A theory of viscoplasticity for fabric-reinforced composites (Q5955256)

The author considers composite structures which are constructed by impregnating sheets of fabric with a matrix material, and are formed into a desired shape at a temperature at which the matrix flows easily. The constitutive equations are formulated for the flow of fabric-reinforced composite materials that exhibit viscoplastic response at the forming temperature. This theory is an analogue, for materials with material symmetries appropriate for fabric-reinforced materials, of the theory of Bingham solids for isotropic materials. In the three-dimensional formulation, it is shown that in the most general case four plasticity parameters and (for linear viscous response) five viscosity parameters are required to characterize the material. However, this number of parameters is substantially reduced if the material possesses any material symmetry. Materials of the considered type are often used in the form of thin sheets, for which plane stress theory is applicable. In this case, the rheological behaviour is described by a single plasticity parameter and by a single viscosity function, even for nonlinear viscous response; these are functions of the current angle between two families of fibres that form the fabric. The plane stress theory is applied to an analysis of the `picture-frame' experiment, and it is shown that, in principle, this experiment provides a method of experimental determination of material response functions. It is observed experimentally in picture-frame tests that the response of some fabric-reinforced materials depends on the direction, as well as on the magnitude and rate, of the shear. This surprising observation is explained by examining symmetry properties of some typical fabric architectures. For some fabrics, the material symmetry that would ensure identical response to positive and negative shears is not present, and so the results of the picture-frame test are consistent with the theoretical analysis.