Finite fracture mechanics fracture criterion for free edge delamination

The interlaminar stresses at the dissimilar interface near the free edges of the composite laminates are weakly singular due to the material mismatch. These stresses can induce delamination between the dissimilar plies. The free edge delamination is investigated in the present study in the framework of Finite Fracture Mechanics. Dimensional analysis is performed to evaluate the two quantities (interlaminar stresses and incremental energy release rate) required for the FFM criterion for any arbitrary load and ply thickness. The non-dimensional functions of these quantities are determined semi-analytically by utilising the expressions derived from dimensional analysis and Finite Element models. The energy release rate is calculated by considering a semi-elliptically shaped crack emanating from the dissimilar interface at the free edge. Since the crack has two dimensions the FFM system of equations leads to infinitely many solutions. Therefore, a hypothesis is made to introduce an additional inequality that the crack extension occurs homothetically, i.e., the crack retains its aspect ratio while extension. The unknown variables (failure load and crack nucleated dimensions) are determined by solving an optimisation problem to find the minimum load corresponding to a specific crack and satisfying both the stress and energy criterion. The prediction of a failure of laminate exhibiting free edge effects using introduced 3D FFM criterion is compared against experimental results from literature and good agreement is attained.