Is there any contradiction between the stress and energy failure criteria in micromechanical tests? Part I. Crack initiation: stress-controlled or energy-controlled?

Abstract

The relationship between energy-based (interfacial toughness, Gic) and stress-based (ultimate shear strength, τult) criteria of interfacial failure in micromechanical tests is investigated within the frames of the Nairn shear-lag approach. To determine which criterion is responsible for interfacial failure in particular fiber-polymer systems, the data obtained in microbond tests for the joints of carbon, glass and aramid fibers with various thermoplastic and thermosetting matrices are analyzed. Experimental relations between the debond force and the embedded fiber length appear to be satisfactorily described by curves plotted according to both theories. It is demonstrated that, in a similar way as a deformed spring can be equally characterized by the reaction force and potential energy, both ultimate shear strength and energy release rate (as well as any combination of those) can be measures of interfacial strength. However, only such function f = f(Gic, τult) can be a real characteristic of the bimaterial interface (rather than of the particular specimen only), which does not depend on the specimen geometry. Theoretical consideration of micromechanical tests has shown that of all geometrical dimensions of a specimen, the fiber diameter, d, has the most prominent effect on the calculated value of the failure criterion. The analysis of data available in literature on microbond experiments with glass fibers having different diameters has revealed that for the glass fiber/epoxy matrix τult is proportional to d-½ and Gic is approximately constant; consequently, interfacial failure can be considered as energy-controlled.