Dislocation emission at fibers-I. Theory of longitudinal punching by thermal stresses

A model predicting the number of prismatic loops dislocation punched at the ends of a cylindrical fiber by thermal mismatch stresses is presented. The longitudinal stress in the fiber is derived as a function of the distance from fiber center using the shear-lag model for the elastic portion of the interface. We show that there is a critical fiber length above which the number of loops is constant. This is because the central part of the fiber is strained by plastic and elastic interfacial shear until it exhibits no mismatch with the matrix. The backstress of the loops on the fiber is derived and the effect of the fiber stress field on the loops is estimated away from the corner singularity. The analysis allows prediction of both the punching distance and the dislocation density in the row of loops. Finally, a parametric study is performed on the system Al/Al₂O₃ and the results are compared to an existing and different model.