Instability of thermal fracture under the conditions of constrained deformation

We study the processes of quasistatic deformation and fracture of brittle materials under the action of rapidly varying temperature fields. As a fracture criterion, we use the condition of attainment of the critical levels of stresses. The analyses of the stressed state and crack growth are performed under the assumptions that the corresponding elements of the stress field are equal to zero on the newly formed free surfaces and that the conditions of the fracture criterion are satisfied at the ends of the crack. It is shown that the process of crack propagation is unstable for the major part of modes of thermomechanical loading: as soon as the critical stresses are attained at a certain point of the body, the crack instantaneously propagates to a critical size corresponding to a new stable state. It is shown that the mechanical overloading of a specimen can substantially weaken the effect of instability of development of the fracture zone. Examples of fracture of elastic brittle bodies are presented. We also perform the numerical analyses of the processes of initiation and propagation of cracks with regard for the plasticity of the material near its heated surface.