Micro-mechanical analysis of composite materials using Phase-Field models of brittle fracture

Failure in fiber-reinforced composites is a complex phenomenon where different damage mechanisms interact and evolve through various scales. Micro-mechanical analysis using the finite element method has become an important alternative to study such failure phenomena and their interactions, by modeling explicitly the fiber, matrix, and fiber-matrix interface. In this work, the predictive capabilities of the finite element method together with the Phase-Field (PF) method for fracture has been assessed. The study compares different PF formulations, energy splits and numerical parameters, using Representative Volume Elements (RVEs) of different sizes, fiber distributions and with different Boundary Conditions (BCs). It is found that even though good approximations can be obtained and meso-scale failure envelopes for transverse loading generated, these are highly dependent on the modeling assumptions and PF parameters. The AT2 formulation combined with Amor's energy split provides the best predictions when compared with an analytical failure surface. The best fit is found for transverse shear-dominated loading, while larger differences are found for compressive loading, whose strength predictions are strongly affected by the PF formulations and energy splits. It is demonstrated that meso-scale strength is conditioned by interface properties as interface damage is the dominant failure initiation mechanism under tensile-dominated loading. On the other hand, PF parameters have a stronger influence on compressive-dominated loading. Finally, it is shown that assuming a perfect fiber-matrix interface has a strong effect on the expected meso-scale strength, as failure is markedly delayed. Accordingly, based on the present results, especial care should be taken in properly assessing all the variables involved in the modeling methodology to draw conclusions from computational micro-mechanical analyses based on the PF approach.