Modeling of fiber circumplacement around a hole using a streamline approach

Abstract

The insertion of holes into laminates can be done by producing a fiber reinforced composite plate and, subsequently, drilling the borehole. Alternatively, we can bypass the fibers around the final hole before injecting the matrix material. In the first case, the spatial distribution of the axis of anisotropy, and the structural tensor concerned, are spatially constant. In the second case, i.e. the fiber circumplacement around the hole, a space-dependent anisotropy has to be considered. Instead of the common approach of defining region-wise constant fiber orientations, we propose a continuous formulation of fiber orientations using streamlines. To estimate the final stress and strain state for a unidirectional composite plate, three-dimensional finite element simulations are performed, where spatially constant transverse isotropy is compared to inhomogeneously distributed fiber orientation around the hole. It will turn out that the resulting stress states lead to both reduced stress amplitudes in loading direction as well as compressive strains in lateral direction. A detailed mathematical derivation of the basic equations accompanies the investigations.