Failure multiscale simulations of composite laminates based on a non-local mean-field damage-enhanced homogenization

A multiscale method is developed to study the failure of carbon fiber reinforced composites.

In order to capture the intra-laminar failure, a non-local mean-field homogenization (MFH) method accounting for the damage evolution of the matrix phase of the composite material [1] is considered. In that formulation, an incremental-secant MFH approach is used to account for the elastic unloading of the fibers during the strain softening of the matrix. In order to avoid the strain/damage localization caused by the matrix material softening, an implicit non-local method [2] was reformulated to account for the composite material anisotropy. As a result, accurate predictions of the composite softening behavior and of the different phases response is possible, even for volume ratios of inclusions around 60%. In particular it is shown that the damage propagation direction in each ply follows the fiber orientation in agreement with experimental data.

The delamination process is modeled by recourse to a hybrid discontinuous Galerkin (DG)/ extrinsic cohesive law approach. As for the extrinsic cohesive law (ECL), which represents the fracturing response only, and for which cohesive elements are inserted at failure onset, the method does not suffer from a mesh-dependent effect. However, because of the underlying discontinuous Galerkin method, interface elements are present since the very beginning of the simulation avoiding the need to propagate topological changes in the mesh with the propagation of the delamination. Moreover, the pre-failure response is accurately captured by the material law though the DG implementation, by contrast to usual intrinsic cohesive laws.

As a demonstration of the efficiency and accuracy of the method, a composite laminate with a quasi-isotropic sequence ([90/45/-45/90/0]S) and an open-hole geometry is studied using the multiscale method [3] and the results are compared to experimental data. The numerical model is found to predict the damage bands along the fiber directions as observed in the experimental samples inspected by X-ray computed tomography (XCT). Moreover, the predicted delamination pattern is found to match the experimental observations.

REFERENCES
[1] L. Wu, L. Noels, L. Adam, I. Doghri, An implicit-gradient-enhanced incremental-secant mean- field homogenization scheme for elasto-plastic composites with damage, International Journal of Solids and Structures, 50, 3843-3860, 2013.
[2] R. Peerlings, R. de Borst, W. Brekelmans, S. Ayyapureddi, Gradient-enhanced damage for quasi-brittle materials. International Journal for Numerical Methods in Engineering, 39, 3391-3403, 1996.
[3] L. Wu, F. Sket, J.M. Molina-Aldareguia, A. Makradi, L. Adam, I. Doghri, L. Noels, A study of composite laminates failure using an anisotropic gradient-enhanced damage mean-field homogenization model, Composite Structures, 126, 246–264, 2015.