A synergistic damage mechanics approach for composite laminates with matrix cracks in multiple orientations

This paper treats the problem of elastic response of composite laminates containing matrix cracks in plies of multiple orientations. The approach taken has been described as synergistic damage mechanics (SDM) and has been previously illustrated for [0m/±θn/0m/2]s[0m/±θn/0m/2]s laminates with cracks of equal density in +θ+θ and -θ-θ plies [Singh, C.V., Talreja, R., 2008. Int. J. Solids Struct. 45(16), 4574–4589]. The current work extends the approach to [0m/±θn/90r]s[0m/±θn/90r]s and [0m/90r/±θn]s[0m/90r/±θn]s laminates with cracks additionally in the 90°-plies. The interaction between the ±θ±θ-cracks and the 90°-cracks is analyzed in terms of the crack surface displacements using a three-dimensional finite element (FE) model and found to be significant only for crack orientations close to 90°. The stiffness degradation of the laminate with all cracking modes simultaneously present is formulated by continuum damage mechanics using a second order tensor characterization of damage. The elastic moduli changes predicted by the SDM procedure are validated by independent three-dimensional FE calculations. For a particular case of quasi-isotropic [0/90/∓45]s[0/90/∓45]s laminate, the elastic moduli predictions are evaluated against experimental data. Finally, a parametric study is performed to examine the effects of ply thickness changes on stiffness properties.