Non–self–similar decohesion along a finite interface of unilaterally constrained delaminations

Abstract

We have presented a novel and unified approach for the analysis of delaminated structures in a compressive load environment. Previous studies have addressed delamination buckling, postbuckling and growth as three separate events with respect to remote load, with an appropriate criterion to demarcate the separate regimes. We show that a unified treatment of this problem is possible so that the evolution of the delaminated areas is obtained as a part of the calculation process. The unified approach is made possible by the introduction of an interface decohesion law that is appealing both as a computational device to regularize an otherwise singular problem, and as a physical model of the decohesion process. This type of modelling is known in fracture mechanics as Barenblatt–Dugdale (BD) models. Employing BD models, we were able to overcome some of the limitations of linear elastic fracture mechanics approaches in predicting general delamination growth. Using a virtual work formulation, the delamination–interphase–substrate system was modelled as one, resulting in a system of integral equations that was solved using an approximate method. The present treatment is new and demonstrates a successful departure from traditional fracture mechanics based concepts that require empirical relations for non–self similar delamination growth studies. The problem formulation places no distinction between the phenomena of buckling (and postbuckling) and non–self–similar growth. That is, the same equations were found to govern the entire behaviour from beginning (starting to load/displace the structure) to end (complete decohesion and/or loss of stiffness) without specification to certain regimes of validity. We have demonstrated that the use of nonlinear elastic foundation models to characterize unilateral constraints and the use of interphase models to analyse delamination decohesion and growth are indeed viable. Non–self–similar delamination growth patterns were simulated without resorting to fracture mechanics concepts and it was found that unilateral contact can occur at buckling or in the postbuckling regime, as well as prior to delamination growth or after delamination growth. Several examples are presented to illustrate this new treatment.