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

Most existing models for the problem of Rbre/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 di_erent 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 speciRed. A new analytical model, including stress non-uniformity in the radial direction and crack interaction, is derived to describe the stress state around Rbre breaks and debonding tips in a single Rbre embedded in an inRnite 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 proRles along both axial and radial directions are pre- sented and compared with results from a numerical model1 available in the literature and also from Rnite-element analysis. Good agreements are achieved. Extensive applications of this approach and the derived model are also discussed.