Study the dynamic crack path in brittle material under thermal shock loading by phase field modeling

A thermal-mechanical coupled phase field fracture model is developed to study the complex dynamic crack propagation path in brittle material under thermal shock loading. By introducing a global continuum phase-field variable to describe the diffusive crack, the coupling between heat transfer, deformation and fracture is conveniently realized. A novel elastic energy density function is proposed to drive the evolution of phase-field variable in a more realistic way. The three-field coupling equations are efficiently solved by adopting a staggered time integration scheme. The coupled phase field fracture model is verified by comparing with three classical examples and is then applied to study the fracture of disk specimens under central thermal shock. The simulations reproduce the three different types of crack paths observed in experiments. It is found that the crack grows through the heating area straightly at lower heating body flux, while branches into two at higher heating body flux loading. The crack branching prefers to occur in the heating area with larger heating radius and prefers to occur outside the heating area with smaller heating radius. Interestingly, the crack branches when propagation speed is at its lowest point, and it always occurs close to the compression region. It is shown that the heterogeneous stress field induced by temperature inhomogeneity may have a strong influence on the crack branching under the thermal shock loading.