The deformation of crystalline materials by dislocation motion takes place in discrete amounts determined by the Burgers vector. Dislocations may move individually or in bundles, potentially giving rise to intermittent slip. This confers plastic deformation with a certain degree of variability that can be interpreted as being caused by stochastic fluctuations in dislocation behavior. However, crystal plasticity (CP) models are almost always formulated in a continuum sense, assuming that fluctuations average out over large material volumes and/or cancel out due to multi-slip contributions. Nevertheless, plastic fluctuations are known to be important in confined volumes at or below the micron scale, at high temperatures, and under low strain rate/stress deformation conditions. Here, we develop a stochastic solver for CP models based on the residence-time algorithm that naturally captures plastic fluctuations by sampling among the set of active slip systems in the crystal. The method solves the evolution equations of explicit CP formulations, which are recast as stochastic ordinary differential equations and integrated discretely in time. The stochastic CP model is numerically stable by design and naturally breaks the symmetry of plastic slip by sampling among the active plastic shear rates with the correct probability. This can lead to phenomena such as intermittent slip or plastic localization without adding external symmetry-breaking operations to the model. The method is applied to body-centered cubic tungsten single crystals under a variety of temperatures, loading orientations, and imposed strain rates.

由位错运动引起的晶体材料的变形以由伯格斯矢量确定的离散量发生。位错可能单独或成束移动，可能导致间歇性滑动。这使塑性变形具有一定程度的可变性，可以解释为是由位错行为的随机波动引起的。然而，晶体塑性 (CP) 模型几乎总是在连续意义上制定，假设波动在大材料体积上平均化和/或由于多滑移贡献而抵消。然而，已知塑性波动在微米级或微米级以下的受限体积、高温和低应变率/应力变形条件下很重要。在这里，我们开发了一种基于停留时间算法的 CP 模型随机求解器，该算法通过在晶体中的一组主动滑移系统之间进行采样来自然地捕捉塑性波动。该方法求解显式 CP 公式的演化方程，这些方程被改写为随机常微分方程并在时间上离散积分。随机 CP 模型通过设计在数值上是稳定的，并且通过以正确的概率在活动塑性剪切速率中采样，自然地打破了塑性滑移的对称性。这可能会导致间歇性滑动或塑性定位等现象，而无需向模型添加外部对称破坏操作。该方法适用于在各种温度、加载方向和施加应变率下的体心立方钨单晶。它们被改写为随机常微分方程并在时间上离散积分。随机 CP 模型通过设计在数值上是稳定的，并且通过以正确的概率在活动塑性剪切速率中采样，自然地打破了塑性滑移的对称性。这可能会导致间歇性滑动或塑性定位等现象，而无需向模型添加外部对称破坏操作。该方法适用于在各种温度、加载方向和施加应变率下的体心立方钨单晶。它们被改写为随机常微分方程并在时间上离散积分。随机 CP 模型通过设计在数值上是稳定的，并且通过以正确的概率在活动塑性剪切速率中采样，自然地打破了塑性滑移的对称性。这可能会导致间歇性滑动或塑性定位等现象，而无需向模型添加外部对称破坏操作。该方法适用于在各种温度、加载方向和施加应变率下的体心立方钨单晶。这可能会导致间歇性滑动或塑性定位等现象，而无需向模型添加外部对称破坏操作。该方法适用于在各种温度、加载方向和施加应变率下的体心立方钨单晶。这可能会导致间歇性滑动或塑性定位等现象，而无需向模型添加外部对称破坏操作。该方法适用于在各种温度、加载方向和施加应变率下的体心立方钨单晶。