(to be submitted for journal publication)
G.H.
Paulino
Z. Dong
Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Newmark Laboratory, 205 North Mathews Avenue, IL 61801, U.S.A.
Abstract
T-stress has significant influence on crack growth direction. This work is the first application of singular integral equation approach to investigate T-stress in functionally graded materials (FGMs). The problem under consideration is a crack located in a FGMs strip with arbitrary material property gradient direction. The crack is parallel to the upper and lower boundaries and subjected to self-equilibrating crack surface loadings. The problem is solved under plane strain and plane stress considering four basic types of boundary conditions: semi-infinite, fixed, mixed and traction-free. The upper and lower boundaries can be chosen from these four basic types of boundary conditions separately, leading to 16 sets of boundary combinations. The T-stress converges slowly upon the number of collocation points using standard Gauss-Chebyshev quadrature formulae. The improved integral method used in this work gives quickly converged and high accurate numerical results for T-stresses. At the same time, the improved integral method provides a general way to further refine the numerical results of SIFs.
Key words: Functionally graded
material, T-stress, stess intensity factor, integral equation method, mixed
mode crack problem