A phase-field model for thermo-elastic fracture in quasicrystals

Abstract

In this paper, a thermo-elastic phase-field model for brittle fracture in quasicrystals is developed. The kind of quasicrystals is not preset, so this model is suitable for almost all thermo-elastic quasicrystal solids. The phonon force and thermal load trigger the variation of the phonon elastic energy, and then drive crack initiation and propagation. The thermal conductivity in the cracked region is assumed to be degraded, which means cracks are adiabatic. For the static penny-shaped crack problem, the results based on the present model agree well with the existing analytical solution. For the quasi-static crack problems, both the tensile/shear fracture in a thermal environment and the thermal shock cracking failure can be dealt with by the present model. Several examples of 1D hexagonal and 2D decagonal quasicrystals are performed to evaluate the effects of thermal load and phason elastic field. The simulation results show that the thermal load can influence the peak force and fracture displacement. For the single-edge notched tension test, the effect of the thermal load on the peak force is small, but it on the fracture displacement is obvious. For the single-edge notched shear test, the thermal load has an obvious influence on both the peak force and fracture displacement. For the thermal shock cracking problem, the phason elastic field has a significant effect on the cracking time and crack number. The present model can serve as a powerful tool to simulate various thermo-elastic fracture problems in quasicrystals.