Numerical calculation of stress intensity factors in functionally graded materials

The finite element method is studied for its use in cracked and uncracked p lates made of functionally graded materials. The material property variatio n is discretized by assigning different homogeneous elastic properties to e ach element. Finite Element results are compared to existing analytical res ults 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 inhomoge neous 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 approxima tely equal. A simple method, using a relatively coarse mesh, is introduced to calculate the stress intensity factors directly from classical J-integra ls by obtaining \lim(Gamma-->0) J.