A theory of viscoplasticity for fabric-reinforced composites

Some composite structures are constructed by impregnating sheets of fabric with a matrix material, and forming into a desired shape at a temperature at which the matrix flows easily. Here constitutive equations are formulated for flow of fabric-reinforced composite materials that exhibit viscoplastic response at the forming temperature. The theory is the analogue, for materials with material symmetries appropriate for fabric-reinforced materials, of the theory of Bingham solids for isotropic materials. The theory is formulated for general three-dimensional deformations, but simplifies greatly when specialised to the case of plane stress. In this case, the rheological behaviour is described by a single plasticity parameter and a single viscosity; these are functions of the current angle between the two families of fibres that form the fabric. The analysis is applied to the analysis of the 'picture-frame' experiment, and it is shown that this experiment provides a method of measuring the response functions. The effect of symmetry of the fabric architecture is considered, and it is found that for some practical fabric architectures the theory allows the possibility of different responses to in-plane shearing in different shearing directions, as has been observed in picture-frame experiments. (C) 2001 Elsevier Science Ltd. All rights reserved.