Thermally induced buckling and damage evolution in stepped circular bi-laminates
Creators: name: Xu, Shuo
Publisher: name: No Publisher Supplied
Year: 2022

description: Stepped circular bi-laminates are employed in various engineering applications which include, but are not limited to, single sided symmetric composite patches for the repair of cracked aircraft structures, piezoelectric actuators, semi-conductors, and smart structures, etc. These structural components are typically exposed to a thermal environment during their operating life, which results in thermal buckling and delamination of the composite structure due to the differing material properties of the layers, particularly the coefficients of thermal expansion. It is therefore of interest to explore the response of such systems to thermal loading, categorize their behavior, and understand their limits. Toward this end, in the present study we consider the thermo-mechanical buckling behavior of intact stepped circular bi-laminates, the influence of edge damage and contact of the detached layers, and the characteristics of damage propagation on the behavior of the evolving composite structures when subjected to a uniform temperature change.The general equations for thermally driven buckling of stepped circular bi-laminates, contact evolution, and detachment propagation are derived via a variational principle that allows for moving interior boundaries – that is, for the variation of the boundaries as well as the in-plane and transverse displacements. This results in the transversality conditions for contact progression/regression and damage propagation, including self-consistent energy release rates along the delamination front, and self-consistent constitutive equations of the composite structure, as well as the equations of motion and the associated matching and boundary conditions for the composite structure. In addition, a stability criterion is established based on the second variation of the total potential energy of the system in to identify stable and unstable equilibrium configurations.Axi-symmetric deformation and detachment of stepped circular bi-laminates are considered. A loading parameter which couples temperature change and membrane force is identified. The membrane forces are shown to be uniform, and the problem is recast in a mixed formulation expressed in terms of the (uniform) membrane force and the transverse deflection. This is coupled with an integrability condition to insure continuity of the in-plane displacements. Exact, closed form analytical solutions of the moving interior boundaries problem are obtained for damaged circular bi-laminates with various contact situations, as well as for intact composite structures. The explicit forms of the expressions for the critical buckling load, the stability criterion, contact progression/regression and the energy release rates are developed, respectively.Simulations based on the analytical solutions are performed and the phenomenon of buckling is observed for thermally loaded intact stepped circular bi-laminates. The effects of changes in material and geometric parameters on critical temperature are also examined. Thermally induced buckling, contact and its progression/regression, and damage propagation for stepped circular bi-laminates with edge damage under thermal load are studied for clamped-fixed and hinged-fixed support conditions. The corresponding results reveal characteristic behavior, including critical threshold temperatures for buckling, stability of pre- and post-buckling equilibrium configurations, contact behavior of the detached segments of the substructures, and the interaction of thermal buckling, contact progression/regression, and damage evolution. Sling-shot buckling, and sling-shot buckling accompanied by buckle trapping, are observed as well.The mathematical models and solutions presented herein are applicable to the design and utilization of composite structures belonging to the class of interest.