An energy based approach for reliability analysis of delamination growth under mode I, mode II and mixed mode I/II loading in composite laminates

Since there are many uncertainty sources in composite laminates such as fiber and matrix material properties, reliability analysis of laminates under specific loading modes has been of significant importance in many applications. This paper represents a method for reliability analysis of E-Glass/Epoxy composite laminates in the presence of the most common and catastrophic failure mode in macro-scale, i.e. delamination under mode I, mode II, and mixed mode I/II using an energy based approach for the first time. Limit state functions for the reliability analysis of delamination growth under mode I, mode II, and mixed mode I/II loading are formulated based on energy release rate along with the interlaminar fracture toughness in each of the mentioned modes. Having random variables and limit state functions determined based on energy, the reliability assessment is carried out using first order reliability method (FORM) and second order reliability method (SORM) and the obtained results are verified by Monte Carlo Simulation (MCS). Finally, the effects of different modes of delamination including mode I, mode II, and mixed mode I/II on the reliability of delamination growth in composite laminates are obtained. It is indicated that the reliability of E-Glass/Epoxy composite laminates in mode I delamination has its lowest value, while in mode II has the highest. Amongst the considered random variables in mode I, mode II, and mixed mode I/II, thickness of the laminate is the most effective one in the reliability of mentioned composite laminates under different delamination modes.