Statistical Analysis for Interface Fracture and Delamination Failure of Composites

A methodology for measuring the interface fracture toughness of a crack between two isotropic, homogeneous materials and a delamination between two laminae of unidirectional composite materials of differing directions is presented. Four cases are considered. Two isotropic material pairs are described: glass/epoxy and two ceramic clays. Similar studies are presented for two cross-ply laminates: 0°/90° and +45°/-45°.
The Brazilian disk specimen was used to carry out mixed mode fracture tests. The load and crack or delamination length at fracture were measured and used in a finite element analysis to determine the displacement field. An interaction energy or M-integral was used to determine the stress intensity factors at failure. These in turn were employed to obtain the critical interface energy release rate G_ic and one phase angles ψ in two dimensions or two phase angles ψ and ϕ in three dimensions which measure the mode mixity. For the M-integral and for each interface crack or delamination, the first term of the asymptotic solution of the field quantities is required. For two isotropic materials, these solutions are well known. For the laminates described here, they were determined by the Stroh and Lekhnitskii formalisms. A failure criterion determined from first principles is presented. The values of G_ic and ψ in two dimensions or ψ and ϕ in three dimensions are used to specify the criterion for each material pair. A statistical analysis is presented. Two approaches are taken: one uses the t-statistic to predict a 10% probability of failure; the second uses a standard normal variate to predict a 10% failure probability with 95% confidence.