A J-integral method for calculating steady-state matrix cracking stresses in composites

A general expression for the steady-state matrix cracking stress in reinforced brittle matrix composites is derived using a J-integral analysis. The result is expressed in terms of the stress-displacement relation that characterizes the stretching of crack bridging ligaments. The influence of residual stress is assessed and a condition for spontaneous matrix cracking due to residual tensile stress in the matrix is evaluated. Results of the analysis are compared with independent solutions for composites containing unbonded reinforcing fibers.