Constitutive laws for unidirectional composite materials

Abstract

Failure predictions for a fibre-reinforced composite with unidirectional (UD) plies can only be relied upon provided the stress state is accurately known. This requires a prediction of the constitutive response to be made when the material is loaded. When failure does occur, matrix cracking is frequently the first mode of failure. Cracking results in a reduction of the material properties of the structure and can lead to other forms of damage. In this context, an elasto-plastic constitutive model that can accurately represent the full non-linear mechanical response of UD composites is developed, as well as the implementation of an improved model for matrix cracking. Unlike many existing constitutive models in the literature, the developed model captures some key features that are often neglected in constitutive modelling. These include the effect of hydrostatic pressure on both the elastic and non-elastic response. A novel yield function is formulated specifically for polymer-matrix fibre-reinforced composites, taking into account the presence of fibres in the material. The developed model is able to predict the non-linear response under complex loading combinations, given only the experimental response from two uniaxial tests. A non-associative flow rule is used to capture the pressure sensitivity of the material. The translation of subsequent yield surfaces under complex loading regimes is modelled by the inclusion of a non-linear kinematic hardening rule, which also allows for simulation of material unloading. The implementation of the model as a user defined material subroutine in a commercial finite element package is described. Regarding the modelling of matrix cracking, several methods are available in the literature. These models are reviewed and an existing model is combined with suitable failure criteria for the simulation of stiffness loss and crack accumulation in laminates. This model is then used to make predictions of crack accumulation and loss in stiffness of composite materials.