Thermal shock fracture of a crack in a functionally gradient half-space based on the memory-dependent heat conduction model

•Memory-dependent heat conduction model is used for the thermoelastic problem.•A insulated crack in a functionally gradient half-space under thermal impact is investigated.•Effects of time delay, kernel function and nonhomogeneity parameters on the temperature and SIFs are analyzed.•The present results are compared with those based on Fourier and CV heat conduction model. In the present study, we consider a thermoelastic half-space made of a functionally gradient material with an insulated crack, which is subjected to a thermal impact. The memory-dependent heat conduction model is adopted for analysis. By using the Fourier and Laplace transforms, the thermoelastic problem is formulated in terms of singular integral equations which can be solved numerically. Effects of the time delay, kernel function, and nonhomogeneity parameters on the temperature and stress intensity factor are analyzed. Our results are also compared with those based on the Fourier and CV heat conduction models, which can be viewed as two special cases of the present model. In conclusion, the memory-dependent derivative and nonhomogeneity parameters play an essential role in controlling the heat transfer process.