3-D rate dependent micromechanical model for polymer composites
Fibre reinforced polymeric composites are in high demand in automotive and aviation industries to improve fuel efficiency. However, the dynamic behaviour of composites is not very well understood. Furthermore, dynamic loading together with the anisotropic nature and complex nonlinear behaviour of polymer composites results in a complex failure behaviour. This behaviour is of significant importance to account for in automobile crash simulation and impact modeling of aircraft structures.
In this thesis, a micromechanics based constitutive model is developed to predict the nonlinear behaviour and failure of unidirectional fibre reinforced polymer composites subjected to compressive dynamic loading. The carbon fibres are assumed to be hyperelastic transversely isotropic. For the matrix, a viscoelastic-viscoplastic constitutive model with hardening enhanced by continuum damage is advocated. A three parameter Maxwell model is used for the linear viscoelastic behaviour of the matrix. The nonlinear viscoplastic behaviour is introduced by coupling a Perzyna-type Bingham/Norton model with an intralaminar matrix continuum damage model. The pressure dependence of the onset of plastic yielding in matrix shear dominated response under compressive loading is also considered. The proposed model is formulated in a geometrically nonlinear description that separates the fibre and the matrix contributions. The model draws from computational homogenization of the unidirectional ply level response,with the matrix and the fibres as subscale constituents. A major feature is that the subscale constituents are coupled via isostrain and isostress assumptions parallel and transverse to the fibres, respectively. An improved isostress formulation is proposed to include in a better way longitudinal fibre shear response. The elastic response is improved by considering a non-uniform stress distribution in the matrix. For intralaminar damage growth, a continuum damage enhanced formulation of Lemaitre type is proposed. This model is combined with a surface based cohesive model that describes interlaminar delamination.
Based on the model, the shear induced failure behaviour in compression of the composite material is characterized. Finite element simulations are conducted to validate observed rate dependent properties of off-axis loaded unidirectional composites and angle-ply laminates. The predictions of the finite element simulations are compared to published experimental results of different material systems under compression loading at different strain rates. The results obtained are in reasonable agreement with the experiments. Typical applications are carbon/epoxy composites, where unidirectional carbon fibres are embedded in a polymer matrix. In the future, the model is possible to extend to orthotropic plies and textile reinforced composites. The model is micromechanically motivated, hence it is also possible to extend for rate dependent fibres, e.g. glass fibres.