的分布：位错网络演化的对数正态行为和剪切带形成的韦伯统计。

Figure 11 

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So far, we have considered how localization of plasticity underneath indents is giving rise to statistical data sets that are possibly unique enough for a mechanistic classification. Most of these approaches have used data sets limited to a couple of hundred indentation curves. This is expected to change, as forefront automated nanoindentation allows measurements of tens of thousands of data sets within practical time frames (184). These high-speed methods have been used mainly for hardness and indentation modulus mapping across multiphase materials, such as steel (185), concrete (186), Cu–W nanocomposites (187), and intermetallics (188). However, applying them to spatially map first- and higher-order statistics is expected to yield completely new insights into local structure–property relationships and spatially confined plasticity, since proximities to grain and phase boundaries or dislocation cell walls are expected to affect the statistics of all signatures of localized plasticity discussed so far. Indeed, at the single-indent level, changes of the pop-in behavior near grain boundaries have already been discussed in the literature (189), where ledges in the boundaries are believed to serve as dislocation sources that can act at significantly lower stresses than within the crystal. Our expectation is that state-of-the-art high-speed nanoindentation mapping will provide deep insights into slip localization in the vicinity of grain boundaries, phase boundaries, or other microstructural features that significantly affect initiation stresses and subsequent stochastic network evolution. This thrilling avenue will provide direct insights into statistically relevant sites of early plastic activity in polycrystalline metals, constituting the next level of correlative structure–property assessment after hardness and elasticity mapping in combination with emerging machine-learning advances (190, 191).
迄今为止，我们已经探讨了压痕下方塑性局部化的统计数据集是如何产生的，这些数据集可能足够独特，可以进行机理分类。这些方法大多使用的数据集仅限于几百条压痕曲线。这种情况有望改变，因为前沿的自动化纳米压痕技术可以在实际时间内测量数万个数据集（184）。这些高速方法主要被用于多相材料（如钢 185、混凝土 186、Cu–W 纳米复合材料 187 和金属间化合物 188）的硬度和压痕模量映射。然而，将这些方法应用于空间统计映射，有望为局部结构-性能关系和空间受限塑性提供全新的见解，因为晶粒和相边界或位错胞壁的邻近性预计会影响迄今为止讨论的所有局部塑性特征的统计规律。 确实，在单压痕尺度上，晶界附近突跳行为的变化在文献中已被讨论过（189），其中认为晶界中的台阶可以作为位错源，其作用应力显著低于晶体内部。我们预期，最先进的高速纳米压痕映射将深入揭示晶界、相界或其他显著影响起始应力和后续随机网络演化的微观结构特征附近的滑移定位。这条激动人心的发展方向将直接提供多晶金属中早期塑性活动统计相关位置的信息，构成在硬度和弹性映射与新兴机器学习进步相结合（190, 191）之后的结构-性能评估的下一层次。

Similar to nanoindentation, microcompression probes small volumes and therefore measures the response of single crystalline subvolumes of the polycrystalline aggregate. However, in comparison with nanoindentation, larger and finite volumes are sampled in microcompression, thereby assessing truncated bulk defect statistics that, together with exhaustion hardening and source strengthening, cause the well-known size effect in strength (192). Studying size-affected strengthening has offered mechanistic insights relevant to the micrometer and submicrometer scale, including strain-rate dependencies (193, 194) and activation volumes (194, 195), which, however, are not immediately related to strain localization. A more relevant second size effect in this context is the persistent presence of stress–strain (force–displacement) discontinuities, which are a direct signature of slip or localized plasticity. Exceeding 1% in strain for a micrometer-sized crystal, the stress–strain discontinuities may appear large, but one should not forget that the absolute magnitudes are in the nanometer range. Therefore, nanoscale intermittent slip localization due to dislocation network fluctuations cannot be resolved in bulk experimentation. Microcompression allows probing such fluctuations and, like nanoindentation, provides unique insights into specific microstructural processes.
与纳米压痕类似，微压缩测试小体积，因此测量多晶聚集体中单晶亚体积的响应。然而，与纳米压痕相比，微压缩测试中采样的体积更大且有限，从而评估截断的体缺陷统计，这些缺陷与耗尽强化和源强化共同导致众所周知的强度尺寸效应（192）。研究受尺寸影响的强化提供了与微米和亚微米尺度相关的机理见解，包括应变率依赖性（193，194）和激活体积（194，195），然而这些与应变局部化并无直接关系。在此背景下，更相关的第二种尺寸效应是应力-应变（力-位移）不连续性的持续存在，这是滑移或局部塑性的直接特征。对于微米级晶体，当应变超过 1%时，应力-应变不连续性可能显得较大，但不应忘记其绝对值处于纳米范围。 因此，由于位错网络波动引起的纳米级间歇滑移定位无法在宏观实验中解析。微压缩实验能够探测此类波动，与纳米压痕实验类似，为特定微观结构过程提供了独特的见解。

Figure 12a is an exemplary depiction of a force–displacement curve obtained during microcompression of a cylindrical gold single crystal. The curve is composed of smoothly advancing segments and abrupt jumps. The smooth segments reflect, within the experimental resolution of much less than 1 nm, continuous plastic strain localization without any spatiotemporal fluctuations. A force–displacement instability, occurring at Weibull distributed stresses (196), instead signifies a collective dislocation event that mediates length changes much faster than the applied deformation rate. Much attention has been given to the non-Gaussian statistical properties of the magnitude of these abrupt slip events (197, 198), where power laws or truncated power laws describe the fluctuations we allude to in the introductory part of this section. This is remarkable, since such statistics do not have a well-defined mean, an assumption traditionally relied upon in phenomenological models. Showing various degrees of scale-free dislocation activity, the detailed functional form (power-law exponents and cut-off functions) describing the fluctuation magnitudes gives insight into the material-specific long-range correlated collective dislocation activity (199, 200) or dislocation source activity if one isolates the largest events captured by the statistics (201). Such fundamental discoveries were only possible due to small-scale deformation experiments and the ability to separately investigate intermittent slip and smooth flow, thereby demonstrating the coexistence of uncorrelated Gaussian and correlated non-Gaussian (or even scale-free) dislocation activity (166, 202).
图 12a 展示了在微压缩圆柱形金单晶过程中获得的力-位移曲线的示例。该曲线由平滑推进段和突然跳跃段组成。平滑段反映了在远小于 1 纳米的实验分辨率范围内，连续塑性应变局部化且没有任何时空波动。在韦伯分布应力（196）处发生的力-位移不稳定性，反而表示一种集体位错事件，该事件介导的长度变化速度远快于施加的变形速率。人们已对这种突然滑移事件的幅度非高斯统计特性给予了极大关注（197，198），其中幂律或截断幂律描述了本节引言部分所指的波动。这一点很显著，因为这些统计特性没有明确的均值，而现象学模型传统上依赖于这一假设。 展现出不同程度的无标度位错活动，描述波动幅度的详细函数形式（幂律指数和截断函数）为理解特定材料的远程相关集体位错活动（199, 200）或位错源活动提供了见解，如果通过统计隔离出最大事件（201）。这些基础性发现仅因小尺度变形实验和能够分别研究间歇性滑移和平滑流动而成为可能，从而证明了不相关高斯和相关非高斯（甚至无标度）位错活动的共存（166, 202）。

Figure 12  图 12  Insights gained from intermittent microplasticity and slip probed with microcompression. (a) A typical intermittent force–displacement curve for a deforming microcrystal, here being [001]-oriented Au. Panel adapted from Reference 208 with permission from Elsevier. The insets show a postdeformation scanning electron microscope image of a deformed crystal and a time-resolved profile of a displacement jump, which originates from a slip event. (b) A deformation map derived from both Au and Nb microcrystal deformation indicating why intermittent stress–strain behavior is not expected at the bulk scale under regular testing conditions, based on data from Reference 205. (c) The peak velocity of velocity profiles, as shown in the inset in panel a, plotted as a function of the testing temperature. An Arrhenius construction indicates essentially athermal slip. Panel adapted from Reference 166 (CC BY 4.0). (d) A distribution of slip peak velocities for slip on pristine slip planes and for slip for already activated slip planes. Panel adapted with permission from Reference 210; copyright 2022 American Physical Society. Abbreviations: bcc, body-centered cubic; fcc, face-centered cubic.
通过微压缩探查间歇性微塑性和滑移所获得的见解。(a) 变形微晶的典型间歇性力-位移曲线，此处为[001]取向的 Au。面板改编自参考文献 208，经 Elsevier 许可使用。插图显示了变形晶体的变形后扫描电子显微镜图像和位移跳跃的时间分辨轮廓，该位移跳跃源于滑移事件。(b) 根据参考文献 205 的数据，从 Au 和 Nb 微晶变形中推导出的变形图，表明在常规测试条件下，在大尺度上不会出现间歇性应力-应变行为。(c) 面板 a 插图所示速度轮廓的峰值速度，作为测试温度的函数绘制。阿伦尼乌斯构造表明基本上是无热滑移。面板改编自参考文献 166 (CC BY 4.0)。(d) 纯净滑移面和已激活滑移面的滑移峰值速度分布。面板经参考文献 210 许可改编；版权 2022 美国物理学会。缩写：bcc，体心立方；fcc，面心立方。

Figure 12 

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Going a step beyond the fluctuation magnitudes, it is possible—with experimental precautions—to derive the time-resolved signature of the collective dislocation rearrangements during slip. The inset in Figure 12a shows such a velocity profile that can be used to quantify the collective slip dynamics. The details of velocity profiles provide, if averaged sufficiently, subtle differences in how collective dislocation motion proceeds (a) in fcc and bcc crystals (203) or high-entropy alloys (204), (b) in the presence of different preexisting dislocation structures, or (c) due to crystal orientation (199). In fact, velocity profiles provide an answer to the question of why the spatiotemporal slip fluctuations of Figure 12a are not seen in a general bulk experiment: Despite large scatter, peak velocities of the collective dynamics are finite, meaning they can couple to the externally applied rate. Figure 12b summarizes this based on the data for Au and Nb microcrystals (205), outlining sample-size dependent transition regimes in strain rate. Since a given strain rate becomes an increasingly large absolute deformation rate, a situation will arise with increasing sample size in which the underlying collective dynamics enters driven slip deformation. This time scale and rate competition offer a rationale for the absence of similar plastic stress–strain fluctuations in typical bulk experiments. Even though the deformation map in Figure 12b ignores the effect of the surface-to-volume ratio or the presence of internal truncation length scales, this interpretation aligns well with the transition from serrated to nonserrated flow of bulk metallic glasses (206) or dynamic strain aging (207).
超越波动幅度，通过实验注意事项，可以推导出位错集体重排在滑移过程中的时间分辨特征。图 12a 中的插图显示了可用于量化集体滑移动力学的速度分布。速度分布的细节，如果足够平均，可以提供集体位错运动过程的微妙差异：(a) 在面心立方和体心立方晶体或高熵合金中；(b) 在不同预先存在的位错结构存在时；或(c) 由于晶体取向。事实上，速度分布回答了为什么图 12a 中的时空滑移波动在一般体块实验中看不到的问题：尽管存在较大散射，集体动力学的峰值速度是有限的，这意味着它们可以与外加速率耦合。图 12b 基于 Au 和 Nb 微晶数据(205)总结了这一点，概述了与应变率相关的样品尺寸依赖性转变区域。 随着给定的应变速率逐渐变成越来越大的绝对变形速率，在样品尺寸不断增加的情况下，基础集体动力学将进入驱动滑移变形的状态。这个时间尺度和速率竞争为典型体实验中缺乏类似的塑性应力-应变波动提供了理由。尽管图 12b 中的变形图忽略了表面积与体积比或内部截断长度尺度的影响，但这种解释与体金属玻璃从锯齿状到非锯齿状流动的过渡（206）或动态应变时效（207）非常吻合。

Another way of exploiting the independent accessibility of smooth, presumably Gaussian, dislocation activity and the correlated non-Gaussian component is to track the spatiotemporal slip dynamics across temperature. This has recently revealed the coexistence of athermal and thermally activated screw-dislocation plasticity in a bcc lattice (166). With decreasing deformation temperature, Nb evidences an almost unaltered slip velocity of the collective events, which is demonstrated in Figure 12c in the form of an Arrhenius construct that returns an effective barrier energy of approximately 0.04 eV. This is an order of magnitude lower than what is derived from the smooth deformation component of the same experiments (209) and raises the question of whether there is a fundamental bimodality in the dislocation network evolution during slip. Relying on DDD simulations, compelling evidence for athermal screw-dominated slip avalanches in highly stressed regions was found. In these local environments of high stress, the Peierls potential is no longer the rate-limiting factor during collective dislocation rearrangement.
利用光滑、推测为高斯型的位错活动与相关非高斯成分的独立可及性，另一种方法是追踪跨越温度的时空滑移动力学。这最近揭示了体心立方晶格中无热激活与热激活螺位错塑性共存的现象（166）。随着变形温度的降低，Nb 表现出集体事件的滑移速度几乎未发生改变，这在图 12c 中以阿伦尼乌斯结构的形式呈现，该结构返回了约 0.04 eV 的有效势垒能。这比从相同实验的平滑变形成分中推导出的结果低一个数量级（209），并引发了关于位错网络演化过程中是否存在根本性双峰性的问题。通过 DDD 模拟，在高应力区域发现了非热激活螺主导的滑移雪崩的有力证据。在这些高应力局部环境中，佩尔斯势不再是集体位错重排过程中的限速因素。

These briefly sketched examples demonstrate how a micromechanical experiment and the tracking of localized slip can provide novel insights into deformation mechanisms that are relevant for bulk plasticity. A question that has been ignored so far is how slip localization extends spatially in the probed volume. Any stress–strain instability reveals only the net displacement magnitude, and gleaned from postmortem slip line analysis, an implicit assumption of single slip plane activation has prevailed. As recently shown via in situ experimentation (210), a single stress–strain instability can originate from a multitude of complex slip processes involving one to many different slip planes, even though the net magnitude is the same. This clearly demonstrates how a population of dislocation sources with sufficiently close strengths is present such that not only the weakest source becomes active, which would result in highly localized slip on one given slip plane. Furthermore, it was found that large fast slip events are linked to the activation of previously inactive slip planes, whereas reactivation mediates smaller slip magnitudes at a slower rate. Figure 12d demonstrates this for slip localization in an fcc solid-solution high-entropy alloy (210), implying that any dislocation debris left behind after slip suppresses subsequent slip dynamics. While at first glance, this might seem to be a finding of purely fundamental value, the immediate relevance to structural stability and failure becomes clear when considering that the suppression of fast collective dynamics directly translates to a suppression of the extreme events that give rise to the non-Gaussian power-law statistics. Being nothing more than a hypothesis at this point, it is very likely that collective-correlated dislocation dynamics (i.e., avalanches) with a high net Burgers vector content give rise to slip localization that leads to strong internal stress fluctuations and concentrations. This has, in fact, been suggested on the basis of cyclic loading, where strongly non-Gaussian components of the strain localization could be linked to microcrack initiation (211). If correct, extreme events of strain localization should come into focus when designing damage tolerant alloys. What kind of obstacles, and therefore structure–property relationships, are the most efficient to suppress these rare but extreme strain localization events remains unclear, as complex microstructures including grain boundaries, solid solutions, precipitates, and irradiation structures continue to bear their signatures (202, 212–214). Being a powerful method to directly track strain localization due to (weakly) correlated dislocation activity, microcompression will continue to play a central role in unraveling the details of spatially confined plasticity and slip, as well as their relationship to local failure initiation.
这些简要的例子展示了如何通过微观力学实验和局部滑移的追踪，为与块体塑性相关的变形机制提供新的见解。目前尚未被关注的问题是，在探测的体积中，滑移的局部化如何扩展空间。任何应力-应变不稳定性仅揭示了净位移的大小，而从死后滑移线分析中得知，一直盛行着单一滑移面激活的隐含假设。正如最近通过原位实验（210）所示，单一应力-应变不稳定性可能源于一个涉及一个或多个不同滑移面的复杂滑移过程，即使净位移大小相同。这清楚地表明，存在足够接近强度的位错源群体，以至于不仅最弱的源被激活，这会导致在某一给定滑移面上产生高度局部化的滑移。此外，研究发现，大规模快速滑移事件与先前未激活滑移面的激活有关，而重新激活则以较慢的速率介导较小的滑移量。 图 12d 展示了在面心立方固溶高熵合金（210）中的滑移定位现象，这意味着滑移后留下的任何位错碎屑都会抑制后续的滑移动力学。虽然乍一看这可能似乎是一个纯粹的基礎性发现，但考虑到快速集体动力学的抑制直接转化为对产生非高斯幂律统计的极端事件的抑制，其与结构稳定性和失效的即时相关性就变得清晰。目前这还只是一个假说，但它很可能表明，具有高净伯格斯矢量含量的集体相关位错动力学（即雪崩）会导致滑移定位，从而引发强烈的内部应力波动和集中。事实上，这一观点已在循环加载的基础上被提出，其中应变定位的强非高斯分量可以与微裂纹萌生（211）相关联。如果正确，那么在设计和开发耐损伤合金时，应变定位的极端事件应当成为关注的焦点。 什么样的障碍，因此结构-性能关系，最有效地抑制这些罕见但极端的应变局部化事件仍然不清楚，因为包括晶界、固溶体、析出物和辐照结构的复杂微观结构继续保留它们的特征（202，212-214）。作为直接追踪（弱）相关位错活动引起的应变局部化的强大方法，微压缩将继续在揭示空间受限塑性及其与局部失效起始的关系的细节中发挥核心作用。

Modeling subgranular slip localizations with most conventional deformation models, even the most mechanically sophisticated, is challenging. First, the discrete nature of slip localization is inherently inhomogeneous, rendering most classical micromechanical formulations inapplicable. Second, intensification of slip is naturally a multiscale process, initiating at some fine nanoscale region and extending across the grain before intensifying to detectable levels at the micrometer scale and larger. Application of standard coarse-graining modeling techniques for slip localization can, therefore, be problematic. Finally, slip localization events do not occur in isolation. Mutual interactions with other slip localization processes at variable distances within the same grain or in the neighboring grains can affect their development.
使用最常规的变形模型模拟亚晶粒滑移局部化具有挑战性。首先，滑移局部化的离散性本质上是不均匀的，这使得大多数经典细观力学公式不适用。其次，滑移的强化本质上是一个多尺度过程，始于某些纳米尺度区域，扩展到晶粒内部，然后在微米尺度及更大尺度上强化到可检测水平。因此，应用标准的粗化建模技术来模拟滑移局部化可能会存在问题。最后，滑移局部化事件并非孤立发生。同一晶粒内或邻近晶粒中不同距离的其他滑移局部化过程的相互作用会影响其发展。

CP theory has served as a basis for modeling slip localization. Of the many polycrystalline deformation modeling tools, the ones that best meet the challenges above combine CP and a full-field mechanical approach, such as the finite element method (CP-FE) or an FFT scheme (CP-FFT) (215, 216). These models require as input an explicit, spatially resolved description of the material microstructure (e.g., grain connectivity, shape, relative size, orientation) and return the spatially resolved mechanical response and strain evolution of the grain structure. As another asset for modeling slip localization formation, for every compute point, inside every grain, these models determine crystallographic slip activity while under the constraint of deforming neighboring grains.
连续介质力学理论为滑移定位建模提供了基础。在众多多晶变形建模工具中，最能应对上述挑战的是结合连续介质力学和全场力学方法（如有限元方法（CP-FE）或快速傅里叶变换方案（CP-FFT））（215, 216）。这些模型需要输入材料微观结构的明确、空间分辨的描述（例如，晶粒连接性、形状、相对尺寸、取向），并返回晶粒结构的空间分辨力学响应和应变演化。作为建模滑移定位形成的另一优势，对于每个计算点，在每个晶粒内部，这些模型在变形相邻晶粒的约束下确定晶体学滑移活动。

In all such models, a nonnegative, nonzero stress, denoted by τ, for activating slip in the grains must be prescribed. Traditionally, it is presumed that τ does not change or increase with the rate of slip. To model the formation of slip localization, however, most models adopt a softening law for τ. Softening means that τ decays with increasing amounts of slip and, when applied to slip localization, is intended to represent the consequence of heat generation due to dissipation of the plastic work that is performed by the several fast-moving, like-signed dislocations in the slip localization. Some models predefine a planar region inside the model grain(s) wherein τ decreases with the slip rate (217, 218) ( Figure 13a,c ). Other models allow the degree of softening to depend on the amount of accumulated slip with no assumptions on localization paths (13) ( Figure 13b ). Alternatively, the model by Ahmadikia et al. (218) introduced a crystallographic planar region in which slip was permitted to localize, and whether localization occurred depended on the material, microstructure, and loading intensity and direction ( Figure 13c ).
在所有这些模型中，必须规定一个非负的非零应力τ，用于激活晶粒中的滑移。传统上，假定τ不随滑移速率变化或增加。然而，为了模拟滑移局部化的形成，大多数模型采用τ的软化定律。软化意味着τ随滑移量的增加而衰减，当应用于滑移局部化时，旨在表示由快速移动的、同号的位错在滑移局部化中耗散的塑性功所产生热量的后果。一些模型预先定义模型晶粒内部的一个平面区域，其中τ随滑移速率降低（217, 218）（图 13a,c）。其他模型允许软化程度取决于累积滑移量，而对局部化路径不做假设（13）（图 13b）。或者，Ahmadikia 等人（218）的模型引入了一个晶体学平面区域，允许滑移局部化，而是否发生局部化则取决于材料、微观结构和加载强度及方向（图 13c）。

Figure 13  图 13  (a) Modeling of slip localization using crystal plasticity simulations shows regions of planar slip within grains, also observed in the experiment. Panel adapted from Reference 217 with permission from Elsevier. (b) Pathways for localization during deformation (slip and kinking) are mapped by massively parallel fast Fourier transform simulations. Panel adapted from Reference 13 with permission from Elsevier. (c) A region of finite thickness is introduced in which a slip band is eligible to form. If the material and external conditions are suitable, for instance, the resolved shear stress (RSS) on a slip band, a slip could localize in this region. Panel adapted from Reference 218 with permission from Elsevier.
(a) 利用晶体塑性模拟对滑移局部化进行建模，显示了晶粒内的平面滑移区域，实验中也观察到了这些区域。该面板根据参考文献 217 改编，并经 Elsevier 授权使用。(b) 通过大规模并行快速傅里叶变换模拟，绘制了变形（滑移和弯曲）期间的局部化路径。该面板根据参考文献 13 改编，并经 Elsevier 授权使用。(c) 引入一个有限厚度的区域，在该区域内，滑移带有可能形成。如果材料和外部条件适宜，例如滑移带上的 resolved shear stress (RSS)，滑移可能在这个区域内局部化。该面板根据参考文献 218 改编，并经 Elsevier 授权使用。

Figure 13 

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Slip localizations are modeled at the subgranular scale, enabling direct comparison with surface measurements of slip localizations in deformed materials. Because microstructural information below the surface is commonly lacking, 3D modeled microstructures often choose to extend the surface structure in the out-of-plane direction, creating a columnar structure. Figure 14a shows the measured strain accumulated across a slip localization obtained from HR-DIC. The amount of accumulated peaks in the center of the grain is lowest where the slip localization meets the grain boundaries. For the same microstructure, the model applies the same strain-state far field by starting from zero and building it up at the same rate as in the experiment. The grains initially deform homogeneously but eventually slip localize. At the same level (0.61% strain), the accumulated slip profile across the slip localization calculated by the model agrees with the measured one. The predicted local stress fields indicate that the neighboring grains resist the shear imposed by slip localization and react by generating a back stress in the grain with the slip localization. The back stress is strongest at the slip localization–grain boundary junction. This back stress can prevent neighboring slip localizations from developing within the same grain.
滑移局部化在亚晶粒尺度上被建模，从而能够与变形材料中滑移局部化的表面测量结果进行直接比较。由于表面以下的微观结构信息通常缺乏，三维模型化的微观结构常常选择在面外方向上扩展表面结构，形成柱状结构。图 14a 显示了从高分辨率数字图像相关（HR-DIC）技术获得的滑移局部化区域的累积应变测量结果。在晶粒中心累积峰值最低的位置，滑移局部化与晶界相遇。对于相同的微观结构，模型通过从零开始并以与实验相同的速率逐步构建，应用相同的远场应变状态。晶粒最初均匀变形，但最终发生滑移局部化。在相同水平（0.61%应变）下，模型计算的滑移局部化区域内的累积滑移分布与测量结果一致。预测的局部应力场表明，邻近晶粒抵抗滑移局部化施加的剪切力，并通过在发生滑移局部化的晶粒中产生反应力来做出反应。 背应力在滑移定位-晶界连接处最强。这种背应力可以阻止同一晶粒内相邻的滑移定位发展。

Figure 14  图 14  Correlation between experimental and numerical measurements. (a) Experimentally captured microstructure is used as input. The slip localization event is explicitly described in a crystal plasticity simulation. The slip intensity along the profile of the slip event is accurately captured by the model. Panel adapted from Reference 218 with permission from Elsevier. (b) Crystal plasticity model permitting the development of an explicit slip event predicted the onset of SB formation and its development in intensity as a result of the parent orientation and surrounding neighboring grains. This blocked SB induces significant stress and lattice rotation in the neighboring grain. Panel adapted from Reference 218 with permission from Elsevier. Abbreviations: IPF, inverse pole figure; LD, loading direction; SB, slip band; TRSS, twin-plane resolved shear stress.
实验测量与数值计算的相关性。(a) 实验捕获的微观结构被用作输入。晶体塑性模拟中明确描述了滑移定位事件。模型精确地捕捉了滑移事件沿轮廓的滑移强度。面板改编自参考文献 218，经 Elsevier 许可。(b) 允许显式滑移事件发展的晶体塑性模型预测了孪晶带形成的开始及其强度的发展，这是由于母相取向和周围相邻晶粒的结果。这种受阻的孪晶带在相邻晶粒中诱导了显著的应力和晶格旋转。面板改编自参考文献 218，经 Elsevier 许可。缩写：IPF，倒极图；LD，加载方向；SB，滑移带；TRSS，孪晶面解理剪切应力。

Figure 14 

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The stress concentrations that develop ahead of a slip localization in the neighboring grain can cause slip systems and other deformation mechanisms that would not otherwise occur or are unexpected. One example that has been studied is deformation twinning (216, 219). The character of the localized stress from the localization can trigger twins of variants that would not be preferred by average stress in the grain. In some rare instances, a 3D feature called a microvolume (105, 106) forms in a grain neighboring another grain containing a slip localization ( Figure 6b,c ). It is characterized as a local plume-shaped zone encompassing large stresses and lattice rotations and is associated with slip localizations that tend to nucleate cracks in cyclic loading (33, 220). With the experimental microstructure, the CP-FE slip localization model by Latypov et al. (221) predicted the formation of microvolumes of similar extent and amount of reorientation in the neighboring grain as seen experimentally ( Figure 14b ). By combining these calculations with other simulations for alternative, hypothetical neighboring grain orientations, the analysis showed that microvolumes form when the slip localization is exceptionally intense and the neighboring grain orientation responds by activating multiple slip systems within the microvolume.
在邻近晶粒中滑移局部化前方形成的应力集中可能导致滑移系统和其他变形机制的产生，而这些机制原本不会发生或出乎意料。一个已被研究过的例子是变形孪晶（216, 219）。局部化产生的应力特征可以触发孪晶变体的形成，而这些变体在晶粒中的平均应力下不会被优先选择。在某些罕见情况下，在含有滑移局部化的邻近晶粒中会形成一种称为微体积的三维特征（105, 106）（图 6b,c）。它被描述为一种包含高应力和晶格旋转的局部羽状区域，并与那些在循环加载中倾向于形成裂纹的滑移局部化相关（33, 220）。通过实验微观结构，Latypov 等人（221）提出的 CP-FE 滑移局部化模型预测了在邻近晶粒中形成与实验观察到的相似范围和重排程度的微体积（图 14b）。 通过将这些计算与其他模拟结合，模拟了替代的、假设的相邻晶粒取向，分析表明，当滑移局部化异常强烈且相邻晶粒取向通过在微体积内激活多个滑移系统做出响应时，会形成微体积。

Although slip localization is confined to form within a crystallographic slip plane of a grain, the slip localization in different grains can appear to link up across grain boundaries, forming a piecewise chain that can span from 2 to 20 grains (59). CP simulations allowing for slip localization to possibly form in one grain while being bounded to other grains have been conducted (218). The comparison with observation revealed that the propensity for slip localization in one grain strongly depends on the orientation of its neighboring grains. For high-angle grain boundaries, the slip localization is weak, signifying that grain deformation occurs homogeneously throughout the grain. For low-angle grain boundaries, intense slip localization is promoted, achieving strain levels like those seen experimentally.
尽管滑移局部化局限于在晶粒的晶体学滑移面上形成，但不同晶粒中的滑移局部化似乎可以通过晶界连接起来，形成可以跨越 2 到 20 个晶粒的片段链（59）。已经进行了 CP 模拟，允许滑移局部化可能在一个晶粒中形成，同时被其他晶粒限制（218）。与观察结果的比较表明，一个晶粒中滑移局部化的倾向强烈取决于其相邻晶粒的取向。对于高角度晶界，滑移局部化较弱，表明晶粒变形在整个晶粒中均匀发生。对于低角度晶界，促进了强烈的滑移局部化，实现了与实验中观察到的应变水平相似的应变水平。

The latest advances in slip localization modeling have revealed the important influence of material and microstructural properties. The models have proven helpful in isolating the roles of one property among the many degrees of freedom that are associated with material and microstructure. Two examples are discussed below.
滑移定位建模的最新进展揭示了材料及微观结构特性的重要影响。这些模型已证明有助于在材料及微观结构的众多自由度中分离出某一特性的作用。下面讨论两个例子。

The plastic deformation of grains in hcp materials is anisotropic, sensitive to the lattice orientation of the grain. If a grain is oriented such that the stress must drive a hard mode of slip and thus is hard to plastically deform, then its orientation is a so-called hard orientation. A soft orientation is the opposite, wherein the stress activates the easier slip modes, which are usually basal or prismatic modes. In high-performance hcp alloys, such as those based on Ti or Mg, slip localizations are most often aligned with the basal or prismatic modes (59, 222). A simple bicrystal model was set up with the parent grain allowing either a basal or prismatic slip localization to form when stressed and a neighboring grain of arbitrary orientation (218). The calculation of the critical strain to localization ϵloc, in which the slip localization sustains twice the strain as the rest of the grain, was repeated for the full space of orientations for the neighboring grains. The relatively harder neighbors resisted the slip localization, causing a larger back stress in the parent grain in the vicinity of but outside the slip localization. The back stress lowers the driving force for new slip localizations in the parent grain, encouraging the slip localization to accommodate even further increases in applied deformation.
六方晶格材料中晶粒的塑性变形具有各向异性，且对晶粒的晶格取向敏感。如果晶粒的取向使得应力必须驱动硬滑移模式，从而导致塑性变形困难，那么这种取向被称为硬取向。相反，软取向则激活了更容易的滑移模式，这些模式通常是基面或棱柱面滑移模式。在高性能六方晶格合金中，如基于钛或镁的合金，滑移定位通常与基面或棱柱面滑移模式一致（59, 222）。建立了一个简单的双晶模型，其中母晶粒在受力时允许形成基面或棱柱面滑移定位，而相邻晶粒的取向任意（218）。对临界应变至定位 ϵloc 的计算重复进行，该计算中滑移定位承受的应变是晶粒其他部分的 twice，即两倍。相对较硬的相邻晶粒会抵抗滑移定位，导致母晶粒在滑移定位附近但位于滑移定位区域外的区域产生更大的反应力。 背应力降低了母晶粒中新滑移定位的驱动力，促使滑移定位进一步适应施加变形的增加。

Shortly after yielding, strong polycrystalline materials usually exhibit some amount of strain hardening, defined as an increase in flow stress with deformation. Concomitantly, the local slip strength τ to activate slip in the grains increases with strain as well. Higher values of τ are usually associated with stronger materials. With a simple bicrystal model for slip localization, the competition between hardening in the parent grain volume and local softening in its slip localization and the role of τ were investigated.
在屈服后不久，强多晶材料通常会表现出一定程度的应变硬化，定义为随着变形的增加，流动应力的增加。同时，激活晶粒中滑移的局部滑移强度τ也随着应变增加。较高的τ值通常与更强材料相关。通过一个简单的双晶模型来研究滑移定位的硬化竞争、母晶粒体积中的硬化、其滑移定位中的局部软化以及τ的作用。

Compared with commercially pure Ti (CP-Ti), Mg is the weaker material, wherein the local τ to activate slip in any of the slip modes in Mg is lower than that in CP-Ti (216, 223). Slip localization calculations found that Mg requires substantially higher ϵloc for the onset of localization and accumulates less strain within the slip localization than the stronger material, CP-Ti. For some grain neighbor orientations in Mg, slip localization did not even form within the 1% applied strain, indicating that conditions do exist where slip localization is not preferred over homogeneous slip in the grain. Further, with the model, the role of elastic anisotropy can be isolated. It was shown that the stronger elastic anisotropy in CP-Ti, compared with that in Mg, contributes to the accumulation of more strain in the slip localization in CP-Ti.
与商业纯钛（CP-Ti）相比，镁是较弱的材料，其中镁中激活任何滑移模式的局部τ低于 CP-Ti（216, 223）。滑移局部化计算发现，镁需要显著更高的ϵloc 才能开始局部化，并且在其滑移局部化中积累的应变比更强材料 CP-Ti 少。对于镁中的一些晶粒邻位取向，滑移局部化甚至在 1%的施加应变内都没有形成，这表明存在滑移局部化并不优于晶粒中均匀滑移的条件。此外，通过该模型可以分离弹性各向异性的作用。研究表明，与镁相比，CP-Ti 更强的弹性各向异性导致其在滑移局部化中积累更多的应变。