A theoretical model for computing the interstitial solute concentration and the interstitial solute-induced stress field in a three-dimensional finite medium with any arbitrary elastic fields was developed. This model can be directly incorporated into two-dimensional or three-dimensional discrete dislocation dynamics simulations, continuum dislocation dynamics simulations, or crystal plasticity simulations. Using this model, it is shown that a nano-hydride can form in the tensile region below a dissociated edge dislocation at hydrogen concentration as low as χ0=5×10−5, and its formation induces a localized hydrogen elastic shielding effect that leads to a lower stacking fault width for the edge dislocation. Additionally, the model also predicts the segregation of hydrogen at Σ109(13 7 0)/33.4∘ symmetric tilt grain boundary dislocations. This segregation strongly alters the magnitude of the shear stresses at the grain boundary, which can subsequently alter dislocation-grain boundary interactions and dislocation slip transmissions across the grain boundary. Moreover, the model also predicts that the hydrogen concentration at a mode-I central crack tip increases with increasing external loading, higher intrinsic hydrogen concentration, and/or larger crack lengths. Finally, linearized approximate closed-form solutions for the solute concentration and the interstitial solute-induced stress field were also developed. These approximate solutions can effectively reduce the computation cost to assess the concentration and stress field in the presence of solutes. These approximate solutions are also shown to be a good approximation when the positions of interest are several nanometers away (i.e. long-ranged elastic interactions) from stress singularities (e.g. dislocation core and crack tip), for low solute concentrations, and/or at high temperatures.

中文翻译：

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预测具有任意弹性场的有限体积中的溶质浓度和溶质诱导应力的理论框架

建立了计算任意弹性场的三维有限介质中间隙溶质浓度和间隙溶质诱导应力场的理论模型。该模型可以直接合并到二维或三维离散位错动力学仿真，连续位错动力学仿真或晶体可塑性仿真中。使用该模型表明，在氢浓度低至χ0= 5×10-5的情况下，纳米氢化物可以在解离的边缘位错以下的拉伸区域中形成，并且其形成引起局部氢弹性屏蔽效应，从而导致边缘错位的堆垛层错宽度较小。此外，该模型还预测了氢在Σ109（13 7 0）/33.4∘对称倾斜晶界位错处的偏析。这种分离强烈地改变了晶界处的切应力的大小，其随后可以改变位错-晶界相互作用和位错滑移在整个晶界上的传递。此外，该模型还预测，随着外部载荷的增加，固有氢浓度的增加和/或裂纹长度的增加，I型中心裂纹尖端处的氢浓度会增加。最后，针对溶质浓度和间隙溶质引起的应力场，建立了线性近似的封闭形式解。这些近似解可以有效地减少在溶质存在下评估浓度和应力场的计算成本。