An elastic-interface model for buckling-driven delamination growth in composite panels under bending

Delamination is a major failure mode for composite laminates. Such phenomenon can have multiple causes, such as manufacturing defects and low-energy impacts. Delamination cracks propagate under both static and cyclic loads [1]. In this paper, we analyse the delamination growth promoted by local buckling in a laminate subjected to four-point bending [2]. The model considers the specimen as an assemblage of sublaminates of different thicknesses, partly connected through an elastic interface, consisting of a continuous distribution of normal and tangential springs. In particular, the specimen is subdivided into three zones with different behaviour: a first zone, between the support and the load application point, where the laminate is schematised as a single extensible and flexible beam undergoing small elastic deformations; a second zone, between the load application point and the delamination front, in which the laminate consists of two sublaminates connected by the elastic interface, modelled as extensible and flexible beams, again under small deformations; one last zone, where the two sublaminates are considered as extensible and flexible beams undergoing large displacements. The different modelling assumptions in the three zones are justified by the lower stiffness of the delaminated region, which turns out to be the region with higher compression and slenderness. The model is described by a system of differential equations, accompanied by suitable boundary conditions. The differential problem is solved analytically and the value of the critical load of instability is determined through the numerical solution of a suitable transcendental equation. The model provides an overall non-linear mechanical response. In the post-critical regime, also the energy release rate and mode mixity are evaluated. Such quantities are then compared with the fracture toughness to predict the growth of the delamination crack.