基于光滑有限元法的热-弹相场断裂研究

With the rapid development of high-speed aircraft, the influence of high temperature on the strength and failure modes of structure needs to be considered. The phase-field fracture method provides a powerful tool for simulating fracture problems; and the cell-based finite element method (CS-FEM) is an efficient numerical method wildly used in mechanical analysis. Hence, in this paper, the phase-field fracture modeling is used to simulate the coupled thermo-elastic fracture problem which is implemented with the CS-FEM. The basic theories of thermal conduction and phase-field modeling are briefly reviewed. The governing equations are derived. The variational formula and the linearization of the three-field coupled system are presented. The numerical implementation of thermo-elastic phase-field fracture modeling with CS-FEM is provided. And then, the calculation programs are written to perform two classical numerical tests with staggered strategy in MATLAB software. First, the typical 2D tensile fracture behavior of edge-notched square specimens under thermo-mechanical loading is calculated. The results show that, for specimens in tension, the temperature difference between the upper and the lower surfaces can advance or delay the crack initiation without considering the influence of temperature on the fracture toughness. The results are in good agreement with the finite element calculation ones. The CS-FEM costs less time and is a little more efficient than the FEM. Second, the multi-crack propagation and failure behavior of the ceramic plate under thermal shock is simulated by this proposed method. It is found that the number and length of cracks are affected by the temperature difference between the inside and the outside, and the numerical results agree well with the experimental ones. This work is an extension of the CS-FEM based on the phase-field method and can provide an effective way for simulating coupled thermo-elastic fracture behavior.