A novel axisymmetric variational analysis of stress transfer into fibreS through a partially debonded interface

Abstract

Most existing models for the problem of fibre/matrix stress-transfer through a partially debonded interface roughly solve the stress distribution in the debonded zone, neglecting the presence of the perfectly bonded zone. However the stress interactions between two zones is what makes the problem essentially different from the stress-transfer problem for a perfectly bonded interface. This paper suggests a variational approach based on the principle of minimum complementary energy not only in a perfectly bonded zone but also in a zone with a discontinuous interface. The debonded interface is treated as an external boundary on which a presumed interfacial shear stress is specified. A new analytical model, including stress non-uniformity in the radial direction and crack interaction, is derived to describe the stress state around fibre breaks and debonding tips in a single fibre embedded in an infinite matrix. For the presumed shear stress at the debonded interface the minimisation procedure renders the most accurate closed-form solution (under used assumptions) for both interactive zones. Finally, the ‘best’ shear stress distribution at the debonded interface is found by using Coulomb’s friction law and simple numerical iterations. The stress profiles along both axial and radial directions are presented and compared with results from a numerical model [1] available in the literature and also from finite-element analysis. Good agreements are achieved. Extensive applications of this approach and the derived model are also discussed.