A variational approach for predicting initiation of matrix cracking and induced delamination in symmetric composite laminates under in-plane loading

Abstract

Abstract This paper discusses the formation of matrix cracking and induced delaminations in a [ ϕ m ( 2 ) / ψ n ( 1 ) ] s $[\phi _m^{(2)}/\psi _n^{(1)}]s$ laminate subject to arbitrary in-plane loading using a variational approach. To this end, the effects of delaminations coming from the tips of transverse cracks in the middle sublaminates are considered to specify the critical crack density points and finally understand which modes of damage are prospects for various lay-ups in the presence of transverse cracks as well as induced delamination. After deriving a very good approximation of the principle of minimum complementary energy by considering complex equations, the stress fields are provided. In this analysis, a unit cell in the ply level of a composite laminate containing both matrix cracking and delamination is considered. Then, the values of the admissible stresses and compliance of cracked laminate are employed to evaluate the energy release rate of each mentioned damage mode. Eventually, the graphs for different lay-ups in such symmetric laminate are drawn, which indicate important points for designers in practical applications. Afterwards, the effects of thickness on the dislocation of critical crack density points are checked. It can be emphasized that the current approach opens a new insight for perceiving the composites’ structural behavior in vulnerable positions.