In this paper, we have investigated void growth in von Mises materials which contain realistic porous microstructures. For that purpose, we have performed finite element calculations of cubic unit-cells which are subjected to periodic boundary conditions and include porosity distributions representative of three additively manufactured metals. The initial void volume fraction in the calculations varies between 0.00564% and 1.75%, the number of actual voids between 14 and 5715, and the pores size from $2.3\mathrm{\mu }\text{m}$ to $110\mathrm{\mu }\text{m}$. Several tests with different void sizes and positions have been generated for each of the three porous microstructures considered, and for each test we have performed several realizations with different spatial arrangement of the voids. The simulations have been carried out with random spatial distributions of pores and with clusters of the same size and different void densities. The macroscopic stress state in the unit-cell is controlled by prescribing constant triaxiality and Lode parameter throughout the loading. Calculations performed exchanging the loading directions for a given distribution of void sizes and positions have shown that the porous microstructure makes the macroscopic strain softening of the unit-cell (slightly) anisotropic. Moreover, the results obtained with the realistic porous microstructures have been compared with unit-cell calculations having an equivalent single central pore, and with calculations in which the material behavior is modeled with Gurson plasticity. It has been shown that both initial void volume fraction and spatial and size distribution of voids affect the macroscopic response of the porous aggregate and the void volume fraction evolution. Moreover, the calculations with random spatial distribution of voids have brought out that different tests of the same microstructure carry significant variations to the effective behavior of the porous aggregate, and that the interaction between neighboring pores dictates the volume evolution of individual voids, especially at higher macroscopic triaxiality. The calculations with clusters have shown that pores clustering promotes localization/coalescence due to increased interaction between the voids, which results in an increased growth rate of voids in clusters with large number of pores. Moreover, the results for the evolution of the distribution of plastic strains in the unit-cell have provided quantitative indications of the role of porous microstructure on the development of heterogeneous plastic strain fields which promote macroscopic strain softening. Namely, the accelerated growth rate of the plastic strains near the voids which indicates the onset of localization/coalescence has been shown to occur earlier as the number of voids in the microstructure increases.

在本文中，我们研究了包含真实多孔微结构的 von Mises 材料中的空隙增长。为此，我们对受周期性边界条件影响的立方晶胞进行了有限元计算，并包括代表三种增材制造金属的孔隙率分布。计算中的初始空隙体积分数在 0.00564% 和 1.75% 之间变化，实际空隙数在 14 和 5715 之间，孔径从$\mathrm{2个}.\mathrm{3个}\mathrm{\mu }\text{米}$到$110\mathrm{\mu }\text{米}$. 对于所考虑的三种多孔微结构中的每一种，都生成了具有不同孔隙大小和位置的多个测试，并且对于每个测试，我们都执行了具有不同孔隙空间排列的多个实现。模拟是在孔的随机空间分布和相同尺寸但不同空隙密度的簇下进行的。通过在整个加载过程中规定恒定的三轴度和 Lode 参数来控制晶胞中的宏观应力状态。针对给定的空隙尺寸和位置分布交换加载方向进行的计算表明，多孔微观结构使晶胞的宏观应变软化（略微）各向异性。而且，已将使用真实多孔微结构获得的结果与具有等效单个中心孔的晶胞计算以及使用 Gurson 塑性对材料行为建模的计算进行了比较。已经表明，初始空隙体积分数和空隙的空间和尺寸分布都会影响多孔聚集体的宏观响应和空隙体积分数的演变。此外，空隙随机空间分布的计算表明，相同微观结构的不同测试对多孔聚集体的有效行为具有显着差异，并且相邻孔隙之间的相互作用决定了单个空隙的体积演变，尤其是在较高的宏观三轴性。簇的计算表明，由于空隙之间的相互作用增加，孔隙聚集促进了定位/聚结，这导致具有大量孔隙的簇中空隙的生长速率增加。此外，晶胞中塑性应变分布演变的结果提供了多孔微观结构对促进宏观应变软化的异质塑性应变场发展的作用的定量指示。即，随着微观结构中空隙数量的增加，表明局部化/聚结开始的空隙附近塑性应变的加速生长速率已被证明会更早发生。这导致具有大量孔隙的簇中空隙的生长速率增加。此外，晶胞中塑性应变分布演变的结果提供了多孔微观结构对促进宏观应变软化的异质塑性应变场发展的作用的定量指示。即，随着微观结构中空隙数量的增加，表明局部化/聚结开始的空隙附近塑性应变的加速生长速率已被证明会更早发生。这导致具有大量孔隙的簇中空隙的生长速率增加。此外，晶胞中塑性应变分布演变的结果提供了多孔微观结构对促进宏观应变软化的异质塑性应变场发展的作用的定量指示。即，随着微观结构中空隙数量的增加，表明局部化/聚结开始的空隙附近塑性应变的加速生长速率已被证明会更早发生。晶胞中塑性应变分布演变的结果提供了多孔微观结构对促进宏观应变软化的异质塑性应变场发展的作用的定量指示。即，随着微观结构中空隙数量的增加，表明局部化/聚结开始的空隙附近塑性应变的加速生长速率已被证明会更早发生。晶胞中塑性应变分布演变的结果提供了多孔微观结构对促进宏观应变软化的异质塑性应变场发展的作用的定量指示。即，随着微观结构中空隙数量的增加，表明局部化/聚结开始的空隙附近塑性应变的加速生长速率已被证明会更早发生。