Modeling of 2D cracked FGMs under thermo-mechanical loadings with the numerical manifold method

In this work, the numerical manifold method (NMM) is further exploited to study the fracture behavior of two-dimensional functionally graded materials (FGMs) subjected to thermo-mechanical loadings. For this purpose, the steady-state heat conduction simulation of the cracked FGMs is firstly performed, and then the computed temperatures are input into the thermoelastic modeling to acquire the mechanical fields and the fracture parameters. The major difficulty of the problem, i.e., the representation of the discontinuities or singularities of thermal and mechanical fields (e.g., the temperature, heat fluxes, displacements and stresses) around cracks is cleared via bi-cover systems of the NMM. By means of the domain-independent interaction integral, the thermal stress intensity factors (TSIFs) are obtained. To verify the proposed method, four numerical cases with raising complexity are tackled on mathematical covers inconsistent with all physical boundaries. The nice agreement between our results and the existing ones well demonstrates the superiority of the NMM. Besides, the effects of the material gradients and crack configurations on the TSIFs are also inspected.