Dynamic stress transfer in fibrous composites with damage

A micromechanical model is developed in order to study the dynamically induced stress distribution in fibrous composites with damage. Damage is taken in the form of either a broken fiber or a matrix crack normal to the fiber direction. The unidirectionally reinforced periodic composite, when loaded in the axial (fiber) direction is modeled as a concentric cylindrical system subjected at its outer boundaries to vanishing radial displacement and shear stress. Guided by the symmetry and the fiber-matrix interface continuity conditions, we first assume an approximate radial dependence of some of the field variables. Therefore, we reduce the two dimensional field equations that hold in both the fiber and the matrix together with their interface conditions to a quasi-one-dimensional system, which automatically satisfies all interface and radial boundary conditions. The resulting simple system retains the integrity of the distribution in the fiber and the matrix, individually, with their interaction reflected in well-defined transfer terms. The system is suitable for treating a variety of situations. Besides the case of damage free composites, the cases of broken fibers and cracked matrix are treated by invoking appropriate boundary conditions at the crack faces. Also simple analytical expressions are derived for the crack width opening for both the fiber break and the matrix crack. For our numerical illustration, we subject the composite slab to an axial cyclic loading with varying frequency. We compare results obtained for broken fibers and cracked matrix with the damage free composite system.