Numerical method for thermoelastic contact of coated materials with thermal imperfections based on a modified conjugate gradient method

Thermal imperfections may arise at the coating–substrate interface during manufacturing processes such as fusion welding or additive layer deposition. The evaluation of thermoelastic contact behavior in coating–substrate systems is essential for reliability assessment. Combining the discrete convolution–fast Fourier transform (DC–FFT) algorithm, a modified conjugate gradient method (CGM) is developed to establish a thermoelastic contact model for an elastic sphere sliding on coated materials with low-conductivity (LC) and high-conductivity (HC) imperfection interfaces. Compared with the conventional CGM, the modified CGM demonstrates good convergence and computational efficiency in handling heat partitioning under various magnitudes of thermal imperfections. The contact model is also validated through comprehensive analysis of thermoelastic responses and heat partition behavior. Numerical results based on the present contact model reveal that thermal imperfections significantly influence the profile of temperature, pressure, and stress component distributions. Specifically, LC imperfection causes obvious jumping behaviors of temperature and in-plane stress at the coating–substrate interface, and HC imperfection leads to a significant decay rate of temperature and in-plane stresses within the coating layer. Furthermore, the existence of imperfections affects the sensitivity of the temperature increase to system parameters compared with that under thermally perfect conditions.