Peak force as function of the embedded length in pull-out and microbond tests: effect of specimen geometry

We have derived the equations which explicitly express the peak force, F max, and the apparent interfacial shear strength, τ app, measured in the pull-out and microbond tests, as functions of the embedded length. Three types of test geometries were considered: (1) a fiber embedded in a cylindrical block of the matrix material; (2) microbond test with spherical matrix droplets; and (3) pull-out test in which the matrix droplet had the shape of a hemisphere. Our equations include the local interfacial shear strength (IFSS), τ d, and the frictional interfacial stress, τ f, as parameters; the effect of specimen geometry appeared in the form of dependency of the effective fiber volume fraction on the embedded length. The values of τ d and τ f were determined by fitting our theoretical curves to experimental F max (l e) plots by using the least squares method. Our analysis showed how the local IFSS and the frictional interfacial stress affected the measured F max and τ app values. In particular, it was revealed that intervals of embedded lengths could exist in which frictional interfacial stress had no effect on F max and τ app, even if the τ f value was high. We also derived an equation relating the scatter in the interfacial strength parameters (τ d and τ f) to the scatter in τ app, which is experimentally measurable, and proposed a procedure to determine the standard deviations of τ d and τ f from experimental pull-out and/or microbond test data.