A micromechanical model for the failure and damage assessment of woven composites

A micromechanical model is advanced in order to study the stress transfer and associated damage and failure in classes of conventional and textile type fibrous composites. Unidirectionally reinforced matrix with straight and undulated fibers define the repeating constructing cell for conventional and textile composites, respectively. Starting with the case of straight reinforcement, we approximate and model the actual discrete composite as a concentric cylindrical system. For axisymmetric loading, and upon adopting some appropriate restrictions on the radial behavior of some field quantities, an elasticity-based procedure reduces the two-dimensional field equations, which hold in both fiber and matrix components together with the appropriate interface, symmetry and boundary conditions, to a quasi-one-dimensional system. This analysis is further extended to cases involving undulated fibers. Based upon local directions (slopes) of the undulated fibers, the linear transformation is used to obtain local stress distributions along the undulated fibers. The total stress field is found to be combinations of these local stresses and the inherent contributions obtained from the transformations of the normal loads along the undulated directions in the absence of reinforcement. This simple system retains total account of the system's physics and presents itself in the form of coupled partial differential equations in the longitudinal displacements and stresses of both the fiber and matrix components.; According to this model, damage is simulated in the form of stress free boundary conditions. Perpetuation of damage is based upon the maximum normal stress criterion. The adverse effect of such damage on the stiffness properties of the composite is predicted. Results show the favorable effect of undulation in decreasing the rate of property degradation with increasing damage. The model is quite general and has been applied to several situations. These include response to static loading, and other vibration and wave propagation applications. Confidence in our modeling procedure has been confirmed by comparisons with whatever available analytical models, experimental data and finite element calculations.