Thermally nonlinear analysis of propagating cracks under generalized thermal shock

Abstract

In this paper, the thermally nonlinear response of stationary and moving cracks in isotropic media subjected to a hyperbolic thermal shock in the framework of the eXtended Finite Element Method (XFEM) is examined. For this purpose, the thermally nonlinear fully coupled Lord-Shulman (LS) model is considered as governing equations. In addition, two cases of material properties, temperature-dependent (TD) and temperature-independent (TID), are assumed. The geometry, including a predefined crack, is modeled using the XFEM for spatial discretization. For modeling the dynamic crack growth within the XFEM, the Maximum Tangential Stress (MTS) criterion is modified based on the stress field near the tip of a growing crack to calculate the dynamic crack growth angle. Besides, the nonlinear form of the Newmark integration scheme is implemented for the numerical integration in the time domain. Finally, a method based on one of the Barnet-Lothe tensors for isotropic materials is employed to extract the stress intensity factors (SIFs). In the provided examples, the effects of thermal nonlinearity, the temperature-dependency of material properties, and the LS relaxation time on the crack propagation path are explored.