Variational approach to the stress-transfer problem through partially debonded interfaces in a three-phase composite

Abstract

In our previous study (Wu W, Verpoest I, Varna J. Compos Sci Technol 1998;58(12):1863–77) of the stress-transfer problem around a single fibre, we presented a variational approach based on the principle of minimum complementary energy, not only in the perfectly bonded zone but also in the zone with a discontinuous interface of a two-phase composite. This approach is adapted in this paper to derive an accurate axisymmetric analytical model for the description of the stress state around the fibre breaks and partially debonded interfaces of a three-phase composite with a fibre, coating and matrix. The debonded fibre/coating interface is treated as a special external boundary on which a presumed interfacial shear stress with some free parameters is specified. Once the parameters are given, minimisation of complementary energy can be applied for both debonded- and bonded-interface zones together, to extract the most accurate closed-form solution. The shear stress at the debonded interface (the right values of free parameters) is finally found by substituting the calculated radial stresses in the Coulomb friction law and minimising the discrepancy by a simple numerical iteration. As the minimisation procedure is applied for the both debonded and bonded zones simultaneously, the strong interaction of the two zones is correctly described. This model also includes the matrix axial stress non-uniformity in the radial direction. The stress profiles along both axial and radial directions are presented and closely compared with the results from a finite element model and both agree quite well. A number of applications of this model are also discussed.