Non-local damage model for 3D woven composites exhibiting size effect
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Our work aims to improve a continuum damage model developed specifically for 3D woven composites by accounting for an energetical size effect occurring on the compressive critical energy release rate associated. For aeronautical parts made of 3D woven composites, such as the FAN blades, it was shown that under a flexural mode of solicitation, the face loaded in a compressive mode is the limiting factor due to carbon fibers kinking. Additionally, the need for larger composite parts has pointed out the criticality of considering size effects on the structural properties to failure. For the studied material, a quasi-brittle failure due to a non-negligible fracture process zone at the crack tip creates a deterministic size effect on the compressive strength. New developments are added to the Onera Damage Model for compression [1]. Based on experimental observations, we introduce in the local material behaviour law a post-softening residual crushing stress. The formulation of the law allows us to dissociate the dissipated energy associated with fibres kinking from the energy dissipated during the crushing phase. To capture the size effect and ensure mesh-objective finite element simulations, the model is coupled with a nonlocal implicit gradient regularization method [2] with two characteristic lengths, associated respectively with tensile and compressive fibre yarn failure. The nonlocal formulation delocalizes the equivalent strain driving the damage variables and is solved through a staggered scheme involving two coupled Z-Set simulations (mechanical equilibrium and Helmholtz-type nonlocal problem). The model parameters are identified from a comprehensive experimental campaign including tension and compression tests on dog-bone specimens, Double Edge Notched Tension/Compression and Compact Tension/Compression specimens of various sizes. This model coupled with a non-local regularization method should allow us to estimate both tensile and compressive strengths for stable and unstable crack propagation, with respect to the energetic size effect. REFERENCES [1] F. Laurin, Transfert vers l’industrie de modèles avancés pour la prévision de la tenue de structures composites aéronautiques, Habilitation à diriger des recherches de l’ENS Cachan, 2015. pp.3391-3403, 1996. [2] R.H.J. Peerlings, R. De Borst, W.A.M. Brekelmans, and J.H.P. De Vree, Gradient enhanced damage for quasi-brittle materials, Int. J. Numer. Meth. Engng., Vol. 39, pp.3391-3403, 1996.
