Please cite this article as: Vyas, G.M., Pinho, S.T., Robinson, P., Constitutive modelling of fibre-reinforced composites with unidirectional plies using a plasticity-based approach, Composites Science and Technology (2011), doi: 10.1016/j.compscitech.2011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Constitutive modelling of fibre-reinforced composites with unidirectional plies using a plasticity-based approach AbstractThis paper presents the development of a constitutive model able to accurately represent the full non-linear mechanical response of polymer-matrix fibre-reinforced composites with unidirectional (UD) plies under quasi-static loading. This is achieved by utilising an elasto-plastic modelling framework. The model captures key features that are often neglected in constitutive modelling of UD composites, such as the effect of hydrostatic pressure on both the elastic and non-elastic material response, the effect of multiaxial loading and dependence of the yield stress on the applied pressure.The constitutive model includes a novel yield function which accurately represents the yielding of the matrix within a unidirectional fibre-reinforced composite by removing the dependence on the stress in the fibre direction. A non-associative flow rule is used to capture the pressure sensitivity of the material. The experimentally observed translation of subsequent yield surfaces is modelled using a non-linear kinematic hardening rule. Furthermore, evolution laws are proposed for the non-linear hardening that relate to the applied hydrostatic pressure. * Corresponding author Email address: gv04@imperial.ac.uk (G.M. Vyas) Preprint submitted to ElsevierMultiaxial test data is used to show that the model is able to predict the nonlinear response under complex loading combinations, given only the experimental response from two uniaxial tests.

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More fundamental test methods are needed to assist the development of physically based and truly predictive simulation tools for composite materials under crash conditions. In this paper, a unidirectional flat specimen that can be used to validate the predicted behaviour from a simulation to the physical behaviour in the experiment is developed. A systematic experimental investigation is conducted to evaluate the influence of the trigger geometry on the crushing response by selecting two trigger types and different trigger angles. For longitudinal crushing, the traditional bevel trigger leads to out-of-plane failure by splaying with a limited amount of in-plane fracture, while the proposed trigger achieves a high amount of compressive fragmentation failure. For transverse crushing, the symmetry of the proposed new trigger improves the specimen stability during the crushing process. It is also observed that the weft threads of the unidirectional fabric reinforcement used for the tests have a strong influence on the longitudinal crushing response. The boundary conditions of the test and the information on the specimen failure gleaned from video recordings and microscopic inspections are discussed in order to facilitate a future correlation with modelling results.

This article showcases the authors’ predictions for Part B of the second World Wide Failure Exercise. Predictions are made using the failure criteria published in the submission for Part A. In several cases, the original predictions are found to match the experimental data well and no revisions are made. A novel constitutive model for unidirectional composite materials is used to improve predictions for cases involving multidirectional laminates.

This paper showcases the authors’ predictions for the 13 challenging test cases of the third World Wide Failure Exercise. The cases involve the prediction of lamina biaxial stress–strain curves, matrix cracking and delamination in various cross-ply and quasi-isotropic laminates under uniaxial loading, variation of thermal expansion coefficient of a laminate with matrix cracking, bending of a general laminate, loading-unloading behaviour and the strength of various thin and thick laminates containing an open hole. The laminates were made of various glass and carbon fibre/epoxy materials. The constitutive model is based on plasticity theory, includes hydrostatic pressure effects and accounts for multiaxial load combination effects. The failure criteria distinguish between matrix failure, fibre kinking and fibre tensile failure. In-situ strengths are used for matrix failure. Propagation of failure takes into consideration the fracture energy associated with each failure mode and, for matrix failure, the accumulation of cracks in the plies. The model is used to make blind predictions of all test cases from the third World-Wide Failure Exercise.