An improved analysis of the stresses in a single-fibre fragmentation test: I. Two-phase model

In order to improve the analysis of the single-fibre fragmentation test, a modified variational analysis, based on the principle of minimum complementary energy, has been derived to describe the stress states around breaks in a single fibre embedded in an infinite matrix. The variational analysis includes the nonuniform stress distribution in the radial direction of the matrix cylinder, and allows for crack interaction. The stress profiles along the interface between the fibre and matrix are presented and compared with the prediction by the variational approach presented by Nairn. The predictions are also compared with the results from finite element analysis and good agreement is obtained. While the present analysis is more accurate than existing analytical models, it leads to very simple final expressions. Thus, it is convenient to be used for data reduction of the single-fibre fragmentation test results. In particular, it can be easily generalized to a three-phase model, including an interphase between fibre and matrix. The extensive applications of this model are also presented.