Differential geometry and the forming of aligned fibre composites

In this paper it is shown that certain aspects of the forming of aligned fibre composites into complex shapes can be treated as a mapping problem. By application of differential geometry theory we show that the required in-plane shear to form an ideal complex shape is related to part curvature and the initial fibre placement. In order to draw fibre mappings for various complex shaped parts we present several new algorithms which are used with existing computer-aided design software. A particularly powerful aspect of the algorithm allows complex curvature parts to be approximated using flat facets. Finally, results from room temperature forming experiments are given which demonstrate broad agreement with theory, and a specific correlation between the calculated ideal in-plane shear and the observed fibre misalignment.