Modelling crack growth in fibre-reinforced cementitious materials

Although the classic Griffith-Orowan one-parameter model cannot be used to describe the crack growth in fiber-reinforced cementitious materials, elastic fracture mechanics is valid. The characteristic of fiber-reinforced materials is the development of stable crack growth because of the resistance due to bridging fibers. The main difficulty in modelling this crack growth is that it is non-linear because the crack closure forces depend upon the crack opening which is in turn dependent partly on the closure stresses. Exact solutions for crack growth are therefore difficult. After reviewing past attempts at satisfactory practical solutions a simple approximate method is described. In this method, the exact stress displacement relationship is linearized and it is assumed that the crack flanks in the fiber bridging zone remain straight. With the assumption that equilibrium crack growth occurs when the effective stress intensity factor at the tip of the continuous matrix crack reaches a critical value K_Ic, it is only necessary to use iteration to find the length of the fully developed fiber bridging zone that produces the critical crack mouth opening.