The scientific literature has shown the strong effect of void size on material response. Several yield functions have been developed to incorporate the void size effects in ductile porous materials. Based on the interface stresses of the membrane around a spherical void, a Gurson-type yield function, which includes void size effects, is coupled with the bifurcation theory for the prediction of plastic strain localization. The constitutive equations as well as the bifurcation-based localization criterion are implemented into the finite element code ABAQUS/Standard within the framework of large plastic deformations. The resulting numerical tool is applied to the prediction of forming limit diagrams (FLDs) for an aluminum material. The effect of void size on the prediction of FLDs is investigated. It is shown that smaller void sizes lead to an increase in the ductility limits of the material. This effect on the FLDs becomes more significant for high initial porosity, due to the increase of void-matrix interface strength within the material.

中文翻译：

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使用空隙尺寸相关模型和分叉方法预测多孔材料的成形极限

科学文献表明空隙尺寸对材料响应有很强的影响。已经开发了几种屈服函数以将空隙尺寸效应纳入可延展的多孔材料中。基于球形空隙周围膜的界面应力，将包含空隙尺寸效应的 Gurson 型屈服函数与分岔理论相结合，用于预测塑性应变局部化。本构方程以及基于分岔的定位准则在大塑性变形框架内被实施到有限元代码ABAQUS/Standard中。所得数值工具用于预测铝材料的成形极限图 (FLD)。研究了空隙尺寸对 FLD 预测的影响。结果表明，较小的空隙尺寸会导致材料延展性极限的增加。由于材料内空隙-基质界面强度的增加，对于高初始孔隙率，这种对 FLD 的影响变得更加显着。