Quantitative linkage between the stress at dislocation channel – Grain boundary interaction sites and irradiation assisted stress corrosion crack initiation

doi:10.1016/j.actamat.2019.02.032

Acta Materialia

Volume 170, 15 May 2019, Pages 166-175
第 170 卷，2019 年 5 月 15 日，第 166-175 页

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Abstract 摘要

Localized deformation has emerged as a key factor in the crack initiation process for irradiated steels, as cracks are observed to nucleate preferentially at these sites. Using high resolution electron backscatter diffraction (HREBSD), the local stress tensor surrounding the dislocation channel-grain boundary interaction sites was quantified and coupled with fully determined grain boundary plane orientation information to determine, for the first time, the relationship between grain boundary normal stress and intergranular crack initiation in irradiated austenitic stainless steel. A Fe

13Cr

15Ni alloy was strained in simulated boiling water reactor, normal water chemistry after quantifying the residual stress tensor at discontinuous dislocation channel – grain boundary interaction sites where grain boundaries were determined to be well oriented with respect to the loading axis. Local stresses at the grain boundary were observed to reach magnitudes greater than 1.5 GPa at a distance of 200 nm from the intersection between the dislocation channel and the grain boundary. A pseudo-threshold stress of 0.9 GPa was measured, below which no cracking was observed. As the stress acting normal to the grain boundary increased above this value, the susceptibility to cracking increased with the cracking fraction reaching 100% at the high end of the stress range. This study shows for the first time that not only does intersection between discontinuous dislocation channels and grain boundaries result in peak local stresses, but the magnitude of the local tensile stress drives the crack initiation process.
局部变形已成为辐照钢裂纹萌生过程中的关键因素，因为观察到裂纹优先在这些位置形核。通过使用高分辨率背散射电子衍射（HREBSD），量化了位错通道-晶界相互作用位置周围的局部应力张量，并结合完全确定的晶界平面取向信息，首次确定了辐照奥氏体不锈钢中晶界法向应力与沿晶裂纹萌生之间的关系。对一种 Fe

13Cr

15Ni 合金在模拟沸水反应堆的正常水化学条件下进行应变，在晶界取向相对于加载轴良好的不连续位错通道-晶界相互作用位置处，量化了残余应力张量。观察到晶界处的局部应力在位错通道与晶界交点 200 nm 处达到 1.5 GPa 以上的量级。测量到一个伪阈值应力 0.9 GPa，低于该应力值未观察到裂纹萌生。当垂直于晶界的应力超过该值时，裂纹敏感性增加，裂纹比例在应力范围的高端达到 100%。这项研究首次表明，不仅不连续位错通道与晶界的交点会产生峰值局部应力，而且局部拉伸应力的幅度驱动着裂纹萌生过程。

Graphical abstract 图示摘要

Keywords 关键词

Austenitic steels

Electron backscattering diffraction (EBSD)

Residual stresses

Molecular dynamics (MD)

Irradiation assisted stress corrosion cracking (IASCC)

奥氏体钢电子背散射衍射（EBSD）残余应力分子动力学（MD）辐照辅助应力腐蚀裂纹（IASCC）

1. Introduction 1. 引言

Nuclear reactor internal components are exposed to high temperatures, stresses, a corrosive environment, and significant radiation fields which lead to premature failure of many components. Irradiation assisted stress corrosion cracking (IASCC) has been identified as an important failure mechanism for austenitic stainless steels [1], which is a primary structural material used in current generation reactors as well as a candidate material for generation IV reactor concepts [2]. Failure of reactor components results in a high financial burden due to both replacement costs as well as reactor down time. As the licensing lifetime of reactors is increased to 60 or 80 years [3], it is becoming increasingly important to understand the underlying mechanisms controlling the failure modes of internal core components. Although IASCC has been observed and studied in both boiling water reactors (BWR) and primary water reactors (PWR) since the early 1960's [4], the underlying mechanisms governing the cracking behavior is still not well understood.
核反应堆内部组件暴露于高温、应力、腐蚀环境和强辐射场中，导致许多组件过早失效。辐照辅助应力腐蚀开裂（IASCC）已被确定为奥氏体不锈钢的重要失效机制[1]，这种材料是当前一代反应堆的主要结构材料，也是第四代反应堆概念候选材料[2]。反应堆组件的失效由于更换成本和反应堆停堆时间而造成巨大的经济负担。随着反应堆的许可寿命增加到 60 或 80 年[3]，理解控制内部核心组件失效模式的基本机制变得越来越重要。尽管自 20 世纪 60 年代初以来，IASCC 已在沸水反应堆（BWR）和压水反应堆（PWR）中被观察到和研究[4]，但控制裂纹行为的潜在机制仍然没有被充分理解。

Radiation damage during typical reactor operation results in a complex number of dynamic interactions between point defects and other evolving microstructural changes, making it difficult to isolate the cause of cracking susceptibility. As damage level increases, so do the populations of loops, precipitates, and degree of radiation induced segregation (RIS) [[5], [6], [7]]. Studies performed by Busby et al. [8] used a series of annealing treatments to preferentially remove specific defects in the microstructure in an attempt to isolate the effect of individual components of the microstructure on cracking susceptibility. The changes in cracking susceptibility could not be attributed to the observed changes in the microstructure after annealing, further detailing the complex nature of IASCC and showing that no single microstructural feature could explain the phenomenon.
在典型反应堆运行期间产生的辐射损伤，导致点缺陷与其他逐渐变化的微观结构之间出现复杂的动态相互作用，使得难以分离裂纹敏感性的成因。随着损伤程度的增加，环状缺陷、析出物和辐射诱导偏析（RIS）的种群数量也随之增加[[5], [6], [7]]。Busby 等人[8]进行的研究采用了一系列退火处理，旨在优先去除微观结构中的特定缺陷，以分离微观结构各组成部分对裂纹敏感性的影响。退火后裂纹敏感性的变化无法归因于微观结构的变化，进一步阐明了 IASCC 的复杂性，并表明没有单一的微观结构特征能够解释这一现象。

In recent years, localized deformation has been highlighted as a potentially key component in the crack initiation process. The defect clusters that evolve during irradiation act as hard barriers to dislocation motion resulting in a change in deformation mode from homogeneous slip to localized heterogeneous deformation. For a dislocation to move through an irradiated matrix, the critical resolved shear stress must be high enough to move the dislocation through the array of defects acting as hard barriers. As the first slip system is activated within a grain, dislocations interact with the defect microstructure and partially annihilate the hard barriers as they propagate [[9], [10], [11]]. The material in the wake of the first mobile dislocations is left relatively defect free compared to the rest of the matrix, allowing easier transmission of dislocations in this softer region. Therefore, subsequent dislocations will preferentially move in a narrow band mostly cleared of defects and all of the deformation experienced by the material will be isolated to these dislocation channels.
近年来，局部变形被强调为裂纹萌生过程中的一个关键因素。辐照过程中形成的缺陷团簇充当位错运动的硬障碍，导致变形模式从均匀滑移转变为局部非均匀变形。位错要穿过辐照后的基体，临界解理应力必须足够高，才能使位错穿过作为硬障碍的缺陷阵列。当晶粒内的第一个滑移系统被激活时，位错与缺陷微观结构相互作用，并在其扩展过程中部分抵消硬障碍[[9], [10], [11]]。第一个可移动位错留下的材料，与基体其他部分相比，相对缺乏缺陷，使得位错更容易在这个较软的区域传播。因此，后续位错将优先移动在一个缺陷大多被清除的狭窄带状区域，而材料所经历的变形将完全局限于这些位错通道。

McMurtrey et al. [12] identified two families of dislocation channel-grain boundary interaction (DC-GB) types: discontinuous channels, where the channels are completely arrested at the grain boundary and continuous channels, where dislocations were transmitted across the boundary into the adjacent grain. The cracking susceptibility at discontinuous channel sites was a factor of six greater than continuous channel sites, which is believed to be caused by the high local tensile stress generated by the pile-up of dislocations at the boundary. West et al. [13] presented additional evidence that local stresses at the grain boundary contribute significantly to the crack initiation process. For a set of austenitic stainless steels, it was observed that the cracking susceptibility was heavily weighted toward boundaries with a measured trace angle close to 90 degees with respect to the loading axis, which is an indication that the stress component acting normal to the grain boundary plane is important for crack initiation. However, these studies do not take into account the grain boundary plane angle in order to resolve the stress in a direction acting perpendicular to the boundary. A collection of constant stress experiments on neutron irradiated O-ring samples have shown a threshold behavior with respect to the applied stress with the lower limit for initiation existing at 40% of the yield stress of the material. This implies that a critical amount of stress is required to initiate cracks in irradiated stainless steels.
麦克马特里等[12]确定了两种位错通道-晶界相互作用（DC-GB）类型：不连续通道，其中通道在晶界处完全停止，以及连续通道，其中位错穿过晶界进入相邻晶粒。不连续通道处的开裂敏感性比连续通道处高六倍，这被认为是由位错在晶界处堆积产生的高局部拉伸应力引起的。韦斯特等[13]提供了进一步证据，表明晶界处的局部应力对裂纹萌生过程有显著贡献。对于一组奥氏体不锈钢，观察到开裂敏感性主要倾向于晶界，其测量迹线角相对于加载轴接近 90 度，这表明垂直于晶界平面的应力分量对裂纹萌生很重要。然而，这些研究没有考虑晶界平面角度，以解决垂直于晶界方向的应力。对中子辐照 O 型环样品进行的一系列恒定应力实验显示，在施加应力方面表现出阈值行为，裂纹起始的下限存在于材料屈服应力的 40%。这意味着辐照不锈钢中产生裂纹需要达到临界应力。

Recent advances in high resolution electron backscatter diffraction (HREBSD) has allowed for the quantification of local stresses with spatial resolution on the order of 100 nm. The cross-correlation technique developed by Wilkinson, Meaden, and Dingley [14] measures small changes in the Kikuchi diffraction pattern and relates them to residual strains in the material. By coupling these residual strains with material specific anisotropic elasticity coefficients, the entire residual stress tensor can be calculated. (for a detailed explanation of the technique see Refs. [[15], [16], [17]].) Using this technique, local stresses near dislocation pile-ups have been observed in both commercial purity titanium [18,19] and austenitic stainless steel [20]. In both cases high local stress fields were observed in the immediate vicinity of the pile-up of dislocations at the boundary, and little to no stress elevation was observed at sites where dislocations were transmitted across the boundary.
高分辨率背散射电子衍射（HREBSD）的最新进展使得能够在 100 nm 的空间分辨率下定量分析局部应力。Wilkinson、Meaden 和 Dingley[14]开发的相关技术通过测量 Kikuchi 衍射图案的微小变化，并将其与材料中的残余应变相关联。通过将这些残余应变与材料特有的各向异性弹性系数相结合，可以计算出整个残余应力张量。（有关该技术的详细解释，请参阅参考文献[[15], [16], [17]]。）利用该技术，研究人员在商业纯钛[18,19]和奥氏体不锈钢[20]中的位错堆积附近观察到了局部应力。在这两种情况下，在边界处位错堆积的立即邻近区域观察到了高局部应力场，而在位错穿过边界的位置几乎没有观察到应力升高。

In this study, HREBSD is coupled with the fully determined grain boundary orientation to calculate for the first time, the stress acting normal to the grain boundary at the DC-GB site. This stress is then compared to cracking behavior at analyzed sites to determine the stress dependence of IASCC initiation in austenitic stainless steel.
在本研究中，HREBSD 与完全确定的晶界取向相结合，首次计算了 DC-GB 位点的晶界法向应力。然后将该应力与分析位点的开裂行为进行比较，以确定奥氏体不锈钢中 IASCC 启裂的应力依赖性。

2. Methods 2. 方法

2.1. Experimental methods
2.1. 实验方法

The alloy selected for this study was a lab purity stainless steel produced by General Electric Global Research with a nominal composition as shown in Table 1. This alloy was selected due to its moderate IASCC susceptibility. Bulk alloy was subjected to cold rolling and a homogenizing heat treatment (1200 °C, 2 h) before a final solution annealing treatment of 950 °C for 30 min resulting in an average grain size of 25 μm. Square gauge section tensile bars were electrical discharge machined (EDM) with dimensions as shown in Fig. 1a. Prior to irradiation, samples were mechanically polished in stages from 320 to 1200 grit SiC paper. Electropolishing with a solution of 10% perchloric acid and 90% methanol was performed at 30 V and −40 °C for 60 s to produce a mirror finish on the surface of each sample.
本研究选用的合金是由通用电气全球研发中心生产的实验室纯度不锈钢，其名义成分如表 1 所示。选择该合金是因为其具有适中的 IASCC 敏感性。块状合金在冷轧后进行了均匀化热处理（1200 °C，2 小时），然后进行最终溶液退火处理（950 °C，30 分钟），最终获得平均晶粒尺寸为 25 μm。方形标距拉伸试样通过电火花加工（EDM）制成，尺寸如图 1a 所示。在辐照前，样品通过从 320 到 1200 目的 SiC 纸分阶段进行机械抛光。在 30 V 和-40 °C 下，使用 10%高氯酸和 90%甲醇的溶液进行电解抛光 60 秒，以在每个样品表面产生镜面光洁度。

Table 1. Alloy composition.
表 1. 合金成分。

Alloy Composition (wt%) 合金成分（wt%）
Cr	Ni	C	Mn 锰	Si	P	Fe
13.41	15.04	0.02	1.03	0.10	0.01	Bal.

Samples were irradiated using 2.0 MeV protons with a tight temperature control of ±7.3 °C (2σ) about 360 °C to a total dose of 5 dpa and a dose rate of 1.0 × 10⁻⁵ dpa/s at the University of Michigan Ion Beam Laboratory (MIBL). Displacement damage was calculated at 60% of the depth of the Bragg peak (12 μm) using the quick Kinchin-Pease formulation in the SRIM simulation program [21] and a displacement energy of 40 eV. The damage profile for this alloy is shown in Fig. 1b.
样品在密歇根大学离子束实验室（MIBL）使用 2.0 MeV 质子进行辐照，温度控制在 360 °C 上下±7.3 °C（2σ），总剂量为 5 dpa，剂量率为 1.0 × 10^10 dpa/s。位移损伤使用 SRIM 模拟程序中的快速 Kinchin-Pease 公式计算，在布喇格峰深度 60%（12 μm）处，位移能量为 40 eV。该合金的损伤分布如图 1b 所示。

Post irradiation, a Bruker hardness indenter was used to place a square array of indents onto the central 7 mm of each tensile bar, dividing it into ten 1.5 mm × 0.7 mm regions. The depth of each indent was measured using a Olympus LEXT confocal laser microscope before collecting EBSD scans of each individual region using a Phillips XL30 FEG SEM and TSL OIM 5 with a hexagonal grid and a step size of 0.7 μm 4–5 μm of material was then removed from the sample surface, as measured by changes in the indent depth, using 20 nm colloidal silica before rescanning the same ten regions. Through mechanical polishing, the centroid of the hardness indent does not change, so aligning the indents before and after the polishing step will reveal the degree to which each grain boundary has moved due to the polishing. The angle each grain boundary makes with respect to the sample surface is measured using the lateral shift of the grain boundary measured between two EBSD maps and the change in indent depth. A sample grain boundary structure after aligning the two EBSD maps has been shown in Fig. 2a. The angle between the vector pointing normal to each grain boundary and the loading axis is then calculated by using this grain boundary plane angle measurement and measurements of the grain boundary trace angle (angle between the surface trace and the loading axis) taken from the initial EBSD scan.
辐照后，使用 Bruker 硬度压头在每个拉伸试样的中心 7 毫米区域制作方形压痕阵列，将其划分为十个 1.5 毫米×0.7 毫米的区域。在收集每个区域的 EBSD 扫描之前，使用 Olympus LEXT 共聚焦激光显微镜测量每个压痕的深度。然后从试样表面移除 4-5 微米的材料，通过测量压痕深度的变化来确认，使用 20 纳米的胶体二氧化硅进行移除，并对相同的十个区域进行重新扫描。通过机械抛光，硬度压痕的质心不会改变，因此对抛光前后的压痕进行对准，可以揭示每个晶界由于抛光而移动的程度。使用两个 EBSD 图之间晶界横向位移和压痕深度变化来测量晶界相对于试样表面的角度。对准后的两个 EBSD 图所显示的试样晶界结构如图 2a 所示。通过使用晶界平面角度测量值和初始 EBSD 扫描中获取的晶界迹线角度测量值（表面迹线与加载轴之间的角度），计算出每个晶界法线向量与加载轴之间的角度。

Samples were then subjected to constant extension rate tensile (CERT) tests at a strain rate of 1 × 10⁻⁷ s⁻¹ to a total plastic strain of 4.5% in a high purity argon environment at 288 °C to produce dislocation channels without the influence of a corrosive environment. SEM and confocal laser images were used to document the location and character of dislocation channels after straining. Specific grain boundaries were selected for this study based on the orientation of the grain boundary with respect to the loading axis and the presence of discontinuous channels since well oriented random high angle boundaries (RHABs) with intersecting discontinuous channels show the highest susceptibility to cracking. Since the primary focus of this paper is to link the observed stress state with the cracking susceptibility rather than analyze the barriers to slip at different grain boundary types, all low angle (misorientation <15°) and CSL boundaries were avoided for HREBSD analysis. This was done to ensure that the GB cohesive strengths and barriers to dislocation propagation between the analyzed RHABs did not vary dramatically from site to site.
随后，样品在 288 °C 的高纯氩气环境中进行恒定应变速率拉伸（CERT）试验，应变速率为 1 × 10 ⁻⁷ s ⁻¹ ，直至总塑性应变为 4.5%，以在不受腐蚀环境影响的情况下产生位错通道。通过扫描电子显微镜（SEM）和共聚焦激光图像记录了应变后位错通道的位置和特征。本研究根据晶界相对于加载轴的方向以及是否存在不连续通道，选择了特定的晶界。由于取向良好且随机分布的高角度晶界（RHABs）与相交的不连续通道显示出最高的开裂敏感性，因此选择了这些晶界。由于本文的主要重点是建立观测到的应力状态与开裂敏感性之间的联系，而不是分析不同晶界类型的滑移障碍，因此所有低角度（错配角<15°）和晶体取向对称边界（CSL）边界均避免用于高分辨率电子背散射衍射（HREBSD）分析。这是为了确保所分析的 RHABs 之间的晶界 cohesive strengths 和位错传播障碍在不同位置之间没有显著差异。

20 nm colloidal silica solution was used to remove ∼200 nm of material to minimize the effect of beam shadowing during EBSD analysis. EBSD scans were performed near DC-GB interaction sites of a ∼400 μm² area with a square grid and 100 nm step size. Kikuchi patterns were collected at each step in the scan and were analyzed offline using the CrossCourt4 (CC4) software package developed by BLG Vantage. The cross correlation software was run using 50 ROIs distributed uniformly across each pattern and single crystal anisotropic elasticity coefficients for stainless steel [22]. A remapping feature in CC4 was implemented during analysis at each boundary to decrease the effect of minor lattice rotation on calculated stress values [23]. All points with a calculated mean angular error by the CC4 program above 10⁻³ rad were removed from analysis due to the large calculation errors for these points. CC4 is able to calculate the full stress tensor using the small changes in the Kikuchi band structure and the assumption that the stress acting normal to the sample surface is zero since it is unconstrained. This tensor is then rotated with respect to the sample coordinate system such that the principle stresses are aligned with the grain boundary plane measurement made prior to HREBSD analysis.
使用 20 nm 胶体二氧化硅溶液去除约 200 nm 材料，以最小化 EBSD 分析期间束影效应。在约 400 μm ² 区域内的 DC-GB 相互作用位点附近进行 EBSD 扫描，采用方形网格和 100 nm 步长。在每个扫描步骤中收集 Kikuchi 图案，并使用 BLG Vantage 开发的 CrossCourt4 (CC4)软件包进行离线分析。交叉相关软件使用均匀分布在每个图案上的 50 个 ROI 和不锈钢的单晶各向异性弹性系数[22]运行。在每次边界分析时，CC4 实现了重映射功能，以减少晶格微小旋转对计算应力值的影响[23]。由于这些点的计算误差较大，所有由 CC4 程序计算出的平均角误差超过 10 ⁻³ 弧度的点均被从分析中移除。CC4 能够利用 Kikuchi 带结构的微小变化，并假设垂直于样品表面的应力为零（因为不受约束），从而计算完整的应力张量。该张量随后相对于样品坐标系进行旋转，使得主应力与 HREBSD 分析前测量的晶界平面对齐。

A final CERT experiment was performed in simulated BWR environment (288 °C, 1500 psi, dissolved oxygen concentration of 2 ppm, and conductivity controlled at 0.2 μS/cm) to add an additional 1.5% plastic strain to induce cracking. Surface oxides were removed so that any small surface cracks would be easily visible. The cracking behavior of this sample was then related to the measured local stresses acting on each grain boundary.
最后进行了一次 CERT 实验，在模拟沸水堆环境（288°C，1500 psi，溶解氧浓度为 2 ppm，电导率控制在 0.2 μS/cm）中进行，以增加 1.5%的塑性应变来诱发表面开裂。移除了表面氧化物，以便任何微小的表面裂纹都能被清晰地观察到。然后，将此样品的开裂行为与作用在每个晶界上的测量局部应力相关联。

2.2. MD simulation methods
2.2. MD 模拟方法

For comparison with the experimental results, a simulation study was conducted using a thin-film polycrystal with 6 grains. The shapes and orientations of these grains were made to match a cluster of grains analyzed experimentally. The sample has an average grain size of 160 nm, a thickness of 10 nm, and contains ∼100 million atoms. The sample was generated using a Voronoi construction technique [24]. The Molecular Dynamics (MD) computational testing was performed using the LAMMPS implementation [25] with a time step of 1fs and a Noose-Hoover barostat and thermostat [26]. Periodic boundary conditions were used in the x- and y-directions and free surfaces were used in z.
为了与实验结果进行比较，进行了一项模拟研究，使用了具有 6 个晶粒的薄膜多晶材料。这些晶粒的形状和取向被设置为与实验分析的一组晶粒相匹配。样品的平均晶粒尺寸为 160 纳米，厚度为 10 纳米，包含约 1 亿个原子。样品是使用 Voronoi 构造技术生成的[24]。分子动力学（MD）计算测试是使用 LAMMPS 实现[25]，时间步长为 1 飞秒，并使用 Noose-Hoover 压力统计器[26]。在 x 轴和 y 轴方向上使用周期性边界条件，而在 z 轴方向上使用自由表面。

The relatively large grain size (for MD) avoids specific nano-crystalline effects such as grain boundary sliding during deformation. It is an intrinsic limitation of MD simulation that timescales are shorter than they would be in experiment, so the strain rates used in the simulation are necessarily much faster than in the experiment. Another limitation in the simulation technique used is the fact that it requires empirical interatomic potentials. The empirical nature of these potentials makes it difficult to describe the specific austenitic stainless steel used in the experiments as most interatomic potentials for Fe typically describe the BCC phase. For this reason a model FCC interatomic potential was used. Specifically, the EAM method [27] was used to describe atomic interactions with an interatomic potential developed for FCC Ni [28].
相对较大的晶粒尺寸（对于分子动力学）避免了变形过程中的特定纳米晶效应，如晶界滑移。分子动力学模拟的一个固有局限性是时间尺度比实验中的要短，因此模拟中使用的应变速率必然比实验中快得多。模拟技术中另一个局限性在于它需要经验原子间势。这些势的经验性质使得难以描述实验中使用的特定奥氏体不锈钢，因为大多数用于铁的原子间势通常描述的是体心立方相。因此，使用了模型面心立方原子间势。具体来说，使用了 EAM 方法[27]来描述原子间相互作用，该方法是使用为面心立方镍[28]开发的原子间势开发的。

After an initial relaxation procedure, the simulated grain cluster underwent virtual strain controlled tensile deformation at 300 K and a strain rate of 3 × 10⁷ s⁻¹. At strain intervals of 0.2%, snapshots of the strained samples were quenched from 300 K to 1 K in 50ps. This procedure removes the effects of thermal fluctuations and resulted in values of the local stress state of every atom, allowing atomic resolution visualization of the stress fields. Estimating per-atom stress in standard units (GPa) required an estimate of the atomic volume. For simplicity, this value was assumed to be the atomic volume of the perfect FCC lattice, using a lattice parameter of 3.52 Å. The grain boundary normal stress, σ_x’, was determined for each atom in the vicinity of the dislocation – grain boundary interaction site using the transformation as follows:
在初始弛豫过程后，模拟的晶粒团簇在 300 K 和 3 × 10^8 s^-1 的应变率下经历了虚拟应变控制拉伸变形。在 0.2%的应变间隔内，对受应变样品的快照从 300 K 淬火至 1 K，耗时 50 ps。该过程消除了热涨落的影响，并得到了每个原子的局部应力状态值，从而实现了应力场的原子分辨率可视化。估算每个原子的应力值（以 GPa 为单位）需要估计原子体积。为简化计算，假设该值为完美面心立方晶格的原子体积，晶格参数为 3.52 Å。通过以下转换公式，确定了位错-晶界相互作用位点上每个原子的晶界法向应力σ_2'：(1)

σ_{x'} = \frac{σ_{x} + σ_{y}}{2} + \frac{σ_{x} - σ_{y}}{2} \cos 2 θ + τ_{x y} \sin 2 θ

where θ is the angle between the x-direction in the simulation and the GB normal (x’). To minimize the effect of atom to atom variation in the calculated stress, a 30 atom moving average was used to calculate the stress at each distance away from the grain boundary. Visualizations of individual atomic stresses were made using the OVITO software package and the tracking of individual dislocations was done using DXA dislocation extraction algorithm within the same software [29].
其中θ是模拟中的 x 方向与晶界法线（x'）之间的夹角。为了减小计算应力中原子间差异的影响，使用了一个 30 个原子的移动平均来计算每个距离晶界的应力。使用 OVITO 软件包对单个原子的应力进行了可视化，并在同一软件中使用 DXA 位错提取算法对单个位错进行了跟踪[29]。

As the sample is deformed, grain boundaries and triple junctions emit dislocations of the Shockley partial type. These dislocations travel across grains and reach another grain boundary. Because of the time limitations of the MD technique, the effect of only a few dislocations is observable at a particular intersection region, rather than the continuous arrival of a large number of dislocations which is the case in the experimental study. Upon arrival, the dislocations pile up against the grain boundary and in some cases these dislocations are transmitted into the adjacent grain. For comparison with the experiments, a specific interaction site was selected and observed where incoming dislocations were arrested at the grain boundary at lower levels of strain, and subsequently transmitted at higher levels of strain. During accumulation of dislocations, the stress was shown to increase monotonically, and then relieve itself once transmission occurred. The chosen grain boundary had a misorientation of ∼35° and was of mixed tilt and twist character. The mechanism of transmission of dislocation is influenced by the specific grain and boundary geometry, but for this case involve a residual Burgers vector that is incorporated into the grain boundary.
随着样品变形，晶界和三重结发出肖克利部分型位错。这些位错穿越晶粒并到达另一个晶界。由于分子动力学技术的时效限制，在特定交点区域可观察到的仅是少数位错的影响，而不是实验研究中大量位错的连续到达。位错到达后，会堆积在晶界上，在某些情况下这些位错会传入相邻晶粒。为了与实验结果进行比较，选择了一个特定的相互作用位点进行观察，其中入射位错在较低应变水平下被晶界阻挡，而在较高应变水平下随后被传递。在位错积累过程中，应力被证明是单调增加的，一旦发生传递，应力就会缓解。所选晶界具有约 35°的取向差，并具有混合倾斜和扭转特征。位错传递的机制受具体的晶粒和边界几何形状的影响，但在此情况下涉及一个残余伯格斯矢量，该矢量被纳入晶界。

3. Results 3. 结果

3.1. Grain boundary plane orientation
3.1. 晶界平面取向

The objective of this study is first, to calculate the total stress acting normal to specific grain boundaries and then analyze the effect this stress has on their cracking susceptibility. To accomplish this task, grain boundaries were specifically chosen for analysis which were well oriented with respect to the loading axis since these specific sites would have the largest normal stress component during CERT testing. Using both the grain boundary trace angle (the angle between the loading direction and the line made by the grain boundary on the sample surface) and the grain boundary plane angle (the angle between the sample surface normal and the grain boundary plane) it is possible to define a vector which points normal to the grain boundary. The angular difference between this grain boundary normal vector and the loading direction is defined as the grain boundary normal offset angle, α. 50 grain boundaries were selected that had a cosine(α) value greater than 0.6 and a set of 25 grains were selected with cosine(α) values ranging from 0.2 to 0.5 to evaluate the influence of grain boundary normal stress caused directly by the applied load. The measurements of this grain boundary normal angle are made possible by the determination of the grain boundary angle with respect to the sample surface through serial sectioning. Fig. 2a shows the overlay between the same region before and after polishing with colloidal silica. Some grain boundaries show significant displacement, while others appear to be minimally displaced or not at all, suggesting that these latter boundaries are oriented almost perpendicular to the surface. Since this measurement is made using two finite points, it is not possible to determine any amount of curvature in the boundary, and for the sake of resolving stresses onto the boundary, it is assumed that the boundary is perfectly planar. Fig. 2b shows the distribution of measured grain boundary plane angles over the central 7 mm of the irradiated region. Due to the finite number of planar slices used in the calculation and the relatively large spacing between the slices, a plane angle bias arises that under samples low grain boundary plane angles. Grains with very shallow plane angles will be completely bypassed when the serial sections are spaced far apart, like they are in this case. The blue line is a fit showing the theoretical distribution of measured plane angles when taking bias into account. Note the good agreement between the fit and the data, indicating that the plane angle measurement appears to be accurately tracking the plane angles. Since the grain boundary plane angle is determined primarily by the displacement of the grain boundary, measurements of plane angles near 90° contain a significant amount of error. However, since this plane angle must be taken in conjunction with the grain boundary trace angle to obtain the grain boundary normal in the sample reference frame, errors close to ±9° at the high end of the measurement scale do not result in large errors for the calculated cosine(α) values.
本研究旨在首先计算特定晶界上的法向总应力，然后分析该应力对其开裂敏感性的影响。为完成此任务，研究人员选择了与加载轴方向良好匹配的晶界进行具体分析，因为这些特定位置在 CERT 测试期间将具有最大的法向应力分量。通过使用晶界迹线角（加载方向与晶界在样品表面形成的线之间的夹角）和晶界平面角（样品表面法线与晶界平面之间的夹角），可以定义一个指向晶界的法向向量。该晶界法向向量与加载方向之间的角度差定义为晶界法向偏移角，α。研究人员选择了 50 个余弦(α)值大于 0.6 的晶界，以及 25 个余弦(α)值在 0.2 到 0.5 范围内的晶粒，以评估由施加载荷直接引起的晶界法向应力的影响。通过连续切片法确定晶界相对于样品表面的角度，从而实现了晶界法向角的测量。图 2a 显示了同一区域在用胶体二氧化硅抛光前后的叠加情况。部分晶界发生了显著位移，而另一些则似乎位移很小或完全没有位移，这表明后者的晶界几乎垂直于表面。由于该测量使用的是两个有限点，因此无法确定晶界的任何曲率，为了将应力分解到晶界上，假设晶界是完美的平面。图 2b 显示了辐照区域中心 7 毫米范围内测量的晶界平面角分布。由于计算中使用的平面切片数量有限，且切片间距相对较大，导致平面角偏差，使得样品中低晶界平面角的情况被低估。当连续切片间距较大时，平面角非常浅的晶粒会被完全忽略，就像本例中的情况。蓝线是一条拟合曲线，显示了考虑偏置时的测量平面角的理论分布。注意拟合曲线与数据之间的良好吻合，这表明平面角测量似乎能够准确追踪平面角。由于晶界平面角主要由晶界的位移决定，接近 90°的平面角测量包含大量误差。然而，由于这个平面角必须与晶界迹线角结合才能获得样品参考系中的晶界法线，测量尺度高端接近±9°的误差不会导致计算出的 cos(α)值产生较大误差。

3.2. Intrinsic residual stress calculation
3.2. 内禀残余应力计算

Discontinuous channel sites were located by SEM after straining in argon and correlating with previously collected EBSD data. By calculating the Schmid values for each slip system using the EBSD orientation information and using the trace angle of the dislocation channel as a guide, it was possible to isolate the active slip system causing channel formation. An example of a site selected for HREBSD analysis is shown in Fig. 3a. A ∼20 × 20 μm region around the interaction site was selected for EBSD analysis to ensure that an appropriate amount of information was collected on either side of the DC-GB interaction site. The cross-correlation system used to calculate residual stresses relies on the use of a low stress reference pattern, to which all other EBSD patterns collected for a single grain are compared. This pattern is selected to be one far away from any potential stress intensifiers, like grain boundaries, and needs to be of high image quality. A sample reference pattern is selected from the site marked with an X labeled in Fig. 3a, and is shown in Fig. 3b. The individual boxes surrounding the EBSD pattern are regions of interest (ROIs) individually correlated between the reference pattern and all other patterns within a single grain. Only 4 ROIs are needed to fully calculate the residual distortion tensor, with additional ROIs enabling the calculation of a best fit distortion tensor from all permutations of 4 ROIs. Convergence on the true distortion tensor is observed to occur with an ROI count ≥30. Using material specific anisotropic elasticity coefficients, the full stress tensor can be calculated using the best fit distortion tensor. This stress tensor is initially calculated in the sample reference frame, but is rotated such that the principle stresses are aligned with the measured grain boundary normal. The full stress tensor for the site shown in Fig. 3a is shown in Fig. 3c.
在氩气中应变后，通过扫描电镜（SEM）定位不连续通道位置，并与先前收集的 EBSD 数据进行关联。利用 EBSD 取向信息计算每个滑移系统的 Schmid 值，并以位错通道的迹线角作为参考，可以分离出导致通道形成的活性滑移系统。图 3a 展示了用于高分辨率 EBSD 分析的选定位置示例。在相互作用位置周围选择了一个约 20×20 μm 的区域进行 EBSD 分析，以确保在 DC-GB 相互作用位置两侧收集到适当的信息量。用于计算残余应力的互相关系统依赖于使用低应力参考图案，将所有为单个晶粒收集的 EBSD 图案与之进行比较。该图案应选择远离任何潜在应力集中因素（如晶界）的位置，并且需要具有高图像质量。从图 3a 中标记为 X 的位置选择了一个样本参考图案，如图 3b 所示。围绕 EBSD 图案的每个方框是感兴趣区域（ROIs），这些区域在参考图案和单个晶粒内的所有其他图案之间进行单独关联。仅需 4 个 ROIs 即可完全计算残余畸变张量，增加 ROIs 能够从 4 个 ROIs 的所有排列组合中计算出最佳拟合畸变张量。当 ROIs 数量≥30 时，观察到会收敛到真实的畸变张量。使用材料特定的各向异性弹性系数，可以利用最佳拟合畸变张量计算完整的应力张量。该应力张量最初在样品参考系中计算，但会旋转，使主应力与测量的晶界法线对齐。图 3a 所示位置的完整应力张量显示在图 3c 中。

The magnitude and rate at which the stress dissipates when moving into the adjacent grain is of critical importance and is measured as a function of distance from the grain boundary for each σ₁₁ plot. In total, 75 grain boundaries with discontinuous channels and 15 sites with continuous dislocation channels were scanned using HREBSD. For the specific stress tensor presented in Fig. 3c, the σ₁₁ stress has been plotted as a function of distance from the grain boundary along a line extending perpendicular to the grain boundary. The data is shown in Fig. 4. At all sites with discontinuous channels present, the tensile stress is highest at the grain boundary and slowly decays as the distance into the adjacent grain increases. This elevated stress is limited to the first couple micrometers from the grain boundary, and decays down to the same background level of stress which is centered around 0 MPa.
当应力向相邻晶粒移动时，其衰减的幅度和速率至关重要，并且通过每个σ ₁₁ 图作为距离晶界的函数进行测量。总共使用 HREBSD 扫描了 75 个具有不连续通道的晶界和 15 个具有连续位错通道的位点。对于图 3c 中所示的具体应力张量，σ ₁₁ 应力沿着垂直于晶界延伸的线作为距离晶界的函数进行了绘制。数据如图 4 所示。在所有存在不连续通道的位点，拉伸应力在晶界处最高，随着距离相邻晶粒的增加而缓慢衰减。这种升高的应力仅限于距离晶界前几微米处，并衰减至与 0 MPa 中心相同的背景应力水平。

Due to the finite spatial resolution of the EBSD scan, it is impossible to determine the exact location of the grain boundary. In addition to this, often times EBSD patterns taken near the grain boundary will have interaction volumes that encompass both grains, resulting in a pattern that contains visible Kikuchi band structures from each grain. During the cross-correlation process, these additional bands are interpreted as extreme departures from the reference pattern and can cause very large errors in the stress calculation. To avoid of these errors, the peak stress value quoted for each scan is taken at a distance of ∼200 nm from the grain boundary. This eliminates the use of any pixels in the EBSD scan which are directly adjacent to the neighboring grain. The magnitude of the tensile stresses at discontinuous channel intersections, measured 200 nm from the grain boundary, ranged from 0.35 GPa to 1.58 GPa. In Fig. 4, the dashed red lines bounding the stress data represent the maximum and minimum stress values measured for the full collection of 75 discontinuous channel interaction sites measured by HREBSD.
由于 EBSD 扫描的空间分辨率有限，无法确定晶界的确切位置。此外，在靠近晶界处获取的 EBSD 图案通常具有包含两个晶粒的交互体积，导致图案中包含来自每个晶粒的可见 Kikuchi 带结构。在互相关过程中，这些额外的带被解释为与参考图案的极端偏差，并可能导致应力计算中产生非常大的误差。为了避免这些误差，每个扫描所引用的峰值应力值取距离晶界约 200 nm 处。这消除了 EBSD 扫描中直接邻近相邻晶粒的任何像素的使用。在距离晶界 200 nm 处测量的不连续通道交叉点的拉伸应力大小范围为 0.35 GPa 至 1.58 GPa。在图 4 中，界定应力数据的虚红线表示 HREBSD 测量的全部 75 个不连续通道交互位点所测得的最大和最小应力值。

Theoretical work by Eshelby et al. [30] produced an analytical solution to the pile-up of dislocations at an immovable barrier, similar to the case here in which dislocations channels are blocked by a grain boundary. In the Eshelby model, the number of dislocations, n, are constrained to lie in the same slip plane under the combined action of their mutual repulsion and the force of an applied stress. The resulting stress field on the other side of the stationary barrier was found to be closely approximated by a 1/r^1/2 dependence, where r is the distance from the dislocation pile-up. Due to this expected form of the stress profile, each stress distribution was fit with a least squares algorithm to a function with the form:
Eshelby 等人[30]的理论工作给出了一个关于位错在固定障碍物处堆积的分析解，类似于此处位错通道被晶界阻挡的情况。在 Eshelby 模型中，位错数量 n 在它们相互排斥力和外加应力的共同作用下被约束在同一滑移面上。研究发现，静止障碍物另一侧产生的应力场近似为 1/r ^1/2 的依赖关系，其中 r 是位错堆积的距离。由于预期的应力分布形式，每个应力分布都通过最小二乘算法拟合到一个具有如下形式的函数：(2)

σ = A + \frac{K}{\sqrt{r + B}} [G P a]

where σ denotes the grain boundary normal stress and K is the stress intensity factor that describes resistance to slip transfer of this particular grain boundary. The factor A is introduced to allow for uncertainty in the stress state of the reference pattern used during offline cross correlation analysis and B allows for uncertainty in the exact location of the grain boundary beneath the resolving limit of the EBSD step size. This analysis is similar to that used by Britton et al. [18] on the stress distributions near blocked slip bands at grain boundaries in commercial purity titanium. For each discontinuous channel site, the Eshelby fit was applied. For the full set of 75 HREBSD scans, the magnitude of the K fitting parameter ranged between 0.33 and 1.36.
其中σ表示晶界法向应力，K 是描述该晶界滑移转移抗性的应力强度因子。引入因子 A 是为了考虑离线交叉相关分析中参考图案应力状态的不确定性，B 则允许晶界在 EBSD 步长分辨率极限以下的确切位置存在不确定性。这项分析与 Britton 等人[18]在商业纯钛晶界附近受阻滑移带应力分布所使用的分析方法相似。对于每个不连续通道位置，应用了 Eshelby 拟合。对于全部 75 组 HREBSD 扫描，K 拟合参数的幅度范围在 0.33 至 1.36 之间。

For the sites with continuous channels, no elevated stresses were observed, and the profiles remained relatively flat regardless of distance from the grain boundary. These continuous profiles typically have tensile stresses that fluctuate around 0 MPa with a magnitude ranging from −200 MPa to 200 MPa. The maximum stress at the discontinuous sites was close to an order of magnitude greater than the tensile stresses observed at the continuous channel sites. Since the continuous sites did not show stress elevation near the grain boundary, a linear fit was plotted through the raw data at these particular sites. The calculated σ₁₁ for one analyzed continuous channel site is plotted as a function of distance from the grain boundary in Fig. 5. The dashed red lines above and below the presented data show the upper and lower limits of the calculated stresses at continuous channel sites.
对于具有连续通道的位错通道-晶界相互作用位点，未观察到应力升高，且无论距离晶界远近，其轮廓均保持相对平坦。这些连续轮廓通常具有在 0 MPa 附近波动的拉伸应力，其幅值在−200 MPa 到 200 MPa 之间。不连续位点的最大应力比连续通道位点的拉伸应力高出一个数量级。由于连续位点在晶界附近未显示应力升高，通过这些特定位点的原始数据绘制了线性拟合曲线。图 5 展示了所分析的连续通道位点之一计算得到的σ ₁₁ 值随距离晶界的变化关系。呈现数据上下方的虚红线分别表示连续通道位点计算应力的上限和下限。

When compared to the stress profiles observed at discontinuous channel interaction sites, there is a clear difference in the depth profileof the induced stress depending on the character of the dislocation channel interaction at the grain boundary. The stress profiles near continuous channel – grain boundary interaction sites were also observed in the study performed by Johnson et al. [20] and followed a similar trend. The stress tensor at sites where dislocations had been transmitted across the grain boundary was calculated and observed to be similar in magnitude to that of the boundary prior to deformation. It is important to keep in mind that the snapshot after slip transmission does not impart any information about the stress state at the grain boundary prior to the transmission event. Continuous channels were observed using MD simulations alongside the HREBSD measurements, and interactions between dislocations and the grain boundary did not result in an increase in the residual stress after transmission into the adjacent grain.
与在非连续通道相互作用位点上观察到的应力分布相比，根据晶界处位错通道相互作用的特性，诱应力在深度分布上存在明显差异。Johnson 等人[20]的研究中也观察到了靠近连续通道-晶界相互作用位点的应力分布，并呈现出相似的趋势。计算了位错已穿过晶界的位点的应力张量，发现其大小与变形前的晶界应力相近。需要注意的是，滑移传递后的快照并不能提供有关传递事件前晶界应力状态的信息。通过分子动力学模拟和 HREBSD 测量，观察到了连续通道，并且位错与晶界的相互作用在传递到相邻晶粒后并未导致残余应力的增加。

3.3. Relation between GB normal stress and cracking susceptibility
3.3. 晶界法向应力与开裂敏感性之间的关系

Straining in a simulated BWR environment added an additional mechanical dependent on the orientation of the grain boundary with respect to the loading axis. Therefore, the total tensile stress acting normal to the grain boundary during straining in water is a sum of the internal stress and that due to the applied load, resolved onto the GB plane. The crystallographic orientation of the deforming grain and the geometric orientation of the grain boundary itself are combined as the product between the cosine of the angle between the grain boundary normal vector and the axis of loading, and the Schmid factor of the grain containing the dislocation channels, against which the stress is plotted. A large value for this product denotes a favorably oriented grain boundary where the deforming grain has a slip system that is crystallographically well oriented with respect to the loading axis. It is assumed that if the Schmid factor is high, then it will be easier to propagate dislocations and the higher degree of plastic deformation will result in higher levels of residual stress as measured by HREBSD. Of the 75 original grain boundaries under investigation, intergranular cracking was observed at 26 sites. An example of typical crack morphology is shown in Fig. 6.
在模拟沸水堆环境中产生的应变，增加了与晶界相对于加载轴的方向相关的机械依赖性。因此，在水中的应变过程中，垂直作用于晶界上的总拉伸应力是内部应力和由于施加的载荷所产生的应力之和，这些应力被分解到晶界平面上。变形晶粒的晶体学取向和晶界本身的几何取向相结合，表现为晶界法向量与加载轴之间夹角的余弦值与包含位错通道的晶粒的 Schmid 因子的乘积，应力被绘制在这个乘积上。这个乘积的较大值表示晶界取向有利，其中变形晶粒的滑移系统在晶体学上与加载轴很好地对齐。假设如果 Schmid 因子较高，那么位错更容易传播，更高的塑性变形程度将导致更高的残余应力水平，如通过 HREBSD 测量所示。在所研究的 75 条原始晶界中，有 26 个位置观察到沿晶开裂。典型的裂纹形貌如图 6 所示。

In addition to the HREBSD analyzed sites, 75 sites with continuous channels were selected randomly and plotted alongside the HREBSD data. Based on the previous HREBSD analysis near continuous channel – grain boundary interaction sites, it is assumed that the component of residual stresses due to dislocation activity is 0 MPa, leaving only the applied stress component. Both sets of data are plotted together in Fig. 7 with closed circles denoting sites where crack initiation was observed and open circles denoting intact grain boundary sites. Cracking was only observed at sites well oriented with respect to the loading axis and that had discontinuous channels intersecting the grain boundary. The magnitude of the included error bars in Fig. 7 were determined using the errors in calculated stress when using a different reference pattern during cross-correlation coupled with errors associated with determining the exact grain boundary orientation which then affects the resolved stress acting normal to the boundary during CERT straining. The data set shown in blue therefore has errors from both the HREBSD measurement and uncertainty in the orientation of the grain boundary while the red data set only has errors associated with grain boundary geometry since the stress state found at a continuous DC-GB interaction site does not show a local elevation in tensile stress.
除了 HREBSD 分析的位置外，还随机选择了 75 个具有连续通道的位置，并与 HREBSD 数据一起绘制。基于先前在连续通道-晶界相互作用位置附近的 HREBSD 分析，假设由于位错活动引起的残余应力分量为 0 MPa，仅保留施加应力分量。两组数据在图 7 中一起绘制，实心圆表示观察到裂纹起始的位置，空心圆表示完整的晶界位置。裂纹仅在那些与加载轴方向良好匹配且具有与晶界相交的不连续通道的位置观察到。图 7 中包含的错误条宽度是通过使用交叉相关期间的不同的参考模式计算应力时的误差，结合确定精确晶界方向的误差来确定的，这会影响在 CERT 应变期间垂直于边界作用的解析应力。因此，蓝色数据集既存在 HREBSD 测量误差，也存在晶界取向的不确定性，而红色数据集仅存在与晶界几何相关的误差，因为连续的直流-晶界相互作用位点的应力状态并未显示出局部拉伸应力的升高。

4. Discussion 4. 讨论

4.1. Comparison of GB normal stress profiles with MD simulations
4.1. 晶界法向应力分布与 MD 模拟的比较

The grain boundary normal stress at dislocation-grain boundary interaction sites was studied using molecular dynamics simulations as described in detail by Johnson et al. [20] Digitally straining the virtual samples activated dislocation sources, propagating dislocations through the grain until they were arrested at a grain boundary opposite the initial source. At the grain boundaries where dislocation motion was halted, an increase in tensile stress was observed at the interaction site. An example map showing the tensile stress acting normal to the grain boundary of a region near a dislocation-grain boundary interaction site in the MD simulation is presented in Fig. 8. Due to the magnification selected to more clearly visualize the stress state generated by the dislocations, the nucleation site of the dislocations is not within the observation window. The dislocations generated during this straining were of the Shockley partial type and propagated across grain 2, ultimately reaching the boundary between grains 1 and 2. The incoming Shockley partials have a Burgers vector of 1/6[121] in the lower grain which has a Schmid factor of 0.38. The partial transmitted into the upper grain has a Burgers vector of 1/6[−211] and has a Schmid factor of 0.34. Prior to dislocation interaction with the grain boundary, the local tensile stresses are very low as shown in Fig. 8a. Up to 3% virtual strain, the deformation is accommodated by uniform elongation of the grain. This results in low levels of stress both at the grain boundary and in the grain interior. Above 3% strain, dislocations are generated at the grain boundary and propagate across the grain, ultimately intersecting another grain boundary and halting motion. Stresses increased dramatically as dislocations propagated into the boundary as the virtual strain in the digital sample was increased, reaching peak magnitudes near 3.5 GPa at the grain boundary. At levels of strain greater than 4%, slip transmission across the grain boundary was observed. The slip transmission event resulted in significant stress reduction at the grain boundary, returning the stress at the grain boundary back to background levels, in agreement with the experimental results shown in Fig. 5. The stress field observed in Fig. 8c after slip transfer has occurred is nearly identical to the stress profile in 8a prior to any dislocation interaction at the grain boundary.
在位错-晶界相互作用位点上，晶界法向应力通过分子动力学模拟进行研究，具体细节由 Johnson 等人[20]详细描述。通过数字应变虚拟样品激活位错源，使位错在晶粒中传播，直到在初始源对面的晶界处停止。在位错运动停止的晶界处，观察到相互作用位点的拉伸应力增加。图 8 展示了 MD 模拟中一个靠近位错-晶界相互作用位点的区域，其晶界法向拉伸应力的示例图。由于选择了放大倍数以更清晰地可视化位错产生的应力状态，位错的成核位点不在观察窗口内。在此应变过程中产生的位错为肖克利部分位错，它们穿过晶粒 2，最终到达晶粒 1 和晶粒 2 之间的晶界。入射的肖克利分位错在较低晶粒中具有 1/6[121]的柏格斯矢量，该晶粒的 Schmid 因子为 0.38。传入上晶粒的分位错具有 1/6[−211]的柏格斯矢量，其 Schmid 因子为 0.34。在位错与晶界相互作用之前，局部拉伸应力非常低，如图 8a 所示。在高达 3%的虚拟应变下，变形通过晶粒的均匀伸长来适应。这导致晶界和晶粒内部的应力水平较低。超过 3%应变后，位错在晶界处产生并沿晶粒传播，最终与另一晶界相交并停止运动。随着数字样品中虚拟应变的增加，位错向晶界传播时应力急剧增加，在晶界处达到峰值约 3.5 GPa。在超过 4%的应变水平下，观察到滑移通过晶界传播。滑移传递事件导致晶界处的应力显著降低，使晶界处的应力恢复到背景水平，与图 5 所示实验结果一致。滑移传递发生后，图 8c 中观察到的应力场与晶界处位错相互作用前 8a 中的应力分布几乎相同。

Fig. 8d shows the progression of the GB normal stress as a function of applied virtual strain, measured at a fixed distance of 4 nm from the grain boundary. After slip transmission, the normal stress acting at the grain boundary is reduced by a factor of 6.2. If this same factor is applied to the HREBSD results, the near GB stress value would drop from 1.5 GPa to 0.24 GPa, which is smaller than the typical errors associated with the HREBSD measurement. This low stress amplification near continuous channels was also observed by Guo et al. [19] where no stress elevation was observed near slip transmission sites in titanium. This is consistent with the observations made with HREBSD, which show a very low residual stress at locations where slip transmission has occurred. The act of transmitting dislocations into the adjacent grain is a significant stress relief mechanism, resulting in these sites being at a significantly lower level of stress than the discontinuous sites, which helps to explain why a significant level of cracking was observed at the discontinuous DC-GB sites while no cracking was observed at the sites which had a continuous channel present at the grain boundary.
图 8d 显示了晶界法向应力随施加的虚拟应变的演变，测量位置距离晶界固定为 4 nm。滑移传递后，晶界处的法向应力降低了 6.2 倍。如果将相同的倍数应用于 HREBSD 结果，近晶界应力值将从 1.5 GPa 降至 0.24 GPa，这小于 HREBSD 测量中通常的误差范围。Guo 等人[19]也观察到了这种在连续通道附近低应力放大的现象，他们在钛中未观察到滑移传递位置附近存在应力升高。这与 HREBSD 的观测结果一致，后者显示在滑移传递发生的位置处残余应力非常低。位错传递到相邻晶粒的行为是一种重要的应力释放机制，导致这些位置的应力水平显著低于不连续位置，这有助于解释为什么在不连续的 DC-GB 位置观察到显著开裂，而在晶界存在连续通道的位置未观察到开裂。

Both the transmission of dislocations and crack initiation offer a way for the crystal system to alleviate the build-up of stresses. Because of this, there is a direct competition between the critical value of stress necessary to initiate intergranular cracks and the stress required to transmit∖nucleate dislocations in the adjacent grain. However, it is difficult at this time to make any definitive statements about the threshold of stress required to propagate dislocations in the irradiated matrix due to the nature of the present study. For this analysis, the stress state in the grain boundary immediately prior to channel nucleation is required, which isn't possible for these finite interrupted straining steps. The stress required to transmit∖nucleate dislocations is also going to be a function of the local grain boundary structure and defect microstructure which are both unavailable to the MD and experimental analysis techniques used for this study. For the MD simulations, there is no simulated effect of radiation damage on the dislocation mobility nor are there any effects due to the high temperature water environment which is necessary for any intergranular cracking to occur.
位错传输和裂纹萌生都为晶体系统提供了一种缓解应力积累的方式。正因如此，在晶界裂纹萌生的临界应力值与邻近晶粒中传输/萌生位错的应力之间存在直接竞争。然而，由于本研究的特点，目前难以对辐照基质中位错传播所需的应力阈值做出任何明确的陈述。对于这项分析，需要获取通道萌生前晶界处的应力状态，但这对于这些有限的中断应变步骤来说是不可能的。传输/萌生位错所需的应力也将是局部晶界结构和缺陷微观结构的函数，而这些对于本研究使用的分子动力学和实验分析技术来说都是不可获取的。在分子动力学模拟中，没有模拟辐射损伤对位错迁移率的影响，也没有考虑高温水环境的影响，而高温水环境是任何晶界裂纹发生所必需的。

4.2. Pseudo-threshold for crack initiation
4.2. 裂纹起始的伪阈值

To better visualize the cracking data presented in Fig. 7, the cracking fraction was calculated as a function of the grain boundary normal stress, divided into uniform bins of width 0.15 GPa, and plotted in Fig. 9. Note that there exists a lower bound for crack initiation near 0.9 GPa. Below this value of GB normal stress, no crack initiation was observed, suggesting that for a given heat there is a minimum value of normal stress on the grain boundary required to initiate cracks. Once above this threshold there is scatter in the data resulting in some locations with higher stresses which do not show any crack initiation. However, as the total stress acting normal to the grain boundary increases, so does the susceptibility to cracking. Increasing the stress acting on the grain boundary results in a higher probability of cracking, with the sites above 1.65 GPa having a cracking fraction of 100%. Further, the fact that internal stresses are near zero for boundaries with slip continuity and none of these 75 boundaries cracked, provides powerful evidence for a strong dependence of cracking susceptibility on the grain boundary normal stress.
为了更好地可视化图 7 中所示的断裂数据，将断裂分数作为晶界法向应力的函数进行计算，并按 0.15 GPa 的宽度均匀划分，然后在图 9 中绘制。请注意，在 0.9 GPa 附近存在裂纹萌生的下限。当晶界法向应力低于此值时，未观察到裂纹萌生，这表明对于给定的热处理条件，晶界上存在一个最小法向应力值才能萌生裂纹。一旦超过这个阈值，数据出现散布，导致某些位置应力较高但未发生裂纹萌生。然而，随着垂直作用于晶界的总应力增加，裂纹敏感性也随之增加。增加作用于晶界的应力会提高裂纹萌生的概率，其中超过 1.65 GPa 的区域的断裂分数为 100%。此外，对于具有滑移连续性的边界，内部应力接近零，且这 75 个边界均未开裂，这为裂纹敏感性对晶界法向应力的强依赖性提供了强有力的证据。

These results provide a more fundamental explanation of the observations of a “threshold” stress for cracking of irradiated O-ring samples in primary water at 320 °C [31]. These constant load experiments only provide the time to failure of the O-ring sample and the applied stress resulting in failure. However, they also show a distinct threshold, above which cracking in this environment occurs and below which there is no cracking. Highly controlled interrupted 4-point bend tests have also been performed on neutron irradiated material in a similar aqueous environment and showed a similar “threshold” stress for initiating cracks, but with the added benefit of being able to characterize the dislocation channel structure and evolution at different steps in the straining process [32]. It was observed that dislocation channel formation either preceded or occurred simultaneously with cracking, and these cracks were found to originate at discontinuous DC-GB interaction sites. Results of our study suggest that the grain boundary normal stress at DC-GB sites is the key factor controlling IASCC in these other experiments as well.
这些结果为在 320 °C 主水环境中辐照 O 型环样品开裂的“阈值”应力观察提供了一个更根本的解释[31]。这些恒定载荷实验仅提供了 O 型环样品的失效时间和导致失效的应力。然而，它们也显示了一个明显的阈值，高于该阈值在此环境中发生开裂，低于该阈值则没有开裂。在类似的水环境中对中子辐照材料进行了高度控制的间歇四点弯曲试验，也显示出类似的“阈值”应力来引发开裂，但额外的好处是能够表征不同应变过程中位错通道结构和演变[32]。观察到位错通道的形成要么先于开裂发生，要么与开裂同时发生，并且发现这些开裂起源于不连续的 DC-GB 相互作用位点。我们研究的结果表明，在 DC-GB 位点的晶界法向应力是控制这些其他实验中 IASCC 的关键因素。

Without the influence of irradiation, deformation in this alloy is limited to homogeneous planar slip, which results in finely spaced individual slip bands [33]. Tensile bar samples strained in simulated BWR water for this study also included non-irradiated sections along the gauge length adjacent to the irradiated zone. In these non-irradiated regions, dislocation channels did not form, nor was any degree of intergranular crack initiation observed. Similar HREBSD measurements were made in a non-irradiated austenitic stainless steel with similar composition, and showed only moderate increases in stress at slip band – grain boundary interaction sites [34]. Since only GB trace angles were taken into account when resolving the calculated stresses onto the grain boundary, the stated stress are overestimated. Even so, the highest observed tensile stress in this study was 0.73 GPa well below the established 0.9 GPa crack initiation threshold observed here. Without the change in microstructure from irradiation and the subsequent change in deformation mode, local stresses high enough to eclipse the lower bound of the crack initiation threshold are not produced. However, it must be emphasized that this is not a purely mechanical problem, and the corrosive water environment in which these experiments take place plays a key role in the IASCC process which cannot be neglected. Additional straining in an inert environment does not yield any intergranular fracture, meaning the high stresses generated by dislocation pile-up at grain boundaries is a necessary, but not sufficient condition to induce intergranular cracking in this alloy.
在没有辐照影响的情况下，该合金的变形仅限于均匀平面滑移，这导致形成间距很小的单个滑移带[33]。本研究中在模拟沸水反应堆水中进行拉伸试验的拉伸棒样品，在辐照区附近的标距长度上也包含未辐照区域。在这些未辐照区域，未形成位错通道，也未观察到任何沿晶裂纹的萌生。在成分相似的未辐照奥氏体不锈钢中也进行了类似的 HREBSD 测量，结果显示滑移带-晶界相互作用位点的应力仅适度增加[34]。由于在将计算应力分解到晶界时仅考虑了晶界迹线角，因此所声明的应力被高估了。即便如此，本研究中观察到的最高拉伸应力为 0.73 GPa，远低于此处观察到的 0.9 GPa 的裂纹萌生阈值。由于辐照引起的微观结构变化以及随后的变形模式变化，没有产生足以超过裂纹萌生阈值下限的局部应力。然而必须强调，这并非一个纯粹力学问题，这些实验进行的腐蚀性水环境在 IASCC 过程中起着关键作用，这一点不可忽视。在惰性环境中施加额外应变并不会产生沿晶断裂，这意味着晶界处位错堆积产生的高应力是引发该合金沿晶断裂的必要条件，但不是充分条件。

The data in Fig. 9 shows that there is not a sharp cut-off in the stress for cracking, suggesting that there are other factors that are important in the crack initiation process. Local variations in grain boundary chemistry and oxide formation, as observed by Rigen et al. [35], could potentially account for variation in the cracking susceptibility for those boundaries with a moderate level of tensile stress. However, the increase in cracking fraction with tensile stress highlights the importance of stress as the dominant factor driving the crack initiation process, with other factors, like local grain boundary chemistry and aqueous environment, playing a secondary role. When the local stresses reach a high enough magnitude, cracking occurs regardless of local variations in the grain boundary chemistry.
图 9 中的数据显示，裂纹的应力并没有明显的截止点，这表明在裂纹萌生过程中还有其他重要因素。正如 Rigen 等人[35]观察到的，晶界化学成分的局部变化和氧化物形成，可能解释了那些具有中等拉伸应力的晶界在裂纹敏感性方面的差异。然而，随着拉伸应力的增加，裂纹比例的提高突出了应力作为主导因素在裂纹萌生过程中的重要性，而其他因素（如局部晶界化学成分和水环境）则扮演次要角色。当局部应力达到足够高的程度时，裂纹发生，而不管局部晶界化学成分如何变化。

5. Conclusions 5. 结论

High resolution electron backscatter diffraction, combined with grain boundary plane orientation determined via serial sectioning technique were used to calculate the stress tensor at specific discontinuous dislocation channel – grain boundary sites in austenitic stainless steel. The magnitude of the stress normal to the grain boundary reached values greater than 1.7 GPa at 200 nm from the grain boundary and was dependent on both the geometric orientation of the grain boundary and the slip plane containing the dislocation channel. Subsequent incremental straining resulted in intergranular crack initiation at dislocation channel – grain boundary sites that was then correlated to the normal stress on the grain boundary at that site. A pseudo-threshold for crack initiation was observed at ∼0.9 GPa, below which no crack initiation was observed. Above this minimum value, the cracking susceptibility increased with stress, reaching 100% for the highest stress range. MD simulations confirmed low stress at continuous sites is due to the nucleation of channels from previously high stress discontinuous sites. The results of this study provide for the first time, a quantitative link between the normal stress at discontinuous dislocation channel – grain boundary sites and the probability of initiating irradiation assisted stress corrosion cracks.
高分辨率背散射电子衍射技术，结合通过连续切片技术确定的晶界平面取向，被用于计算奥氏体不锈钢中特定不连续位错通道-晶界位点的应力张量。晶界法向应力的大小在距离晶界 200 纳米处达到 1.7 吉帕以上的值，并且取决于晶界的几何取向以及包含位错通道的滑移面。随后的增量应变导致在位错通道-晶界位点发生沿晶裂纹萌生，随后将其与该位点的晶界法向应力相关联。观察到裂纹萌生的伪阈值约为 0.9 吉帕，低于该值未观察到裂纹萌生。高于此最小值，裂纹敏感性随应力增加，在最高应力范围内达到 100%。分子动力学模拟证实，连续位点的低应力是由于从先前高应力的不连续位点形成的通道的形核所致。这项研究首次建立了连续位错通道-晶界位点的法向应力与辐照辅助应力腐蚀裂纹萌生概率之间的定量关系。

Acknowledgements 致谢

The authors would like to acknowledge the Michigan Ion Beam Laboratory for providing irradiated samples and Advanced Research Computing at Virginia Tech for providing computational resources and technical support that have contributed to the results reported within this paper. URL: http://www.arc.vt.edu. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under grant DE-FG02-08ER46525.
作者感谢密歇根离子束实验室提供辐照样品，以及弗吉尼亚理工大学先进研究计算中心提供计算资源和技术支持，这些资源促进了本论文所报告的结果。URL: http://www.arc.vt.edu。这项工作由美国能源部科学办公室、基础能源科学项目资助，资助号为 DE-FG02-08ER46525。

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N. Hashimoto, T.S. Byun
Deformation-induced martensite formation and dislocation channeling in neutron-irradiated 316 stainless steel
JNM (J. Nucl. Med.), 367–370 (2007), p. 960
View PDF View article View in Scopus Google Scholar
[11]
J.S. Robach, I.M. Robertson, B.D. Wirth, A. Arsenlis
In-situ transmission electron microscopy observations and molecular dynamics simulations of dislocation-defect interactions in ion-irradiated copper
Philos. Mag. A, 83 (2003), p. 955
View in Scopus Google Scholar
[12]
M.D. McMurtrey, G.S. Was, B. Cui, I.M. Robertson, L. Smith, D. Farkas
Strain localization at dislocation channel-grain boundary intersections in irradiated stainless steel
Int. J. Plast., 56 (2014), p. 219
View PDF View article View in Scopus Google Scholar
[13]
E.A. West, M.D. McMurtrey, Z. Jiao, G.S. Was
Role of localized deformation in irradiation-assisted stress corrosion cracking initiation
Metall. Mater. Trans., 43 (2012), p. 136
View in Scopus Google Scholar
[14]
A.J. Wilkinson, G. Meaden, D.J. Dingley
High-resolution elastic strain measurement from electron backscatter diffraction patterns: new levels of sensitivity
Ultramicroscopy, 106 (2006), p. 307
View PDF View article View in Scopus Google Scholar
[15]
A.J. Wilkinson, G. Meaden, D.J. Dingley
High resolution mapping of strains and rotations using electron backscatter diffraction
Mater. Sci. Technol., 22 (2006), p. 1271
View in Scopus Google Scholar
[16]
J. Kacher, C. Landon, B.L. Adams, D. Fullwood
Bragg's law diffraction simulations for electron backscatter diffraction analysis
Ultramicroscopy, 109 (2009), p. 1148
View PDF View article View in Scopus Google Scholar
[17]
D. Fullwood, B. Adams, J. Basinger, T. Ruggles, A. Khosravani, C. Sorensen, J. Kacher
Strain and Dislocation Gradients from Diffraction: Spatially-Resolved Local Structure and Defects
(2014), pp. 405-437
Crossref View in Scopus Google Scholar
[18]
T.B. Britton, A.J. Wilkinson
Stress fields and geometricall necessary dislocation density distributions near the head of a blocked slip band
Acta Mater., 60 (2012), p. 5773
Google Scholar
[19]
Y. Guo, T.B. Britton, A.J. Wilkinson
Slip band-grain boundary interactions in commercial-purity titanium
Acta Mater., 76 (2014), p. 1
View PDF View article Google Scholar
[20]
D.C. Johnson, B. Kuhr, D. Farkas, G.S. Was
Quantitative analysis of localized stresses in irradiated stainless steels using high resolution electron backscatter diffraction and molecular dynamics modeling
Scripta Mater., 116 (2016), pp. 87-90
View PDF View article View in Scopus Google Scholar
[21]
R.E. Stoller, M.B. Toloczko, G.S. Was, S. Dwaraknath, F.A. Garner
On the use of SRIM for computing radiation damage exposure
Nucl. Instrum. Methods Phys. Res. B, 310 (2013), p. 75
View PDF View article View in Scopus Google Scholar
[22]
K. Benyelloul, H. Aourag
Elastic constants of austenitic stainless steel: investigation by the first-principles calculations and the artificial neural network approach
Comput. Mater. Sci., 67 (2013), p. 353
View PDF View article View in Scopus Google Scholar
[23]
T.B. Britton, A.J. Wilkinson
High resolution electron backscatter diffraction measurements of elastic strain variations in the presence of larger lattice rotations
Ultramicroscopy, 114 (2012), pp. 82-95
View PDF View article View in Scopus Google Scholar
[24]
D. Farkas
Atomistic simulations of metallic microstructures
Curr Opin Solid St M, 17 (2013), pp. 284-297
View PDF View article View in Scopus Google Scholar
[25]
S. Plimpton
Fast parallel algorithms for short-range molecular dynamics
J. Comput. Phys., 117 (1995), pp. 1-19
View PDF View article View in Scopus Google Scholar
[26]
G. Bussi, T. Zykova-Timan, M. Parrinello
Isothermal-isobaric molecular dynamics using stochastic velocity rescaling
J. Chem. Phys., 130 (2009)
Google Scholar
[27]
M.S. Daw, M.I. Baskes
Embedded-atom method - derivation and application to impurities, surfaces, and other defects in metals
Phys. Rev. B, 29 (1984), pp. 6443-6453
View in Scopus Google Scholar
[28]
A.F. Voter, S.P. Chen
High temperature ordered intermetallic alloys
MRS Symposia Proceedings, 82 (1987), p. 175
Google Scholar
[29]
A. Stukowski
Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool
Model Simul Mater Sc, 18 (2010)
Google Scholar
[30]
J.D. Eshelby, F.C. Frank, F.R.N. Nabarro
Equilibrium of linear arrays of dislocations
Philos. Mag. A, 42 (1951), p. 351
Crossref Google Scholar
[31]
R.W. Bosch, M. Vankeerberghen, R. Gerard, F. Somville
Crack initiation testing of thimble tube material under PWR conditions to determine a stress threshold for IASCC
JNM (J. Nucl. Med.), 461 (2015), pp. 112-121
View PDF View article View in Scopus Google Scholar
[32]
K.J. Stephenson, G.S. Was
The role of dislocation channeling in IASCC initiation of neutron irradiated stainless steel
JNM (J. Nucl. Med.), 481 (2016), pp. 214-225
View PDF View article View in Scopus Google Scholar
[33]
P.R. Swann
Dislocation substructure vs. transgranular stress corrosion susceptibility of single phase alloys
Corrosion, 19 (1963)
Google Scholar
[34]
D.C. Johnson, M.D. McMurtrey, G.S. Was
Quantitative stress measurements near blocked slip bands in austenitic stainless steel using high resolution electron backscatter diffraction
Microscopy and Microanalysis Proceedings, 21 (2015), pp. 1017-1018
Google Scholar
[35]
M. He, D.C. Johnson, G.S. Was, I.M. Robertson
The role of grain boundary microchemistry in irradiation-assisted stress corrosion cracking of a Fe-13Cr-15Ni alloy
Acta Mater., 138 (2017), pp. 61-71
View PDF View article View in Scopus Google Scholar

Cited by (73)

Anisotropy investigation of an ECAP-processed Mg-Al-Ca-Mn alloy with synergistically enhanced mechanical properties and corrosion resistance
2022, Journal of Alloys and Compounds
Anisotropy of a 32-pass equal channel angular pressing (ECAP) processed Mg-3.7Al-1.8Ca-0.4Mn (wt%) alloy with synergistically enhanced mechanical properties and corrosion resistance was investigated. Compared with coarse α-Mg grains and discontinuous network Al₂Ca phase in as-cast alloy, the ECAP alloy exhibits homogeneous fine α-Mg grains (~2.6 µm), but refined Al₂Ca particles show different distribution in three planes, which is network in the extrusion plane (EP), uniform in normal plane (NP) and bandlike in transverse plane (TP). Refinement of microstructure after ECAP resulted in the synergistically enhanced mechanical and corrosion performances in three planes (directions). Moreover, due to grain refinement, the protective film was easily produced on the ECAP alloy, resulting in different corrosion mechanisms developed between ECAP and as-cast alloys. The main factors effecting anisotropic properties of ECAP alloy are Al₂Ca distribution and texture of α-Mg. Based on the anisotropy investigations, grain size in several microns and high (0001) basal texture density are necessary to realize RE-free Mg-Al-Ca-Mn alloys with synergetic high strength and good corrosion performance.
An atomistic-to-microscale computational analysis of the dislocation pileup-induced local stresses near an interface in plastically deformed two-phase materials
2022, Acta Materialia
Taking the two-phase material as a model system, here we perform atomistic-to-microscale computational analysis on how the dislocations pileup is formed at a buried interface through two-dimensional concurrent atomistic-continuum simulations. One novelty here is a simultaneous resolution of the $μ$ m-level dislocation slip, the pileup-induced stress complexity, and the atomic-level interface structure evolution all in one single model. Our main findings are: (i) the internal stresses induced by a pileup spans a range up to hundreds of nanometers when tens of dislocations participate the pileup; (ii) the resulting stress concentration decays as a function of the distance, $r$ , away from the pileup tip, but deviates from the Eshelby model-based $1 / r^{0.5}$ , where the interface was assumed to be rigid without allowing any local structure reconstruction; and (iii) the stress intensity factor at a pileup tip is linearly proportional to the dislocation density nearby the interface only when a few dislocations are involved in the pileup, but will suddenly ”upper bend” to a very high level when tens of or more dislocations arrive at the interface. The gained knowledge can be used to understand how the local stresses may dictate the plastic flow-induced phase transformations, twinning, or cracking in heterogeneous materials such as polycrystalline steel, Ti-, Mg-, high entropy alloys, fcc/bcc, fcc/hcp, and bcc/hcp composites, containing a high density of interfaces.
Quantitative study of the effect of grain boundary parameters on the slip system level Hall-Petch slope for basal slip system in Mg-4Al
2020, Acta Materialia
Citation Excerpt :
Recently, the development of high-resolution electron backscatter diffraction (HR-EBSD) technique provides the possibility of measuring the stress components locally in materials with the spatial resolution on the order of 100 nm [49]. Using this technique, the local stress concentration, ahead of dislocation pile-ups, has been successfully examined in commercial purity titanium [50–52], irradiated steel [53,54], and unalloyed Mg [55]. In this work, HR-EBSD measurements are analyzed using a continuum dislocation pile-up model to calculate the micro-Hall-Petch coefficient of the basal slip system for nine different grain boundaries in a deformed Mg-4Al sample.
Several theoretical studies have reported that the geometry and structure of grain boundaries in polycrystalline materials could impose a significant effect on the Hall-Petch slope. However, experimental observations are primarily limited by the ability of the techniques to accurately quantify the grain boundary strength and validate these theoretical models. Using high-resolution electron backscatter diffraction (HR-EBSD), the local stress tensor ahead of a slip band blocked by a grain boundary was quantified and coupled with a continuum dislocation pile-up model to assess the barrier strength of specific grain boundaries to specific slip systems, referred to as micro-Hall-Petch coefficient. For basal slip system in a deformed Mg-4Al alloy, the micro-Hall-Petch coefficient $(k_{μ}^{b a s a l})$ varied significantly, from 0.054 to 0.184 $MPa - m^{1 / 2}$ for nine different grain boundaries. These results were correlated with geometric descriptors of the respective grain boundaries, with three-dimensional GB profile additionally measured via focused ion beam milling. It was found that the angle between the two slip plane traces on the grain boundary plane was the most sensitive parameter affecting $k_{μ}^{b a s a l}$ , followed by the angle between the slip directions. A functional form for calculation of $k_{μ}^{b a s a l}$ depending on these two angles is proposed to augment crystal plasticity constitutive models with slip resistance dependent on some measure of the grain size. The method allows a new pathway to calibrate grain size strengthening parameters in crystal plasticity models, allowing further computational investigations of the interrelationship between texture, grain morphology, and the Hall Petch effect.
Corrosion behavior and mechanism of Cr–Mo alloyed steel: Role of ferrite/bainite duplex microstructure
2019, Journal of Alloys and Compounds
This study presents a systematic investigation of the corrosion behavior and corrosion mechanism of a novel ultralow-carbon Cr–Mo alloyed ferrite/bainite duplex steel rebar. Electrochemical tests revealed the studied steel rebar to have satisfactory corrosion resistance in an NaCl medium, similar to 430 stainless steel and better than 403 stainless steel. The formation of a Cr-dominated bilayer-structured oxidation passive film endows the steel with excellent passivity. During long-term exposure, the Cr–Mo alloyed steel presented no tendency of pitting corrosion. Meanwhile, the formation of a Cr–Mo enriched rust layer inhibited penetration of the corrosive medium, efficiently delaying corrosion propagation in the steel matrix. Given its excellent anticorrosion performance, this novel alloyed steel rebar has great application potential in marine concrete structures. Electron probe microanalyzer, transmission electron microscope, and electron backscattered diffraction analysis of the rebar matrix revealed the bainite phase to have lower Cr–Mo content but more crystal defects than the ferrite phase, leading to the lower potential and higher corrosion tendency of the bainite phase. Microgalvanic corrosion between the bainite phase (anode) and ferrite phase (cathode) caused prior breakdown of the passive film on the bainite phase, stimulating corrosion initiation of this Cr–Mo alloyed duplex steel.
An insight into oversaturated deformation-induced sigma precipitation in Super304H austenitic stainless steel
2019, Materials and Design
A new mechanism of the deformation-promoted precipitation of the sigma phase during aging at 650 °C in nanocrystallized Super304H austenitic stainless steel was proposed for its extremely early nucleation and subsequently fast growth. Unlike the reports of sigma phase nucleation at the recrystallizing grain boundaries in other deformed steels, the sigma phase was found to nucleate before recrystallization during aging in the over-saturated shot-peened Super304H steel at stress concentrations with high distortion energy (nanograin boundaries, twinning intersections and interfaces of dispersion strengthening phases like Nb(C,N)). The high-distortion areas favored the segregation of chromium and consequently facilitated the structure transformation from face-centered cubic austenite to topologically close-packed sigma phase. Sigma phase particles were found to grow slowly in the early stage of aging due to the residual compressive stress field in the deformed austenite matrix, and began to grow abnormally quickly to be 1–2 μm in size at the recrystallizing boundaries when recrystallization commences, due to both the release of residual compressive stress at the recrystallized region and the fast chromium diffusion at the deformed nanostructure region. To avoid the occurrence of sigma phases, the degree of surface deformation should be controlled to be lower than the deformation saturation value.
Constructing function domains in NiTi shape memory alloys by additive manufacturing
2022, Virtual and Physical Prototyping

View all citing articles on Scopus

View Abstract

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View in Scopus Google Scholar

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E.A. West, M.D. McMurtrey, Z. Jiao, G.S. Was
Role of localized deformation in irradiation-assisted stress corrosion cracking initiation
Metall. Mater. Trans., 43 (2012), p. 136
View in Scopus Google Scholar

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A.J. Wilkinson, G. Meaden, D.J. Dingley
High-resolution elastic strain measurement from electron backscatter diffraction patterns: new levels of sensitivity
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View PDF View article View in Scopus Google Scholar

[15] [15]
A.J. Wilkinson, G. Meaden, D.J. Dingley
High resolution mapping of strains and rotations using electron backscatter diffraction
Mater. Sci. Technol., 22 (2006), p. 1271
View in Scopus Google Scholar

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J. Kacher, C. Landon, B.L. Adams, D. Fullwood
Bragg's law diffraction simulations for electron backscatter diffraction analysis
Ultramicroscopy, 109 (2009), p. 1148
View PDF View article View in Scopus Google Scholar

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D. Fullwood, B. Adams, J. Basinger, T. Ruggles, A. Khosravani, C. Sorensen, J. Kacher
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T.B. Britton, A.J. Wilkinson
Stress fields and geometricall necessary dislocation density distributions near the head of a blocked slip band
Acta Mater., 60 (2012), p. 5773
Google Scholar

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Y. Guo, T.B. Britton, A.J. Wilkinson
Slip band-grain boundary interactions in commercial-purity titanium
Acta Mater., 76 (2014), p. 1
View PDF View article Google Scholar

[20] [20]
D.C. Johnson, B. Kuhr, D. Farkas, G.S. Was
Quantitative analysis of localized stresses in irradiated stainless steels using high resolution electron backscatter diffraction and molecular dynamics modeling
Scripta Mater., 116 (2016), pp. 87-90
View PDF View article View in Scopus Google Scholar

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R.E. Stoller, M.B. Toloczko, G.S. Was, S. Dwaraknath, F.A. Garner
On the use of SRIM for computing radiation damage exposure
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View PDF View article View in Scopus Google Scholar

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K. Benyelloul, H. Aourag
Elastic constants of austenitic stainless steel: investigation by the first-principles calculations and the artificial neural network approach
Comput. Mater. Sci., 67 (2013), p. 353
View PDF View article View in Scopus Google Scholar

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T.B. Britton, A.J. Wilkinson
High resolution electron backscatter diffraction measurements of elastic strain variations in the presence of larger lattice rotations
Ultramicroscopy, 114 (2012), pp. 82-95
View PDF View article View in Scopus Google Scholar

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D. Farkas
Atomistic simulations of metallic microstructures
Curr Opin Solid St M, 17 (2013), pp. 284-297
View PDF View article View in Scopus Google Scholar

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S. Plimpton
Fast parallel algorithms for short-range molecular dynamics
J. Comput. Phys., 117 (1995), pp. 1-19
View PDF View article View in Scopus Google Scholar

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G. Bussi, T. Zykova-Timan, M. Parrinello
Isothermal-isobaric molecular dynamics using stochastic velocity rescaling
J. Chem. Phys., 130 (2009)
Google Scholar

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M.S. Daw, M.I. Baskes
Embedded-atom method - derivation and application to impurities, surfaces, and other defects in metals
Phys. Rev. B, 29 (1984), pp. 6443-6453
View in Scopus Google Scholar

[28] [28]
A.F. Voter, S.P. Chen
High temperature ordered intermetallic alloys
MRS Symposia Proceedings, 82 (1987), p. 175
Google Scholar

[29] [29]
A. Stukowski
Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool
Model Simul Mater Sc, 18 (2010)
Google Scholar

[30] [30]
J.D. Eshelby, F.C. Frank, F.R.N. Nabarro
Equilibrium of linear arrays of dislocations
Philos. Mag. A, 42 (1951), p. 351
Crossref Google Scholar

[31] [31]
R.W. Bosch, M. Vankeerberghen, R. Gerard, F. Somville
Crack initiation testing of thimble tube material under PWR conditions to determine a stress threshold for IASCC
JNM (J. Nucl. Med.), 461 (2015), pp. 112-121
View PDF View article View in Scopus Google Scholar

[32] [32]
K.J. Stephenson, G.S. Was
The role of dislocation channeling in IASCC initiation of neutron irradiated stainless steel
JNM (J. Nucl. Med.), 481 (2016), pp. 214-225
View PDF View article View in Scopus Google Scholar

[33] [33]
P.R. Swann
Dislocation substructure vs. transgranular stress corrosion susceptibility of single phase alloys
Corrosion, 19 (1963)
Google Scholar

[34] [34]
D.C. Johnson, M.D. McMurtrey, G.S. Was
Quantitative stress measurements near blocked slip bands in austenitic stainless steel using high resolution electron backscatter diffraction
Microscopy and Microanalysis Proceedings, 21 (2015), pp. 1017-1018
Google Scholar

[35] [35]
M. He, D.C. Johnson, G.S. Was, I.M. Robertson
The role of grain boundary microchemistry in irradiation-assisted stress corrosion cracking of a Fe-13Cr-15Ni alloy
Acta Mater., 138 (2017), pp. 61-71
View PDF View article View in Scopus Google Scholar

Outline 概要

Cited by (73) 被引用次数 (73)

Figures (10) 图 (10)

Tables (1) 表格 (1)

Acta Materialia

Abstract 摘要

Graphical abstract 图示摘要

Keywords 关键词

1. Introduction 1. 引言

2. Methods 2. 方法

2.1. Experimental methods
2.1. 实验方法

2.2. MD simulation methods
2.2. MD 模拟方法

3. Results 3. 结果

3.1. Grain boundary plane orientation
3.1. 晶界平面取向

3.2. Intrinsic residual stress calculation
3.2. 内禀残余应力计算

3.3. Relation between GB normal stress and cracking susceptibility
3.3. 晶界法向应力与开裂敏感性之间的关系

4. Discussion 4. 讨论

4.1. Comparison of GB normal stress profiles with MD simulations
4.1. 晶界法向应力分布与 MD 模拟的比较

4.2. Pseudo-threshold for crack initiation
4.2. 裂纹起始的伪阈值

5. Conclusions 5. 结论

Acknowledgements 致谢

References

Cited by (73)

Anisotropy investigation of an ECAP-processed Mg-Al-Ca-Mn alloy with synergistically enhanced mechanical properties and corrosion resistance

An atomistic-to-microscale computational analysis of the dislocation pileup-induced local stresses near an interface in plastically deformed two-phase materials

Quantitative study of the effect of grain boundary parameters on the slip system level Hall-Petch slope for basal slip system in Mg-4Al

Corrosion behavior and mechanism of Cr–Mo alloyed steel: Role of ferrite/bainite duplex microstructure

An insight into oversaturated deformation-induced sigma precipitation in Super304H austenitic stainless steel

Constructing function domains in NiTi shape memory alloys by additive manufacturing

Full length article 全文Quantitative linkage between the stress at dislocation channel – Grain boundary interaction sites and irradiation assisted stress corrosion crack initiation位错通道-晶界相互作用位点的应力与辐照辅助应力腐蚀裂纹萌生的定量联系

Abstract 摘要

Graphical abstract 图示摘要

Keywords 关键词

1. Introduction 1. 引言

2. Methods 2. 方法

2.1. Experimental methods2.1. 实验方法

2.2. MD simulation methods2.2. MD 模拟方法

3. Results 3. 结果

3.1. Grain boundary plane orientation3.1. 晶界平面取向

3.2. Intrinsic residual stress calculation3.2. 内禀残余应力计算

3.3. Relation between GB normal stress and cracking susceptibility3.3. 晶界法向应力与开裂敏感性之间的关系

4. Discussion 4. 讨论

4.1. Comparison of GB normal stress profiles with MD simulations4.1. 晶界法向应力分布与 MD 模拟的比较

4.2. Pseudo-threshold for crack initiation4.2. 裂纹起始的伪阈值

5. Conclusions 5. 结论

Acknowledgements 致谢

References

Full length article 全文
Quantitative linkage between the stress at dislocation channel – Grain boundary interaction sites and irradiation assisted stress corrosion crack initiation
位错通道-晶界相互作用位点的应力与辐照辅助应力腐蚀裂纹萌生的定量联系

2.1. Experimental methods
2.1. 实验方法

2.2. MD simulation methods
2.2. MD 模拟方法

3.1. Grain boundary plane orientation
3.1. 晶界平面取向

3.2. Intrinsic residual stress calculation
3.2. 内禀残余应力计算

3.3. Relation between GB normal stress and cracking susceptibility
3.3. 晶界法向应力与开裂敏感性之间的关系

4.1. Comparison of GB normal stress profiles with MD simulations
4.1. 晶界法向应力分布与 MD 模拟的比较

4.2. Pseudo-threshold for crack initiation
4.2. 裂纹起始的伪阈值