Determination of a general close form relation for crack density and induced delamination evolution in cross ply laminates under uniaxial loading condition based on an extended shear lag model

In the present study, using a precise shear lag parameter in an extended shear lag model, by considering the effects of out of plane shear stresses, the stress fields distribution as well as strain fields and displacement distributions will be obtained for a typical [0m/90n]s cross ply composite laminate containing a specified matrix cracking density. Then, the stiffness degradation due to existence of matrix cracking in these cross-ply composite laminates will be evaluated and specific damage parameters, which affect the stiffness matrix of composite ply, will be defined. Furthermore, using the concept of fracture mechanics by applying two different criteria including the maximum stress and strain energy release rate, the matrix cracking initiation and evolution as well as induced delamination propagation will be studied. Finally, a closed form relation will be presented which predicts the evolution of matrix cracking under uniaxial loading conditions in cross-ply composite laminates. At last, the obtained results by present study will be compared with available semi-analytical and experimental results. The obtained results reveal that the proposed closed form relations by the authors have a less difference with experimental results in comparison with the previous semi analytic results.