Free edges at bilayered compounds—a short analytical and numerical reconsideration

Abstract

In this contribution, the local stress field very close to the free edges of bilayered compounds is reconsidered. Special emphasis is laid on the fulfilment of the boundary conditions. The bilayer character is represented by two areas in a homogeneous strip, where one of these areas is loaded by a homogeneous eigenstrain. Bilayered compounds are important components in several kinds of electronics and mechanical engineering applications. Positions of the intersection of the interface with free edges are prone to crack initiation. An easy-to-handle semi-analytical concept is presented, which allows estimating the maximum shear stress in the interface and its rapid dropping down very near to the free edges. The stress distributions in the immediate vicinity of the intersection of the interface with the free edges for generalized plane strain situations (as appearing along the side edges of a bilayered strip, sufficiently far away from the strip end), for plane stress situations (as appearing at the end of a bilayered beam), and in an axisymmetric setting (as appearing at the edge of a bilayered circular disc) are investigated. Already published approaches and results for these stress states are reviewed critically.