Non-uniform stress distribution and deformation bifurcation of thin film/substrate system subjected to gradient temperature

Stresses in thin films or coatings control the reliability of the thin film/substrate structure. By considering a circular thin film/substrate system subjected to gradient temperature, we derive relations between the non-uniform stresses in film and temperature, and between the non-uniform system curvatures and temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “non-local” part which reflects the effect of temperature of other points on the location of scrutiny. Furthermore, the deformation bifurcation behavior of the thin film/substrate system is analyzed. As the thermo-mismatch strain in the thin film increases, the system may transit to a biaxial curvature state (non-spherical deformation), in other words, the bifurcation of curvature will occur.