On the Use of Shear-Lag Methods for Analysis of Stress Transfer in Unidirectional Composites

The “shear-lag” analysis method is frequently used for analysis of stress transfer between the fiber and the matrix in composites. The accuracy of shear-lag methods has not been critically assessed, in part because the assumptions have not been fully understood. This paper starts from the exact equations of elasticity for axisymmetric stress states in transversely isotropic materials and introduces the minimum assumptions required to derive the most commonly used shear-lag equations. These assumptions can now be checked to study the accuracy of shear-lag analysis on any problem. Some sample calculations were done for stress transfer from a matrix into a broken fiber. The shear-lag method did a reasonable job (within 20%) of predicting average axial stress in the fiber and total strain energy in the specimen provided the shear-lag parameter most commonly used in the literature is replaced by a new one derived from the approximate elasticity analysis. The shear-lag method does a much worse job of predicting shear stresses and energy release rates. Furthermore, the shear-lag method does not work for low fiber volume fractions.