| A single fragment from a single fiber fragmentation test specimen is analyzed using Bessel-Fourier series stress functions. The fiber in this analysis can be either a transversely isotropic material or an isotropic material, and the fiber/matrix interface is assumed imperfect using an approach originally proposed by Hashin. The solution satisfies equilibrium equations, compatibility conditions, and the most boundary conditions. The fiber's axial stress at the crack surface is satisfied approximately--only the average stress is zero. The interface quality parameter D{dollar}sb{lcub}rm s{rcub}{dollar} can be measured quantitatively by comparing the theoretical stress transfer profile along the fiber fragment to Raman Spectroscopy results. The fracture mechanics energy method is used for interpreting single fiber fragmentation test result (crack density vs. applied strain). During fragmentation of HM carbon fibers in an epoxy matrix, the released energy is larger than the amount needed to fracture the fiber. The remaining excess released energy may cause other damage in the specimen, such as interfacial debonding. Equating the total energy released by fiber fracture and interfacial debonding to the energy absorbed by the fracture surfaces, the fiber fracture toughness, G{dollar}sb{lcub}rm fc{rcub}{dollar}, and the interfacial debonding toughness, G{dollar}sb{lcub}rm dc{rcub}{dollar}, can be determined from single fiber fragmentation test results. |
