Shear Stress at a Film-Substrate Interface Due to Mismatch Strain

摘要

The elastic stress distributions that develop when a thin film of one material is bonded to a half space of a second material under conditions with a mismatch strain that results in a state of residual stress. The origin of the mismatch strain may be temperature change, chemical reaction, remote applied loading on the substrate, or some other source. The distribution of shear stress at the interface is determined for the case when the film is thin enough to be idealized as a membrane. A semi-infinite film is considered first to examine in detail the concentration of shear stress near the edge. Then, a periodic array of film segments is considered , and the dependence of the stress distribution and the stress concentration factor on spacing and material parameters is determined. The special case of an isolated film segment is studied by taking the spacing distance to be very large compared to the segment width. All problems are cast in the form of a singular integral equation for the distribution of shear stress at the interface, and this integral equation is solved numerically for the cases of interest. Representative results are also presented for the distribution of mean stress and resolved shear stress in the substrate due to the mismatch strain. Finally, the limitations of the film idealization of the substrate are discussed.