This paper presents an analytical solution for a semi-infinite interface crack between two infinite isotropic elastic layers under general edge loading conditions. The problem is solved analytically except for a single real scalar, which is extracted from a numerical solution for a specific loading case. Two applications of the basic solution are discussed: interface cracking driven by residual stress in a thin film on a substrate, and an analysis of a test specimen proposed for measuring interface toughness.
The mathematical problem involves two elastic layers with a semi-infinite crack along the negative x₁-axis. The layers have thicknesses h and H, with material 1 above the interface and material 2 below. The crack tip is at the origin, and the uncracked bimaterial layer is considered as a composite beam with a neutral axis offset from the bottom of layer 2. The structure is loaded with forces and moments per unit thickness, leading to two equilibrium constraints among the six load parameters.
The stress fields for the problem are shown to be the same as those for a simplified problem when the interface crack is superimposed. This allows the number of load parameters controlling the crack tip singularity to be reduced to two: P and M. These are defined in terms of the load parameters and dimensionless constants from Appendix III.
The general nature of the edge loads allows for the solution of special practical problems. Two sample problems are considered: one involving residual stress in thin films, and another involving a four-point bending test specimen for measuring interface toughness. The test specimen is extended to include a longitudinal load to assess its feasibility for measuring toughness over a range of mixed-mode interface intensity factors. The crack is approximated by the system in Fig. 3b when it is long compared to the thickness of the top layer but still within the central region of the specimen. This system is a special loading case of the system in Fig. 1a.This paper presents an analytical solution for a semi-infinite interface crack between two infinite isotropic elastic layers under general edge loading conditions. The problem is solved analytically except for a single real scalar, which is extracted from a numerical solution for a specific loading case. Two applications of the basic solution are discussed: interface cracking driven by residual stress in a thin film on a substrate, and an analysis of a test specimen proposed for measuring interface toughness.
The mathematical problem involves two elastic layers with a semi-infinite crack along the negative x₁-axis. The layers have thicknesses h and H, with material 1 above the interface and material 2 below. The crack tip is at the origin, and the uncracked bimaterial layer is considered as a composite beam with a neutral axis offset from the bottom of layer 2. The structure is loaded with forces and moments per unit thickness, leading to two equilibrium constraints among the six load parameters.
The stress fields for the problem are shown to be the same as those for a simplified problem when the interface crack is superimposed. This allows the number of load parameters controlling the crack tip singularity to be reduced to two: P and M. These are defined in terms of the load parameters and dimensionless constants from Appendix III.
The general nature of the edge loads allows for the solution of special practical problems. Two sample problems are considered: one involving residual stress in thin films, and another involving a four-point bending test specimen for measuring interface toughness. The test specimen is extended to include a longitudinal load to assess its feasibility for measuring toughness over a range of mixed-mode interface intensity factors. The crack is approximated by the system in Fig. 3b when it is long compared to the thickness of the top layer but still within the central region of the specimen. This system is a special loading case of the system in Fig. 1a.