On the Interaction of Damage Evolution and Thermal Buckling in Stepped Circular Bilaminates

Abstract

The behavior and evolution of stepped circular bi-laminates with edge damage are studied for structures subjected to uniform thermal load. The problem is formulated as a moving intermediate boundaries problem in the calculus of variations, where the boundary of an evolving region of damage emanating from the edge of the smaller substructure, as well as the boundary of a progressing/regressing region of sliding contact adjacent to the intact region of the composite structure are each allowed to vary along with the displacements. This yields the associated transversality conditions that define the locations of the propagating boundaries that correspond to equilibrium configurations of the evolving composite structure, as well as the equations of equilibrium and the associated interior and exterior boundary conditions. Various configurations of contact of the detached segments of the composite structure and the associated behavior are considered, and the influence and progression of contact on the overall evolution of the composite structure are assessed. Closed-form analytical solutions to the geometrically nonlinear problem are obtained, and expressions for the critical buckling load are developed. The explicit forms of the total energy release rate along the delamination front, as well as of the conditions for propagation of the contact zone boundary, are obtained from the analytical solutions and the corresponding transversality conditions. Results of numerical simulations based on the analytical solutions are presented and are seen to unveil a rich evolution process involving contact progression/recession and metamorphosis, buckling, and detachment progression during the prebuckling phase, during sling-shot buckling, and during the postbuckling phase, depending on the material properties of the sublaminates, the geometry of the sublaminates, the initial size of the damage, and the strength of the interfacial bond. Characteristic behavior of damage propagation is found to be quite robust and is seen to include stable propagation, stable followed by unstable progression, arrest, and catastrophic propagation.