On a matrix cracking model using Coulomb’s friction law

A matrix cracking model is developed based upon Coulomb friction law instead of a constant frictional shear stress usually assumed in the matrix cracking analyses. A Lamé formulation incorporated with Coulomb friction law is adopted to solve the elastic states of fiber/matrix stress-transfer through a frictionally constrained interface in the slipping region and a modified shear lag model is applied to evaluate the elastic responses in the intact region. By using an energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber reinforced composite is formulated in terms of the frictional coefficient rather than the frictional shear stress usually equated in the matrix cracking stress formulations. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model will be compared with those predicted by the constant frictional shear stress models. The effect of Poisson contraction caused by stress redistribution between the fiber and matrix on the matrix cracking mechanics will be shown and discussed in the present analysis.