Micromechanics of multiple cracking: Part I Fibre analysis

Fibre-reinforced brittle materials exhibiting a strain-hardening tensile behaviour undergo a multiple cracking process. A micromechanical analysis of a straight smooth fibre, bridging one or several cracks in a multiply-cracked composite is introduced, taking into account the full or elastic bond, gradual debonding, and frictional sliding of the fibre. Equilibrium is satisfied by means of a two-fibre system introducing a symmetry fibre within the segment. Equations for different debonding cases are derived. The fibre ends are analysed using a simplified approach, the validity of which is discussed. The system equations are derived from the compatibility condition of equal crack widths. Two examples are analysed to study the effects of crack spacing.