A modified shear lag analysis is proposed for a unidirectional brittle-matrix composite under longitudinal tensile loading. It is assumed that the matrix, having a lower ultimate strain than the fiber, fails by transverse cracking. The analysis was conducted for a cylindrical element of matrix with a single fiber with various boundary conditions. Closed form solutions were obtained for stress distributions in the matrix and fiber as a function of applied stress and constituent properties in each case. In addition, the matrix crack density, debonded length, and reduced axial stiffness of the damaged model of two matrix cracks were obtained in closed form as a function of applied stress and constituent properties. The shear lag parameter is only a function of geometry and shear moduli of the constituents. The basic assumptions used in the analysis are that the shear stress in the fiber varies linearly and in the matrix varies according to an inverse function of a second-degree polynomial in the radial direction. The analysis can take into account residual stresses in the material.
The predicted stress-strain and stress versus matrix crack density curves were compared with experimental results for a silicon carbide/glass ceramic (SiC/CAS) composite subjected to monotonic loading. The predictions in general are in good qualitative agreement with experimental results. In particular, the saturation crack density measured is very close to the predicted value.