Mode II dominant fracture of layered composite beams and wide-plates: a homogenized structural approach

Abstract

Brittle delamination fracture under Mode II dominant conditions in unidirectional composite and layered beams and wide-plates is studied using a homogenized structural model based on a zigzag approach. The model captures the unstable propagation of cracks, snap-back and snap-through instabilities, the effects of the interaction of multiple cracks on the macrostructural response and of the layered structure on the energy release rate. The layered structure and the delaminations are described by introducing local enrichments, in the form of zigzag functions and cohesive interfaces, to a classical first-order shear deformation plate theory. The model applies to layers with principal material directions parallel to the geometrical axes, depends on only three displacement variables and the solution of specific problems requires only in-plane discretization, for any numbers of layers and delaminations. Closed form solutions are derived for the energy release rate in bi-material beams and applications are presented to homogeneous, bi-material and layered, simply supported and cantilever, bend-beams, with one and two delaminations.