Numerical calculation of stress intensity factors in functionally graded materials

The finite element method is studied for its use in cracked and uncracked plates made of functionally graded materials. The material property variation is discretized by assigning different homogeneous elastic properties to each element. Finite Element results are compared to existing analytical results and the effect of mesh size is discussed. Stress intensity factors are calculated for an edge-cracked plate using both the strain energy release rate and the J-contour integral. The contour dependence of J in an inhomogeneous material is discussed. An alternative, contour independent integral (J) over tilde is calculated and it is shown numerically that (J) over tilde, the strain energy release rate G, and the limit of J as Gamma approaches the crack tip (where Gamma is the contour of integration) are all approximately equal. A simple method, using a relatively coarse mesh, is introduced to calculate the stress intensity factors directly from classical J-integrals by obtaining \lim(Gamma-->0) J.