In this paper, a micromechanics model is developed to model the fiber fragmentation test using single fiber composite specimens (SFC). The SFC specimen considered here consists of a single brittle (SiC) fiber embedded in a ductile (Al) matrix. The goal is to predict the longitudinal constitutive behavior of the composite as damage occurs and to determine if the interfacial strength can be estimated from the fiber fragment length at a given effective strain.
Before the fiber fractures, the fiber-matrix interface is assumed perfect. During fiber fracture, the interface is damaged. An imperfect interface model is then employed. When the fiber fractures, the fragments are assumed to be uniformly distributed such that the fragment lengths are equal at each given load level. The Weibull strength distribution was used to relate the fiber fragment length to the tensile strength of the brittle fiber. An increase in the applied effective strain causes successive fractures in the fiber, in that the fragments become increasingly shorter. The length of the fiber fragments at a given level of effective strain is dependent upon the interfacial shear strength.
The finite element method was used to provide numerical solutions for the state of stress and fiber length at a given applied effective strain for each SFC, and to allow a better understanding of the interaction of each component. The numerical solutions were used to construct effective stress-strain curves showing the constitutive behavior and effective strain-fiber fragment length plots of each SFC modeled. Classical elasticity and mechanics of materials modeling techniques were also used to derive analytical solutions for the state of stress in each SFC. Approximate longitudinal stress-strain relationships were developed from these analytical solutions.