Determination of Stress Concentration Factor of Around Arbitrary Cracking in Thermo-elastic Solids

A novel finite element capable of arbitrary cracking in solids under coupled thermo mechanical loading has been formulated and implemented into the commercial software package ABAQUS as a user-defined element. The thermal mechanical augmented finite element method (TM-AFEM) is an extension of the Augmented Finite Element Method (AFEM) which includes temperature degrees of freedom (DoFs) so steady-state or transient temperature evolution and their direct effects on fracture processes in solids can be explicitly considered. The formulation incorporates a thermomechanical cohesive zone model (TMCZM) to account for load and heat transfer across the intra-element weak and strong discontinuities (i.e., material interfaces&cracks). A novel condensing method is used to express the internal DoFs, both mechanical and thermal, as explicit functions of the external DoFs. It has been demonstrated through several numerical examples that, the TM-AFEM can provide a general framework for realistic simulation of thermal fracture problems both at single elemental level and at structural level. The advantages of the TM-AFEM include: (1) arbitrary crack initiation and propagation without a priori knowledge of the crack path; (2) greatly improved numerical efficiency as compared to similar advanced methods such as XFEM or PNM because the TM-AFEM does not need extra external DoFs for crack evolution; and (3) the capability of accounting for multiple, complex crack evolution and interactions.