Closed-Form Fracture Analysis Based on First Order Shear Deformable Plate Theory

Enjuto, P., Graesser, D.L., Mabson, G.E., and Weckner, O.

2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA SciTech Forum, (AIAA 2018-2248), 8 – 12 January 2018, Kissimmee, Florida.

The application of two-dimensional or three-dimensional elasticity theory to the analysis of interfacial cracks between dissimilar materials results in coupling between fracture modes. This coupling is a consequence of the oscillatory behaviour of stresses and displacements resulting from physically inadmissible interpenetration of the crack surfaces near the crack tips. Generally, the study of delaminations in composite laminates makes use of laminate theory. Nevertheless, most laminate models fail to assist in the determination of the individual components of the energy-release rate.

Based on a sub-laminate model, expressions for individual energy-release rates are derived. By dividing the laminate into sub-laminates in both delaminated and un-delaminated regions and adopting transverse shear-deformable laminate theory for each of the sub-laminates, general expressions for total energy-release rate and its individual components are derived. The energy-release rates are expressed explicitly in terms of the stress resultant jumps and the derivatives of the relative displacements between the upper and lower surfaces of the delamination at its tip.