A general meso-scale (“GM”) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.

建立了一般的中尺度（“ GM”）晶体可塑性（CP）模型，该模型考虑了几何上必要的位错（GND）的低阶（应变硬化）和高阶（内应力）效应。这是可预测的：没有调用任意参数或长度标度，也没有特别设置采用数值技术。它使用通用应力场方程来确定GND含量，并使用一种新颖的协调技术来强制弹性远程奇异缺陷场与应用的弹塑性场保持一致。该模型便于在商业有限元程序中实施，而无需特殊元素，特殊边界条件或使用元素形状函数。GM模拟以提高的准确性确认了先前发表的关于Hall-Petch效应，Bauschinger效应和无弹性的预测。还可以预测以前无法预测的现象：单晶Ta晶体的无弹性和滞后性以及应变硬化停滞。内部应力（高阶效应）在大尺度下占主导地位，而在小尺度上，GND密度硬化（低阶效应）占主导地位。