Mixed-mode fracture of orthotropic functionally graded materials using finite elements and the modified crack closure method

A finite element methodology is developed for fracture analysis of orthotropic functionally graded materials (FGMs) where cracks are arbitrarily oriented with respect to the principal axes of material orthotropy. The graded and orthotropic material properties are smooth functions of spatial coordinates, which are integrated into the element stiffness matrix using the isoparametric concept and special graded finite elements. Stress intensity factors (SIFs) for mode I and mixed-mode two-dimensional problems are evaluated and compared by means of the modified crack closure (MCC) and the displacement correlation technique (DCT) especially tailored for orthotropic FGMs. An accurate technique to evaluate SIFs by means of the MCC is presented using a simple two-step (predictor–corrector) process in which the SIFs are first predicted (e.g. by the DCT) and then corrected by Newton iterations. The effects of boundary conditions, crack tip mesh discretization and material properties on fracture behavior are investigated in detail. Many numerical examples are given to validate the proposed methodology. The accuracy of results is discussed by comparison with available (semi-) analytical or numerical solutions.