Fiber-reinforced brittle-matrix composites: Discontinuous phenomena and optimization of the components

In the field of Fracture Mechanics of fiber-reinforced composites, the problem of minimum reinforcement and catastrophic (snap-back) or hyper-strength structural behavior is investigated, in order to improve the material design through an optimization of the components. A Fracture Mechanics approach makes it possible to analyze the composite post-cracking behavior and, unlike the classical strength theory, to explain certain discontinuous phenomena, that are experimentally verified, such as the snap-back and snap-through instabilities, together with size-scale effects. In particular, the fundamental secondary-phase role played by the fiber volume fraction is investigated by means of the Bridged Crack Model, in order to highlight how the fracture toughness of the brittle matrix is improved by means of the fiber bridging action affecting the matrix micro-and macro-cracks, so as to prevent their coalescence, opening and growth. These bridging toughening mechanisms are due to debonding, sliding and frictional pulling-out between the matrix and the high-resistance fibres, or to yielding of the low-resistance ductile fibres. Moreover, the effect of the size scale is found to be fundamental for the global structural behaviour, which can range from ductile to catastrophic simply with the variation of a dimensionless brittleness number, NP, which is a function of the toughness of the matrix, of the yielding or slippage limit of the reinforcement, of the volume fraction of the reinforcement, and of the characteristic structural size.