Thermal generalized stress intensity factors in 2-D domains

Computation of thermal generalized stress intensity factors (TGSIFs) in linear thermo-elastic two-dimensional problems with singular points subjected to steady-state temperature distribution is addressed. The stress tensor in the vicinity of singular points exhibits singular behavior characterized by the strength of the singularity and the associated TGSIFs. The p-version of the finite element method is first used to compute the temperature field, usually exhibiting singular behavior of the fluxes in the vicinity of the singular point, then imposed in the elastic analysis as thermal loading, exciting the TGSIFs. A post-processing technique based on the complementary weak form in conjunction with Richardson extrapolation is applied to extract the TGSIFs. Importantly, the proposed method is applicable, not only to singularities associated with crack tips, but also to multi-material interfaces and non-homogeneous materials. Numerical results of crack-tip singularities (mode I, mode II and mixed modes) and singular points associated with a two-material inclusion and a 90° dissimilar materials wedge, are presented.