The Effects of Poisson Contraction on Matrix Cracking in Brittle-Matrix Composites

The effects of Poisson contraction on matrix cracking in unidirectional fiber-reinforced brittle-matrix composites are studied in this paper. The fibers, initially held in the matrix by a compressive pressure due to the thermal expansion mismatch, are subjected to frictional slipping over the matrix as soon as a fiber-bridged crack is formed. The friction between the fibers and the matrix is assumed to follow the Coulomb friction law. A shear-lag model, which includes the Poisson contraction and the friction due to the relative fiber/matrix slipping, is adopted to calculate the stress and strain fields in the fibers and matrix. Using the energy balance approach, a relation for the critical matrix cracking stress for propagating of a semi-infinite fiber-bridged crack is derived. The results obtained show that the Poisson contraction has a strong effect on the predicted matrix cracking stress in brittle-matrix composites, especially in composites with a stiff matrix.