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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.

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Studying the behavior of composite materials reveals that various types of failure modes occur when material experiences different loading conditions, which may have a significant impact on performance and properties of a structure. In this research, we study the mechanical response of orthogonal multi-layers by considering different failure modes at micro-scale and their development in macro-scale. For this purpose, the effect of the emergence and growth of fiber separation and subsequent formation of matrix cracks are investigated in the micro-scale. Furthermore, interlayer separation caused by leaving the matrix are studied in macro-scale. To model the separation of fiber matrix which is the first dominant failure mode, the sticky area method is used. The model verification and obtained results are compared with the previous research. Then, XFEM method is used to take into account the failure mode of matrix. Finally, using of the sticky area method, we are able to simulate the separation of matrix layers. The FE-program Abaqus via its user scripting interface (Python) are employed in this research for modeling of fibers embedded into matrix.