Improved Constitutive Model for Mesoscale Modelling of Unidirectional Composites

Abstract

This era of science and technology has seen widespread use of composite materials for a variety of applications ranging from the defense sector to the transport and construction sectors. Composites are mainly comprised of fibres impregnated with a polymeric matrix and have a superior strength to weight ratio as compared to traditional construction materials like concrete and steel. The strength of the fibres is much larger than that of the matrix. Also, the fibres exhibits elastic brittle behaviour while the matrix shows a nonlinear plastic behavior before damage occurs. Thus the overall response of the material is subjective to which direction it is loaded. In reality a multitude of stresses act simultaneously on any structure and it is quite challenging to develop a constitutive formulation for the composite material that can predict the stresses in these mixed modes accurately. This thesis aims at providing an improved constitutive formulation for the prediction of the material behavior of unidirectional composites. The constitutive formulation builds up on the existing knowledge of an isotropic invariant based yield function. The motive is to improve the performance of this constitutive law for better predicting the behavior under combined stress states, particularly in the presence of fibre stresses. Even thought the fibres behave completely elastic, the matrix surrounding the fibres is much weaker and tends to deform inelastically. The moment at which the yield stresses are developed in the matrix is also dependant on the level of stress in the fibres. To capture this behavious, two different yield criterion are formulated and testing in this project. First an additive split of the stress tensor helps to separate the fibre and matrix stress components along the fibre(`1') direction. The fibre stress is always elastic whilst the matrix stress component can behave inelastic. This matrix stress component is taken into account in the new constitutive laws. The first constitutive law is a modified version of the transversely isotropic invariant formulations as proposed by Vogler et al. and the second constitutive law is an anisotropic yield function proposed by Tsai Wu. The invarants are reformulated with the matrix stress tensor while keeping the same functional form as that of the transversely isotropic invariant formulation . Again, the split in stress tensor is performed and used in association with the anisotropic yield function. The derivations of all the constitutive relations is presented extensively in the third chapter. Followed by the formulations is the calibration of both the constitutive laws using the hardening curves derived from the micromodel simulations. The micromodel serves as the equivalent experimental test setup for the mesomodels presented in this project. Calibration of the mesomodels is a complex task in itself and the various trials were performed to determine the yield stress parameters that calibrate the models. Having calibrated the models, both the mesomodels are subjected to basic load cases and combined load cases. The MTIF model gives more consistent results than the TW model, however TW model performs better in the combined stress state of longitudinal axial tension and longitudinal in-plane shear. Finally, the effect of the fibre stresses on the plastic behavior of the matrix is being captured but to different extents in both the models. Neither of the models is able to match the micromodel results for all simulations. The sensitivity of the yield stress parameters is brought to light and are the main cause for the overestimating behavior of the TW model. Lastly, all the observations were concluded followed by some recommendations for the future work.