Mechanical Modeling of Multilayered Films on an Elastic Substrate—Part I: Analysis

In this paper the basic residual stress problem for multilayered or multiple films on an elastic substrate is considered. The stresses may be caused by a homogeneous temperature variation or slow thermal cycling and by far field mechanical loading. The films are approximated by orthotropic membranes and the substrate is assumed to be an elastic continuum. The interfacial zone is modeled by either an ideal interface or a homogeneous shear layer. The primary interest in the paper is in examining stress concentrations or singularities near the film ends. For the two interface conditions considered, this is done by varying the film/substrate contact angle. Also studied are strain energy release rate for the propagation of an interfacial crack and the direction and the magnitude of the maximum cleavage stress for a possible crack initiation in the substrate. The basic modeling and analysis are considered in Part I. Part II of the paper is devoted to the presentation and discussion of the results.