Modeling fracture of multidirectional thin-ply laminates using an anisotropic phase field formulation at the macro-scale

Abstract

An equivalent single layer approach to model fracture events of multidirectional balanced thin-ply laminates via the use of the Phase Field method is explored. The inherent anisotropic nature of a multidirectional laminate is taken into account through the use of a structural tensor, defined from scaled directional vectors, which can account for the variation in fracture toughness of the laminates in varying directions. The scaling constants are defined using the lay-up of the laminate and the intra-laminar fracture toughness of the lamina, minimizing the number of input parameters required while also alleviating the structural tensor of a pure numerical and geometric meaning. They have a significant effect in the solution, and are here related to materials properties, not only providing a new perspective on their definition but also allowing the reduction of the number of numerical parameters used to calibrate the anisotropic PF model. The numerical implementation of the proposed formulation is performed using a simple and robust thermal analogy in Abaqus by exploiting the use of an anisotropic conductivity matrix that plays the role of the structural tensor in the anisotropic phase field formulation, which reduces the complexity of the simulations. Experimental results, based on open-hole tension and double edge-notched tension, are reproduced via simulation validating the model for size effects and for the response to off-axis loading. Successful prediction of notch size effects in multidirectional composite laminates is achieved by means of an equivalent single layer approach, incl. the off-axis open-hole tension strengths of a directional thin-ply laminate. All numerical strength predictions were well within acceptable errors of the respective experimental values.