The numerical manifold method for crack modeling of two-dimensional functionally graded materials under thermal shocks

Abstract

Profiting from its bi-cover systems, i.e., the mathematical cover and the physical cover, the numerical manifold method (NMM) is superior in crack modeling. In this work, the NMM is further extended to study thermal shock fracture behavior of two-dimensional functionally graded materials (FGMs). The discontinuity of temperature and displacement fields across crack surface is naturally represented by the NMM, while the singularity of the heat fluxes and stresses at the crack tip is captured through the use of associated asymptotic terms in the NMM local functions. The temperatures are firstly obtained through transient heat transfer simulation and then stepwisely imported into the thermoelastic counterpart to compute the mechanical quantities. The thermal stress intensity factors (TSIFs) are obtained through the domain-independent interaction integral. For verification, several numerical examples with increasing complexity are tested and the NMM results match well with the available published solutions. Moreover, the influences of the material gradation of the FGMs and the crack geometries on the TSIFs are also revealed.