A Numerical Modelling of Mixed Mode Crack Initiation and Growth in Functionally Graded Materials

The main objective of this work is to present a numerical modeling of crack propagation path in isotropic functionally graded materials (FGMs) under mixed-mode loadings. The displacement extrapolation technique (DET) and the maximum circumferential stress (MCS) criterion are investigated in the context of crack growth in functionally graded beam subject to three and four bending conditions. Using the Ansys Parametric Design Language (APDL), the variation continues of the material properties are incorporated by specifying the material parameters at the centroid of each finite element (FE) and the crack direction angle is evaluated as a function of stress intensity factors (SIFs) at each increment of crack extension. In this paper, two applications are investigated using an initial crack perpendicular and parallel to material gradient, respectively. The developed approach is validated using available numerical and experimental results reported in the literature.

本研究的主要目标是提出一种针对复合型载荷下各向同性功能梯度材料（FGMs）裂纹扩展路径的数值建模方法。针对受三点弯曲与四点弯曲作用的功能梯度梁的裂纹扩展问题，本文对位移外推法（DET）与最大周向应力（MCS）准则展开了研究。借助ANSYS参数化设计语言（APDL），通过在每个有限元（FE）的形心处指定材料参数，实现了材料属性的连续变化；同时将裂纹扩展每一步增量下的裂纹方向角，以应力强度因子（SIFs）为函数进行求解。本文分别设置垂直于和平行于材料梯度方向的初始裂纹，开展了两项应用案例研究。所提出的建模方法通过文献中已公开的数值与实验结果完成了有效性验证。