Finite element evaluation of mixed mode stress intensity factors in functionally graded materials

This paper is directed towards :nite element computation of fracture parameters in functionally graded material (FGM) assemblages of arbitrary geometry with stationary cracks. Graded :nite elements are developed where the elastic moduli are smooth functions of spatial co-ordinates which are integrated into the element sti=ness matrix. In particular, stress intensity factors for mode I and mixed-mode two-dimensional problems are evaluated and compared through three di=erent approaches tailored for FGMs: path-independent J ∗ k -integral, modi:ed crack-closure integral method, and displacement correlation technique. The accuracy of these methods is discussed based on comparison with available theoretical, experimental or numerical solutions