Analytical solution of the thermoelastic problem of the asymmetric collinear nano-cracks in one-dimensional hexagonal quasicrystals: Analytical solution of the thermoelastic problem

The presence of multiple nano-cracks and their interactions may lead to damage to the structure and devices of materials. The plane thermoelastic problem of two asymmetric collinear nano-cracks in the aperiodic plane of one-dimensional hexagonal quasicrystals (1DHQs) is studied using the Young–Laplace equation and the classical Kachanov method. The thermal conductivity of the medium inside the crack is considered, and the interaction coefficient between cracks is introduced. The analytical expressions for the temperature, the stress intensity factors (SIFs), and the strain energy density factor (SEDF) are obtained using the Fourier integral transform method. The numerical results discussed the effects of size effects, surface effects, coupling effects and thermal conductivity on temperature, SIFs and SEDF. The results indicated that the temperature difference between the upper and the lower surface increases with the increase of the external loads. The interaction between cracks is more significant when the crack spacing is less than the length of any nano-crack. The surface effects can suppress crack propagation, and the influence of mode I SIFs on crack propagation is more significant than that of mode II thermal stress intensity factors (TSIFs). The results of the thermal fracture mechanism of quasicrystal materials at the micro- and nano-scales will benefit from the main conclusions of this paper.