Al&met-A method for predicting the state of stress in a finite body consisting of two isotropic material layers, including a ch~cte~~tion of the singular stress state at the intersection of the interface with a stress-free boundary, is presented. The prediction of the "free edge stress" is accomplished using elastic stress intensity parameters. Arbitrary two-dimensional geometries with mechanical and thermal loading and plane strain or plane stress behavior are addressed. The approach consists of coupling the finite element solution of two unattached layers to a singular integral representation of distributed dislocations along the interface of two semi-infinite layers. Coupling of the two methods occurs along the interface, where displacement compatibility is enforced, and at the finite boundary, where correction forces are defined to eliminate the tractions from the semi-infinite dislocation solution. The stress intensity factors at the free edge interface are derived from the singular integral solution.
1. I~RODUCTIO~ THE FREE EDGE STRESS PROBLEM
A MAJOR concern in determining the strength, response and reliability of layered components is the structural integrity of the interface between the layers. Debonding of layers can occur anywhere along a material interface, but of great interest is delamination that initiates at a stress-free boundary. This problem is particularly difficult to address, since the elastic solution predicts a stress state that is singular, i.e. the stress components tend to infinity or are undefined.
Although linear elasticity predicts singular stresses at the free edge interface, these high stresses are relieved in a physical sense by some type of nonlinear behavior, such as yielding and plastic defo~ation.
However, much success has been found in the prediction of singular stresses by applying linear theory with an appropriate interpretation of the singularity.
The free edge stress problem has been studied extensively. Solutions to this problem and other problems of a localized nature have taken the form of analytical approaches, numerical methods, and hybrid or combined methods.
Many analytical approaches have been utilized to predict the form of the singularity at the vertex of a two-dimensional, semi-infinite, composite wedge, based on the material properties of the two materials and the wedge angle [l-lo]. These approaches result in characteristic equations whose solutions determine the form of the singularities.
Analytical studies have been performed to predict the edge stresses for several idealized confi~rations.
Erdogan and Bakioglu [I l] define stress intensity factors for periodically arranged bonded dissimilar semi-infinite layers. Lu and Erdogan [12] considered two semi-infinite dissimilar layers. These studies are limited by their semi-infinite geometry and lack of general loading capability.
Numerical methods have been utilized to predict interlaminar stresses near a free edge between isotropic layers. The finite element method has emerged as the predominant numerical tool in analyzing the edge problem. This method has limitations such as lack of convergence and poor accuracy near areas of singularity, i.e. in the elements along the interface nearest the edge.
The surface integral method has recently been developed for solving problems in solid mechanics that have a localized nature [13]. The surface integral method uses governing integral