This work investigates the void surface effects on the macroscopic yield criterion of ductile materials embedded with nanosized spherical cavities. The solid matrix is treated as an isotropic, von Mises, incompressible and rigid-perfectly plastic material. Based on the trial velocity field proposed by Gurson and the first-order Taylor approximations of the equivalent volume strain rate, surface strain rate and curvature change rate, a limit analysis is conducted for the spherical representative volume element under the application of an arbitrary macroscopic strain rate loading. The void surface effects enter into the mechanics and physics of the yield criterion through a plastic surface model of the Steigmann–Ogden type. In addition to the plastic dissipation in the solid matrix that is conventionally included in the classical solution, those due to residual surface stress, surface tensile strength and surface bending strength are also taken into account in order to address the void surface effects. A closed-form plastic dissipation is provided, based on which analytical parametric equations are developed for the macroscopic mean and equivalent stresses. The governing parameters of void surface plasticity are three dimensionless ratios among surface material properties, void radius and the bulk yield strength. The inclusion of residual surface stress leads to a simple translation of the classical yield surface along the mean stress axis. For the surface tensile strength, the yield surface experiences a bidirectional expansion. In contrast, the surface bending strength tends to expand the yield surface only along the equivalent stress axis.

这项工作研究了孔隙表面对嵌入纳米级球形空腔的韧性材料宏观屈服准则的影响。固体基质被视为各向同性，冯·米塞斯（von Mises），不可压缩且刚性完美的塑料材料。基于Gurson提出的试验速度场以及等效体积应变率，表面应变率和曲率变化率的一阶泰勒近似，在任意宏观应变作用下对球形代表体积元进行了极限分析。费率加载。空隙表面效应通过Steigmann–Ogden类型的塑性表面模型进入屈服准则的力学和物理学。除了传统解决方案中通常包含的固体基质中的塑性耗散之外，为了解决空隙表面效应，还考虑了由于残余表面应力，表面抗拉强度和表面弯曲强度而产生的那些应力。提供了一种封闭形式的塑性耗散，在此基础上针对宏观平均应力和等效应力建立了解析参数方程。空孔表面可塑性的控制参数是表面材料性能，空孔半径和体积屈服强度之间的三个无量纲比率。包含残余表面应力会导致经典屈服面沿平均应力轴的简单平移。对于表面抗拉强度，屈服面经历双向膨胀。相反，表面弯曲强度倾向于仅沿等效应力轴扩展屈服面。为了解决空隙表面效应，还考虑了表面抗张强度和表面弯曲强度。提供了一种封闭形式的塑性耗散，在此基础上针对宏观平均应力和等效应力建立了解析参数方程。空孔表面可塑性的控制参数是表面材料性能，空孔半径和体积屈服强度之间的三个无量纲比率。包含残余表面应力导致经典屈服面沿平均应力轴的简单平移。对于表面抗拉强度，屈服面经历双向膨胀。相反，表面弯曲强度倾向于仅沿等效应力轴扩展屈服面。为了解决空隙表面效应，还考虑了表面抗张强度和表面弯曲强度。提供了一种封闭形式的塑性耗散，在此基础上针对宏观平均应力和等效应力建立了解析参数方程。空孔表面可塑性的控制参数是表面材料性能，空孔半径和体积屈服强度之间的三个无量纲比率。包含残余表面应力会导致经典屈服面沿平均应力轴的简单平移。对于表面抗拉强度，屈服面经历双向膨胀。相反，表面弯曲强度倾向于仅沿等效应力轴扩展屈服面。