On the optimal direction of short metal fibres in brittle matrix composites

Abstract

In the composite materials considered in this paper the fibres bridge the cracks in the matrix and control their propagation. The ability to sustain large cracks before complete failure is of primary importance in several applications. This quality formulated as the fracture energy is chosen as an objective function for optimization. Five different components of the fracture energy are expressed by simplified formulae, derived from the assumed behaviour of fibres in the cracked matrix. The angle of the orientation of the parallel fibres system is the only design variable. The optimization problem is solved by derivation with respect to that angle. An element subjected to axial tension is considered for the maximum of fracture energy and the optimum angle of fibres is determined. Several examples for steel fibres reinforced cements are calculated and discussed. The proposed approach may be further developed using adequate formulae and assumptions for various kinds of fibre reinforced materials.