A higher-order gradient crystal plasticity theory applicable to three-dimensional problems is reduced to a plane strain version to be used for the analysis of the deformation of face-centered cubic (FCC) crystals at a particular orientation that the out-of-plane plastic deformation cancels out. Plane strain conditions have been frequently quoted in the literature on theoretical crack problems and experimental studies on FCC crystals since effective information on the fundamental deformation behavior of such materials under multiaxial states of stress and strain is obtained. The present plane strain theory is formulated with planar pseudo slip systems that are contractions of the crystallographic slip systems $\left\{111\right\}〈110〉$ of FCC crystals. The resultant theory is purely two-dimensional, but it involves the nature of FCC crystal deformation, i.e., effects of latent hardening, cross slip, and backstresses (equivalently, internal stresses with the opposite sign) associated with the distribution of the edge and screw components of the geometrically necessary dislocations.

适用于三维问题的高阶梯度晶体可塑性理论简化为平面应变版本，用于分析面外立方（FCC）晶体在面外特定方向上的变形塑性变形抵消了。平面应变条件在理论裂纹问题和FCC晶体的实验研究中经常被引用，因为获得了有关此类材料在多轴向应力和应变状态下基本变形行为的有效信息。当前的平面应变理论是用平面伪滑移系统来表达的，该系统是晶体滑移系统的收缩。$\left\{111\right\}〈110〉$FCC晶体。最终的理论纯粹是二维的，但它涉及FCC晶体变形的性质，即潜在硬化，交叉滑移和与边缘和螺钉分布相关的背应力（等效地，内部应力带有相反符号）的影响。几何上必要的位错的组成部分。