Elsevier

Corrosion Science  腐蚀科学

Volume 85, August 2014, Pages 428-435
第 85 卷，2014 年 8 月，第 428-435 页
Corrosion Science

Grain boundary structure and intergranular stress corrosion crack initiation in high temperature water of a thermally sensitised austenitic stainless steel, observed in situ
晶界结构和热敏化奥氏体不锈钢在高温水中的晶间应力腐蚀裂纹萌生，原位观察

https://doi.org/10.1016/j.corsci.2014.04.050Get rights and content  获取权利和内容
Full text access  全文访问

Highlights  要点

  • •
    Stress corrosion crack initiation in high temperature water has been observed for the first time in situ.
    首次在原位观察到高温水中的应力腐蚀裂纹萌生。
  • •
    Grain boundary normal stress is predicted using 3D grain boundary and grain orientation data.
    利用 3D 晶界和晶粒取向数据预测晶界法向应力。
  • •
    Initiation coincided with the most highly stressed, sensitised grain boundary.
    萌生发生在应力最高、敏化的晶界上。
  • •
    This is a foundation for modelling effects of thermo-mechanical processing on IGSCC initiation.
    这是模拟热机械加工对 IGSCC 起始影响的模型基础。

Abstract  摘要

The development of an intergranular stress corrosion crack initiation site in thermally sensitised type 304 austenitic stainless steel has been observed in situ in high temperature oxygenated water using digital image correlation of time-resolved optical observations. The grain boundary normal stresses were calculated using the Schmid-Modified Grain Boundary Stress (SMGBS) model of Was et al., applying three-dimensional data for the grain boundary planes and grain orientations. The initiation site coincided with the most highly stressed sensitised boundary, demonstrating the importance of the combined contributions to crack initiation of grain boundary structure and plastic strain incompatibility.
通过使用时间分辨光学观察的数字图像相关技术，在高温富氧水中原位观察了热敏化 304 奥氏体不锈钢中沿晶应力腐蚀裂纹起始位置的发展。利用 Was 等人的 Schmid-Modified Grain Boundary Stress (SMGBS)模型计算了晶界法向应力，该模型采用晶界平面和晶粒取向的三维数据。起始位置与最应力集中的敏化晶界相吻合，这表明晶界结构和塑性应变不匹配对裂纹起始的综合贡献非常重要。

Graphical abstract  图示摘要

Keywords  关键词

A. Stainless steel
C. Intergranular corrosion
C. Stress corrosion

A. 不锈钢 C. 沿晶腐蚀 C. 应力腐蚀

1. Introduction  1. 引言

Intergranular stress corrosion cracking (IGSCC) requires a susceptible material, an applied stress and a corrosive environment [1]. In order to design resistant materials or manage IGSCC by predicting the likelihood of failure during service, it is necessary to quantify the influences of microstructure, loading and environment on both initiation (e.g. frequency of initiation sites, probability of initiation with time) and also propagation (e.g. fracture mechanics) [2]. The development of predictive models for IGSCC has therefore been a long-standing goal of corrosion research [3], [4], [5]. In austenitic stainless steels that are sensitised by thermal aging or fast neutron irradiation, the susceptibility of a microstructure to IGSCC is affected by the grain boundary structure and the local deformation. The factors that have been identified as influencing intergranular crack initiation include the Schmid factors in the adjacent grains [6], [7], [8], [9], [10], the grain boundary inclination to the tensile axis [7], [10] and the structure of the grain boundaries [11], [12], [13], [14].
晶间应力腐蚀开裂（IGSCC）需要易感材料、施加的应力和腐蚀环境[1]。为了设计耐蚀材料或通过预测服役期间失效的可能性来管理 IGSCC，有必要量化微观结构、载荷和环境对起始（例如起始位点的频率、随时间变化的起始概率）以及扩展（例如断裂力学）的影响[2]。因此，IGSCC 预测模型的开发一直是腐蚀研究的一个长期目标[3]、[4]、[5]。在热老化或快中子辐照敏化的奥氏体不锈钢中，微观结构对 IGSCC 的敏感性受晶界结构和局部变形的影响。已被确定为影响晶间裂纹起始的因素包括相邻晶粒中的 Schmid 因子[6]、[7]、[8]、[9]、[10]、晶界与拉伸轴的倾角[7]、[10]以及晶界的结构[11]、[12]、[13]、[14]。
To develop predictive models, it is important that these factors are properly described, based on full understanding of the physical mechanisms of degradation. For instance, it has been widely observed that the susceptibility to intergranular fracture, such as via IGSCC, is determined by the crystallography of the grain boundaries (see for example [11], [12], [13]). Predictive models have been created to describe intergranular degradation based on the distribution of “special” and “random” grain boundaries. The “Grain Boundary Engineering” (GBE) concept introduced by Watanabe [11] proposed making resistant materials by increasing the fraction of “special” grain boundaries. However, the limited experimental data make the definition of a “special” grain boundary quite difficult. The CSL or coincidence site lattice model [15] is commonly used to describe the crystallographic relationship between adjacent grain crystal lattices, based on the general observation that boundaries with ∑ ⩽ 29 are often more resistant to degradation mechanisms such as cavitation, sensitization, fracture and stress-corrosion cracking [16]; consequently a “special” grain boundary is often classified to have a CSL value less than or equal to ∑29, whilst “random” grain boundaries have values above ∑29 and are considered to have a lower resistance.
为了开发预测模型，重要的是基于对降解物理机制的全面理解，正确描述这些因素。例如，人们已经广泛观察到，晶间断裂的敏感性，如 IGSCC，是由晶界的晶体学特性决定的（例如[11]、[12]、[13]）。基于“特殊”和“随机”晶界的分布，已经创建了预测模型来描述晶间降解。Watanabe[11]引入的“晶界工程”（GBE）概念提出通过增加“特殊”晶界的比例来制造耐腐蚀材料。然而，有限的实验数据使得“特殊”晶界的定义相当困难。 CSL（ coincidence site lattice）模型[15]通常用于描述相邻晶粒晶体晶格之间的晶体学关系，其基于普遍观察到的现象：∑⩽29 的边界通常对空化、敏化、断裂和应力腐蚀开裂等退化机制具有更高的抗性[16]。因此，“特殊”晶界通常被归类为具有小于或等于∑29 的 CSL 值，而“随机”晶界则具有大于∑29 的值，被认为具有较低的抗性。
This classification is an approximation: Gertsman and Bruemmer [14] observed IGSCC in a thermally sensitised type 304 austenitic steel, tested in a high-temperature water environment (simulated PWR, Pressurised Water Reactor, environment), finding that only the ∑3 grain boundaries were “special” and that not all of these were resistant to IGSCC; the ∑9 and ∑27 were also found to crack. Rahimi et al. [17] also observed that microstructure plays an important role in intergranular cracking during an in situ stress corrosion cracking experiment on thermally sensitised type 304 stainless steel, tested in acidified potassium tetrathionate solution; the majority (88%) of grain boundaries that failed were ‘random’ grain boundaries (∑ > 29), which was above the expected proportion in the microstructure (57%), but also 10% of the cracked boundaries were ∑3; all proportions are by number of boundaries.
这种分类是一种近似：Gertsman 和 Bruemmer[14]在高温水环境（模拟压水堆环境）中测试了一种热敏化 304 奥氏体钢，观察到了晶间应力腐蚀裂纹（IGSCC），发现只有∑3 晶界是“特殊”的，但这些晶界并非全部都抵抗 IGSCC；∑9 和∑27 晶界也被发现开裂。Rahimi 等人[17]也在热敏化 304 不锈钢的酸化四硫酸钾溶液中进行原位应力腐蚀裂纹实验时观察到，微观结构在晶间开裂中起着重要作用；失效的晶界中大多数（88%）是“随机”晶界（∑ > 29），这高于微观结构中预期的比例（57%），但也有 10%的开裂晶界是∑3；所有比例均按晶界数量计算。
The CSL-based GBE approach is incomplete [18] since it does not take into consideration the grain boundary plane, which plays an important role in determining grain boundary properties. A grain boundary requires five degrees of freedom to define its geometry; two degrees of freedom define the physical orientation of the grain boundary plane and the other three degrees of freedom represent the crystal misorientation across the grain boundary (i.e. the CSL description). King et al. [19] were the first to observe in situ in 3D the interaction between microstructure and IGSCC, using diffraction contrast tomography to measure the grains’ orientation and shape in a thermally sensitised austenitic steel, combined with tomographic observations of stress corrosion cracking (tested in acidified potassium tetrathionate solution); the grain boundaries that had a higher resistance to IGSCC were not necessarily low ∑ boundaries, but were boundaries that were oriented close to the low {hkl} Miller index planes, such as coherent twin boundaries. Thermal sensitization is caused by intergranular carbide precipitation and the associated decrease in chromium concentration at grain boundaries; Jones et al. [20] observed that carbide precipitation in stainless steel is selective to the grain boundary plane rather than just the CSL description; incoherent ∑3 twins were not immune to precipitation while precipitation did not occur at coherent ∑3 twin boundaries. Low {hkl} planes may thus be less susceptible to sensitization.
基于 CSL 的 GBE 方法是不完整的[18]，因为它没有考虑晶界平面，而晶界平面在决定晶界特性中起着重要作用。晶界需要五个自由度来定义其几何形状；两个自由度定义晶界平面的物理取向，另外三个自由度代表晶界处的晶体取向偏差（即 CSL 描述）。King 等人[19]首次使用衍射衬度断层扫描技术，在三维尺度下观察了微观结构与 IGSCC 之间的相互作用，测量了敏化奥氏体钢中晶粒的取向和形状，并结合应力腐蚀开裂的断层扫描观察（在酸性四硫酸钾溶液中测试）；对 IGSCC 具有更高抗性的晶界不一定是低∑晶界，而是那些取向接近低{hkl}米勒指数平面的晶界，例如 coherent twin boundaries。 热敏化是由沿晶界碳化物析出以及由此导致的晶界处铬浓度降低引起的；Jones 等人[20]观察到，不锈钢中的碳化物析出具有选择性，倾向于晶界平面而非仅限于 CSL 描述；非协调的∑3 孪晶并非不受析出影响，而析出则未发生在协调的∑3 孪晶界上。因此，低{hkl}晶面可能对热敏化具有较低敏感性。
Plastic deformation in austenitic stainless steel is heterogeneous and influenced by the local environment of the grains [21]. The Schmid factor [22], which expresses the geometrical relationship between the direction of the applied force and the shear deformation mode, is commonly used to describe local plastic deformation in crystalline materials, since incompatibility of Schmid factor between adjacent grains can be responsible for damage initiation. For instance, in fatigue a strong correlation is observed between strain and intergranular crack initiation; Rho et al. [6] in a study of intergranular cavitation from low cycle high temperature fatigue of a Nb-A286 alloy observed accelerated cavitation at high angle grain boundaries due to the strain incompatibility arising from the tendency to yield in adjacent grains. McMurtrey et al. [7] studied irradiation-assisted stress corrosion cracking of proton-irradiated Fe–13Cr–15Ni austenitic steel, tested in a simulated BWR (boiling water reactor) high temperature water environment, and deduced that intergranular crack initiation depended on slip continuity. Fukuya et al. [8] studied grain separation in cold worked and neutron-irradiated type SU2316 stainless steels strained at elevated temperatures, concluding that the tendency for grain boundary separation increased with the increase of Schmid factor mismatch (i.e. difference in Schmid factor of the adjacent grains). The same trend was observed by West et al. [9], [10] in a study of proton-irradiated type 316L steel strained in supercritical water, in which intergranular cracking tended to occur where grains of higher Schmid factor were adjacent to grains with a low Schmid factor. Several studies [7], [9], [10] also noted the grain boundary inclination to the tensile axis was a contributing factor to IGSCC.
奥氏体不锈钢的塑性变形具有非均匀性，并受晶粒局部环境的影响[21]。Schmid 因子[22]，用于表达施加力的方向与剪切变形模式之间的几何关系，通常被用来描述晶体材料的局部塑性变形，因为相邻晶粒间 Schmid 因子的不匹配可能是损伤起始的原因。例如，在疲劳过程中观察到应变与沿晶裂纹起始之间存在强相关性；Rho 等人[6]在对 Nb-A286 合金低循环高温疲劳引起的沿晶气孔进行研究时，观察到由于相邻晶粒屈服趋势导致的应变不匹配，在高角度晶界处加速了气孔的形成。McMurtrey 等人[7]研究了质子辐照 Fe–13Cr–15Ni 奥氏体钢的辐照辅助应力腐蚀开裂，试验在模拟沸水反应堆（BWR）高温水环境中进行，并推断沿晶裂纹起始依赖于滑移连续性。Fukuya 等人 [8] 研究了冷加工和中子辐照的 SU2316 不锈钢在高温下的晶界分离现象，得出晶界分离的倾向随着 Schmid 因子不匹配的增加而增强（即相邻晶粒的 Schmid 因子差异增大）。West 等人[9], [10]在研究超临界水中辐照的 316L 不锈钢时也观察到了同样的趋势，其中晶间裂纹倾向于发生在 Schmid 因子较高的晶粒与 Schmid 因子较低的晶粒相邻的地方。多项研究[7], [9], [10]还指出，晶界与拉伸轴的倾角是 IGSCC 的一个影响因素。
The Schmid-Modified Grain Boundary Stress (SMGBS) model, proposed by West and Was [9] incorporates these factors by considering the combined effects of the grain boundary plane orientation and grain orientations through their Schmid factors. The model’s basic assumption is that intergranular cracking depends on the tensile stress that acts normal to the grain boundary (i.e. the normal stress); intergranular crack nucleation is more likely at grain boundaries that are highly stressed. The model, presented in full in reference [9], is outlined briefly below.
西斯特和瓦斯[9]提出的 Schmid 修正晶界应力（SMGBS）模型通过考虑晶界平面取向和晶粒取向的 Schmid 因子的综合效应来包含这些因素。该模型的基本假设是晶间开裂取决于垂直作用于晶界（即法向应力）的拉伸应力；晶间裂纹萌生更可能发生在高度受力的晶界。该模型在参考文献[9]中完整呈现，以下简要概述。
The normal stress (σN) acting on a grain boundary due to tensile yield in one grain is described as
由于一个晶粒的拉伸屈服而在晶界上作用的法向应力（σ N ）描述为(1)σN=σfgcosα2where σfg is the tensile stress required to yield the individual grain and α is the angle between the grain boundary plane normal and the tensile axis (Fig. 1), which can be obtained by trace analysis of the grain boundary on orthogonal planes with respect to the tensile direction as described by West and Was [9] and Alexandreanu and Was [23].
其中σ fg 是使单个晶粒屈服所需的拉伸应力，α是晶界平面法线与拉伸轴之间的夹角（图 1），可通过西斯特和瓦斯[9]以及亚历山大努和瓦斯[23]描述的相对于拉伸方向在正交平面上对晶界进行迹线分析来获得。(2)α=cos-1cot2φ+cot2θ+11/2
  1. Download: Download full-size image
    下载：下载完整尺寸图像

Fig. 1. Definition of parameters required to calculate the normal stress on a grain boundary in the SMBGS model.
图 1. 计算 SMBGS 模型中晶界法向应力的参数定义。

To address the effects of texture, expressed as the average Schmid factor of the material, mavg, the tensile flow stress (σf) of the polycrystalline material is related to a nominal tensile yield stress (σy),
为解决织构的影响，以材料平均 Schmid 因子 m avg 表示，多晶材料的拉伸流变应力（σ）与名义拉伸屈服应力（σ y ）相关，(3)σf=σy∝1mavghence the tensile stress required to yield an individual grain, σfg, with Schmid factor mg is:
因此，使具有 Schmid 因子 m g 的单个晶粒（σ fg ）屈服所需的拉伸应力为：(4)σfg=σfmavgmg
Normalising by the flow stress and assuming that the stress acting on a grain boundary depends on the average yield behaviour of the adjacent grains, with Schmid factors mg1 and mg2, the effective normal stress acting on a grain boundary is [9]:
通过流变应力进行归一化，并假设晶界上的应力取决于相邻晶粒的平均屈服行为，其 Schmid 因子分别为 m g 1 和 m g 2 ，作用在晶界上的有效法向应力为[9]：(5)σN=mavg21mg1+1mg2cosα2
The model was first applied to characterise intergranular cracking of irradiated type 316L stainless steel, tested at 400 °C in supercritical water, [9], in which experimental data on crack populations were examined as function of the Schmid factor and surface trace inclination. Data were not available on the actual grain boundary orientations in three dimensions, and so an assumed probabilistic distribution of relative grain boundary orientations was used. It was concluded that the tendency for intergranular cracking increased with the normal stress of the grain boundary. A subsequent work [24] considered the role of grain boundary and grain orientations on slip continuity, observing that intergranular crack initiation in proton-irradiated stainless steel, tested in slow strain rate conditions in high temperature de-oxygenated water (supercritical water reactor environment), observed that the probability of crack initiation was described by both SMGBS model and the probability of slip discontinuity. Slip discontinuity, which encourages strain concentrations at grain boundaries, provides a mechanical mechanism to aid corrosion at sensitised grain boundaries. The authors noted that the propensity for slip discontinuity was higher when the normal stress acting on the grain boundary was above a critical value; the normal stress is described by the SMGBS model, thus there is a phenomenological correlation between the SMGBS description of a grain boundary and the slip discontinuity. The SMGBS model has some limitations, as it does not consider the properties or structure of the grain boundary; only the orientation of the grain boundary plane and the deformation of the adjacent grains are addressed. The precise role of the grain boundary structure in slip discontinuity is complex, since this affects the absorption and transmission of strain [25]. Nonetheless, the SMGBS provides a useful framework for analysis. Consequently, in the current study, the grain boundary plane orientation has been characterised by direct measurement via sectioning of grain boundaries and the SMGBS model has been applied using knowledge of the crystal orientations of the adjacent grains. Furthermore, in situ observations have been used to identify the initiation site of an intergranular stress corrosion crack that developed in high temperature oxygenated water. The objective of the study was to test whether the SMGBS model could explain the occurrence of IGSCC at an identified initiation site.
该模型首先应用于表征辐照 316L 不锈钢的晶间开裂，在 400°C 的超临界水中进行测试[9]，其中分析了裂纹数量与 Schmid 因子和表面痕迹倾角的关系。由于缺乏实际晶界方向的三维数据，因此使用了假设的相对晶界方向概率分布。研究得出晶界正常应力越大，晶间开裂的趋势越强。后续研究[24]考虑了晶界和晶粒取向对滑移连续性的影响，观察到在高温脱氧水（超临界水反应堆环境）中，在慢应变率条件下测试的质子辐照不锈钢的晶间开裂起始概率，既可以用 SMGBS 模型描述，也可以用滑移不连续性的概率描述。滑移不连续性会促使晶界处产生应变集中，为敏化晶界处的腐蚀提供了一种机械机制。 作者指出，当晶界上的正应力超过临界值时，滑移不连续的倾向更高；正应力由 SMGBS 模型描述，因此晶界的 SMGBS 描述与滑移不连续之间存在现象学相关性。SMGBS 模型存在一些局限性，因为它不考虑晶界的性质或结构；仅考虑了晶界平面的取向和相邻晶粒的变形。晶界结构在滑移不连续中的精确作用很复杂，因为这与应变的吸收和传递有关[25]。尽管如此，SMGBS 提供了一个有用的分析框架。因此，在本研究中，通过晶界切片进行直接测量来表征晶界平面取向，并利用相邻晶粒的晶体取向知识应用 SMGBS 模型。此外，利用原位观察来确定在高温富氧水中形成的沿晶应力腐蚀裂纹的起始位置。 该研究的目的是测试 SMGBS 模型能否解释在已确定的起始位置发生 IGSCC 的现象。

2. Experimental details  2. 实验细节

The material was a hot-rolled type 304 austenitic stainless steel (Cr:18.15, Ni:8.60, C:0.055, Mn:1.38, P:0.032, S:0.005, Si:0.45, N:0.038, Fe:Bal, wt.%) with an initial thickness of 13 mm. The microstructure and sensitisation behaviour of this particular plate have been fully described in [26], [27]. The sample was sensitised for 24 h at 650 °C to reduce its resistance to intergranular corrosion before cutting to its final dimensions of approximately 90 mm × 10 mm × 7 mm (L × W × T). The tensile surface was mechanically polished, then electro-polished in a 92% acetic acid and 8% perchloric acid mix at 42 V for 60 s, followed by electro-etching in the same solution at 13 V for 20 s to provide a speckle surface pattern that was suitable for digital image correlation analysis of optical micrographs.
该材料为热轧型 304 奥氏体不锈钢（Cr:18.15, Ni:8.60, C:0.055, Mn:1.38, P:0.032, S:0.005, Si:0.45, N:0.038, Fe:余量, wt.），初始厚度为 13 mm。该特定板材的微观结构和敏化行为已在文献[26]、[27]中详细描述。样品在 650 °C 下敏化 24 小时以降低其对晶间腐蚀的抵抗能力，然后切割成最终尺寸约为 90 mm × 10 mm × 7 mm（L × W × T）。拉伸表面经过机械抛光，然后在 92%醋酸和 8%高氯酸混合溶液中于 42 V 下电解抛光 60 秒，随后在同一溶液中于 13 V 下电解腐蚀 20 秒，以提供适合光学显微图像数字图像相关分析的斑点表面图案。
The stress corrosion test was conducted using a windowed autoclave with a four-point bend specimen loaded for 30 days under a static stress of 200 MPa, which is above the room temperature yield stress. The autoclave environment was 250 °C high purity water with a dissolved oxygen content of 1000 p.p.b. at 50 atmospheres pressure (5.5 μS/m feed-water conductivity). The autoclave and its optical system have been described in [28]; briefly it allows high-resolution in situ optical observation of the stressed tensile surface of the test specimen during autoclave operation.
应力腐蚀试验使用带窗口的加压釜进行，试样为四点弯曲试样，在 200 MPa 的静态应力下加载 30 天，该应力高于室温屈服应力。加压釜环境为 250°C 的高纯水，溶解氧含量为 1000 p.p.b.，压力为 50 个大气压（给水电导率 5.5 μS/m）。加压釜及其光学系统已在文献[28]中描述；简而言之，它允许在加压釜运行过程中对试验试样的受应力拉伸表面进行高分辨率原位光学观察。
After the stress corrosion test, the tensile surface was polished with colloidal silica until a final mirror surface was obtained, in order to enable electron backscatter diffraction (EBSD) analysis. EBSD data were collected using a JOEL-6500F SEM and the TSL OIM DC v4 software with standard parameters; a voltage of 20 kV and a probe current of approximately 1 nA were used. The camera binning was 2 × 2 with an exposure time of approximately 0.5 s. A grid was mapped with an area of 600 × 1400 μm, at a step size of 0.3 μm. The Schmid factor was calculated for the 12 slip systems of the face centred cubic lattice;<0 1 1>{1 1 1}, with respect to the tensile loading direction. The slip system with the maximum resolved stress was identified as the primary active slip system, and its Schmid factor was reported.
应力腐蚀试验后，对拉伸表面进行硅溶胶抛光，直至获得镜面，以便进行电子背散射衍射（EBSD）分析。使用 JOEL-6500F 扫描电子显微镜和 TSL OIM DC v4 软件收集 EBSD 数据，采用标准参数；电压为 20 kV，探针电流约为 1 nA。相机分幅为 2 × 2，曝光时间约为 0.5 s。网格映射区域为 600 × 1400 μm，步长为 0.3 μm。计算了面心立方晶格的 12 个滑移系统<0 1 1>{1 1 1}相对于拉伸加载方向的 Schmid 因子；确定最大分应力滑移系统为主要活性滑移系统，并报告了其 Schmid 因子。
Digital image correlation (DIC) is a technique that maps the displacements between successive images using contrast from features. Measurement of crack opening displacements via DIC can detect and quantify cracks that would otherwise be invisible; it is particularly useful for the in situ study of stress corrosion cracking [29], [17], [30]. Sub-micron displacements can be readily measured under the operating conditions of the windowed autoclave [31], which has previously been used to study corrosion fatigue short crack behaviour [28]. The images, captured at almost daily intervals with a ×20 objective lens, had a field of view of approximately 450 μm × 450 μm at an image pixel size of 0.23 μm. These were analysed by DIC using the Davis Strain Master 2D software (version 7.2) with a final interrogation subset size of 64 × 64 pixels at an overlap of 87%. The uncertainty in the displacement measurements in these conditions has been estimated to be better than 0.07 μm [28].
数字图像相关（DIC）是一种利用特征对比来映射连续图像间位移的技术。通过 DIC 测量裂纹张开位移可以检测并量化原本不可见的裂纹；它特别适用于应力腐蚀开裂的原位研究[29], [17], [30]。在窗口式高压釜的操作条件下，亚微米位移可以轻易测量[31]，该高压釜此前已用于研究腐蚀疲劳短裂纹行为[28]。使用×20 物镜几乎每日拍摄图像，图像视场约为 450 μm × 450 μm，像素大小为 0.23 μm。这些图像通过 Davis Strain Master 2D 软件（版本 7.2）进行 DIC 分析，最终查询子集大小为 64 × 64 像素，重叠率为 87%。在这些条件下位移测量的不确定性估计优于 0.07 μm[28]。

3. Results and analysis  3. 结果与分析

A single stress corrosion crack was first detected using DIC after 22 days from the start of the experiment; no cracking was visible otherwise. A series of maps of the maximum principal strain obtained at different time intervals by DIC analysis is presented in Fig. 2. The strains, which are calculated from the gradients of measured displacement vectors, give a qualitative indication of the crack opening displacement; the reference image for DIC was recorded at the start of the test. The strain maps are superposed on an optical image of the surface that was recorded at 30 days, after significant crack propagation that caused a large increase in the crack opening displacement. This shows the regions of high strain due to the crack opening approximately correspond to the intergranular crack path; positional uncertainty arises due to the coarse displacement grid, which is a consequence of the large interrogation subset (∼15 μm) required for sub-pixel displacement measurements. The crack initiation site, which was judged by the locally increasing magnitude of its crack opening displacement, is marked in Fig. 2 by a rectangle: the maximum measured crack opening at the initiation site was 0.2 μm at Day 22, 0.6 μm at Day 24 and 0.9 μm at Day 26. The same position is shown in the scanning electron microscope observation (Fig. 3a) of the specimen surface, which was polished after the test.
在实验开始 22 天后，首次使用 DIC 检测到单条应力腐蚀裂纹；其他时间点未见裂纹。图 2 展示了通过 DIC 分析在不同时间间隔获得的最大主应变的一系列图。这些应变是根据测量位移矢量的梯度计算得出的，可定性指示裂纹张开位移；DIC 的参考图像是在测试开始时记录的。应变图叠加在 30 天时记录的表面光学图像上，此时裂纹已显著扩展，导致裂纹张开位移大幅增加。这表明由于裂纹张开引起的高应变区域大致对应于沿晶裂纹路径；由于位移网格较粗，存在位置不确定性，这是需要大尺寸查询子集（~15 μm）进行亚像素位移测量的结果。通过其裂纹张开位移局部增大的判断，裂纹起始位置在图中已标记。 2 通过矩形显示：在裂纹起始位置测得的最大裂纹开口在 22 天时为 0.2 μm，24 天时为 0.6 μm，26 天时为 0.9 μm。相同位置在测试后抛光后的样品表面扫描电子显微镜观察中显示（图 3a）。
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Fig. 2. Visualisation of crack openings at different time intervals, represented as strains calculated from the digital image correlation measured displacements. The crack initiation site is indicated by the red rectangle. The strain map is superposed on an optical observation of the sample at the end of the test. The strain scale is qualitative and indicates the magnitude of crack opening displacement; dark blue represents low strain and red represents high strain. The maximum crack opening increased from 0.2 μm at Day 22–0.9 μm at Day 26. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
图 2. 不同时间间隔的裂纹开口可视化，表示为从数字图像相关测量的位移计算出的应变。裂纹起始位置由红色矩形指示。应变图叠加在测试结束时的样品光学观察上。应变刻度是定性的，表示裂纹开口位移的大小；深蓝色代表低应变，红色代表高应变。最大裂纹开口从 22 天的 0.2 μm 增加到 26 天的 0.9 μm。（对于本图例中颜色引用的解释，读者请参阅本文的网页版本。）

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Fig. 3. (a) Scanning electron microscopy observation of the tensile surface, polished after testing. The crack initiation site is marked by the red rectangle and (b) example FIB-milled trench across a grain boundary to measure the trace orientation angles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
图 3. (a) 拉伸表面扫描电子显微镜观察，测试后抛光。裂纹起始位置用红色矩形标记，(b) 跨越晶界的 FIB 铣削沟槽示例，用于测量痕迹取向角。（对于本图例中颜色引用的解释，读者请参阅本文的网络版本。）

The purpose of the analysis that follows is to investigate whether the mechanically-driven SMGBS model, informed by 3D characterisation of grain boundaries, can explain the observed initiation site; the expectation is that the initiation site should be significantly different from the general population of grain boundaries. Two populations of grain boundaries on the sample surface were considered. These comprised (i) 50 randomly selected grain boundaries from three different areas of the sample that had not failed; these were all located 5–10 grains distant from the initiation site and (ii) 25 grain boundaries along the crack path, which included the initiation site. These will be referred to as the “intact” set (i), and “cracked” set (ii) boundaries respectively. Focused ion beam (FIB) milling was used to cut a trench across each boundary (Fig. 3b) in order to expose the grain boundary trace on two orthogonal planes and to allow the measurement of the angles θ and φ (tilt corrections in the scanning electron microscope images were applied). EBSD analysis, prior to the FIB milling, provided the grain orientations, which were used to calculate the Schmid factor for each grain due to the tensile surface stress. The resulting Schmid factor map, in which the initiation site is marked (Fig. 4) shows the Schmid factors range between 0.27 and 0.5. The error in Schmid factor, based on EBSD angular measurement precision, is 0.01. Several grain boundaries at the initiation site are identified (AA′ to EE′) with Schmid factor mismatch values between 0.01 and 0.17. All had CSL character with ∑ > 29, and the data for these boundaries are summarised in Table 1. The grain boundary character distribution for the randomly selected grain boundaries in the inspected region had a significant population of low ∑CSL boundaries comprising 39% ∑3, 2% ∑9 and 2% ∑27 (all expressed as number fractions, not as proportion of boundary length). This is consistent with data obtained on the same plate by Rahimi et al. [17].
接下来的分析旨在探究机械驱动的 SMGBS 模型，在获得晶界三维表征信息后，是否能够解释观察到的裂纹起始位置；预期该起始位置应与普通晶界群体有显著差异。研究考虑了样品表面两种晶界群体。这些包括（i）从三个未失效样品区域随机选取的 50 条晶界，这些晶界均位于距离起始位置 5-10 个晶粒处；（ii）沿裂纹路径的 25 条晶界，其中包括起始位置。分别将前者称为“完好”组（i），后者称为“裂纹”组（ii）。采用聚焦离子束（FIB）铣削技术，在每个晶界上切割一条沟槽（图 3b），以在两个正交平面上暴露晶界痕迹，并允许测量角度θ和φ（扫描电镜图像中进行了倾斜校正）。 在 FIB 铣削之前进行的 EBSD 分析提供了晶粒取向，这些取向被用于计算由于拉伸表面应力而产生的每个晶粒的 Schmid 因子。所得 Schmid 因子图（图 4）中标记了起始位置，显示 Schmid 因子范围在 0.27 到 0.5 之间。基于 EBSD 角度测量精度，Schmid 因子的误差为 0.01。在起始位置处识别了数条晶界（AA′到 EE′），其 Schmid 因子不匹配值在 0.01 到 0.17 之间。所有这些晶界都具有 CSL 特征，且∑>29，这些晶界的数据汇总于表 1。在检查区域内随机选取的晶界的晶界特征分布中，存在大量低∑CSL 晶界，包括 39%的∑3、2%的∑9 和 2%的∑27（均以数量分数表示，而非边界长度比例）。这与 Rahimi 等人[17]在同一块板上获得的数据一致。
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Fig. 4. (a) Schmid factor map of the region of the crack initiation site; the observed values range from ∼0.27 to 0.5, (b) five grain boundaries (AA′, AB′, CC′, CD′ and EE′) are identified and (c) their positions relative to the strain map indicated.
图 4. (a) 裂纹起始部位的 Schmid 因子图；观测值范围从~0.27 到 0.5，(b) 识别出五个晶界(AA′, AB′, CC′, CD′和 EE′)，(c) 它们相对于应变图的位置。

Table 1. Data for the grain boundaries in the region of the initiation site.
表 1. 起始部位晶界的数据。

Grain boundary  晶界θ (°)φ (°)mg1mg2ΔmσNAngle to closest low index plane (hkl)
与最近低指数晶面(hkl)的夹角
AA′68870.280.450.171.128°:(33¯1)
AB′68860.450.450.010.8639°:(11¯1)
CC′39760.420.460.040.4042°:(21¯1¯)
CD′88780.450.450.010.9541°:(11¯1)
EE′52660.380.460.080.5929°:(32¯2¯)
The Schmid factor values from grains adjacent to the set (i) intact boundaries are compared to those of the larger population of approximately 2000 grains (shown in Fig. 4). The distributions of Schmid factors (Fig. 5) are very similar, indicating that these randomly selected grains in set (i) are sufficiently representative of the Schmid factor distribution for this material. Similarly, the data for the trace angles (θ and φ) for both set (i) intact and set (ii) cracked boundaries were compared (Fig. 6), finding no significant differences. The data for θ and φ for the set (ii) boundaries along the crack path close to the initiation site are presented in Table 1. The uncertainty in these values is estimated to be 3°.
将邻近(i)组完整晶界的晶粒的 Schmid 因子值与约 2000 个晶粒的较大群体（如图 4 所示）的值进行比较。Schmid 因子分布（图 5）非常相似，表明(i)组中随机选取的这些晶粒足以代表该材料的 Schmid 因子分布。同样，比较了(i)组完整晶界和(ii)组裂纹晶界的微量角度（θ和φ）（图 6），发现没有显著差异。沿裂纹路径靠近起始位置(ii)组晶界的θ和φ数据见表 1。这些值的误差估计为 3°。
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Fig. 5. Normalised frequency distributions of the Schmid factor (m) measured for a population of 2000 grains, a randomly selected population of 50 grains adjacent to intact grain boundaries and 25 grains adjacent to the crack path. The Schmid factor data are binned in ranges of 0.2.
图 5. 2000 个晶粒群体的 Schmid 因子（m）的归一化频率分布，包括邻近完整晶界的 50 个随机晶粒和邻近裂纹路径的 25 个晶粒。Schmid 因子数据按 0.2 的范围分组。

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Fig. 6. Cumulative probability distributions of the grain boundary trace angles; (a) θ and (b) φ for the intact and cracked boundaries.
图 6. 晶界微量角度的累积概率分布；(a) θ和(b) φ对于完整和裂纹晶界。

The Schmid factor mismatch, Δm (i.e.|mg1 − mg2|), was calculated for both intact and cracked grain boundary populations. The similar distributions (Fig. 7a) indicate that there is no obvious bias between set (i) and set (ii). The highest mismatch value of 0.17 was obtained in the cracked population; this was for the grain boundary AA′ (Table 1). The SMGBS model was used to calculate the normal stress, σN, for each boundary in the two populations from the measured grain boundary plane and grain orientations; Eq. (5) with the average Schmid factor 0.45 was employed. From the measurement errors in the grain boundary traces, the uncertainty in σN was approximately 2%. The distributions for the two populations of grain boundaries (Fig. 7b) are quite similar; although there is a tendency for higher values to be the set (i) intact boundaries this does not appear significant. The highest value is obtained for boundary AA′ (Table 1) in set (ii). The Schmid factor mismatch and grain boundary stress at individual boundaries are compared in Fig. 7c; the data are scattered with a tendency for higher values to be correlated. Boundary AA′ has the highest value of both and is situated between a pair of grains with low and high Schmid factor (0.28 and 0.45). The relationship between the Schmid factor sum of adjacent grains and the normal stress are shown in Fig. 7d; there is no strong correlation, but boundary AA′ with the highest normal stress has the lowest Schmid factor sum. The calculated normal stress is representative only of conditions up to the point of crack initiation; hence similar distributions for the set (i) intact and set (ii) failed boundaries are expected. After initiation of a crack at one boundary, the deformation field of the propagating crack determines the stresses experienced by those boundaries that subsequently fail, depending on their stress corrosion susceptibility. It is noteworthy, however, that the highest value of normal stress is within the failed boundary population.
Schmid 因子失配，Δm（即|m g 1 − m g 2 |），被计算用于完整和开裂的晶界群体。相似的分布（图 7a）表明，集合（i）和集合（ii）之间没有明显的偏差。开裂群体中获得了最高的失配值 0.17，这是对于晶界 AA′（表 1）。使用 SMGBS 模型从测量的晶界平面和晶向计算两个群体中每个晶界的法向应力σ N ；采用平均 Schmid 因子 0.45 的公式（5）。从晶界迹线的测量误差，σ N 的不确定性约为 2%。两个晶界群体的分布（图 7b）非常相似；尽管集合（i）完整晶界有更高值的趋势，但这并不显著。最高值是在集合（ii）的晶界 AA′（表 1）获得的。Schmid 因子失配和单个晶界的晶界应力在图 7c 中进行了比较；数据是分散的，有较高值相关的趋势。 边界 AA′具有最高值，位于一对具有低和高 Schmid 因子（0.28 和 0.45）的晶粒之间。相邻晶粒的 Schmid 因子之和与正应力的关系如图 7d 所示；两者没有强相关性，但具有最高正应力的边界 AA′具有最低的 Schmid 因子之和。计算的正应力仅代表裂纹萌生点之前的条件；因此，预期(i)完整边界和(ii)失效边界的分布相似。在某个边界萌生裂纹后，扩展裂纹的变形场决定了随后失效的边界所承受的应力，这取决于它们的应力腐蚀敏感性。然而值得注意的是，最高正应力值位于失效边界群体中。
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Fig. 7. Schmid factor mismatch (Δm) and normalised grain boundary stress (σN) data for the intact and cracked grain boundaries; (a) cumulative probability distribution of Schmid factor mismatch, (b) cumulative probability distribution of grain boundary stress, (c) relationship between Schmid factor mismatch and grain boundary stress and (d) relationship between Schmid factor sum and grain boundary stress.
图 7. 完整和开裂晶界的 Schmid 因子失配（Δm）和标准化晶界应力（σ N ）数据；（a）Schmid 因子失配的累积概率分布，（b）晶界应力的累积概率分布，（c）Schmid 因子失配与晶界应力的关系，（d）Schmid 因子总和与晶界应力的关系。

As noted earlier, the SMGBS model does not consider the properties of the grain boundaries, yet there is a requirement for IGSCC of a susceptible grain boundary. Inspection of the failed grain boundaries affirms that the CSL characterisation is an approximation of the degree of susceptibility; the data for grain boundary normal stress are presented in Fig. 8a, identifying those boundaries with ∑ < 29. Of the failed set (ii) boundaries, only 16% had ∑ < 29 and no ∑3, ∑9 or ∑27 boundaries were observed to crack, whereas the proportion of the set (i) intact boundaries with ∑ < 29 was 28%, which is consistent with the general population of boundaries. This indicates that the crack propagates along a path that is influenced by the grain boundary susceptibility. It has been proposed that grain boundaries with orientations close to low Miller {hkl} index planes (i.e. low energy planes) are resistant to sensitisation and IGSCC [32], [19]. To identify such boundaries, the angles between the grain boundary plane normal and those of index planes up to {hkl} = {3 3 2} were calculated; a grain boundary was identified to be close to a particular plane if the angle was less than an arbitrary small value (6°). The data (Fig. 8b) shows that 12% of the intact boundaries were close to such low index planes in either of the adjacent grains, whilst 20% of the cracked boundaries were of this type. None of the cracked boundaries AA′ to EE′ were either low ∑ CSL boundaries or close to any low index plane.
如前所述，SMGBS 模型未考虑晶界的性质，然而对于易感晶界的 IGSCC 存在需求。对失效晶界的检查证实，CSL 表征是对易感程度的一种近似；晶界法向应力的数据如图 8a 所示，标出了∑<29 的晶界。在失效组(ii)晶界中，仅有 16%的晶界∑<29，且未观察到∑3、∑9 或∑27 晶界开裂，而组(i)完好晶界中∑<29 的比例为 28%，这与晶界的总体情况一致。这表明裂纹沿受晶界易感影响路径扩展。已有研究表明，取向接近低密勒指数{hkl}平面（即低能平面）的晶界对敏化和 IGSCC 具有抗性[32][19]。 为识别这些边界，计算了晶界平面法线与指数平面（至{hkl}={3 3 2}）之间的角度；如果角度小于任意小的值（6°），则认为晶界接近于特定平面。数据显示（图 8b），12%的完整边界在相邻晶粒中接近此类低指数平面，而 20%的裂纹边界属于此类。裂纹边界 AA′至 EE′中，没有一个是低∑ CSL 边界，也没有一个接近任何低指数平面。
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Fig. 8. Positions of nominally special boundaries within the cumulative probability distribution of normal grain boundary stress, σN, for intact and cracked boundaries; (a) boundaries with CSL < ∑ 29 and (b) boundaries close to low Miller index planes (the angle to the nearest plane is labelled).
图 8. 完整和裂纹边界在法向晶界应力σ N 的累积概率分布中的名义特殊边界位置；(a) CSL < ∑ 29 的边界和(b)接近低米勒指数平面的边界（与最近平面的角度标注）。

4. Discussion  4. 讨论

The purpose of this study was to apply the SMGBS model to interpret an observation of IGSCC initiation in thermally sensitised type 304 stainless steel. The full three-dimensional data on crack trace angle, the angle between the tensile direction and the grain boundary plane, and also the Schmid factors of the adjacent grains have been used to calculate the grain boundary normal stress, σN. Digital image correlation of in situ optical observations has allowed the initiation site of a high temperature water intergranular stress corrosion crack to be located (Fig. 2); previously this has only been achieved for ambient temperature environments [17]. The precise grain boundary is not determined unambiguously, but on the basis of the local increase in crack opening displacement, the initiation site can be identified to be within a sub-set of grain boundaries: AA′ to EE′ (Fig. 4). Compared to the general population, none of these boundaries is distinctive in terms of the orientation of its adjacent grains when expressed as the Schmid factor of the most stressed slip system (Fig. 5), nor are the orientations of these grain boundaries distinctive with respect to the tensile axis of stress (Fig. 6). In terms of grain boundary structure, these failed boundaries would not be considered special: none are between grains with low ∑ orientation relationships, nor are they close to low Miller index planes in either of their adjacent grains (Table 1); thus they can be expected to be thermally sensitised by carbide precipitation and susceptible to intergranular corrosion.
本研究旨在应用 SMGBS 模型解释热敏化 304 不锈钢中 IGSCC 的萌生现象。利用裂纹迹线角、拉伸方向与晶界平面之间的角度以及相邻晶粒的 Schmid 因子等三维数据，计算晶界法向应力σ N 。原位光学观察的数字图像相关分析，使高温水溶液晶间应力腐蚀裂纹的萌生位置得以定位（图 2）；此前仅能在常温环境下实现这一目标[17]。晶界位置并未明确确定，但基于裂纹开口位移的局部增加，可识别萌生位置位于晶界子集 AA′至 EE′（图 4）内。与普通晶界相比，这些晶界在最大受力滑移系统的 Schmid 因子表示的相邻晶粒取向方面并无显著差异（图）。 5), 这些晶界的取向也并非相对于应力拉伸轴特别显著（图 6）。从晶界结构来看，这些失效的晶界并不被视为特殊：它们都不是位于具有低∑取向关系的晶粒之间，也都不靠近其相邻晶粒中的低米勒指数晶面（表 1）；因此，它们可能因碳化物析出而热敏化，并易受晶间腐蚀。
Considered in terms of grain boundary normal stress and Schmid factor mismatch, some clear patterns emerge: none of boundaries AB′ to EE′ are exceptional when compared to the general populations of intact and failed boundaries; CC′ and EE′ have intermediate values of normal stress and Schmid factor mismatch (Fig. 7); CD′ and AB′ have quite low Schmid factor mismatch (Fig. 7) and although they have high normal stress there are non-special (i.e. sensitised) boundaries with higher stress that are intact (Fig. 8). However, boundary AA′ has the highest Schmid factor mismatch and grain boundary normal stress of all the examined grain boundaries (75 in total) (Fig. 7). It is concluded that boundary AA′ is the initiation site. This is consistent with the requirement for IGSCC of a susceptible boundary and sufficient mechanical stress from localised deformation.
从晶界法向应力和 Schmid 因子不匹配的角度考虑，可以观察到一些明显的模式：与完整和失效晶界的总体分布相比，AB′到 EE′的晶界均无特殊之处；CC′和 EE′的法向应力和 Schmid 因子不匹配值处于中等水平（图 7）；CD′和 AB′的 Schmid 因子不匹配值相当低（图 7），尽管它们具有较高的法向应力，但存在具有更高应力且未失效的特殊（即敏化）晶界（图 8）。然而，在所有检查的晶界（共 75 个）中，AA′晶界具有最高的 Schmid 因子不匹配值和晶界法向应力（图 7）。因此得出结论，AA′晶界是裂纹的起始点。这与易感晶界发生 IGSCC 的要求以及局部变形产生的足够机械应力相一致。
The grain boundary normal stress depends on the relative Schmid factors of the adjacent grains. The data in Fig. 7c show there is a general but scattered trend for σN to increase with increasing Schmid factor mismatch. It has been observed [7], [9] that the Schmid factor sum of the adjacent grains is an important factor in initiation, and it is noticeable that the highest grain boundary stress is also associated with the lowest Schmid factor sum (Fig. 7d). These parameters are roughly correlated due the relationship in Eq. (5). In this experiment the sample was stressed above the bulk yield stress, thus all grains may be assumed to be deform plastically; higher tensile stresses develop in those deforming grains oriented with high Schmid factor, and the localised grain boundary normal stress is increased at boundaries of high Schmid factor mismatch. To illustrate this, the variation of normal stress with grain boundary orientation with respect to the tensile axis is considered for three boundaries of different Schmid factor mismatch and orientation; hard–hard (Δm = 0), soft–soft (Δm = 0) and hard-soft (Δm = 0.23) (Fig. 9). In this case, hard represents a grain with low Schmid factor that is resistant to deformation by the applied stress and soft is the converse. The predicted grain boundary stress increases as the tensile stress becomes normal to the grain boundary plane, but the magnitude is sensitive to the Schmid factor mismatch and also the absolute values of Schmid factor; the highest normal stress to the grain boundary is obtained for the hard–hard combination, but the hard–soft combination causes a higher normal stress than soft–soft. The Schmid factor mismatch or sum are thus incomplete but approximate descriptions of the mechanical force on the grain boundary, which may be better provided by the grain boundary normal stress that is obtained via the SMGBS model. The observation of initiation at boundary AA′ is therefore consistent with the findings of West and Was [9] that intergranular cracking in an irradiated stainless steel occurred preferentially at boundaries that were boundaries perpendicular to the tensile axis and adjacent to low Schmid factor grains; these are the factors that contribute to high normal grain boundary stress.
晶界法向应力取决于相邻晶粒的相对 Schmid 因子。图 7c 中的数据显示，随着 Schmid 因子不匹配的增加，σ值呈现普遍但分散的趋势。已有研究[7]、[9]表明，相邻晶粒的 Schmid 因子之和是裂纹萌生的重要因素，值得注意的是，最高的晶界应力也伴随着最低的 Schmid 因子之和（图 7d）。由于存在式(5)中的关系，这些参数大致相关。在本实验中，样品的应力超过了体屈服应力，因此可以假设所有晶粒都发生塑性变形；在 Schmid 因子较高的变形晶粒中产生更高的拉伸应力，并且在 Schmid 因子不匹配较高的晶界处局部晶界法向应力增加。为了说明这一点，考虑了三种不同 Schmid 因子不匹配和取向的晶界相对于拉伸轴的法向应力变化；硬-硬（Δm = 0）、软-软（Δm = 0）和硬-软（Δm = 0.23）（图 9）。 在这种情况下，硬代表一个 Schmid 因子较低的晶粒，该晶粒对施加的应力变形具有抗性，而软则相反。预测的晶界应力随着拉伸应力变得垂直于晶界平面而增加，但其大小对 Schmid 因子不匹配和 Schmid 因子的绝对值都很敏感；对于硬-硬组合，获得晶界法向应力的最大值，但硬-软组合引起的法向应力高于软-软组合。因此，Schmid 因子不匹配或总和只是对晶界机械力的不完全但近似的描述，而通过 SMGBS 模型获得的晶界法向应力能更好地提供这种机械力。因此，在边界 AA′处观察到的起始现象与 West 和 Was[9]的研究结果一致，即在辐照不锈钢中，沿垂直于拉伸轴且邻近低 Schmid 因子晶粒的晶界优先发生沿晶开裂；这些是导致高晶界法向应力的因素。
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Fig. 9. Variation of grain boundary normal stress, σN, with orientation, φ, relative to the tensile stress, for three different combinations of Schmid factor mismatch and orientation: hard–hard, soft–soft and hard–soft.
图 9. 晶界法向应力σ N 随取向φ相对于拉伸应力的变化，对于三种不同的 Schmid 因子失配和取向组合：硬-硬、软-软和硬-软。

A more sophisticated modelling approach, based on crystal plasticity and full three-dimensional characterisation of the grains and their interfaces (e.g. [33], [34], [35]), which may affect slip continuity and hence the localisation of strain [24], would be appropriate to develop this work further. Nonetheless, the SMGBS model provides a useful framework for a model of the likelihood of crack initiation [9]. The observations obtained here suggest that the SMGBS model should be augmented to include the proportion of susceptible grain boundaries, as not all highly stressed boundaries may fail. This could provide an improved tool to rank the susceptibility of thermo-mechanically microstructures to IGSCC.
一种更复杂的建模方法，基于晶体塑性以及晶粒及其界面的完整三维表征（例如[33]、[34]、[35]），这可能影响滑移连续性并从而影响应变局部化[24]，将适合进一步发展这项工作。尽管如此，SMGBS 模型为裂纹起始可能性模型提供了一个有用的框架[9]。这里获得的观察结果表明，SMGBS 模型应该增加对易损晶界的比例的考虑，因为并非所有高度受力的边界都会失效。这可以提供一个改进的工具来评估热力-机械微结构对 IGSCC 的易损性排序。
Intergranular sensitisation is affected by alloy chemistry [36]; grain boundary structure, as discussed earlier, determines the segregation and precipitation behaviour and this is influenced by thermo-mechanical processing. It is not currently possible to reliably predict the proportion and distribution of susceptible boundaries in sensitised steel, although image analysis of electrochemical tests such as the standard DL-EPR to quantify the networks of such boundaries and their degree of sensitisation [26] offers a route to this. Further observations and analysis such as described in this work would be necessary to quantify the threshold stress for IGSCC initiation, and to determine how this is affected by the degree of sensitisation. Direct analysis of the grain boundary segregation, which could be measured in FIB lift-out sections at selected boundaries, could be coupled with the analysis of grain boundary planes to improve our understanding of the factors that control sensitization. Such data are necessary for predictive models of IGSCC initiation.
晶间敏化受合金化学成分[36]的影响；晶界结构，如前所述，决定了偏析和析出行为，而这一行为受热机械加工的影响。目前尚无法可靠预测敏化钢中易感晶界的比例和分布，尽管通过标准 DL-EPR 等电化学测试的图像分析，可以量化此类晶界的网络及其敏化程度[26]，这为预测提供了途径。为了量化晶间应力腐蚀裂纹（IGSCC）的起始阈值应力，并确定其受敏化程度的影响，需要进一步进行此类工作所述的观察和分析。对晶界偏析的直接分析，可以在选定的晶界处通过 FIB 剥离切片进行测量，这可以与晶界平面的分析相结合，以增进我们对控制敏化因素的理解。这些数据对于 IGSCC 起始的预测模型是必要的。
In summary, in this work the development of an intergranular stress corrosion crack initiation site in thermally sensitised type 304 austenitic stainless steel tested in high temperature oxygenated water has been observed. Digital image correlation of time-resolved in situ optical observations measured the crack opening displacements of the crack, which could otherwise not be observed. Consequently the grain boundaries at the position of initiation site could be identified and characterised to determine how the initiation site differed from other positions in the observed region of the sample. Using EBSD to measure grain orientation and focused ion beam milling to enable grain boundary trace analysis, the grain boundary normal stresses could be calculated using the Schmid-Modified Grain Boundary Stress (SMGBS) model of Was et al. The propensity for thermal sensitisation of the grain boundaries could also be identified, using the measured CSL misorientation of the adjacent grains and the orientation of the grain boundary plane relative to either grain to define the grain boundary structure. Using the SMGBS model, the most highly stressed of the sensitised boundaries was located at the initiation site. The initiation site is a non-special grain boundary, in terms of grain boundary structure, that is inclined with its grain boundary normal close to the tensile stress axis. It is between a pair of grains with low and high Schmid factors (0.28 and 0.45). This demonstrates the importance of the combined contributions to crack initiation of grain boundary structure and plastic strain incompatibility and the suitability of the SMGBS model to provide an estimate of the likelihood of crack initiation. An extension to the model is suggested that could allow it to incorporate the degree of sensitisation that is measured in the microstructure.
总之，在这项工作中，观察了在高温富氧水中测试的热敏化 304 奥氏体不锈钢中沿晶应力腐蚀裂纹萌生位置的发展。通过时间分辨的原位光学观测的数字图像相关技术测量了裂纹的开口位移，这些位移原本无法观察到。因此，可以识别和表征萌生位置处的晶界，以确定该位置与其他观察区域内的位置有何不同。利用 EBSD 测量晶粒取向，并使用聚焦离子束刻蚀进行晶界轨迹分析，根据 Was 等人提出的 Schmid-Modified Grain Boundary Stress (SMGBS)模型计算晶界法向应力。此外，还可以通过测量相邻晶粒的 CSL 取向偏差以及晶界平面相对于任一晶粒的取向来定义晶界结构，从而确定晶界的热敏化倾向。 利用 SMGBS 模型，敏化晶界中最受应力集中的位置位于裂纹起始处。该起始处是一种非特殊晶界，从晶界结构来看，其晶界法线与拉伸应力轴接近。它位于一对 Schmid 因子较低（0.28）和较高（0.45）的晶粒之间。这表明晶界结构和塑性应变不匹配对裂纹起始的综合贡献的重要性，以及 SMGBS 模型在评估裂纹起始可能性方面的适用性。建议对模型进行扩展，使其能够结合微观结构中测量的敏化程度。

5. Conclusion  5. 结论

Intergranular stress corrosion initiation in a thermally sensitised stainless steel, tested in high temperature water has been studied in situ using digital image correlation of optical images, with three-dimensional characterisation to determine the grain boundary structures. The site at which the crack initiated is coincident with the most highly stressed of the characterised grain boundaries, as described by the SMGBS (Schmid-Modified Grain Boundary Stress) model.
在高温水中对热敏化不锈钢的晶间应力腐蚀起始进行了原位研究，采用光学图像的数字图像相关技术，并结合三维表征来确定晶界结构。裂纹起始的位置与 SMGBS（Schmid-Modified Grain Boundary Stress）模型所描述的最高应力晶界相吻合。

Acknowledgements  致谢

The authors thank Prof. Steve Roberts (Department of Materials, Oxford University) for helpful discussions. AS gratefully acknowledges the funding of her research studentship by Areva UK. TJM gratefully acknowledges the support of the Oxford Martin School at the University of Oxford.
作者感谢史蒂夫·罗伯茨教授（牛津大学材料系）的有益讨论。AS 感谢 Areva UK 对其研究奖学金的资助。TJM 感谢牛津大学马丁学院的鼎力支持。

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