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Abstract With the rapid development of high-speed aircraft, the influence of high temperature on the structural strength and the failure mode needs to be considered. The phase field fracture method provides a powerful tool to simulate fracture problems. And the Cell-based finite element method (CS-FEM) is an efficient numerical method which is wildly used in mechanical analysis. Hence, in this paper, phase field fracture model is used to simulate the coupling thermo-elastic fracture problem which is implemented with the CS-FEM. The basic theories of thermal conduction and phase field model 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 thermal-elastic phase field fracture model 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, a typical 2D tensile fracture behavior of edge notched square specimen under thermal-mechanical load is calculated. The results show that, for tensile specimens, 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 result is in a good agreement with the finite element calculation results, and CS-FEM costs less time and is little more efficient than the FEM one. Second, the multi-cracks propagating 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 inside and outside, and the numerical results can agree well with the experimental ones. This work is an extension of the CS-FEM based on phase-field method and it can provide an effective way to simulate thermal-elastic coupling fracture behavior.
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Received: 10 August 2022
Published: 19 June 2023
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2023, Vol. 44 
