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, tau(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), tau(d), and the frictional interfacial stress, tau(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 tau(d) and tau(f) were determined by fitting our theoretical curves to experimental Fmax(le) 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 tau(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 tau(app), even if the tau(f) value was high. We also derived an equation relating the scatter in the interfacial strength parameters (tau(d) and tau(f)) to the scatter in tau(app), which is experimentally measurable, and proposed a procedure to determine the standard deviations of tau(d) and tau(f) from experimental pull-out and/or microbond test data.