In small-scale mechanical tests, such as micropillar compression tests, plastic deformation is often localized in narrow slip traces. These slip traces result from a few dislocation sources with relatively low nucleation stresses that are present in the material. In order to accurately simulate such small-scale experiments, the stochastics of the underlying dislocation network must be taken into account, which is usually done by performing discrete dislocation dynamics simulations. However, their high computational cost generally restricts these simulations to small and simple geometries and small applied displacements. Furthermore, effects of geometrical changes are usually neglected in the small strain formulation adopted. In this study, a discrete slip plane model for simulating small-scale experiments on single crystals is proposed, which takes the most important characteristics of dislocation plasticity for geometries in the micrometer range into account, i.e. the stochastics and physics of dislocation sources. In the model, the properties of all lattice planes are sampled from a probability density function. This results in a heterogeneous flow stress within a single crystal, unlike the uniform properties assumed in conventional crystal plasticity formulations. Moreover, the slip planes can be grouped together in bands via a weakest-link principle. The resulting equations are implemented in a standard crystal plasticity finite element model, using a finite deformation formulation. Within this setting, only the collective dislocation motion on glide planes is modeled, resulting in a significantly lower computational cost compared to frameworks in which the dynamics of individual dislocations are considered. This allows for simulating multiple realizations in 3D, up to large deformations. A small case study on micropillar compression tests is presented to illustrate the capabilities of the model.

在小规模的机械测试中，例如微柱压缩测试，塑性变形通常位于狭窄的滑动轨迹中。这些滑移轨迹是由材料中存在的具有相对较低成核应力的少数位错源引起的。为了准确模拟这种小规模实验，必须考虑底层位错网络的随机性，这通常通过执行离散位错动力学模拟来完成。然而，它们的高计算成本通常将这些模拟限制在小而简单的几何形状和小的应用位移上。此外，在采用的小应变公式中，几何变化的影响通常被忽略。在这项研究中，提出了一种用于模拟单晶小规模实验的离散滑移面模型， 位错源的随机性和物理学。在模型中，所有晶格平面的属性都是从概率密度函数中采样的。这导致单晶内的流动应力不均匀，这与传统晶体塑性公式中假设的均匀特性不同。此外，滑移面可以通过最弱链接原理在带中组合在一起。所得方程在标准晶体塑性有限元模型中使用有限变形公式实现。在此设置中，仅对滑翔平面上的集体位错运动进行建模，与考虑单个位错动力学的框架相比，计算成本显着降低。这允许在 3D 中模拟多个实现，直至大变形。