Multi-phase field modeling for various fracture mechanisms in composites

Abstract

Composite possesses wide spectrum of mechanical responses along with remarkable fracture strength and toughness. Such properties evolve due to combination of different failure mechanisms across multiple phases. Understanding the contribution of these mechanisms on overall behavior is necessary to fabricate the composite with desired fracture properties. Although numerous studies have been performed to correlate the fracture response with crack propagation characteristics, they fail to account several underlying micro-mechanical events. Therefore, in the present study, a multi-phase field fracture model is proposed. We consider that constituents are homogeneously distributed within the matrix, while macro-scale phase field descriptors are utilized to represent the failure of its constituents. Further, the reinforced elements are assumed to be anisotropic in nature with preferential fracture direction. Therefore, by employing the rule of mixture in free energies and applying thermodynamic principles, the governing equations together with evolution laws of phase field parameters are derived. Using multi-field approach and extracting the weak form for governing equations, we develop finite element based numerical framework. Coupled sets of linear equations are solved using staggered scheme in parallel computing architecture. Proposed scheme is verified with analytical solution of a composite where separate evolutions of damage within phases are correlated with emergent stress–strain response. Numerical simulations are performed to predict the mechanical response by interpreting the competitive involvement of fracture mechanisms within matrix and inclusion phases. The present findings and future scopes highlight the predictive capability of the proposed scheme for analyzing fracture behavior of composites.