沿指定应力路径加载的有限元RVE模型研究

Analysis of FEM Cubic Representative Volume Element along Specified Stress Path

在细观尺度上建立能反映材料微观组织结构又能反映统计意义上宏观力学性能的代表性体积单元(Representative Volume Element,RVE),对其进行复杂加载下的数值研究,是目前预测材料宏观力学性能较有效的方法.论文从理论上分析并提供了对正六面体RVE在任意应力状态及任意应力路径下加载及宏观应力、应变计算的方法,用有限元软件ABAQUS实现了数值计算过程,并用此方法对循环加载下缺口圆棒颈部中心和边缘位置进行了RVE分析.结果表明:(1)此方法能准确的控制并实现正六面体RVE在任意应力状态及应力状态路径下加载;(2)通过RVE分析,可用于复杂加载下试样局部细观结构变化的研究.

The representative volume element（RVE）established on the mesoscopic scale,by which the analysis can reflect the behavior of materials with complicated microstructures and macroscopic statistical mechanical properties,is an effective method to predict the mechanical properties.These mechanical properties of materials,such as yield or subsequent yield,plastic flow,hardening,damage and failure,are closely related to their stress states and stress state paths.In this paper,the method of simulating a normal hexahedron RVE with fully periodic boundary conditions under arbitrary stress state with arbitrary loading path to calculate the macroscopic stress and strain in the entire course of the loading is theoretically analyzed.Seven springs are added on the RVE to control the load/unload of each stress component in accordance with the prescribed route and state using the relation between the internal force of spring and spring extension.The calculation is performed by using the general purpose finite element software ABAQUS adding a user subroutine（User subroutine to define multi-point constraints,MPC）to keep RVE under specified（constant or arbitrary）stress state path in the entire course of the loading and unloading.To versify this method,the multi-scale analysis of the special positions of notched round bar under cyclic loading is carried out.Through the numerical analysis,it is confirmed that the proposed method can be used to reveal the relationship between material microstructure,deformation failure mechanism and failure criterion and fatigue properties.The results show that：（1）The method enables us to perform RVE calculations under any specified arbitrary stress state and stress state paths（proportional or non-proportional loading）with high computational efciency and accuracy;（2）The simulation associated with RVE can obtain the microstructure evolution when the macrostructure under complex loading;（3）The result of the RVE model can be used to establish the constitutive equations and further to investigate the influence of stress state and stress state path on the mechanical properties of materials.