Probabilistic energy based model for prediction of transverse cracking in cross-ply laminates (Q1777167)

This paper presents a method to describe transverse cracking of cross-ply laminates \([0^{\circ}n/90^{\circ}m]s\) due to external mechanical and thermal loadings (\(n\) and \(m\) are the number of piles in each layer, \(s\) is the symmetry). These laminates consist of unidirectional fibers with fiber directions in orthogonal adjacent layers. This method is developed through the combination of the variation stress analysis, the energy balance based finite fracture criterion and the probabilistic approach. First, the variational stress analysis is presented. As a result, the complementary energy change due to transverse crack is found. Then, the energy based cracking criterion is stated, using a probability density function (PDF). Stochastic properties are assumed for the specific surface energy, noticing that the energy required for a new crack to appear is related to a random microflow distribution in the material. Both, the ``geometrical'' (i.e. location of newly formed cracks) and ``physical'' (i.e. the critical energy release distribution) probabilities are included in the formulation and analysis. A numerical model of the cracking is established, comparing the specific surface energy, randomly distributed along the laminate, with the mechanical energy release, calculated by using the variational stress analysis and the local finite fracture criterion. The application of the finite fracture criterion leads to modification of PDF of specific surface energy, when different transverse ply thicknesses are considered. In this case, a convolution procedure is required, which leads to a system of coupled equations for new values of PDF parameters. Then, the probabilistic criteria of initial and progressive cracking are obtained. Smooth crack density growth with increasing external load during the initial cracking is explained from the probabilistic point of view. The predicted density growth calculated for different laminates is in good agreement with published test results.