At low strain, geometrically necessary dislocations (GND) confined in the close vicinity of grain boundaries can be approximated as a dislocation wall structure called a GND facet. Analytical solutions derived from Field Dislocations Mechanics (FDM) theory allow calculating the stress components associated with the GND facets but are unable to account for the stress field variation induced by finite size effect. Dislocation dynamics simulation is used to investigate the true stress field of GND facets. The geometry, dimension and dislocation density of three generic types of GND facets (twist, tilt and epitaxial facets) are systematically studied. In all cases, the stress field generated by GND facets is proportional to the surface GND density and its spatial distribution can be recovered using FDM solution combined with two scaling parameters identified from DD simulation results. This calculation procedure can be generalized to any crystal structure by relating the components of the surface Nye’s tensor to the solutions of simple cubic slip systems. Finally, static and dynamic tests are made to validate the calculation of back stress within regular grains bounded by GND facets.

在低应变下，限制在晶界附近的几何上必需的位错（GND）可以近似为位错壁结构，称为GND面。源自场错力学（FDM）理论的解析解决方案允许计算与GND面相关的应力分量，但无法解决有限尺寸效应引起的应力场变化。位错动力学仿真用于研究GND面的真实应力场。系统地研究了GND面的三种通用类型（扭转，倾斜和外延面）的几何形状，尺寸和位错密度。在所有情况下，GND面产生的应力场与表面GND密度成比例，并且可以使用FDM解决方案并结合从DD仿真结果中识别出的两个缩放参数来恢复其空间分布。通过将表面Nye张量的分量与简单三次滑动系统的解相关联，可以将该计算过程推广到任何晶体结构。最后，进行了静态和动态测试，以验证以GND面为边界的常规晶粒内的反应力计算。