In-situ investigation of slip system activation, intergranular plasticity transfer, and deformation heterogeneity of Al-Zn-Mg-Cu alloy

doi:10.1016/j.msea.2024.147604

Materials Science and Engineering: A
材料科学与工程：A

Volume 922, February 2025, 147604
卷 922，2025 年 2 月，147604

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Abstract 摘要

In-situ SEM/EBSD experiments were conducted to investigate the microstructure evolution and plastic accommodation behavior during the plastic deformation of the Al-Zn-Mg-Cu alloy. The activated slip systems are identified through the slip trace analysis, and the criteria for the activation of slip systems during the plastic deformation is provided. Statistical analysis was conducted on the plasticity transfer between adjacent grains, a more comprehensive and systematic basis for determining the occurrence of intergranular slip transmission has been provided, combining the geometrical compatibility factor (

m^{'}

) and residual dislocation information. Experimental analysis found that the Al-Zn-Mg-Cu alloy exhibited significant heterogeneity of deformation both within grains and between grains during the deformation process, and it was closely related to activation of slip systems and the plasticity transfer at the interfaces. Additionally, crystal plasticity simulation, based on real EBSD data, were conducted as a supplementary means of experiment, to comprehensively understand the plastic coordination mechanism from the perspective of micro-scale stress and strain.
原位 SEM/EBSD 实验用于研究 Al-Zn-Mg-Cu 合金在塑性变形过程中的微观结构演变和塑性适应行为。通过滑移迹线分析确定了激活的滑移系统，并提供了塑性变形过程中滑移系统激活的标准。对相邻晶粒间的塑性传递进行了统计分析，结合了几何兼容性因子（

m^{'}

）和残余位错信息，为确定晶间滑移传递的发生提供了更全面和系统的依据。实验分析发现，Al-Zn-Mg-Cu 合金在变形过程中晶粒内和晶粒间均表现出显著的变形异质性，这与滑移系统的激活和界面处的塑性传递密切相关。此外，基于真实 EBSD 数据进行的晶体塑性模拟作为实验的补充手段，从微观尺度应力和应变的角度全面理解了塑性协调机制。

Keywords 关键词

Al-Zn-Mg-Cu alloy

Plastic deformation

In-situ EBSD/SEM

Plasticity transfer

Deformation inhomogeneity

Al-Zn-Mg-Cu 合金塑性变形原位 EBSD/SEM 塑性转移变形不均匀

1. Introduction 1. 引言

Al-Zn-Mg-Cu alloys play an important role in the aerospace, automotive, and rail transportation fields due to their excellent specific strength, fatigue toughness, and machinability [[1], [2], [3]]. In the context of the current industrial lightweighting trend, high-strength aluminum alloys are expected to replace traditional high-density materials in more industrial sectors. Therefore, they have received more research attention as representative lightweight alloy materials.
Al-Zn-Mg-Cu 合金因其优异的比强度、疲劳韧性和可加工性，在航空航天、汽车和轨道交通领域发挥着重要作用[[1], [2], [3]]。在当前工业轻量化趋势的背景下，高强度铝合金有望取代传统高密度材料应用于更多工业领域。因此，作为代表性轻量化合金材料，它们获得了更多的研究关注。

The plastic deformation of Al alloys depends on the activation of dislocation slip systems to coordinate plasticity. Therefore, revealing the activation mechanism of dislocation during the deformation process is of a great significance for controlling the plastic deformation and thereby enhancing deformation capability. Generally, the activation of dislocations is determined by the resolved shear stress of slip systems under the load during the deformation [[4], [5], [6]]. Based on this theoretical foundation, many models are used to predict the plastic behavior. For example, the Sachs model [7] and the Taylor model [8], which assume uniform stress or strain, are very effective in predicting the activation of slip systems for macroscopic material plastic deformation [9,10]. However, the models have shortcomings in description of plastic heterogeneity that commonly exists in material deformation, as it provides a uniform stress distribution during the deformation process, however, this is clearly unrealistic in the actual deformation process of polycrystalline materials [[9], [10], [11]]. Researches have found that there is a plastic deformation heterogeneity between different grains [[12], [13], [14]], and the influence of crystal orientation of polycrystalline materials leads to differences in the effective resolved shear stress for slip systems in different grains. This results in the activation of different types of dislocations and causes discrepancies in crystal rotation pathways and rates [[15], [16], [17]]. Therefore, further exploring the activation behavior of dislocations and their subsequent effects is of a great significance for in-depth understanding of the deformation heterogeneity in polycrystalline materials.
铝合金的塑性变形依赖于位错滑移系统的激活来协调塑性。因此，揭示变形过程中位错的激活机制对于控制塑性变形并从而提高变形能力具有重要意义。通常，位错的激活由变形过程中载荷下滑移系统的分解切应力决定[[4], [5], [6]]。基于这一理论基础，许多模型被用于预测塑性行为。例如，假设均匀应力或应变的 Sachs 模型[7]和 Taylor 模型[8]，在预测宏观材料塑性变形的滑移系统激活方面非常有效[9,10]。然而，这些模型在描述材料变形中常见的塑性非均匀性方面存在不足，因为它们在变形过程中提供均匀的应力分布，然而这在多晶材料的实际变形过程中显然是不现实的[[9], [10], [11]]。研究表明，不同晶粒之间存在塑性变形不均匀性[[12], [13], [14]]，多晶材料的晶体取向影响导致不同晶粒中滑移系统的有效分解切应力存在差异。这导致不同类型的位错被激活，并造成晶体旋转路径和速率的差异[[15], [16], [17]]。因此，进一步探究位错的激活行为及其后续影响，对于深入理解多晶材料的变形不均匀性具有重要意义。

Numerous experimental studies have summarized that the crystal rotation of FCC materials can generally be divided into three modes [13,18,19], as shown in Fig. 1. The grains in region 1, where the crystal orientations are concentrated in the [011] direction on the loading direction orientation distribution map, exhibit a statistical trend of rotation towards the [001]-[

\overline{1}

11] line direction. In Region 2, the majority of areas on [001]-[

\overline{1}

11], and the regions near the [011]-[

\overline{1}

11] line in the direction of [221], exhibit a trend of orientation grain clusters rotating towards the [

\overline{1}

11] direction. Meanwhile, the orientation grain subsets located at the corner in the [001] direction show a rotation trend towards the direction of the [011]-[

\overline{1}

11] line. These statistical regularities consistently indicate that the rotation of crystals or the activation of slip systems is greatly influenced by crystal orientation. Furthermore, in terms of predictive models, the development of crystal plasticity models, such as the viscoplastic self-consistent model, has begun to consider the heterogeneity within a grain [4,20]. The model establishment allows the grains to be subjected to different strains under the action of external loads and boundary conditions, which largely solves the problem of heterogeneous deformation matching between grains of different orientations. However, even so, most of the current predictive methods are still unable to effectively solve the issue of inhomogeneous plasticity within grains.
大量实验研究表明，FCC 材料的晶体旋转通常可分为三种模式[13,18,19]，如图 1 所示。在区域 1 中，晶体取向在加载方向取向分布图上集中在[011]方向上的晶粒，表现出向[001]-[

\overline{1}

11]线方向旋转的统计趋势。在区域 2 中，[001]-[

\overline{1}

11]方向上的大部分区域，以及[221]方向上[011]-[

\overline{1}

11]线附近的区域，显示出取向晶粒簇向[

\overline{1}

11]方向旋转的趋势。同时，位于[001]方向角落的取向晶粒子集表现出向[011]-[

\overline{1}

11]线方向旋转的趋势。这些统计规律始终表明，晶体旋转或滑移系统的激活受晶体取向的极大影响。此外，在预测模型方面，如粘塑性自洽模型等晶体塑性模型的开发，已开始考虑晶粒内部的异质性[4,20]。模型建立使得晶粒在外部载荷和边界条件的作用下承受不同的应变，这很大程度上解决了不同取向晶粒间变形不匹配的问题。然而，即便如此，目前大多数预测方法仍无法有效解决晶粒内部非均匀塑性变形的问题。

Inhomogeneity in intracrystalline plastic deformation delves into another aspect of deformation heterogeneity in polycrystalline materials, specifically the interaction among neighboring grains and the role of grain boundaries in plastic deformation [9,[21], [22], [23], [24]]. A widely accepted understanding is that grain boundaries play a hindering role in the process of dislocation motion, they hinder the transfer of plasticity between two grains, leading to the interruption of plastic deformation between them. Consequently, after deformation, noticeable wrinkling protrusions emerge near the grain boundaries, serving as evident manifestations of uneven deformation, and such disparities in intergranular plastic deformation may even give rise to the nucleation of intergranular cracks [25,26]. Additionally, this kind of plasticity non-coordination often leads to discrepancies in crystal rotation near the grain boundary and the overall interior of individual grains. On the other hand, extensive experimental observations have revealed that the interaction of grain boundaries with dislocations is not merely inhibitory, the phenomenon of dislocations traversing grain boundaries between adjacent grains has been identified through material characterization techniques such as SEM, EBSD, and TEM [[27], [28], [29], [30], [31]]. Over the past few decades, researchers have dedicated their efforts to the research on the mechanisms and assessment of plasticity transmission across grain boundaries, the research work in this area mainly focuses on two aspects. Firstly, utilizing techniques such as EBSD for crystal orientation characterization, involves the analysis of the activated slip systems between adjacent grains, as well as the degree of slip plane coincidence and the angles of the grain boundary plane [9,21,28,32,33], and enables an assessment of the geometric relationships between activated slip systems of neighboring grains, providing insights into the conditions under which plastic transmission occurs. Additionally, employing characterization techniques, such as TEM, allows for the direct observation of the transmission mechanisms of dislocations at interfaces. Studies in this area indicate the complexity of the transformation mechanisms of dislocations at grain boundaries with atomic misalignment in disordered. In addition, it often involves the conversion of dislocation types, migration between different crystal planes, and the residual presence of dislocations at three-dimensional interfaces [30,31,34]. Nevertheless, in the experimental exploration of interface issues, such as grain boundaries, achieving three-dimensional observation is often challenging. Techniques like ion beam-scanning and diffraction contrast tomography scanning can to some extent enhance the depth of characterization [[35], [36], [37]]. However, the precise investigation of crystal boundary distribution information, such as the twist angle and the 3D shape of grain boundaries, remains a challenging technical problem. The lack of accurate description of three-dimensional information about grain boundaries makes it difficult to precisely determine the strain and stress distribution at interfaces during the plastic deformation process of polycrystalline materials.
晶粒内塑性变形的不均匀性深入探讨了多晶材料变形异质性的另一个方面，即相邻晶粒之间的相互作用以及晶界在塑性变形中的作用[9,[21], [22], [23], [24]]。一种广泛接受的理解是，晶界在位错运动过程中起着阻碍作用，它们阻碍了塑性在两个晶粒之间的传递，导致它们之间的塑性变形中断。因此，变形后，在晶界附近会出现明显的褶皱凸起，作为变形不均匀的明显表现，这种晶间塑性变形的差异甚至可能引发晶间裂纹的萌生[25,26]。此外，这种塑性不协调通常会导致晶界附近和单个晶粒内部的晶体旋转出现差异。另一方面，大量的实验观察表明，晶界与位错的相互作用并不仅仅是抑制性的，通过 SEM、EBSD 和 TEM 等材料表征技术已经识别出位错在相邻晶粒间的晶界处穿行的现象[[27], [28], [29], [30], [31]]。在过去的几十年里，研究人员致力于研究晶界处塑性传递的机制及其评估，该领域的研究工作主要集中在两个方面。首先，利用 EBSD 等技术研究晶体取向表征，涉及分析相邻晶粒间激活的滑移系统，以及滑移面重合程度和晶界平面角度[9,21,28,32,33]，从而能够评估相邻晶粒激活滑移系统之间的几何关系，为理解塑性传递发生的条件提供见解。此外，采用透射电子显微镜等表征技术，可以直接观察位错在界面处的传输机制。该领域的研究表明，在无序状态下原子错配的晶界处位错的转变机制具有复杂性。此外，它通常涉及位错类型的转换、在不同晶面之间的迁移，以及三维界面处位错的残留存在[30,31,34]。然而，在实验探索界面问题（如晶界）时，实现三维观察往往具有挑战性。离子束扫描和衍射衬度断层扫描等技术可以在一定程度上增强表征的深度[[35], [36], [37]]。然而，精确研究晶体边界分布信息，如扭转角和晶界的三维形状，仍然是一个具有挑战性的技术问题。对晶界三维信息的准确描述不足，使得在多晶材料塑性变形过程中难以精确确定界面处的应变和应力分布。

In summary, the experimental scheme using SEM/EBSD characterization can more objectively and comprehensively provide statistical results on the activation of dislocations and plasticity transfer behavior during the deformation process. This has important guiding significance for the study of the plasticity mechanism of polycrystalline materials and the design of material microstructures. Therefore, this work explores the issue of deformation heterogeneity of the Al-Zn-Mg-Cu alloy from the perspective of slip system activation and plasticity transfer. The plastic deformation process was comprehensively tracked through an in-situ SEM/EBSD experimental scheme. Additionally the activation of slip systems was determined through slip trace analysis, and criteria for the activation of slip systems was established. Statistical analysis was conducted on the plasticity transfer between grains of different orientations, and the distribution characteristics of dislocations at the grain boundaries were investigated using TEM characterization. The possibility of plasticity transfer occurring at the interfaces was comprehensively evaluated from the perspectives of geometric matching and residual dislocation. Furthermore, although it has been mentioned, the current shortcomings in predictive models for intracrystalline plastic incompatibility and the grain boundary interactions, these limitations predominantly arise due to the intricate mechanisms of grain boundary interactions and the challenges in grain boundary modeling [38]. Nevertheless, it is widely recognized that the crystal plasticity simulations remain an effective complementary approach in the study of the plastic deformation mechanisms of polycrystalline materials, as they can, to some extent, supplement the information that is difficult to obtain experimentally, such as stress distributions. Therefore, in this work, to more comprehensively evaluate the influence of heterogeneous deformation in the plastic deformation process of the Al-Zn-Mg-Cu alloy, we have conducted complementary crystal plasticity calculations based on experiments,. The analysis and research results of this work can play an important guiding role in the in-depth understanding of the heterogeneity of plastic deformation in Al alloys, as well as the mechanisms and determination criteria of plasticity transfer at grain boundaries.
总之，采用 SEM/EBSD 表征的实验方案能够更客观、全面地提供位错激活和塑性转移行为在变形过程中的统计结果。这对研究多晶材料的塑性机制和材料微观结构设计具有重要指导意义。因此，本研究从滑移系统激活和塑性转移的角度探讨了 Al-Zn-Mg-Cu 合金的变形不均匀性问题。通过原位 SEM/EBSD 实验方案，全面追踪了塑性变形过程。此外，通过滑移迹线分析确定了滑移系统的激活，并建立了滑移系统激活判据。对取向不同的晶粒间的塑性转移进行了统计分析，并利用 TEM 表征研究了晶界处位错的分布特征。在界面处发生塑性转移的可能性从几何匹配和残余位错的角度进行了全面评估。此外，尽管已经提及，但当前预测模型在晶内塑性不兼容和晶界相互作用方面的不足，这些限制主要源于晶界相互作用的复杂机制和晶界建模的挑战[38]。然而，人们普遍认为，晶体塑性模拟仍然是研究多晶材料塑性变形机制的一种有效补充方法，因为它们在一定程度上可以补充实验难以获得的信息，例如应力分布。因此，在本工作中，为了更全面地评估非均匀变形对 Al-Zn-Mg-Cu 合金塑性变形过程的影响，我们基于实验进行了补充晶体塑性计算。这项工作的分析和研究结果可以在深入理解铝合金塑性变形的异质性问题，以及晶界处塑性转移的机制和判定标准方面发挥重要的指导作用。

2. Experiment and simulation
2. 实验、模拟

2.1. Experimental details
2.1. 实验细节

The adopted homogenized Al-7.5 wt%Zn-2wt%Mg-2.1 wt%Cu-0.15 wt%Fe alloy ingot, provided by Shandong Nanshan Aluminium co., Ltd, was subjected to a solution treatment at 475 °C for 2 h. In-situ tensile tests were conducted using the Kammrath Weiss Gmbh MZ0-1 Tensile/Compression Module. The module is equipped with tensile force sensor and displacement sensor, without an extensometer. Using electrical discharge machining, a dog-bone-shaped in-situ tensile specimen, of a total length of 35 mm, was cut from the solution-treated material. The in-situ tensile specimen designed in this study has a total length of 35 mm, and the middle section of the specimen is machined into a slender neck shape with approximate dimensions of 1500 μm × 800 μm and a thickness of approximately 1000 μm, ensuring that the observed area is the primary zone for plastic deformation, as illustrated in Fig. 2. During the in-situ tensile process, the stretching rate was 15 μm/s, corresponding to a strain rate of 0.01/s, and the tensile process was interrupted 4 times for the SEM and EBSD characterization.
所采用的均匀化 Al-7.5 wt%Zn-2wt%Mg-2.1 wt%Cu-0.15 wt%Fe 合金锭由山东南山铝业公司提供，在 475 °C 下进行 2 小时固溶处理。采用 Kammrath Weiss Gmbh MZ0-1 拉伸/压缩模块进行原位拉伸试验。该模块配备拉伸力传感器和位移传感器，但没有引伸计。通过电火花加工，从固溶处理材料中切割出总长 35 mm 的狗骨形原位拉伸试样。本研究设计的原位拉伸试样总长为 35 mm，其中试样中间部分加工成细颈形状，尺寸约为 1500 μm × 800 μm，厚度约为 1000 μm，确保观察区域是主要的塑性变形区域，如图 2 所示。在原位拉伸过程中，拉伸速率为 15 μm/s，对应应变速率为 0.01/s，拉伸过程中断 4 次进行 SEM 和 EBSD 表征。

To validate the reliability of the in-situ tensile data and obtain accurate strain-stress information, reference tensile tests were conducted on a Zwick-Z250 mechanical testing machine with a laser extensometer. The same in-situ tensile specimens, of general specimens with a total length of 80 mm and a gauge length of 25 mm were employed.
为验证原位拉伸数据的可靠性并获取准确的应变-应力信息，在 Zwick-Z250 机械试验机上使用激光引伸计进行了参考拉伸试验。采用相同的原位拉伸试样，这些试样为普通试样，总长 80 mm，标距 25 mm。

The specimens underwent mechanical grinding and polishing using diamond suspension and 60 nm OPS suspension. The SEM, EBSD, and EDS characterizations were conducted using a TESCAN Lyra3 electron microscope equipped with an EBSD probe. The initial EBSD characterization covered an area of 800 μm × 600 μm with a scanning step of 1 μm. The acquired EBSD data were analyzed using an in-house MATLAB code based on the MTEX [39] toolbox.
试样使用金刚石悬浮液和 60 nm OPS 悬浮液进行机械研磨和抛光。SEM、EBSD 和 EDS 表征使用配备 EBSD 探头的 TESCAN Lyra3 电子显微镜进行。初始 EBSD 表征覆盖区域为 800 μm × 600 μm，扫描步长为 1 μm。获得的 EBSD 数据使用基于 MTEX [39]工具箱的内部 MATLAB 代码进行分析。

Furthermore, for a more intuitive observation of detailed dislocation information at the grain boundaries after plastic deformation, the TEM characterization was performed on Al-Zn-Mg-Cu alloy subjected to a 10 % strain during tension. The deformed sample underwent grinding, punching, and ion milling at −90 °C. Subsequently, the FEI Talos F200S transmission electron microscope was employed at 200 kV for transmission observations.
此外，为了更直观地观察塑性变形后晶界处的详细位错信息，对经历 10%拉伸应变的 Al-Zn-Mg-Cu 合金进行了 TEM 表征。变形样品在-90°C 下进行了研磨、冲孔和离子减薄处理。随后，使用 FEI Talos F200S 透射电子显微镜在 200 kV 下进行透射观察。

2.2. Crystal plasticity computational framework
2.2. 晶体塑性计算框架

Crystal plasticity simulation using a fast Fourier transform solver (CPFFT) is performed on DAMASK (Dusseldorf Advanced Materials Simulation Kit) [40]. The representative volume element (RVE) model for the crystal plasticity computation was constructed by processing the initial EBSD data of the Al-Zn-Mg-Cu alloy from the in-situ tensile experiment using Dream.3D [41]. DAMASK provides various models that can be used for crystal plasticity simulation, in this work, the classical phenomenological model proposed by Hutchinson [42] was employed to describe the constitutive response of the material. To facilitate the understanding of the subsequently presented material parameters, a brief summary of the model is provided here.
使用快速傅里叶变换求解器（CPFFT）在 DAMASK（杜塞尔多夫先进材料模拟套件）[40]上进行了晶体塑性模拟。晶体塑性计算的代表性体积元素（RVE）模型是通过使用 Dream.3D [41]处理 Al-Zn-Mg-Cu 合金的原位拉伸实验的初始 EBSD 数据构建的。DAMASK 提供了多种可用于晶体塑性模拟的模型，在本工作中，采用了 Hutchinson [42]提出的经典现象学模型来描述材料的本构响应。为了便于理解随后呈现的材料参数，在此简要总结了该模型。

Without considering damage, the deformation gradient F can be decomposed into two parts, namely the elastic deformation gradient

F_{e}

and the plastic deformation gradient

F_{p}

:
不考虑损伤，变形梯度 F 可以分解为两部分，即弹性变形梯度

F_{e}

和塑性变形梯度

F_{p}

：(1)

F = F_{e} F_{p} .

In the elastic portion, the generalized Hooke's law is employed, the second Piola-Kirchhoff stress (S) described in terms of Green-Lagrange strain (E) and the elastic stiffness matrix

C

.
在弹性部分，采用广义胡克定律，用格林-拉格朗日应变 E 描述第二皮奥拉-基尔霍夫应力（S）和弹性刚度矩阵

C

。(2)

{\begin{array}{c} E = \frac{1}{2} ({F^{e}}^{T} F^{e} - I) \\ S = \det F^{e} {F^{e}}^{- 1} σ {F^{e}}^{- T} = C : E \end{array},

in which

σ

represents the Cauchy stress, and for materials with an FCC crystal structure, the elastic stiffness matrix comprises three independent components, namely C₁₁, C₁₂, and C₄₄. For a specific slip system

α (α = 1, \dots, N_{s})

, the slip resistance evolves from an initial value

τ_{0}

. The expression for the shear rate

{\dot{γ}}^{α}

is dependent on the critical resolved shear stress

τ_{c}^{α}

and the resolved shear stress

τ^{α}

associated with the slip system, with
其中

σ

表示柯西应力，对于具有 FCC 晶体结构的材料，弹性刚度矩阵包含三个独立分量，即 C ₁₁ 、C ₁₂ 和 C ₄₄ 。对于特定的滑移系统

α (α = 1, \dots, N_{s})

，滑移阻力从初始值

τ_{0}

演变。剪切速率

{\dot{γ}}^{α}

的表达式取决于临界 resolved shear stress

τ_{c}^{α}

和与滑移系统相关的 resolved shear stress

τ^{α}

，(3)

{\dot{γ}}^{α} = f (τ^{α}, τ_{c}^{α}) = {\dot{γ}}_{0} {| \frac{τ^{α}}{τ_{c}^{α}} |}^{\frac{1}{m}} s g n (τ^{α}),

with

{\dot{γ}}_{0}

and m representing the reference shear and the rate sensitivity constant, respectively. The resolved shear stress of slip system

α

is calculated using the following expression

{\dot{γ}}_{0}

和 m 分别代表参考剪切应力和速率敏感性常数。滑移系统

α

的解析剪切应力通过以下公式计算(4)

τ_{α} = 0.5 C [F_{e}^{T} F_{e} - I] : m^{α} \otimes n^{α},

and

m^{α}

n^{α}

are the unit vector of slip direction and normal to slip plane of slip system

α

, respectively. The hardening behavior between the slip systems is described as

m^{α}

和

n^{α}

分别是滑移系统

α

的滑移方向和滑移平面的单位向量。滑移系统之间的硬化行为描述为(5)

{\dot{τ}}_{c}^{α} = \sum_{β = 1}^{N_{s}} q_{α β} {| {\dot{γ}}^{β} | h_{0} | 1 - \frac{τ^{β}}{τ_{\infty}} |}^{a} s g n (1 - \frac{τ^{β}}{τ_{\infty}}),

where

τ_{\infty}

serves as a boundary value to restrict the infinite growth evolution of the critical shear stress for slip systems due to hardening behavior;

h_{0}

represents the reference hardening coefficient, and a is the hardening exponent, generally lacking explicit physical significance, but capable of influencing the curve's trend in hardening evolution (typically,

a > 1

). When the slip systems are coplanar, the potential hardening coefficient

q_{α β}

= 1, whereas for non-coplanar situations,

q_{α β}

= 1.4.
其中

τ_{\infty}

作为边界值，用于限制由于硬化行为导致滑移系统的临界剪切应力的无限增长演化；

h_{0}

代表参考硬化系数，a 是硬化指数，通常缺乏明确的物理意义，但能够影响硬化演化曲线的趋势（通常，

a > 1

）。当滑移系统共面时，潜在硬化系数

q_{α β}

= 1，而非共面情况下，

q_{α β}

= 1.4。

3. Results 3. 结果

3.1. Microstructure of the raw material
3.1. 原材料微观结构

The microstructural characteristics of the raw material (denoted as I0) are illustrated in Fig. 3. It can be observed that, after a solution treatment at 475 °C for 2 h, the Al-Zn-Mg-Cu alloy retains some intergranular compounds (Fig. 3(a)). Within the characterization region, 88 grains were identified, as depicted in Fig. 3(b), with each grain labeled with a unique number. The information extracted from the IPF map in Fig. 3(b) and the misorientation angle distribution in Fig. 3(c) reveal that the alloy exhibits predominantly high-angle grain boundaries (HAGB), while a small fraction of low-angle grain boundaries (LAGB) with angles below 10° still remains.
原材料（记为 I0）的微观结构特征如图 3 所示。可以看出，经过 475 °C 下 2 小时固溶处理后，Al-Zn-Mg-Cu 合金仍保留一些沿晶化合物（图 3(a)）。在表征区域内，识别出 88 个晶粒，如图 3(b)所示，每个晶粒都标有唯一编号。从图 3(b)的 IPF 图和图 3(c)的取向差角分布中提取的信息表明，该合金主要呈现高角度晶界（HAGB），同时仍残留少量角度低于 10°的低角度晶界（LAGB）。

Additionally, the pole figure distribution is shown in Fig. 3(d), where the center of the pole figure represents the tensile direction, which will be adopted as the standard for the subsequent analysis. Several points on the pole figure exhibit localized orientation concentration, which is attributed to a few significantly larger grains introduced after the solution treatment enhancing the intensity of the multiples of uniform density (mud). However, it can still be observed that the initial material exhibits a relatively random orientation overall.
此外，图 3(d)显示了极图分布，其中极图的中心代表拉伸方向，这将作为后续分析的基准。极图上的几个点表现出局部取向集中，这归因于固溶处理后引入的几个显著更大的晶粒增强了均匀密度倍数（mud）的强度。然而，仍然可以看出初始材料整体上表现出相对随机的取向。

3.2. Mechanical property 3.2. 力学性能

Fig. 4 illustrates the comprehensive tensile curve from an in-situ tensile module, interrupted in-situ tensile curve, and the validation experimental curve from the Zwick-Z250. It can be observed that the yield strength and peak strength values, measured on the in-situ tensile testing platform and the Zwick-Z250 testing machine, are remarkably similar, indicating a reliability of the force data obtained in the in-situ tensile platform. However, a comparison of the data obtained from the in-situ tensile platform and the Zwick-Z250 testing machine reveals that the curve obtained by the in-situ platform exhibits a significantly lower elastic modulus, this discrepancy is evident from the difference in the elastic stage of the curves indicated by the black arrow in Subplot of Fig. 4. The slope of the in-situ curve in the elastic stage is noticeably lower than the slope of the curve obtained in the reference experiment with the Zwick-Z250 testing machine. Even when tested simultaneously on the Zwick-Z250 testing machine, the curve obtained from the in-situ sample exhibits a relatively lower elastic modulus in the elastic stage; however, this difference is noticeably smaller compared to the disparity between the in-situ testing platform and the Zwick-Z250.
图 4 展示了原位拉伸模块的全面拉伸曲线、中断原位拉伸曲线以及来自 Zwick-Z250 的验证实验曲线。可以看出，在原位拉伸测试平台和 Zwick-Z250 测试机上测得的屈服强度和峰值强度值非常相似，这表明原位拉伸平台获得的力数据具有可靠性。然而，将原位拉伸平台和 Zwick-Z250 测试机获得的数据进行比较后发现，原位平台得到的曲线表现出明显较低的弹性模量，这一差异从图 4 子图中的黑色箭头指示的弹性阶段曲线差异中可以看出。原位曲线在弹性阶段的斜率明显低于 Zwick-Z250 测试机进行的参考实验中得到的曲线斜率。即使在 Zwick-Z250 试验机上同时进行测试，原位样品获得的曲线在弹性阶段表现出相对较低的弹性模量；然而，与原位测试平台和 Zwick-Z250 之间的差异相比，这种差异明显更小。

The primary reasons for differences in the elastic stage between the curves are attributed to the disparities in stiffness and measurement methods between the in-situ testing platform and conventional mechanical testing machines. The overall displacement measured by the in-situ testing platform encompasses both the sample displacement and tensile platform deformation. Consequently, this leads to a decrease in the slope of the curve during the elastic stage (F/D, where F represents measured force, and D denotes measured displacement). Additionally, comparing the two sets of contrast experiments on the Zwick-Z250, it was observed that the specially designed in-situ tensile specimens may compromise the stiffness of the testing system to some extent. To correct the elastic phase differences, caused by the stiffness of the in-situ testing platform and measurement, the data of the in-situ tensile platform was processed using the correction scheme provided in Ref. [43]. The corrected results are shown by the red curve in sub-Fig. 4, where it can be observed that the corrected data closely matches the strain-stress characteristics of the Al-Zn-Mg-Cu alloy.
曲线在弹性阶段的差异主要归因于原位测试平台与传统机械测试机之间刚度和测量方法的差异。原位测试平台测量的总位移包括样品位移和拉伸平台变形。因此，这导致弹性阶段曲线的斜率（F/D，其中 F 表示测量力，D 表示测量位移）下降。此外，通过比较 Zwick-Z250 上的两组对比实验，观察到专门设计的原位拉伸样品在一定程度上可能降低测试系统的刚度。为修正由原位测试平台刚度和测量引起的弹性阶段差异，使用 Ref. [43]中提供的修正方案对原位拉伸平台的数据进行处理。修正结果由子图 4 中的红色曲线显示，可以看出修正数据与 Al-Zn-Mg-Cu 合金的应变-应力特性紧密匹配。

3.3. Microstructure evolution
3.3. 组织演变

These four interrupted tensile test are denoted as I1, I2, I3, and I4, and the corresponding strains, after data correction, as described in Section 3.2, are 1 %, 4 %, 10 %, and 18 % respectively, as shown in Fig. 4. Fig. 5 displays the surface morphology, IPF maps, and misorientation information of the Al-Zn-Mg-Cu alloy after each interruptions. From Fig. 4, it can be observed that the material exhibits a stress amplitude of approximately 150 MPa after a 1 % deformation, at this stage, the SEM image in Fig. 5 reveals no significant changes in the surface morphology, the IPF maps and misorientation distribution are nearly identical to the initial microstructure I0. Analysis of results of the geometrically necessary dislocations (GND) density [44], displayed in Fig. 6, reveals a minor increase in dislocation density with a value of 7.05 × 10¹²/m² during this stage. This suggests that the dislocations are in the early stage of nucleation and have not yet caused substantial changes in the microstructure. At a deformation level of 4 %, the SEM images reveal the appearance of surface wrinkles on the sample, as indicated by the red arrows in Fig. 5; this type of wrinkling is caused by the inhomogeneous local plastic deformation, and it can be observed that this phenomenon becomes more pronounced as the deformation level increases. At I2 stage, there is a rapid increase in the low-angle misorientation, and the IPF map shows the emergence of gray lines representing LAGBs. Meanwhile, the dislocation density experiences a significant increase, reaching 13.5 × 10¹²/m², nearly double that of the previous stage. As the specimen continues to deform, the surface wrinkles intensify, as illustrated in Fig. 5(g)(j), resulting in a notable elongation of the region of interest (ROI) as evidenced by the size variation in the IPF maps, Fig. 5(h)(k). The misorientation data indicates that upon reaching 10 % deformation, there is a predominance of LAGBs, the dislocation density increased sharply to 32.8 × 10¹²/m² and 44.8 × 10¹²/m² after stages I3 and I4, respectively. Notably, Fig. 5(j) illustrates that the deformation during the I4 stage results in severe surface wrinkling of the sample, which may introduce some degree of distortion in the GND calculations at this stage. However, it is foreseeable that increased deformation will promote a corresponding rise in dislocation density. Therefore, the dislocation density evolution presented for this stage in Fig. 6 remains of reference value. Furthermore, in the corresponding IPF maps, a discernible color gradients are indicative of the breakdown of the uniform orientation within grain, this phenomenon commonly suggests the initiation of crystal rotation, attributed to the activation and movement of dislocations.
这四个中断拉伸试验分别标记为 I1、I2、I3 和 I4，经过数据校正后的相应应变，如第 3.2 节所述，分别为 1%、4%、10%和 18%，如图 4 所示。图 5 显示了 Al-Zn-Mg-Cu 合金在每次中断后的表面形貌、IPF 图和取向差信息。从图 4 可以看出，材料在 1%变形后表现出约 150 MPa 的应力幅值，在此阶段，图 5 中的 SEM 图像显示表面形貌没有明显变化，IPF 图和取向差分布与初始微观结构 I0 几乎相同。对几何必要位错（GND）密度的结果分析[44]，如图 6 所示，表明在此阶段位错密度略有增加，值为 7.05 × 10^8 /m^2。这表明位错处于成核的早期阶段，尚未引起微观结构的显著变化。在 4%的变形水平下，SEM 图像显示样品表面出现了皱纹，如图中红色箭头所示。 5; 这种褶皱是由不均匀的局部塑性变形引起的，并且可以观察到这种现象随着变形程度的增加而变得更加明显。在 I2 阶段，低角度取向差迅速增加，IPF 图显示出代表亚晶界的灰色线条的出现。同时，位错密度显著增加，达到 13.5 × 10 ¹² /m ² ，几乎是前一阶段的近两倍。随着试样继续变形，表面褶皱加剧，如图 5(g)(j)所示，导致感兴趣区域(ROI)显著拉长，如 IPF 图的大小变化所示，图 5(h)(k)。取向差数据显示，在达到 10%变形时，LAGB 占主导地位，在 I3 和 I4 阶段后，位错密度分别急剧增加到 32.8 × 10 ¹² /m ² 和 44.8 × 10 ¹² /m ² 。值得注意的是，图 5(j)表明 I4 阶段的变形导致试样表面严重褶皱，这可能会在这一阶段 GND 计算中引入一定程度上的畸变。然而，可以预见的是，增加变形将促进位错密度的相应上升。因此，图 6 中展示的该阶段位错密度演变仍然具有参考价值。此外，在相应的 IPF 图中，明显的颜色梯度表明晶粒内均匀取向的破坏，这种现象通常表明晶体旋转的起始，归因于位错的激活和运动。

3.4. Slip system activation and plasticity transfer
3.4. 滑移系激活和塑性转移

As mentioned above, after 4 % deformation, surface wrinkles attributable to plastic inhomogeneity, become noticeable on the sample surface, and as the deformation progresses, the amplitude of the folds increases. Fig. 7 presents a local magnified SEM image of the EBSD observation area, at 4 % deformation (Fig. 7(a)), the presence of slip traces on the sample surface becomes evident, predominantly distributed within the grain and extending to the grain boundaries at this stage. When the deformation reaches 10 % (Fig. 7(b)), the slip traces continue to increase and the surface fluctuations between adjacent grains are obvious, the grains are significantly elongated, and microcracks begin to appear at some grain boundaries where intergranular compounds exist. These microcracks are caused by the rupture of intergranular compounds and will expand with the deformation. As shown in Fig. 8, EDS analysis shows that the main components of these intergranular compounds are Cu and Fe elements; from the elemental composition, it can be inferred that these intergranular compounds should be the ferric-rich phase (Al₇Cu₂Fe) commonly found in Al-Zn-Mg-Cu alloys [45].
如上所述，在 4%变形后，由于塑性不均匀性引起的表面褶皱在样品表面变得明显，随着变形的进行，褶皱的振幅增加。图 7 展示了 EBSD 观测区域的局部放大 SEM 图像，在 4%变形时（图 7(a)），样品表面的滑移痕迹变得明显，主要分布在晶粒内，并延伸至晶界。当变形达到 10%（图 7(b)）时，滑移痕迹继续增加，相邻晶粒之间的表面波动明显，晶粒显著拉长，在存在晶间化合物的晶界处开始出现微裂纹。这些微裂纹是由晶间化合物的断裂引起的，并将随着变形的进行而扩展。如图 8 所示，EDS 分析表明，这些晶间化合物的主体成分是 Cu 和 Fe 元素；从元素成分可以推断，这些晶间化合物应该是铝锌镁铜合金中常见的富铁相（Al ₇ Cu ₂ Fe）[45]。

The experimental results show that material exhibits significant plasticity transfer and intergranular plastic inhomogeneity. Some of the slip trajectories clearly cross the grain boundaries, as evidenced by the green dotted line depicted in Fig. 7(c), and the grain boundary fluctuations between these grains are relatively marginal, indicating a more homogeneous plastic deformation in these areas. Additionally, the example grain boundary marked by the yellow solid line in the figure exhibits grain boundary protrusions, and the slip lines are impeded at the grain boundaries, without any observed plasticity transfer phenomena, In addition to the intergranular plasticity inhomogeneity, experimental results also reveal the occurrence of intragranular plastic heterogeneity in certain grains, as it is illustrated in Fig. 7(b), grains 52 and 37 (refer to Fig. 3(b) for grain numbering) exhibit slip line trajectories on the half-side of the grains.
实验结果表明，材料表现出显著的塑性转移和晶间塑性不均匀性。部分滑移轨迹明显跨越了晶界，如图 7(c)中绿色虚线所示，这些晶粒之间的晶界波动相对较小，表明这些区域的塑性变形更加均匀。此外，图中用黄色实线标记的示例晶界存在晶界凸起，滑移线在晶界处受阻，未观察到任何塑性转移现象。除了晶间塑性不均匀性，实验结果还揭示了某些晶粒中存在晶内塑性不均匀性，如图 7(b)所示，晶粒 52 和 37（晶粒编号参见图 3(b)）在晶粒的半侧表现出滑移线轨迹。

3.4.1. Slip system activation
3.4.1. 滑移系激活

At room temperature, plastic deformation in Al alloy primarily relies on the activation and motion of dislocations. The aforementioned experimental findings indicate that when dislocations reach grain boundaries, phenomena such as transmit across the boundaries or obstruction occur. In the deformed Al-Zn-Mg-Cu alloy, simultaneous occurrences of these plasticity phenomena demonstrates a direct correlation with the heterogeneity of plastic deformation.
在室温下，铝合金的塑性变形主要依赖于位错的激活和运动。上述实验结果表明，当位错到达晶界时，会发生穿过晶界或受阻等现象。在变形的 Al-Zn-Mg-Cu 合金中，这些塑性现象的同时发生与塑性变形的异质性直接相关。

To investigate the activation of slip systems in different grains within the deformation region, slip trace analysis was conducted based on EBSD and SEM results. As an FCC material, taking into account its crystal symmetry, aluminum alloy possesses a total of 12 slip systems. The identification and numbering of these 12 slip systems considered in this work are detailed in Table 1.
为了研究变形区域内不同晶粒中滑移系统的激活情况，基于 EBSD 和 SEM 结果进行了滑移迹线分析。作为一种面心立方材料，考虑到其晶体对称性，铝合金共有 12 个滑移系统。本研究中考虑的这 12 个滑移系统的识别和编号详细见表 1。

Table 1. The slip systems considered in this research and the numbers.
表 1. 本研究考虑的滑移系统及其编号。

No. 编号	1	2	3	4	5	6
Slip system 滑移系统	(111)[01 $\overline{1}$ ]	(111)[ $\overline{1}$ 01]	(111)[1 $\overline{1}$ 0]	( $\overline{1} \overline{1}$ 1)[0 $\overline{1} \overline{1}$ ]	( $\overline{1} \overline{1}$ 1)[101]	( $\overline{1} \overline{1}$ 1)[ $\overline{1}$ 10]
No. 编号	7	8	9	10	11	12
Slip system 滑移系统	(1 $\overline{1} \overline{1}$ )[0 $\overline{1}$ 1]	(1 $\overline{1} \overline{1}$ )[ $\overline{1}$ 0 $\overline{1}$ ]	(1 $\overline{1} \overline{1}$ )[110]	( $\overline{1}$ 1 $\overline{1}$ )[011]	( $\overline{1}$ 1 $\overline{1}$ )[10 $\overline{1}$ ]	( $\overline{1}$ 1 $\overline{1}$ )[ $\overline{1} \overline{1}$ 0]

Fig. 9 illustrates the slip trace analysis results for several example grains (Grain No: 35, 42, 43, 49, 50, 52, 54, 56, 61, 64). For the FCC materials, 12 slip systems are distributed on four densely packed slip planes, with each slip plane corresponding to three slip directions. The identification of slip planes is determined by examining the slip trace on the sample surface, and it is considered that among the identified three coplanar slip systems, the one with the maximum Schmid factor is activated [29,33,37,46]. As shown in Fig. 9(a), at a 4 % deformation, slip traces are observed in five grains, and as the deformation progresses to 10 %, all ten grains exhibit distinct slip traces, with five of them showing multiple sets of slip systems. The information regarding the activated slip systems identified through the slip trace analysis is consolidated in Table 2.
图 9 展示了几个示例晶粒（晶粒编号：35、42、43、49、50、52、54、56、61、64）的滑移迹线分析结果。对于面心立方（FCC）材料，12 个滑移系统分布在四个紧密堆积的滑移面上，每个滑移面对应三个滑移方向。滑移面的识别是通过检查样品表面的滑移迹线来确定的，并且认为在识别出的三个共面滑移系统中，Schmid 因子最大的那个被激活[29,33,37,46]。如图 9(a)所示，在 4%变形时观察到五个晶粒中有滑移迹线，随着变形增加到 10%，所有十个晶粒都表现出明显的滑移迹线，其中五个晶粒显示出多个滑移系统的组合。通过滑移迹线分析识别出的激活滑移系统的信息汇总在表 2 中。

Table 2. Analysis results of the activated slip systems and the corresponding Schmid factor.
表 2. 激活滑移系统的分析结果及对应的 Schmid 因子。

Grain ID 晶粒 ID Euler angle 欧拉角	1st slip system 第一滑移系统 SF and Rank SF 和 Rank	2ed slip system 2ed 滑移系统 SF and Rank SF 和 Rank
35 (334.8, 144.2, 250.2)	S12 −0.4829 and 1 −0.4829 和 1	S6 −0.4793 and 2 -0.4793 和 2
35 (334.8, 144.2, 250.2)	S12 −0.4829 and 1 −0.4829 和 1	S7 0.3488 and 5 0.3488 和 5
42 (351, 154.2, 257.3)	S7 0.4366 and 1 0.4366 和 1	S6 −0.4311 and 3 -0.4311 和 3
43 (134.6, 140.5, 215.2)	S6 −0.4760 and 1 -0.4760 和 1	None
49 (343.8, 146.2, 242.3)	S7 0.4746 and 1 0.4746 和 1	S10 −0.4440 and 2 −0.4440 和 2
49 (343.8, 146.2, 242.3)	S7 0.4746 and 1 0.4746 和 1	S6 −0.4267 and 3 −0.4267 和 3
50 (337.1, 149.4, 236.4)	S7 0.4627 and 1 0.4627 和 1	S6 −0.4445and 2 −0.4445 和 2
52 (314.7, 143.2, 233.9)	S12 −0.4975 and 1 −0.4975 和 1	S6 −0.4817 and 2 −0.4817 和 2
54 (39.5, 143.3, 180.7)	S2 −0.4245 and 1 −0.4245 和 1	None 无
56 (74.6, 148.2, 239.7)	S9 −0.4879 and 1 −0.4879 和 1	None 无
61 (72.4, 141.9, 226.9)	S9 −0.4483 and 1 -0.4483 和 1	None 无
64 (60.4, 139.2, 206.7)	S9 −0.4230 and 1 -0.4230 和 1	None 无

The Schmid factor information for the activated slip systems reveals that the grains exhibiting conspicuous slip traces are initiated by the slip systems with the highest absolute Schmid factor values among the 12 slip systems. Negative values of the Schmid factor indicate that the slip occurs in the opposite direction to the defined one. Analyzing the evolution of slip trajectories for individual grains in Fig. 9, it is evident that the distribution of slip traces occurs within the grains, and as deformation progresses, pre-existing slip traces deepen and extend towards grain boundaries. This phenomenon suggests that the initially activated slip systems are not influenced by the stress state at the interfaces, the characteristics of a uniform crystal orientation after solid solution plays a crucial role in determining the absence of pronounced localized stress concentration within the grains during the initial deformation stages. The slip system with the maximum Schmid factor exhibits the highest effective resolved shear stress, making it reasonable for it to be activated first, so in this scenario, the activation of slip in the slip system is primarily influenced by the applied load. As deformation progresses, the slip traces extend to the grain boundaries. Due to the differences in dislocation motion between the adjacent grains, the grains begin to exhibit pronounced twisting. At this stage, some grains activate two or even three slip systems simultaneously, with the following activated activating slip systems typically having the second or third highest absolute Schmid factors. Analysis results reveal that grains activating the second slip system have an absolute difference in values between the first and second highest Schmid factors that does not exceed 10 %. The largest difference is observed in grain 49, with a difference of 6.49 %. The second highest Schmid factors (non-coplanar slip systems) for the grains 43, 54, 56, 61, and 64, which have not activated the second slip system, are as follows: 0.3810 (S12), −0.3431 (S9), 0.4113 (S6), 0.3077 (S6), and 0.2848 (S2), respectively. Additionally, these grains exhibit differences between their first and second Schmid factors of 19.96 %, 19.18 %, 15.70 %, 31.36 %, and 32.67 %, respectively. These data demonstrate that Schmid factors also serve as indicators for the activation of the subsequent slip system, specifically, the second slip system that activates tends to have Schmid factors that are numerically close to those of the first activated slip system.
Schmid 因子信息显示，表现出明显滑移痕迹的晶粒是由 12 个滑移系统中绝对 Schmid 因子值最高的滑移系统启动的。Schmid 因子为负值表明滑移发生在定义方向的反方向。通过分析图 9 中单个晶粒的滑移轨迹演变，可以明显看出滑移痕迹分布在晶粒内部，随着变形的进行，已有的滑移痕迹加深并向晶界扩展。这种现象表明，最初激活的滑移系统不受界面处应力状态的影响，固溶处理后的均匀晶体取向特性在决定初始变形阶段晶粒内没有出现明显的局部应力集中方面起着关键作用。具有最大 Schmid 因子的滑移系统表现出最高的有效 resolved shear stress，因此它首先被激活是合理的，所以在这种情况下，滑移系统的激活主要受施加载荷的影响。随着变形的进行，滑移迹线延伸到晶界。由于相邻晶粒之间位错运动的差异，晶粒开始表现出明显的扭曲。在这个阶段，一些晶粒同时激活两个甚至三个滑移系统，随后激活的滑移系统通常具有第二高或第三高的绝对 Schmid 因子。分析结果表明，激活第二滑移系统的晶粒，其第一和第二最高 Schmid 因子之间的绝对值差不超过 10%。最大差异出现在晶粒 49，差异为 6.49%。未激活第二滑移系统的晶粒 43、54、56、61 和 64 的第二最高 Schmid 因子（非共面滑移系统）分别为：0.3810（S12）、-0.3431（S9）、0.4113（S6）、0.3077（S6）和 0.2848（S2）。此外，这些晶粒在它们的第一和第二 Schmid 因子之间存在 19.96%、19.18%、15.70%、31.36%和 32.67%的差异。这些数据表明 Schmid 因子也作为后续滑移系统激活的指标，具体来说，激活的第二滑移系统往往具有与首次激活的滑移系统数值相近的 Schmid 因子。

The Schmid factor can indicate the magnitude of effective resolved shear stress for a specific slip system under a given load, so the slip system with the highest Schmid factor tends to be more efficiently activated. The activation of slip systems induces crystal rotation, thereby coordinating plastic deformation. From the deformed grain morphologies shown in Fig. 9(c), it can be observed that grains that activate a single slip system exhibit a single trend in their crystal shape changes. For example, grain 54 demonstrates a complete inversion and tilt of the surface and grains 56, 61, and 64 twist along the direction of slip lines, while grains that activate multiple slip systems experience more complex internal surface distortion with wrinkles, and there are differences in morphology between adjacent grains. Examples of such grains include 35, 42, 49, and 50, where the central region of the grain collapses while the grain boundaries area protrude.
施密特因子可以表示在给定载荷下特定滑移系统所具有的有效分解切应力的大小，因此具有最高施密特因子的滑移系统往往更容易被有效激活。滑移系统的激活会导致晶体旋转，从而协调塑性变形。从图 9(c)所示变形晶粒形貌可以观察到，激活单一滑移系统的晶粒在晶体形状变化上表现出单一趋势。例如，晶粒 54 表现出表面完全反转和倾斜，而晶粒 56、61 和 64 沿滑移线方向扭曲，而激活多个滑移系统的晶粒则经历更复杂的内部表面畸变，出现褶皱，且相邻晶粒之间存在形貌差异。这类晶粒的例子包括 35、42、49 和 50，其中晶粒中心区域坍塌，而晶粒边界区域突出。

3.4.2. Plasticity transfer between adjacent grains
3.4.2. 相邻晶粒间的塑性转移

The in-situ SEM characterization and analysis results show that the slip systems with the highest Schmid factor are the first to activate within the grain. As the deformation progresses, although the multiple slip systems may be activated within individual grains, almost all the slip traces extend to the grain boundaries, and it is observed that the trajectories either pass through or are interrupted at the grain boundaries. The plastic behavior between grains on either side of the grain boundary leads to appearance of relatively flat areas or local wrinkles on the material surface after deformation.
原位 SEM 表征和分析结果表明，具有最高 Schmid 因子的滑移系统首先在晶粒内被激活。随着变形的进行，尽管单个晶粒内可能被激活多个滑移系统，但几乎所有滑移迹线都延伸至晶界，观察到轨迹要么穿过晶界，要么在晶界处中断。晶界两侧晶粒间的塑性行为导致变形后材料表面出现相对平坦的区域或局部褶皱。

Luster and Morris proposed the geometric compatibility factor

m^{'}

, which is commonly employed for the assessment of plasticity transfer ability between the grains [47]. The schematic diagram in Fig. 10(a) provides a visual representation of the parameters involved in evaluation of

m^{'}

, highlighting the crucial role played by the orientation and alignment of slip systems in the plasticity transfer phenomenon:
卢斯特和莫里斯提出了几何兼容性因子

m^{'}

，该因子通常用于评估晶粒间的塑性传递能力[47]。图 10(a)中的示意图直观地展示了评估

m^{'}

所涉及的参数，突出了滑移系统方向和排列在塑性传递现象中的关键作用：(6)

m^{`} = ({\vec{n}}_{i n} ∙ {\vec{n}}_{o u t}) ({\vec{d}}_{i n} ∙ {\vec{d}}_{o u t}) = \cos (Ψ) \cos (κ) .

For the 10 selected grains in Fig. 10, Fig. 16 grain boundaries were numbered based on SEM scan results. A calculation of the

m^{'}

between the activated slip systems on both sides of each grain boundary was conducted. The results have been compiled and integrated into Table 3.
对于图 10 中选定的 10 个晶粒，根据 SEM 扫描结果对晶界进行了编号。对每个晶界两侧的激活滑移系统之间的

m^{'}

进行了计算。结果已汇总并整合到表 3 中。

Table 3. Plasticity transfer conditions and $m^{'}$ for grain boundaries in Fig. 10.
表 3. 图 10 中晶界的塑性传递条件和 $m^{'}$ 。

GB ID	Transfer or not 转移或不转移	Pair and m' 成对和 m'	GB ID	Transfer or not 转移或不转移	Pair and m' 成对和 m'
1 (35/42)	Yes 是	S6-S6:0.9606 S7-S7:0.9571	9 (50/56)	No 否	S7-S9:0.0549 S6-S9:0.7780
2 (42/43)	No 否	S7-S6:0.1161	10 (50/54)	No 否	S7-S2:0.1128 S6-S2:0.3241
3 (42/50)	Yes 是	S6-S6:0.9760 S7-S7:0.9782	11 (64/61)	Yes 是	S9-S9:0.9629
4 (42/49)	Yes 是	S7-S7:0.9782	12 (61/56)	Yes 是	S9-S9:0.9710
5 (49/50)	Yes 是	S7-S7:0.9951 S6-S6:0.9956	13 (56/52)	No 否	S9-S12:0.0008 S9-S6:0.7909
6 (49/52)	No 否	S7-S12:0.2733	14 (61/54)	No 否	S9-S2:0.0310
7 (49/56)	No 否	S7-S9:0.0453 S10-S9:0.0348 S6-S9:0.8096	15 (56/54)	No 否	S9-S2:0.0528
8 (50/43)	No 否	S7-S6:0.1062	16 (54/43)	No 否	S2-S6:0.2960

Based on Fig. 10, it is evident that among the 16 grain boundaries, a total of 6 grain boundaries sequentially exhibit noticeable occurrences of plasticity transfer phenomena. Specifically, the slip trace initiated in grain 42 passes through grain boundaries 3 and 4, connecting with the slip traces initiated in grains 49 and 50. The analysis of slip traces in Fig. 9 reveals that these slip traces correspond to the S7 slip system, which is the first to be activated in grains 42, 49, and 50. According to the analysis results in Table 3, the geometric compatibility factors corresponding to these grain boundaries are determined to be 0.9782 and 0.9760. The values of

m^{'}

range between 0 and 1, and a larger

m^{'}

indicates a higher degree of alignment between the slip planes and slip directions of the grains on either side of the grain boundary. Consequently, plasticity dominated by the corresponding slip system is more likely to be effectively transmitted at the interface. Similarly, a parallel occurrence is observed at grain boundaries 1, 5, 11, and 12. The slip systems, activated first with the high Schmid factor, exhibit significant high

m^{'}

values on both sides as they extend to the grain boundaries. In this study, all these values surpass 0.95.
根据图 10 可知，在 16 条晶界中，共有 6 条晶界依次表现出明显的塑性转移现象。具体来说，晶粒 42 中的滑移迹线通过晶界 3 和 4，连接到晶粒 49 和 50 中起始的滑移迹线。图 9 中滑移迹线的分析表明，这些滑移迹线对应于 S7 滑移系统，该滑移系统是晶粒 42、49 和 50 中首先被激活的。根据表 3 的分析结果，这些晶界的几何兼容性因子被确定为 0.9782 和 0.9760。

m^{'}

的值介于 0 和 1 之间，

m^{'}

值越大表示晶界两侧晶粒的滑移面和滑移方向越一致。因此，由相应滑移系统主导的塑性在界面处更可能被有效传递。类似地，晶界 1、5、11 和 12 也观察到平行发生的情况。首先被激活的滑移系统，在扩展到晶界时，两侧都表现出显著的高

m^{'}

值。在本研究中，所有这些值都超过 0.95。

Additionally, as depicted in Fig. 9(b)(c) and Fig. 10(b)(c), at grain boundaries 1 and 5, the subsequent activated slip system S6 also exhibits plasticity transfer phenomena as they extend to the respective grain boundaries. The computational results in Table 3 indicate that these pairs of slip systems at the corresponding grain boundaries also display higher

m^{'}

. And the grain boundaries where plasticity transfer occurs do not show noticeable protrusions caused by plastic heterogeneity, indicating that the occurrence of plasticity transfer can harmonize the plastic deformation of grains on both sides of the grain boundary.
此外，如图 9(b)(c)和图 10(b)(c)所示，在晶界 1 和晶界 5 处，随后激活的滑移系统 S6 也表现出塑性转移现象，随着它们延伸至相应的晶界。表 3 的计算结果表明，在相应的晶界处，这些成对的滑移系统也显示出更高的

m^{'}

。发生塑性转移的晶界没有出现明显的由塑性不均匀性引起的凸起，这表明塑性转移的发生可以协调晶界两侧晶粒的塑性变形。

The analysis reveals that the grain boundaries exhibiting wrinkles tend to have the adjacent grains with relatively low

m^{'}

values for their respective slip systems. For instance, at grain boundary 10, as deduced from the slip trace analysis in Fig. 9, the activated slip system S2 in grain 54 discontinues its movement upon reaching grain boundary, and there is no evident transfer or exchange of slip trajectory lines with grain 50. With the ongoing deformation, a conspicuous protrusion emerges at grain boundary 10, based on the analysis of data from Tables 3, it is evident that the

m^{'}

for the activated slip system in grain 54 and the two slip systems (S7 and S6) activated in grain 50 are 0.1128 and 0.3241, respectively. The extremely low values of

m^{'}

indicate a poor alignment between the slip planes and directions of the activated slip systems on either side of the grain boundary. In this scenario, the grain boundary hinders the dislocation motion, leading to a lack of plastic coordination between the grains. This, in turn, results in protrusions and even folding phenomena near the boundary. Comparable occurrences manifest at grain boundaries 2, 6, 7, 8, 9, 14, 15, and 16, where the dominant slip systems on both sides of the grains exhibit remarkably low values of

m^{'}

. These grain boundaries, akin to the situation observed at boundary 10, not only undergo folding protrusions but accumulate slip lines intensely at these boundaries, as well. For example, at boundary 7, the slip system S7 in grain 49 and the slip system S9 in grain 56 accumulate significantly at this boundary, contributing to a substantial accumulation of slip lines, and this particular grain boundary exhibits pronounced depression relative to the surrounding areas.
分析表明，出现褶皱的晶界倾向于其相邻晶粒的各自滑移系统具有相对较低的

m^{'}

值。例如，在晶界 10 处，根据图 9 中的滑移迹线分析，晶粒 54 中激活的滑移系统 S2 在到达晶界时停止运动，并且没有明显的滑移轨迹线与晶粒 50 发生转移或交换。随着变形的进行，根据表 3 的数据分析，晶界 10 处出现明显的凸起，晶粒 54 中激活的滑移系统以及晶粒 50 中激活的两个滑移系统（S7 和 S6）的

m^{'}

分别为 0.1128 和 0.3241。

m^{'}

的极低值表明滑移面和晶界两侧激活滑移系统的方向之间缺乏良好的一致性。在这种情况下，晶界阻碍了位错运动，导致晶粒之间缺乏塑性协调，进而导致晶界附近出现凸起甚至折叠现象。在晶界 2、6、7、8、9、14、15 和 16 处出现类似的情形，这些晶界两侧的晶粒主导滑移系统显示出非常低的

m^{'}

值。这些晶界与观察到的晶界 10 的情况相似，不仅出现折叠突起，还在这些晶界处强烈积累滑移线。例如，在晶界 7 处，晶粒 49 中的滑移系统 S7 和晶粒 56 中的滑移系统 S9 在此晶界处显著积累，导致滑移线大量积累，并且这个特定的晶界相对于周围区域表现出明显的凹陷。

The analysis results in Table 3 also reveals that some slip pairs exhibit relatively high

m^{'}

, however, in situ SEM results indicate the absence of plasticity transfer behavior at the corresponding grain boundaries. For instance, at GB 13, the slip system S9 activated in grain 56 and the slip system S6 in grain 52 exhibit a relatively high

m^{'}

with a values of 0.7780, but when the slip system S9 in grain 56 reaches the boundary, no trace of slip system S6 in grain 52 near GB 13 is observed, see Figs. 9 (a-2) and (b-2) for an illustration. Additionally, the

m^{'}

values between the slip system S6 in grains 49 and 50 and the slip system S9 activated in grain 56 are 0.8096 and 0.7780, respectively. However, at both corresponding grain boundaries, there is no occurrence of plasticity transfer between the respective slip systems.
表 3 的分析结果还表明，某些滑移对表现出相对较高的

m^{'}

，然而原位 SEM 结果表明，在相应的晶界处没有塑性转移行为。例如，在晶界 13 处，晶粒 56 中的滑移系 S9 和晶粒 52 中的滑移系 S6 表现出相对较高的

m^{'}

，其值为 0.7780，但当晶粒 56 中的滑移系 S9 达到边界时，未观察到晶粒 52 中靠近晶界 13 的滑移系 S6 的痕迹，参见图 9 (a-2) 和 (b-2) 以说明。此外，晶粒 49 和 50 中的滑移系 S6 与晶粒 56 中激活的滑移系 S9 之间的

m^{'}

值分别为 0.8096 和 0.7780。然而，在相应的晶界处，这些滑移系之间没有发生塑性转移。

3.5. Crystal plasticity simulation results
3.5. 晶体塑性模拟结果

3.5.1. Modeling and parameter calibration
3.5.1. 建模与参数校准

The EBSD data of the initial microstructure was imported into Dream.3D (Version: 6.5.160) for processing and the corresponding IPF map is shown in Fig. 11(a). A comparison with the result obtained through MTEX, as depicted in Fig. 3(b), reveals that Dream.3D processing captures identical microstructure features. The resulting RVE model constructed is shown in Fig. 11(b), the model can accurately represent the initial microstructure characteristics.
初始微观结构的 EBSD 数据被导入 Dream.3D（版本：6.5.160）进行处理，相应的 IPF 图显示在图 11(a)中。与通过 MTEX 获得的结果（如图 3(b)所示）相比，Dream.3D 处理捕捉到了相同的微观结构特征。构建的 RVE 模型如图 11(b)所示，该模型可以准确地表示初始微观结构特征。

The calibrated material parameters used for crystal plasticity simulation of Al-Zn-Mg-Cu alloy have been consolidated in Table 4. The elastic parameters are based on the research results of Kamm et al. [48]. In the process of fitting material parameters, the curve characteristics of both general tensile specimens and specially designed in-situ samples were considered. The simulated strain-stress curves can capture the trend characteristics of both experimental curves, as illustrated in Fig. 11(c), the simulated curves in the plastic deformation stage align well with the mechanical response curve of the in-situ experiment. It can be reasonably considered that the parameters used in the simulation process of this study can capture the plastic response of the Al-Zn-Mg-Cu alloy, and the simulation results can provide a valuable complementary for the in-situ experimental analysis.
用于 Al-Zn-Mg-Cu 合金晶体塑性模拟的校准材料参数已汇总于表 4。弹性参数基于 Kamm 等人[48]的研究结果。在拟合材料参数的过程中，考虑了普通拉伸试样和专门设计的原位样品的曲线特征。模拟的应变-应力曲线能够捕捉实验曲线的趋势特征，如图 11(c)所示，塑性变形阶段的模拟曲线与原位实验的力学响应曲线吻合良好。可以合理地认为，本研究模拟过程中使用的参数能够捕捉 Al-Zn-Mg-Cu 合金的塑性响应，模拟结果可为原位实验分析提供有价值的补充。

Table 4. Calibrated material parameters used for crystal plasticity simulation of Al-Zn-Mg-Cu alloy.
表 4. 用于 Al-Zn-Mg-Cu 合金晶体塑性模拟的校准材料参数。

Parameter 参数	C₁₁	C₁₂	C₄₄	${\dot{γ}}_{0}$	h₀
Values 值	106.9 GPa	60.5 GPa	28.4 GPa	0.001	200 MPa
Parameters 参数	$τ_{0}$	$τ_{\infty}$	m	a
Values 值	60 MPa	250 MPa	20	2.25

3.5.2. Simulated strain and stress characteristics
3.5.2. 模拟的应变和应力特征

As displayed in Fig. 12, during the initial stages of deformation (1 %), strains manifest as a uniform distribution, which is similar with experimental results. When the deformation level reaches 4 %, disparities in the strain distribution become evident which aligns with the microstructure characteristics captured in the in-situ experiment results of Section 3.3, and in comparison to strain variations between grains, the evolution of strain in Fig. 12 indicates minimal differences within individual grains. Strain concentration initiates primarily at the triple junctions (as denoted by the yellow circle in Fig. 12(c)), and with ongoing deformation, the influence of strain concentration at grain boundaries extends into the grain interior. This suggests that the microscale strain distribution within grains is not only influenced by their own orientation but by the neighboring grains as well. Following a trend similar to the exhibited experimental results, the strain concentration features along grain boundaries become more conspicuous with increasing deformation, demonstrating the effective capturing of intergranular plastic strain heterogeneity of the crystal plasticity simulation.
如图 12 所示，在变形的初始阶段（1%），应变表现为均匀分布，这与实验结果相似。当变形程度达到 4%时，应变分布的差异变得明显，这与第 3.3 节原位实验结果中观察到的微观结构特征一致。与晶粒间的应变变化相比，图 12 中的应变演化表明单个晶粒内部的差异很小。应变集中主要始于三重结点（如图 12(c)中黄色圆圈所示），随着变形的持续，晶界处的应变集中影响扩展到晶粒内部。这表明晶粒内部的微观尺度应变分布不仅受其自身取向的影响，还受邻近晶粒的影响。沿着晶界的应变集中特征随着变形的增加而变得更加明显，这表明晶体塑性模拟有效地捕捉了晶间塑性应变异质性。

In addition, during the initial stages of deformation, stress is also uniformly distributed, as illustrated in Fig. 13(a). At a deformation of 1 %, the average equivalent stress value is approximately 150 MPa, closely matching the macroscopic stress values obtained in experiments. As deformation progresses, the stress differences between distinct grains gradually increase, this phenomenon can be primarily attributed to the adaptive effects of deformation resistance induced by grain orientations [19]. Stress concentration firstly occurs near the grain boundaries, primarily due to heterogeneous deformation between different grains and the accumulation of dislocations. As deformation reaches its maximum (18 %), noticeable stress variations between grains become evident. Grains with higher stress do not correspond to higher strain, exemplified by grain 49 exhibiting higher stress but lower strain. Similar outcomes are observed at grain 52, as highlighted in the regions selected by the red dashed boxes in Fig. 13(d). Experimental results indicate that these grains undergo significant fold, as shown in Figs. 5(k) and Fig. 7(c). The SEM and EBSD results reveal severe wrinkles and even the occurrence of fragmented small grains in the region of grain 49, while grain 52 exhibits pronounced intragranular plastic heterogeneity. The pronounced orientation changes leading to formation of kinks, as well as grain fragmentation, will result in a more complex distribution of local stresses, this complexity may explain the disappearance of slip system S6 in grain 49 as deformation continues. However, due to the absence of grain fragmentation effects in the crystal plasticity model, the simulation results fail to capture the evolving trends under the large deformation conditions.
此外，在变形的初始阶段，应力也是均匀分布的，如图 13(a)所示。在 1%的变形下，平均等效应力值约为 150 MPa，与实验中获得的宏观应力值非常接近。随着变形的进行，不同晶粒之间的应力差异逐渐增大，这种现象主要归因于晶粒取向引起的变形抗力的适应性效应[19]。应力集中首先发生在晶界附近，这主要是由于不同晶粒之间的非均匀变形和位错累积所致。当变形达到最大值（18%）时，晶粒之间的应力变化变得明显。应力较高的晶粒并不一定对应应变较高，例如晶粒 49 表现出较高的应力但应变较低。晶粒 52 也观察到类似的结果，如图 13(d)中红色虚线框选定的区域所示。实验结果表明，这些晶粒发生了显著的折皱，如图 5(k)和图 7(c)所示。 SEM 和 EBSD 结果揭示了晶粒 49 区域存在严重的褶皱，甚至出现了碎裂的小晶粒，而晶粒 52 则表现出明显的晶内塑性不均匀性。显著的取向变化导致形成位错环，以及晶粒碎裂，将导致局部应力分布更加复杂，这种复杂性可以解释随着变形的继续，晶粒 49 中滑移系统 S6 的消失。然而，由于晶体塑性模型中缺乏晶粒碎裂效应，模拟结果未能捕捉到在大幅度变形条件下的演变趋势。

The stress values of the grain 38, selected by the green dashed box in Fig. 13(d), are lower than those of grains 49 and 52, but significantly higher than the surrounding grains. Experimental results indicate the absence of severe wrinkles and grain fracture in grain 38, as shown in Fig. 7(b), and SEM results demonstrate plasticity transfer occurring between this grain and adjacent grains, suggesting that plasticity transfer can alleviate stress concentration in grains. Comparative analysis of simulated strain and stress distributions reveals that the occurrence of local plastic behavior can alleviate the micro-scale stress concentrations. Combining with the experimental results, it can be inferred that the occurrence of plasticity transfer not only coordinates the strain between adjacent grains but reduces the level of stress concentration within the grains as well. In contrast, the grains with high stress distributions that fail to undergo plasticity transfer will subsequently experience severe wrinkling and intragranular plastic incompatibility.
晶粒 38 的应力值（如图 13(d)中绿色虚线框所示）低于晶粒 49 和 52，但显著高于周围晶粒。实验结果表明，晶粒 38 没有出现严重的褶皱和晶粒断裂（如图 7(b)所示），SEM 结果展示了该晶粒与相邻晶粒之间发生塑性转移，这表明塑性转移可以缓解晶粒中的应力集中。模拟应变和应力分布的比较分析表明，局部塑性行为的发生可以缓解微尺度应力集中。结合实验结果可以推断，塑性转移的发生不仅协调了相邻晶粒之间的应变，还降低了晶粒内部的应力集中程度。相比之下，那些应力分布较高且未能发生塑性转移的晶粒，随后将出现严重的褶皱和晶粒内塑性不匹配。

4. Discussion 4. 讨论

4.1. The slip transfer criterion
4.1. 滑移转移准则

The analysis of the in-situ tests indicates that the active slip systems between adjacent grains at grain boundaries, where plasticity transfer occurs, often exhibit high values of the

m^{'}

. However, as mentioned above, in-situ SEM results also reveal that certain combinations of slip systems with relatively high

m^{'}

do not undergo plasticity transfer. This suggests that evaluating the plasticity transfer capability of grain boundaries solely based on the geometric relationships between active slip systems is not reliable. Therefore, a more comprehensive assessment of the conditions under which the plasticity transfer occurs in Al-Zn-Mg-Cu alloys is required.
对原位测试的分析表明，在发生塑性转移的晶界处相邻晶粒之间的活跃滑移系统，其

m^{'}

值通常较高。然而，如前所述，原位 SEM 结果也揭示某些相对具有较高

m^{'}

值的滑移系统组合并未发生塑性转移。这表明，仅根据活跃滑移系统之间的几何关系来评估晶界的塑性转移能力是不可靠的。因此，需要更全面地评估 Al-Zn-Mg-Cu 合金中塑性转移发生时的条件。

To directly investigate the response of dislocation slide to grain boundaries during the deformation process of the Al-Zn-Mg-Cu alloy, the same material was stretched to 10 % at an identical strain rate, followed by TEM characterization. Focusing on the distribution of dislocations at grain boundaries after deformation, a comprehensive analysis of the grain boundary regions was performed. The two representative grain boundaries were selected for detailed analysis, as illustrated in Fig. 14. In Figs. 14(a-1)(a-2) and (a-3), grain boundaries with evident dislocation transfer are depicted. As three-dimensional planar defects, the projected width of the grain boundary interface in Fig. 14(a) is approximately 144 nm. The dashed lines in Figs. 14(a-2)(a-3) indicate dislocation lines with a certain curvature, suggesting that dislocations are moving along the grain boundary interface [31]. Notably, the dislocation line in the lower-left grain crosses the grain boundary and connects with the dislocation line in the upper-right grain, indicating effective dislocation motion and transfer during interaction.
为直接研究 Al-Zn-Mg-Cu 合金变形过程中位错滑移对晶界的响应，将相同材料以相同应变速率拉伸至 10%，随后进行 TEM 表征。聚焦于变形后晶界处位错的分布，对晶界区域进行了全面分析。选取了两个具有代表性的晶界进行详细分析，如图 14 所示。在图 14(a-1)(a-2)和(a-3)中描绘了存在明显位错转移的晶界。作为三维平面缺陷，图 14(a)中晶界界面的投影宽度约为 144 nm。图 14(a-2)(a-3)中的虚线表示具有一定曲率的位错线，表明位错沿晶界界面移动[31]。值得注意的是，左下角的位错线穿过晶界并与右上角的位错线相连，表明在相互作用过程中存在有效的位错运动和转移。

In contrast, in Fig. 14(b), there is no obvious evidence of dislocation transfer between the two grains at the grain boundary. As shown in Figs. 14(b-1) and (b-2), this grain boundary, compared to the one in Figs. 14(a-1) where plasticity transfer occurred, has a narrow interface of only about 35 nm projected width. Numerous residual dislocations were found at the boundary, but there is no indication of dislocations transferring. A comparison of the selected area diffraction pattern (SEAD) information at the grain boundary interfaces in Figs. 14(b-2) and Fig. (a-2) reveals that the grain orientation on either side of the boundary in Figs. 14(a-2) exhibits a higher degree of matching, whereas the grain orientations on either side of the interface in Figs. 14(b-2) demonstrate significant differences, indicating a poor aligned relationship. To explore the characteristics of dislocations at the grain boundary, as shown in Figs. 14(b-3), a further high-resolution Transmission Electron Microscopy (HRTEM) characterization was conducted on the green outlined area in Figs. 14(b-1). It can be observed that, compared to the left grain region where no dislocation transfer occurred, the right region exhibits more color contrast due to lattice mismatches caused by dislocation accumulation [49]. Inverse Fast Fourier transformation (IFFT) of the HRTEM results in the red dashed box area in Fig. 14(b) also reveals the presence of numerous pinned dislocations at the boundary region.
相比之下，在图 14(b)中，晶界处两个晶粒之间没有明显的位错转移证据。如图 14(b-1)和(b-2)所示，与发生塑性转移的图 14(a-1)中的晶界相比，该晶界的界面投影宽度仅约 35 纳米，非常狭窄。在晶界处发现了大量残余位错，但没有位错转移的迹象。通过比较图 14(b-2)和图(a-2)中晶界界面处的选区衍射（SEAD）信息，可以发现图 14(a-2)两侧的晶粒取向具有更高的匹配度，而图 14(b-2)两侧的界面晶粒取向则存在显著差异，表明取向关系不佳。为了探究晶界处位错的特征，如图 14(b-3)所示，对图 14(b-1)中绿色框标区域进行了进一步的高分辨率透射电子显微镜（HRTEM）表征。可以观察到，与没有位错转移的左侧晶粒区域相比，右侧区域由于位错累积引起的晶格失配表现出更多的颜色对比[49]。对图 14(b)中红色虚线框区域的高分辨率透射电镜(HRTEM)结果进行逆快速傅里叶变换(IFFT)也揭示了边界区域存在大量被钉扎的位错。

The TEM results reveal that interactions between dislocations and the grain boundary lead to phenomena such as dislocation transmission and pile-ups [30]. From the calculation process, it can be seen that

m^{'}

merely expresses the degree of alignment between the slip planes and slip direction. Numerically, slip systems with higher

m^{'}

values exhibit favorable geometric alignment, contributing to the occurrence of plastic transmission. However, the experimental results in Section 3.4 demonstrate that solely relying on the geometric compatibility factor cannot accurately predict the occurrence of plasticity transmission.
TEM 结果揭示，位错与晶界的相互作用导致位错传递和堆积等现象[30]。从计算过程可以看出，

m^{'}

仅表示滑移面与滑移方向之间的对齐程度。数值上，具有更高

m^{'}

值的滑移系统表现出更有利的几何对齐，有助于塑性传递的发生。然而，3.4 节的实验结果表明，仅依靠几何兼容性因子无法准确预测塑性传递的发生。

When dislocations glide to the grain boundary, atomic mismatch at the grain boundary may hinder the smooth and complete passage of dislocations, preventing plasticity transmission. As illustrated in Fig. 15(a), grain boundaries between grains often exhibit irregular structures with a certain thickness of atomic layers, when dislocations attempt to traverse these irregular structures and propagate towards grains with orientation differences, complex dislocation transformations occur at the grain boundary [31]. In polycrystalline materials, grains and grain boundaries exist in three dimensions, leading to a more intricate reaction of dislocations when crossing the grain boundary. While plasticity transmission would be simplified if dislocations could smoothly traverse the grain boundary, the reality is that dislocations may become partially immobilized at grain boundary, indicating that the energy of the dislocation movement is spent overcoming the hindrance. Analysis of TEM results reveals an accumulation of residual dislocations at grain boundaries where the plastic transmission did not occur. Therefore, the residual dislocation (residual Burgers vectors/rBv)

Δ b = {\vec{b}}_{o u t} - {\vec{b}}_{i n}

, between input dislocation

{\vec{b}}_{i n}

moving to the grain boundary and output dislocation

{\vec{b}}_{o u t}

passing through the grain boundary, needs to be carefully estimated as a crucial parameter to evaluate the ability of dislocations to traverse the grain boundary, The calculation scheme [28] is as follows:
当位错滑移到晶界时，晶界处的原子失配可能会阻碍位错的顺利和完全通过，从而阻止塑性传递。如图 15(a)所示，当位错试图穿越这些不规则结构并向取向不同的晶粒传播时，晶界处会发生复杂的位错转变[31]。在多晶材料中，晶粒和晶界存在于三维空间中，导致位错在穿越晶界时反应更为复杂。如果位错能够顺利穿越晶界，塑性传递将会简化，但现实中位错可能会在晶界处部分被固定，表明位错运动的能量被用于克服阻碍。TEM 结果分析揭示了在塑性传递未发生的晶界处存在残余位错的积累。因此，输入位错

{\vec{b}}_{i n}

移动到晶界和输出位错

{\vec{b}}_{o u t}

穿过晶界之间的残余位错（残余伯格斯矢量/rBv）

Δ b = {\vec{b}}_{o u t} - {\vec{b}}_{i n}

，需要仔细估计，作为评估位错穿越晶界能力的关键参数。计算方案[28]如下：(7)

Δ b / b = {\vec{g}}_{i n} ∙ {\vec{b}}_{i n} - {\vec{g}}_{o u t} ∙ {\vec{b}}_{o u t}

with

{\vec{g}}_{i n}

and

{\vec{g}}_{o u t}

representing the orientation matrices of the grains, while

{\vec{b}}_{i n}

and

{\vec{b}}_{o u t}

donate the Burgers vectors of the input and output dislocations, respectively.
其中

{\vec{g}}_{i n}

和

{\vec{g}}_{o u t}

代表晶粒的取向矩阵，而

{\vec{b}}_{i n}

和

{\vec{b}}_{o u t}

分别代表输入和输出位错的伯格斯矢量。

The computed results in Table 4 reveal a high geometric compatibility factor of 0.8096 between the activated slip system S6 in grain 49 and S9 in grain 56. However, in-situ experimental results indicate the absence of plasticity transfer phenomena at the corresponding grain boundary 7 for the slip systems. Calculating the corresponding rBv yields a value of 11.1213, signifying that the majority of dislocations act as residual dislocations fixed at the grain boundary interface. Notably, a distinct rBv value of 0.4244 is found for the slip system S6-S6 (grain 49-grain 50) where plasticity transmission occurs. The aforementioned observations and associated numerical computation results suggest that, despite the elevated geometric compatibility factor between slip systems S6 in grain 49 and S9 in grain 56, a substantial portion of dislocations forms residual dislocations at the grain boundary during the transmission process, impeding the plasticity transmission. This implies that, besides exhibiting a high geometric compatibility factor, an extremely low rBv value is a crucial condition for effective dislocation penetration through the grain boundary.
表 4 中的计算结果表明，晶粒 49 中的滑移系统 S6 与晶粒 56 中的 S9 之间存在 0.8096 的高几何兼容因子。然而，原位实验结果表明，对于这些滑移系统，相应的晶界 7 上没有观察到塑性转移现象。计算相应的 rBv 值得到 11.1213，这意味着大多数位错作为残定位错固定在晶界界面。值得注意的是，对于发生塑性传递的滑移系统 S6-S6（晶粒 49-晶粒 50），发现了一个独特的 rBv 值 0.4244。上述观察结果及相关数值计算结果表明，尽管晶粒 49 中的滑移系统 S6 与晶粒 56 中的 S9 之间存在较高的几何兼容因子，但在传递过程中，相当一部分位错在晶界处形成残定位错，阻碍了塑性传递。这表明，除了表现出高几何兼容因子外，极低的 rBv 值是有效位错穿透晶界的一个关键条件。

To comprehensively analyze the intrinsic connections between the plasticity transmission and various assessment parameters, a statistical analysis of grains exhibiting distinct slip traces within the characterization region was conducted, along with the Schmid factor, misorientation angle of grain boundary, geometric compatibility factors, and residual dislocation information at the grain boundaries. The results, as depicted in Fig. 16, reveal that all the grain boundaries, where the plasticity transmission was detected, exhibit high geometric compatibility factor values. Fig. 16(a) illustrates that the minimum geometric compatibility factor between the slip systems demonstrating plasticity transmission is 0.9571, with values in close proximity to previously reported threshold criteria (0.9 [28], 0.89 [29], 0.97 [32]).
为了全面分析塑性传递与各种评估参数之间的内在联系，对表征区域内具有不同滑移痕迹的晶粒进行了统计分析，并结合了 Schmid 因子、晶界取向角、几何兼容性因子以及晶界处的残余位错信息。如图 16 所示，结果表明所有检测到塑性传递的晶界均表现出高几何兼容性因子值。图 16(a)说明，表现出塑性传递的滑移系统的最小几何兼容性因子为 0.9571，其值接近先前报道的阈值标准（0.9 [28]、0.89 [29]、0.97 [32]）。

The relationship between different parameters and the misorientation angles at grain boundaries reveals that as the gb misorientation decreases, the probability of high geometric compatibility factors increases. However, it is noteworthy that grain boundaries with higher misorientation angles also exhibit elevated

m^{'}

values. In the context of this research, all grain boundaries where plasticity transmission occurs are situated in regions with relatively low values of gb misorientation, as depicted in Fig. 16(c), the maximum gb misorientation angle for grain boundaries where plasticity transmission occurred in this study is 14.96°. Fig. 16(b) comprehensively evaluates the relationship between

m^{'}

and Schmid factors, it is evident that the scenarios of plasticity transmission and pile-up exhibit a similar trend to the distribution of

m^{'}

, this similarity arises because it was found above that almost all activated slip systems possess the highest Schmid factors, with their numerical values approaching 0.5. Additionally, as illustrated in Fig. 16(c)–a distinctive statistical feature of grain boundaries, where no plasticity transmission occurs, is the remarkably low ratio of

m^{'}

to rBv, with a maximum value of only 0.1088. This phenomenon is attributed to the significantly elevated values of rBv. The values of rBv in all such boundaries exceed 4, as depicted in Fig. 16(d). Conversely, grain boundaries experiencing plasticity transmission simultaneously exhibit high

m^{'}

and lower residual dislocation density. In this study, the numerical values of rBv are consistently below 1.47 for boundaries where plasticity transmission occurs.
不同参数与晶界取向角之间的关系表明，随着晶界取向角的减小，高几何兼容性因子的概率增加。然而值得注意的是，具有较高取向角的晶界也表现出较高的

m^{'}

值。在本研究中，所有发生塑性传递的晶界都位于晶界取向角相对较低的区域，如图 16(c)所示，本研究中发生塑性传递的晶界的最大晶界取向角为 14.96°。图 16(b)全面评估了

m^{'}

与 Schmid 因子的关系，很明显塑性传递和孪晶的情景与

m^{'}

的分布趋势相似，这种相似性是因为之前发现几乎所有激活的滑移系统都具有最高的 Schmid 因子，其数值接近 0.5。此外，如图所示。 16(c)–晶界的一个独特统计特征是，在塑性不发生传递的地方，

m^{'}

与 rBv 的比率显著较低，最大值仅为 0.1088。这种现象归因于 rBv 值的显著升高。在所有这些晶界中，rBv 的值都超过 4，如图 16(d)所示。相反，同时经历塑性传递的晶界表现出较高的

m^{'}

和较低的残余位错密度。在本研究中，塑性传递发生处的晶界，rBv 的数值始终低于 1.47。

4.2. Heterogeneous deformation and crystal rotation
4.2. 不均匀变形和晶体旋转

Existing research indicates that, under applied loading conditions, the direction of crystal rotation with different orientated grain is predictable [13,18], this point to some extent aligns with the experimental results presented in this study, as the crystal orientation distribution determines the effective shear stress of slip systems under specific applied loading tensors, and the slip systems with the maximum Schmid factor exhibit the characteristics of activation first. Therefore, the slip systems with the highest Schmid factor results in the crystal rotation of grains around a specific axis.
现有研究表明，在施加载荷条件下，不同取向晶粒的晶体旋转方向是可预测的[13,18]，这一点在一定程度上与本研究展示的实验结果相符，因为晶体取向分布决定了在特定施加载荷张量下滑移系统的有效剪切应力，而具有最大 Schmid 因子的滑移系统表现出先激活的特征。因此，具有最高 Schmid 因子的滑移系统导致晶粒围绕特定轴旋转。

However, experimental results also reveal that, with an increase in deformation, the Al-Zn-Mg-Cu alloy exhibits pronounced heterogeneity in plastic deformation both between and within grains. After the solution treatment, the material manifests the characteristics of statically recrystallized grains with uniform orientation, and the internal misorientation are all below 0.5°, as shown in Fig. 17(a-1)(b-1)(c-1). From the initial state I0 to the stage I1, the crystal orientation of grain 42 weakly tilts towards the [001] direction, while grain 54 shows a weak rotation towards the line connecting [001] and [011]. As deformation reaches stage I3, the internal misorientation within grains rapidly increase. Grain 54 as a whole tends to rotate towards the [

\overline{1}

11] direction, while grain 42 rotates in the direction of the line connecting [011]-[

\overline{1}

11]. These rotational trends of the grains largely align with the summarized rotational rules of FCC material crystals outlined in the introduction. Moreover, in grains exhibiting cooperative action of multiple slip systems, the crystal rotation becomes even more complex. For instance, grain 42, while rotating towards the [011]-[

\overline{1}

11] line, also exhibits a tendency to rotate towards the [001] direction simultaneously, a phenomenon similarly observed in grain 49 activating multiple slip systems.
然而，实验结果还表明，随着变形的增加，Al-Zn-Mg-Cu 合金在晶粒之间和晶粒内部都表现出明显的塑性变形不均匀性。在固溶处理后，材料表现出具有均匀取向的静态再结晶晶粒的特征，内部取向差均低于 0.5°，如图 17(a-1)(b-1)(c-1)所示。从初始状态 I0 到阶段 I1，晶粒 42 的晶体取向微弱地向[001]方向倾斜，而晶粒 54 则微弱地向连接[001]和[011]的直线旋转。当变形达到阶段 I3 时，晶粒内部的取向差迅速增加。晶粒 54 整体倾向于向[

\overline{1}

11]方向旋转，而晶粒 42 则沿[011]-[

\overline{1}

11]连接线方向旋转。这些晶粒的旋转趋势与引言中总结的 FCC 材料晶体旋转规则大体一致。此外，在多个滑移系统协同作用的晶粒中，晶体旋转变得更加复杂。例如，晶粒 42 在旋转至[011]-[

\overline{1}

11]线的同时，也表现出向[001]方向旋转的趋势，这种现象与晶粒 49 激活多个滑移系统的观察结果相似。

The systematic crystal rotation rule appears to be disrupted as the strain reaches 18 %. Within grain 42, the portion rotating towards the [001] direction continues to increase, and an additional rotational component emerges in grain 54, oriented towards [011]-[

\overline{1}

11]. Particularly noteworthy is grain 49, which does not exhibit a singular trend of rotation towards [

\overline{1}

11] but rather simultaneously rotates towards both [001] and [

\overline{1}

11]. Fig. 17 illustrates that when the strain reaches 18 %, the cumulative misorientation for all grains surpass 10°. However, there are distinct variations in the misorientation between adjacent pixel points, in grain 42, the final difference between the minimum and maximum misorientation values is only 6°, while the orientation gradients in grains 49 and 54 significantly exceed this value. The corresponding grain IPF color gradients reveal noticeable misorientation gap, especially in the lower-right section of grain 49 and the lower-left section of grain 54, exhibiting significant orientation gradients and even severe wrinkling leading to grain fragmentation.
随着应变达到 18%，系统的晶体旋转规则似乎被破坏。在晶粒 42 中，朝向[001]方向旋转的部分持续增加，而在晶粒 54 中，又出现了一个朝向[011]-[

\overline{1}

11]方向的旋转分量。特别值得注意的是晶粒 49，它并未表现出朝向[

\overline{1}

11]的单一旋转趋势，而是同时朝向[001]和[

\overline{1}

11]方向旋转。图 17 表明，当应变达到 18%时，所有晶粒的累积取向差超过 10°。然而，相邻像素点之间的取向差存在明显差异，在晶粒 42 中，最小和最大取向差之间的最终差异仅为 6°，而晶粒 49 和 54 中的取向梯度显著超过这一数值。相应的晶粒 IPF 颜色梯度显示出明显的取向差，特别是在晶粒 49 的右下部分和晶粒 54 的左下部分，这些区域表现出显著的取向梯度和严重的褶皱，甚至导致晶粒碎裂。

Extracting the IPF and orientation distribution information of the three grains showcased in Fig. 17 at the maximum deformation in this experimental study (18 %), the results are depicted in Fig. 18. All three grains exhibit noticeable differences in their internal orientation distributions. Grain 42, analyzed through the color gradient information of the IPF map, is divided into four sub-regions. It is evident that sub-regions B and C, after deformation, still closely resemble the original red color. In contrast, there is a distinct color gradient between sub-regions A, D and sub-regions B. This indicates a significant disparity in the crystal rotation within these two sub-regions compared to the overall rotational trend of grain 42. The results of the analysis in Section 3.4.2 indicate that the sub-regions B and C exhibit a higher

m^{'}

and undergo noticeable plasticity transfer between grain 50 and grain 35. In contrast, sub-regions A and D show no plasticity transfer between the corresponding adjacent grains, namely, grain 43 and grain 38. A similar phenomenon is more pronounced in grains 49 and 54. Sub-regions A and C of grain 49, as well as sub-region B of grain 54, demonstrate a non-progressive color gradient and distinct boundaries of internal deformation (indicated by the cyan dashed line in Fig. 9(c)). Plasticity transfer analysis suggests that the corresponding grains in these regions exhibit weaker plasticity transfer capabilities with adjacent grains. The above analysis indicates that as deformation progresses the plasticity transfer capability between grains influences the coordination of intragranular crystal rotation. Grains with better plasticity transfer capabilities exhibit relatively lower intragranular orientation gradients, demonstrating enhanced plasticity uniformity. Conversely, the weak plasticity transfer capability can lead to significant differences between the crystal orientation at the grain boundaries and within the grains, and even result in grain fragmentation, leading to complexity in the form of crystal rotation.
提取图 17 中三颗晶粒在本次实验研究最大变形程度（18%）下的 IPF 和取向分布信息，结果如图 18 所示。三颗晶粒的内部取向分布存在明显差异。通过 IPF 图的色彩梯度信息分析晶粒 42，将其分为四个亚区。可以看出，变形后亚区 B 和 C 仍与原始红色非常相似。相比之下，亚区 A、D 与亚区 B 之间存在明显的色彩梯度。这表明这两组亚区内的晶体旋转与晶粒 42 的整体旋转趋势存在显著差异。3.4.2 节的分析结果表明，亚区 B 和 C 的

m^{'}

值较高，并在晶粒 50 和晶粒 35 之间发生明显的塑性转移。相比之下，亚区 A 和 D 在相应的相邻晶粒（晶粒 43 和晶粒 38）之间没有发生塑性转移。在晶粒 49 和晶粒 54 中，这种现象更为明显。晶粒 49 的亚区 A 和 C，以及晶粒 54 的亚区 B，显示出非渐进性的颜色渐变和内部变形的明显边界（如图 9(c)中所示的青色虚线）。塑性传递分析表明，这些区域中的相应晶粒与相邻晶粒的塑性传递能力较弱。上述分析表明，随着变形的进行，晶粒之间的塑性传递能力会影响晶粒内晶体旋转的协调性。塑性传递能力较好的晶粒表现出相对较低的晶粒内取向梯度，显示出增强的塑性均匀性。相反，弱的塑性传递能力会导致晶界处和晶粒内部的晶体取向存在显著差异，甚至导致晶粒破碎，从而形成晶体旋转的复杂性。

The crystal plasticity simulation supplemented information about normal stress at the interfaces between adjacent grains, as illustrated in the magnified view in Fig. 19(d), some regions may exhibit opposite stress states. It is worth noting that since the crystal plasticity model establishment process did not explicitly establish a grain boundary characteristic model and phenomenological models lacked a consideration of the underlying physically mechanisms and a description of the plasticity transfer phenomenon, so the simulation results obtained mainly reflect the grain orientation and the corresponding resolved shear stress state of the slip systems, which limits the ability to comprehensively describe the effects of the interactions between dislocations and grain boundaries, and the interactions have been experimentally confirmed in this study to play a critically important role. However, even though not all the factors mentioned in the experiments have been fully considered, the existing simulation results can still indicate that the deformation heterogeneity at the interface, arising from differences in slip system activation among grains with different orientations, leads to dramatic stress states at the interface to those within the grains [50]. This may be attributed to the activation of different slip systems in grains with distinct orientations, which must reach a state of equilibrium as they approach the respective grain boundaries. However, this equilibrium is not solely a function of the slip systems, the role of the grain boundary is critically important - a significant insight derived from our experiments. Therefore, it is reasonable to observe notable differences in the micro-scale stress states on either side of the interface. And during the plastic deformation, the accumulation and entanglement of dislocations also lead to stress concentrations. Additionally, different mechanisms of the grain boundaries on dislocation motion lead to greater disparities in stress distribution. Grain boundaries with strong plasticity transmission capabilities result in a more uniform strain distribution on both sides of the interface, leading to smaller stress differentials between interface and internal part of grain. Conversely, residual dislocations and poor deformation continuity at the grain boundaries with poorer plasticity transfer capability would lead to stress concentrations. In addition, the high local stress state can induce complex dislocation behaviors, which further contributes to the complexity of crystal rotation in these local regions, thereby resulting in more severe intergranular plastic deformation heterogeneity. The severe heterogeneous deformation at the interfaces is the primary cause leading to grain fragmentation. The in-situ experimental results have revealed the complexity of crystal rotation and the occurrence of grain fragmentation at these types of grain boundaries, and the influence of the deformation heterogeneity can extend into the grain interiors, further triggering severe intragranular deformation heterogeneity.
晶体塑性模拟补充了相邻晶粒界面处正应力的信息，如图 19(d)的放大视图所示，某些区域可能表现出相反的应力状态。值得注意的是，由于晶体塑性模型建立过程未明确建立晶界特性模型，且现象学模型缺乏对潜在物理机制和塑性转移现象的考虑，因此获得的模拟结果主要反映了晶粒取向及相应滑移系统的解析切应力状态，这限制了全面描述位错与晶界相互作用的影响的能力，而本研究通过实验已证实这些相互作用起着至关重要的作用。然而，尽管实验中未充分考虑所有因素，现有的模拟结果仍可表明，界面处的变形不均匀性——源于不同取向晶粒间滑移系激活的差异——导致界面处的应力状态与晶粒内部的应力状态存在显著差异[50]。这可归因于不同取向晶粒中不同滑移系的激活，当它们接近各自的晶界时必须达到平衡状态。然而，这种平衡并不仅仅取决于滑移系，晶界的作用至关重要——这是我们实验得出的重要见解。因此，观察到界面两侧的微观尺度应力状态存在显著差异是合理的。此外，在塑性变形过程中，位错的累积和缠结也会导致应力集中。此外，晶界对位错运动的机制不同，导致应力分布存在更大差异。具有强塑性传递能力的晶界导致界面两侧的应变分布更加均匀，从而减小了界面与晶粒内部之间的应力差。相反，塑性传递能力较差的晶界处残留位错和变形连续性差会导致应力集中。此外，高局部应力状态会诱导复杂的位错行为，这进一步增加了这些局部区域的晶体旋转复杂性，从而导致更严重的晶间塑性变形不均匀性。界面处严重的非均匀变形是导致晶粒碎裂的主要原因。原位实验结果揭示了这类晶界处晶体旋转的复杂性和晶粒碎裂的发生，变形不均匀性的影响可以延伸至晶粒内部，进一步引发严重的晶内变形不均匀性。

5. Conclusions 5. 结论

In this study, the in-situ SEM/EBSD characterization techniques were employed to track and analyze the plastic behavior of Al-Zn-Mg-Cu alloy. Complemented by crystal plasticity simulations, this work has comprehensively investigated the slip systems activation, plasticity transfer and especially their effect of deformation heterogeneity during the deformation process. Statistical analyses and calculations of plastic behavior in the characterized region were conducted at the grain level. The key conclusions drawn from this research are as follows:
在本研究中，采用原位 SEM/EBSD 表征技术追踪和分析 Al-Zn-Mg-Cu 合金的塑性行为。结合晶体塑性模拟，这项工作全面研究了滑移系统激活、塑性转移及其对变形过程变形异质性的影响。对表征区域内的塑性行为进行了颗粒级别的统计分析与计算。本研究的核心结论如下：

1.
In the plastic deformation stage of Al-Zn-Mg-Cu alloy materials, there is a significant increase in dislocation density. Crystal rotation becomes pronounced, and due to the hindering effect of grain boundaries on dislocation motion, a distinct phenomenon of plastic inhomogeneity manifests. As deformation progresses, microcracks initiated by the fracture of ferric-rich phase first appear in the intergranular regions.
在 Al-Zn-Mg-Cu 合金材料的塑性变形阶段，位错密度显著增加。晶体旋转变得明显，由于晶界对位错运动的阻碍作用，出现了明显的塑性不均匀现象。随着变形的进行，富铁相断裂引起的微裂纹首先在晶间区域出现。
2.
The activation of slip systems within grains is primarily determined by the Schmid factor, the slip system with the highest Schmid factor in a grain is typically the first to activate. In grains where the secondary slip system is activated, the difference between the Schmid factor of the subsequent slip system and the highest Schmid factor is relatively small. In this study, the results indicate that the difference does not exceed 10 %.
晶粒内滑移系统的激活主要由 Schmid 因子决定，晶粒内 Schmid 因子最高的滑移系统通常是首先激活的。在激活了次级滑移系统的晶粒中，后续滑移系统的 Schmid 因子与最高 Schmid 因子之间的差异相对较小。在本研究中，结果表明该差异不超过 10%。
3.
The grains that undergo plasticity transfer exhibit relatively high geometric compatibility factor, but geometric compatibility factor alone cannot serve as the sole criterion for determining whether plasticity transfer occurs. Through the comprehensive analysis, this study found that plasticity transfer occurs between grains that simultaneously exhibit high geometric compatibility factors and low residual dislocation values. The statistical experimental results of this study indicate that the thresholds for these two indicators are 0.9571 and 1.47, respectively.
发生塑性转移的晶粒表现出相对较高的几何兼容因子，但几何兼容因子本身不能作为判断塑性是否转移的唯一标准。通过综合分析，本研究发现塑性转移发生在同时具有较高几何兼容因子和较低残余位错值的晶粒之间。本研究的统计实验结果表明，这两个指标的门限值分别为 0.9571 和 1.47。
4.
The trend of crystal rotation becomes more complex in grains where the multiple slip systems are active, and the differences in plasticity transfer capability between grains can affect the crystal orientation evolution. The crystal plasticity simulation results indicate that the occurrence of local strain can effectively alleviate stress concentration during the plastic deformation, and stress gap are observed at grain boundaries.
在多组滑移系统活跃的晶粒中，晶体旋转的趋势变得更加复杂，而晶粒间塑性传递能力的差异会影响晶体取向的演变。晶体塑性模拟结果表明，局部应力的出现可以有效地缓解塑性变形过程中的应力集中，并在晶界处观察到应力间隙。
5.
During the plastic deformation, high plasticity transfer capability grain boundaries result in relatively small differences in strain and stress distribution among grains, while absence of plasticity transfer can lead to localized stress amplification, thereby increasing the complexity of crystal rotation in that local region, resulting in more severe intergranular plastic heterogeneity. Heterogeneous deformation at grain boundaries and neighboring grains also affects the evolution of intragranular crystal rotation, and the influence of these interacting factors becomes particularly pronounced with increasing deformation.
在塑性变形过程中，高塑性传递能力的晶界导致晶粒间的应变和应力分布差异相对较小，而塑性传递的缺失会导致局部应力放大，从而增加该局部区域的晶体旋转复杂性，导致更严重的晶间塑性不均匀性。晶界及其邻近晶粒的变形不均匀性也会影响晶内晶体旋转的演变，随着变形的增加，这些相互作用因素的影响变得更加显著。

CRediT authorship contribution statement
CRediT 作者贡献声明

Luyi Han: Writing – original draft, Software, Methodology, Investigation, Data curation. Dejin Wei: Validation, Investigation. Yanan Yu: Validation, Investigation. Zhengfeng Lv: Project administration. Zhaohui Yan: Project administration. Guoqun Zhao: Project administration, Funding acquisition, Conceptualization. Guangchun Wang: Writing – review & editing, Supervision, Project administration, Funding acquisition.
吕怡：撰写——初稿，软件，方法，研究，数据管理。魏德军：验证，研究。余岩：验证，研究。吕正峰：项目管理。闫兆辉：项目管理。赵国群：项目管理，资金获取，概念化。王广春：撰写——审阅与编辑，指导，项目管理，资金获取。

Declaration of competing interest
利益冲突声明

The authors have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
作者没有已知的利益冲突或个人关系可能影响本论文报告的工作。

Acknowledgments 致谢

The authors greatly acknowledge the financial support of the Key Research and Development Program of Shandong Province, China (Grant No. 2021ZLGX01) and the National Natural Science Foundation of China (Grant No. 51735008).
作者非常感谢山东省重点研发计划（项目编号 2021ZLGX01）和中国国家自然科学基金（项目编号 51735008）的资金支持。

Data availability 数据可用性

Data will be made available on request.
数据将根据要求提供。

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Cited by (6)

Effect of epitaxial growth microstructure on the stress corrosion cracking propagation behavior of fusion zone in 316L-316LN stainless steel weld joint
外延生长微观结构对 316L-316LN 不锈钢焊缝熔合区应力腐蚀开裂扩展行为的影响
2025, Corrosion Science 2025，腐蚀科学
The stress corrosion crack (SCC) initiation and propagation behaviors at fusion zone of the 316 L (filler metal)-316LN (base metal) stainless steel weld joint in high-temperature (320°C) and high-pressure (15 MPa) water were investigated by small punch test with a punch displacement rate of 0.0001 mm/min. The results indicated that at room temperature, the heat-affected zone (HAZ) manifested a 38.79 % hardness elevation relative to the base metal, consequently directing fracture initiation to the weld metal. By contrast, under high-temperature and high-pressure water, the HAZ showed markedly increased susceptibility to SCC, with subsequent fracture localization shifting to the HAZ itself, accompanied by a 30.7 % reduction in strength. The epitaxial growth crystallization characteristic of the weld joint govern the SCC propagation trajectories of the fusion zone. Weld metal adjacent to the fusion boundary maintains crystallographic continuity with the partially melted base metal grains through epitaxial growth, which fundamentally determines crack propagation paths. Intergranular cracks originating in the HAZ were observed to propagate across the fusion boundary along these continuous crystalline structures into the weld metal, rather than following the fusion line. Meanwhile, in addition to the intergranular cracks, cracking propagated along slip bands were also found in the weld metal and HAZ, which was related to the formation of extrusion-induced slip steps on the material surface. The slip deformation mechanism induced critical oxide layer fractures, creating discontinuities in the oxide layer that served as preferential nucleation sites for SCC. However, intergranular cracking emerged as the predominant failure mechanism observed in weld joint fractures.
Tailoring microstructure and mechanical properties of IN738LC fabricated by laser powder bed fusion through processing parameter optimization
通过优化工艺参数来调整 IN738LC 激光粉末床熔融制造的结构和力学性能
2025, Optics and Laser Technology
2025, 光学与激光技术
IN738LC has been widely used in hot-end components owing to its excellent high-temperature performance, while it has still suffered from metallurgical defects during laser powder bed fusion (LPBF) due to its high crack sensitivity. This study investigated forming behavior, microstructure evolution and mechanical property of LPBF-processed IN738LC samples at different parameters (laser power of 150–300 W, scanning speed of 500–1500 mm/s). The result indicated that the decrease in energy density caused the width and depth of the melt pool to decrease and eventually broke into droplets, leading to an increase in porosity. As the scanning speed increases, the microstructure changes from irregular columnar/cellular dendrites to all distributed as columnar dendrites, exhibiting epitaxial growth. An optimal process window was finally obtained at a laser power of 200 W and a scanning speed of 1000 mm/s, which achieved excellent forming quality (the porosity of 0.01 %) and mechanical properties (microhardness of 445.5 HV, ultimate tensile strength of 1335 MPa and elongation of 19.3 %). This study provides process basis for subsequent studies of IN738LC fabricated by LPBF.
Fatigue crack growth rate investigation of cold rolled and aged Al-Mg-Zn alloy
冷轧和时效 Al-Mg-Zn 合金的疲劳裂纹扩展速率研究
2025, International Journal of Fatigue
2025, 国际疲劳杂志
This research explored the fatigue crack growth rate (FCGR) characteristics correlating with microstructure of Solution heat treated (SHT), SHT + peak aged (PA), SHT + 45 % cold rolled (CR), SHT + 60 % warm rolled (WR) and SHT + PA + 90 % CR Al-Mg-Zn alloy. The findings indicate that artificial aging and cold rolling process decelerate fatigue crack initiation because of precipitation hardening and work hardening as well as grain boundary strengthening, respectively. Utilizing the Paris model, fatigue crack growth rates during the linear extension stage were analyzed. Analysis of crack paths via scanning electron microscope (SEM) techniques revealed ductile fracture(dimples) in case of SHT and SHT + 60 % WR sample, while ductile and brittle mix fracture (dimples and facets) in case of SHT + PA and SHT + 45 % CR sample, whereas brittle fracture (river pattern, facets) in case of SHT + PA + 90 % CR sample were observed. The broadening of precipitate peaks in the X-ray diffraction (XRD) graph of SHT + PA + 90 % CR indicates a rise in dislocation density which is 11.1 $\times 10^{14} m^{- 2}$ . The microstructural evolution is characterized using optical −microscopy, EBSD and transmission electron microscopy (TEM) techniques. Rod like shape η″ precipitates were observed in TEM images in the case of SHT + PA + 90 % CR sample. Through the partition of IPF image it was observed that higher volume fraction of recrystallized grains was formed in SHT + 60 % WR sample, whereas nano-meter to micrometer size sub grains were formed in the case of SHT + PA + 90 % CR sample. It was observed through orientation distribution function that SHT + 45 % CR is showing strong brass ({110} < 112 > ) texture, whereas SHT + 60 % WR sample is showing strong rotated cube({001} < 110 > ) texture, while 90 % CR sample is showing strong brass({110} < 112 > ), strong Cu({112} < 111 > ) and strong S({123} < 634 > ) texture. Mechanical properties are assessed through tensile, hardness, and fracture tests. The highest values for Vickers hardness (226 HV), tensile strength (526 MPa), and conditional elastic–plastic fracture toughness (J_Q) (344.54 kJ/m²) were obtained after SHT (470 °C) for a duration of 8 h), PA (140 °C for a duration of 21 h) and 90 % CR.
Grain-scale micromechanical behaviors of hexagonal titanium utilizing in-situ high-energy diffraction microscopy and crystal plasticity finite element simulations
六方钛的晶粒尺度微观力学行为：利用原位高能衍射显微镜和晶体塑性有限元模拟
2025, International Journal of Plasticity
2025，《塑性力学国际杂志》
Coupling crystal plasticity finite element (CPFE) simulations with in-situ characterization techniques offers a robust framework for exploring the micromechanical behavior of polycrystalline metals. In this study, we tracked the evolution of the complete elastic strain tensor and orientation rotation of hundreds of grains in a hexagonal titanium (Ti) sample under uniaxial tension using in-situ high-energy diffraction microscopy (HEDM). These experimental observations were systematically compared to CPFE simulations instantiated with experimentally characterized results. It was found that CPFE simulations successfully replicate the macroscopic stress-strain response and texture evolution of polycrystalline Ti, however, only partially capture grain-scale micromechanical behaviors, particularly regarding grain-resolved elastic strains and orientation rotations. Detailed grain-to-grain comparison metrics reveal that incorporating residual stresses into CPFE models significantly improves the predictive accuracy of micromechanical behaviors. Moreover, simulations involving pyramidal <a> slip systems with high critical resolved shear stress, show slightly enhanced predictive performance. Further analyses of individual grains showcase how residual stresses and slip systems selections influence the micromechanical behaviors, highlighting the importance of the grain-scale stress state in determining deformation mechanisms. To understand the role of strain gradient effects in grain-scale stress heterogeneity, a non-local dislocation-based CPFE model was further compared to the phenomenological model discussed above. Although pronounced localized stresses and altered deformation mechanisms were observed near grain boundaries, the dislocation-based CPFE model still cannot significantly improve the predictions of grain-scale micromechanical behaviors. This work deepens the fundamental understanding of deformation mechanisms in hexagonal metals, and offers valuable insights into micromechanical modeling of polycrystalline materials.
Improving the microstructure and properties of a high-alloyed Al-Zn-Mg-Cu alloy by optimizing the initial temperature of Pre-recovery multi-stage solution treatment (P-MST)
通过优化预恢复多阶段溶液处理（P-MST）的初始温度，改善高合金化 Al-Zn-Mg-Cu 合金的微观结构和性能
2025, Materials Science and Engineering A
2025，材料科学与工程 A
This study proposed a new strategy to improve the microstructure and properties of Al-Zn-Mg-Cu alloy via optimizing the initial temperature of pre-recovery multi-stage solution treatment (P-MST, T0°C/12h + 350 °C/12h + 450 °C/2h + 460 °C/2h + 470 °C/2h). This optimization facilitated the adjustment of dislocation density, element solubility, and grain size, resulting in a significant increase in mechanical properties and corrosion resistance. The research found that during the T0°C/12h + 350 °C/12h stage, as the T0 temperature increased, the alloy's dislocation density initially decreased before rising again. The minimum point was achieved at T0 of 300 °C, which led to the lowest driving force for grain growth in the subsequent MST, resulting in the smallest grain size and best corrosion resistance in the T6-aging state. Additionally, during the T0°C/12h and T0°C/12h + 350 °C/12h stages, with a rise in T0 temperature, the average size of the second phase gradually increased. The highest elemental solubility of the matrix after MST occurred at T0 of 300 °C, promoting the alloy to demonstrate the maximum aging precipitation strengthening. Nevertheless, at T0 of 250 °C, the alloy, after T6-aging treatment, presented the lowest dislocation density, thereby achieving the highest strain-hardening capacity and plasticity. At T0 of 250 °C and 300 °C, the alloy exhibited superior properties, with the yield strength of 774 MPa and 803 MPa, the ultimate tensile strength of 802 MPa and 823 MPa, the elongation of 10.1 % and 6.9 %, and the corrosion current density of 1.37 × 10⁻⁶ A cm⁻² and 2.44 × 10⁻⁶ A cm⁻² in 3.5 wt % NaCl solution, respectively.
Mechanical properties and microstructure evolutions of the SLM fabricated Al-Mg-Mn-Sc-Zr alloy when deforming at elevated temperatures
SLM 制备的 Al-Mg-Mn-Sc-Zr 合金在高温变形时的力学性能和微观结构演变
2025, Materials Characterization
2025, 材料表征
The Al-Mg-Mn-Sc-Zr alloy is fabricated by selective laser melting (SLM), and the tensile deformation behaviors at 20 °C ∼ 300 °C are studied. The results indicate that the alloy exhibits significant softening when deformed at elevated temperatures. When the tensile temperature increases from 20 °C to 300 °C, the peak strength decreases from 592 MPa to 167 MPa, and the elongation increases from 13.6 % to 23.9 %, respectively. The decrease in strength is mainly due to the reduction in densities of dislocations and grain boundaries, as well as the weakening of pinning effects of dispersed Al₃(Sc,Zr) particles. The increase in elongation can be attributed to the alleviation of local stress concentration and enhancement on dislocation slip frequency during thermal deformation. In addition, the typical bimodal grain structures of the SLM alloys result in different deformation behaviors. The coarse grains usually deform preferentially under high temperatures due to their higher Schmid factors and lower strength. The unavoidable pore defects formed during the printing process will weaken the alloy's uniform plastic deformation ability and result in a deterioration of elongations, especially when the pore size further increases at higher temperatures. As a result, the improvement on elongations of the SLM fabricated Al-Mg-Mn-Sc-Zr alloys when deforming at elevated temperatures is not as significant as that of alloys fabricated by traditional methods.

View Abstract 查看摘要

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Outline 概要

Cited by (6) 被引用 (6)

Figures (19) 图 19

Tables (4) 表格 (4)

Materials Science and Engineering: A
材料科学与工程：A

Abstract 摘要

Keywords 关键词

1. Introduction 1. 引言

2. Experiment and simulation
2. 实验、模拟

2.1. Experimental details
2.1. 实验细节

2.2. Crystal plasticity computational framework
2.2. 晶体塑性计算框架

3. Results 3. 结果

3.1. Microstructure of the raw material
3.1. 原材料微观结构

3.2. Mechanical property 3.2. 力学性能

3.3. Microstructure evolution
3.3. 组织演变

3.4. Slip system activation and plasticity transfer
3.4. 滑移系激活和塑性转移

3.4.1. Slip system activation
3.4.1. 滑移系激活

3.4.2. Plasticity transfer between adjacent grains
3.4.2. 相邻晶粒间的塑性转移

3.5. Crystal plasticity simulation results
3.5. 晶体塑性模拟结果

3.5.1. Modeling and parameter calibration
3.5.1. 建模与参数校准

3.5.2. Simulated strain and stress characteristics
3.5.2. 模拟的应变和应力特征

4. Discussion 4. 讨论

4.1. The slip transfer criterion
4.1. 滑移转移准则

4.2. Heterogeneous deformation and crystal rotation
4.2. 不均匀变形和晶体旋转

5. Conclusions 5. 结论

CRediT authorship contribution statement
CRediT 作者贡献声明

Declaration of competing interest
利益冲突声明

Acknowledgments 致谢

Data availability 数据可用性

References

Cited by (6)

Effect of epitaxial growth microstructure on the stress corrosion cracking propagation behavior of fusion zone in 316L-316LN stainless steel weld joint
外延生长微观结构对 316L-316LN 不锈钢焊缝熔合区应力腐蚀开裂扩展行为的影响

Tailoring microstructure and mechanical properties of IN738LC fabricated by laser powder bed fusion through processing parameter optimization
通过优化工艺参数来调整 IN738LC 激光粉末床熔融制造的结构和力学性能

Fatigue crack growth rate investigation of cold rolled and aged Al-Mg-Zn alloy
冷轧和时效 Al-Mg-Zn 合金的疲劳裂纹扩展速率研究

Grain-scale micromechanical behaviors of hexagonal titanium utilizing in-situ high-energy diffraction microscopy and crystal plasticity finite element simulations
六方钛的晶粒尺度微观力学行为：利用原位高能衍射显微镜和晶体塑性有限元模拟

Mechanical properties and microstructure evolutions of the SLM fabricated Al-Mg-Mn-Sc-Zr alloy when deforming at elevated temperatures
SLM 制备的 Al-Mg-Mn-Sc-Zr 合金在高温变形时的力学性能和微观结构演变

In-situ investigation of slip system activation, intergranular plasticity transfer, and deformation heterogeneity of Al-Zn-Mg-Cu alloy原位研究 Al-Zn-Mg-Cu 合金滑移系激活、晶间塑性传递和变形非均匀性

Abstract 摘要

Keywords 关键词

1. Introduction 1. 引言

2. Experiment and simulation2. 实验、模拟

2.1. Experimental details2.1. 实验细节

2.2. Crystal plasticity computational framework2.2. 晶体塑性计算框架

3. Results 3. 结果

3.1. Microstructure of the raw material3.1. 原材料微观结构

3.2. Mechanical property 3.2. 力学性能

3.3. Microstructure evolution3.3. 组织演变

3.4. Slip system activation and plasticity transfer3.4. 滑移系激活和塑性转移

3.4.1. Slip system activation3.4.1. 滑移系激活

3.4.2. Plasticity transfer between adjacent grains3.4.2. 相邻晶粒间的塑性转移

3.5. Crystal plasticity simulation results3.5. 晶体塑性模拟结果

3.5.1. Modeling and parameter calibration3.5.1. 建模与参数校准

3.5.2. Simulated strain and stress characteristics3.5.2. 模拟的应变和应力特征

4. Discussion 4. 讨论

4.1. The slip transfer criterion4.1. 滑移转移准则

4.2. Heterogeneous deformation and crystal rotation4.2. 不均匀变形和晶体旋转

5. Conclusions 5. 结论

CRediT authorship contribution statementCRediT 作者贡献声明

Declaration of competing interest利益冲突声明

Acknowledgments 致谢

Data availability 数据可用性

References

In-situ investigation of slip system activation, intergranular plasticity transfer, and deformation heterogeneity of Al-Zn-Mg-Cu alloy
原位研究 Al-Zn-Mg-Cu 合金滑移系激活、晶间塑性传递和变形非均匀性

2. Experiment and simulation
2. 实验、模拟

2.1. Experimental details
2.1. 实验细节

2.2. Crystal plasticity computational framework
2.2. 晶体塑性计算框架

3.1. Microstructure of the raw material
3.1. 原材料微观结构

3.3. Microstructure evolution
3.3. 组织演变

3.4. Slip system activation and plasticity transfer
3.4. 滑移系激活和塑性转移

3.4.1. Slip system activation
3.4.1. 滑移系激活

3.4.2. Plasticity transfer between adjacent grains
3.4.2. 相邻晶粒间的塑性转移

3.5. Crystal plasticity simulation results
3.5. 晶体塑性模拟结果

3.5.1. Modeling and parameter calibration
3.5.1. 建模与参数校准

3.5.2. Simulated strain and stress characteristics
3.5.2. 模拟的应变和应力特征

4.1. The slip transfer criterion
4.1. 滑移转移准则

4.2. Heterogeneous deformation and crystal rotation
4.2. 不均匀变形和晶体旋转

CRediT authorship contribution statement
CRediT 作者贡献声明

Declaration of competing interest
利益冲突声明