Evaluation of Interfacial Stresses in a Bilayer Shell Subjected to Intrinsic Stress

Abstract

A method to computationally determine the interfacial contact pressure and shear stress in bilayers has been evaluated. The method uses “Tied-Contact Pair” conditions between two shell surfaces of a coating and a substrate in Abaqus, which constitutes a bilayer circular disk. This method was evaluated for three cases: free expansion (simply supported at the center), fixed edge, and pinned outer edge. The results were validated with previous work. The displacements obtained were typically in the range of 2–3% of the theoretical values for the linear simulations. Comparisons were made between the theoretical stress values and the radial, tangential stresses obtained at the interfacing surfaces of the bilayer from the tied model. This provided a method to perform a preliminary investigation of the interfacial stresses at the interfacing shell surface, namely the normal contact pressure and shear stress as well as the radial & tangential stresses of the constituent layers for these two shell surfaces. The non-linear SAX2 shell element type was used in this simulation. A second model which uses “Mesh-Tie Constraints” in Abaqus was also investigated. The values obtained for both these models was found to match each other. However, the difficulty with the “Mesh-Tie Constraints” method was that it did not allow the interfacial stresses to be computed explicitly; a problem not encountered with the “Tied-Contact Pair” approach. A convergence study was performed to establish convergence of the model. This method holds promise to study the complex interfacial stress developed in multi-layered coatings typically encountered for Physical Vapor Deposition (PVD) processes.