Thermo-mechanically coupled sliding contact shakedown analysis of functionally graded coating-substrate structures

The sliding contact shakedown map composed of elastic shakedown limit and elastic limit is significant to the further optimization of functionally graded (FG) coating parameters. The friction heat induced by the relative sliding velocity of contact pairs can cause thermal stress and changes in contact parameters. Nevertheless, the influence of thermo-mechanically coupled effect on the sliding contact shakedown map of FG coating-substrate structures keeps unrevealed. Therefore, a mathematical optimization model is proposed to draw the shakedown map considering the temperature-dependent friction coefficient and yield stress. Based on the thermo-elasto-perfectly plastic material model and multilayered approximation of FG coating, the required thermo-elastic stress field with the temperature-dependent friction coefficient is obtained by employing the conjugate gradient method and discrete convolution-fast Fourier transform algorithm. The results show that the friction heat can cause the decreases of elastic shakedown limit and elastic limit, and increasing the sliding velocity can enhance the decreases. Moreover, the friction heat can elevate the residual tensile stress near the surface and weaken the residual compressive stress at a large depth from the surface. Meanwhile, the temperaturedependence of friction coefficient can cause the increases of elastic shakedown limit and elastic limit, but the introduction of temperature-dependent yield stress brings no obvious change to the shakedown curves due to the slight thermally-induced change of yield stress. Additionally, decreasing the distribution gradient index can not only improve elastic limit and elastic shakedown limit at large friction coefficients, but also reduce the distribution of residual tensile stress near the surface.