We present a crystal plasticity constitutive relation for the description of experimentally observed non-Schmid crystallographic slip in a class of ternary carbides and nitrides commonly referred to as MAX phases. In the constitutive relation, we assume that the evolution of the slip system strength in MAX phases has two components – a classical component that depends on the Taylor cumulative shear strain and a non-Schmid component that depends on the stress normal to the slip plane. The non-Schmid crystal plasticity constitutive relation is then used to carry out finite element simulations of micropillar compression of single crystals of two MAX phases, Ti₂AlC and Ti₃AlC₂. The finite element simulations not only quantitatively predict the stress – strain response of a wide range of crystallographic orientations of the micropillars but also rationalize the non-uniform deformation and the deformed shape of the micropillars observed in the experiments for the two materials. Parametric studies are also carried out to quantify the role of the non-Schmid effect and understand the effects of key experimental parameters on the stress – strain response of the micropillars of the two MAX phases.

我们提出了晶体塑性本构关系，用于描述在通常称为 MAX 相的一类三元碳化物和氮化物中实验观察到的非施密德晶体滑移。在本构关系中，我们假设 MAX 相中滑移系统强度的演变具有两个分量——一个依赖于泰勒累积剪切应变的经典分量和一个依赖于垂直于滑动平面的应力的非施密德分量。然后使用非施密德晶体塑性本构关系对两个 MAX 相 Ti ₂ AlC 和 Ti ₃ AlC _{2单晶的微柱压缩进行有限元模拟}. 有限元模拟不仅定量地预测了微柱的各种晶体取向的应力 - 应变响应，而且还合理化了在两种材料的实验中观察到的微柱的非均匀变形和变形形状。还进行了参数研究以量化非施密德效应的作用，并了解关键实验参数对两个 MAX 相的微柱的应力-应变响应的影响。