A kinematically enhanced constitutive model for progressive damage analysis of unidirectional fiber reinforced composites

Abstract

The application of fiber reinforced laminated composite structures has been increasing steadily in many engineering disciplines due to their high specific strength and stiffness, corrosion resistance, exceptional durability and many other attractive features over the last few decades. A comprehensive strength and failure assessment of these structures made of composite materials is extremely important for a reliable design of these structures and it has been a major focus of many researchers in this field for a long time. To the best of our knowledge, the majority of the existing studies based on macro based continuum approach are particularly focussed on capturing the effective elastic properties and final failure envelop of the composite material, while the subsequent post-yield inelastic behaviour or the entire nonlinear response is often overlooked. Composite structures with such diverse applications can be subjected to complex loading conditions such as impacts, severe dynamic loads or extreme thermal loads which can lead to a significant damage or complete failure of these structures. It is therefore essential to predict the entire nonlinear response and failure of these structures in many situations for a better design with higher confidence. This problem is quite challenging, specifically with a macro based continuum approach, as the actual failure initiates at the micro scale in the form of matrix cracking, fiber rupture or fiber-matrix interface failure which propagate gradually, accumulate together and finally manifested as macroscale structural failure. Thus tracking the details on the entire failure evolution process from microscale to macroscale is necessary for accurately modelling the structural failure. A detailed micromechanical modelling approach, where all constituents are explicitly modelled, can capture all these microscale failure processes and their evolutions in details but such modelling strategy is not computationally feasible for failure analysis for large structures due to a huge gap between micro/fiber and macro/structural scales. Thus the analysis of these structures requires an innovative modelling approach that can represent and capture the essential features of these microscale failure details, while at the same time, should be computationally efficient like a macro based continuum model for undertaking large scale structural analysis. In this study, a new three-dimensional kinematically enhanced macro-based constitutive model is developed which is applicable at the lamina/ply scale of these laminated composite structures. A novel analytical technique is developed for upscaling the nonlinear response from the fiber/micro scale to the ply scale which is the key for achieving such precise modelling of composites with feasible computational resources. The proposed approach utilized a strategy of strain field enhancements kinematically to account for different rate of deformations in the local fields within a fiber reinforced composite (FRC) ply. Based on these considerations, closed-form analytical expressions are derived which can be used conveniently to express the average macro strain increments of the entire volume element in terms of strain increments in the local fields and vice versa. This modelling strategy provides an opportunity to incorporate both fiber and matrix constitutive responses as well as their interactions into the overall ply response. To this end, a thermodynamics-based continuum model is developed using damage mechanics and plasticity theory to capture the constitutive response of the matrix. This has incorporated two predominant failure mechanisms in the matrix, which are permanent plastic deformation and loss of stiffness. For the fiber-matrix interface that includes interfacial debonding, an anisotropic damage model is developed to account for the directional dependence of the softening response in FRC ply due to fiber debonding failure. The proposed approach and models are developed in incremental forms, allowing the applications in both linear and nonlinear ranges of behaviour. Their verification with available analytical and numerical approaches together with the validation against a wide range of experimental data show both features and good potentials of the proposed approach.