The ductile failure of crystalline materials is strongly linked to the growth of intragranular voids. The estimation of the overall yield criterion thus requires to take into account the anisotropic plastic behavior of the single crystal. In the framework of the kinematic limit-analysis approach, this problem has been considered up to now with Gurson-type isotropic trial velocity fields. In the present work, a different class of piecewise constant velocity fields is proposed based on a detailed analysis of FFT numerical results on the strain localization in porous single crystals with periodic distributions of voids. This original approach is implemented for the model 2D problem of a square or hexagonal array of cylindrical voids in a hexagonal close-packed single crystal with in-plane prismatic slip systems. For equibiaxial loadings, the assumption of discontinuous velocity field provides a good approximation of the smooth jumps observed in the numerical results. Consistently, this new proposal leads to a significant improvement on the macroscopic yield stress with respect to the estimate based on an isotropic velocity field. Our theoretical estimate almost coincides with the FFT numerical results for all the unit-cells and crystalline orientations considered.

结晶材料的延性破坏与晶内空隙的生长密切相关。因此，总产量标准的估计需要考虑单晶的各向异性塑性行为。在运动学极限分析方法的框架内，这个问题迄今为止已经被考虑在 Gurson 型各向同性试验速度场中。在目前的工作中，基于对具有周期性空隙分布的多孔单晶中应变局部化的 FFT 数值结果的详细分析，提出了不同类别的分段恒速场。这种原始方法是针对具有面内棱柱滑移系统的六边形密排单晶中的方形或六边形圆柱形空隙阵列的二维模型问题实施的。对于等双轴载荷，不连续速度场的假设提供了数值结果中观察到的平滑跳跃的良好近似。始终如一地，与基于各向同性速度场的估计相比，这一新提议导致宏观屈服应力的显着改善。我们的理论估计几乎与所有考虑的晶胞和晶体取向的 FFT 数值结果一致。