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

In the present paper an attempt is made to describe transverse cracking of cross-ply ([0°n/90°m]s) laminates subjected to an external applied load and a temperature change. For this purpose a new method is suggested which was developed on the basis of the energy balance based finite fracture criterion suggested by Hashin (1996) [Hashin, Z., 1996. J. Mech. Phys. Solids 44, 1129]. In this approach the value of the specific surface energy (the critical energy release rate) is assumed to be dependent on a random microdamage distribution in the material. Hence, it is assumed to be a random function of location. A new probabilistic technique is developed to take this randomness into consideration. It is shown that only one unknown probabilistic function is required, namely the probability density function of the specific surface energy. This is determined by fitting the external stress and the corresponding crack density to experimental data for any specific laminated system. The cracking process for any other laminate made of the same material may be predicted by the suggested method. Numerical simulation of progressive cracking process is described, which provides the probability density function for inter-crack distances as well as the crack density growth with increasing external loading. A simple probabilistic progressive cracking criterion is developed as well. The predicted crack density growth calculated for various laminates is in good agreement with published experimental results.