Three-dimensional singular stress field near a partially debonded cylindrical rigid fiber

Asymptotic solutions to a class of problems pertaining to the stress fields in the neighborhood of a circular cylindrical partially debonded infinitely rigid fiber (inclusion) in a homogeneous isotropic linearly elastic matrix (plate), subjected to far-field extension-bending (mode I), inplane shear-twisting (mode II) and torsional (mode III) loadings, are presented. Two different combinations of boundary conditions are considered: (i) infinitely rigid fiber with partial axisymmetric debond, and (ii) infinitely rigid fiber with partial axisymmetric frictionless slip (Comninou type contact zone). Introduction of the Comninou type contact zone at the circumferential tip of an infinitely rigid fiber–matrix axisymmetric interfacial debond eliminates the oscillatory character of the deformation in the case of mode I/II loading, and the stress singularity altogether in the case of mode III loading. Numerical results presented include, whenever applicable, the effect of Poisson’s ratio on the computed eigenvalue(s).