Determination of T-stress for thermal cracks in homogeneous and functionally graded materials with the numerical manifold method

•Thermal T-stress in cracked homogenous and functionally graded materials is studied.•Numerical manifold method and interaction integral is combined for T-stress extract.•Our solutions are in nice agreement with the available reference ones.•New T-stress results for inclined, multiple and intersecting cracks are reported. T-stress plays an important role in the fracture of various materials, and is frequently adopted as a second fracture parameter in addition to the stress intensity factor. In this paper, the T-stresses for cracks in both homogeneous and functionally graded materials under thermal loadings are computed by the numerical manifold method (NMM), which is very suitable for crack modeling due to the use of bi-cover systems. After the calculation of temperature and displacement fields by the NMM solver, the T-stress is extracted through the domain-independent interaction integral. The proposed method is verified through two benchmark problems and then applied to study three more complex cases where the effects of material parameters and crack configurations on the T-stress are further examined.