A three-phase model of the single-fiber composite fragmentation test is proposed to evaluate viscoelasticity, stress distributions and interface fracture toughness. Based on the three-parameter standard linear solid model, a unit cell is established under periodic boundary conditions to study viscoelasticity considering the interface effect. Under the thermal residual stress and the tensile load, a three-dimensional (3D) theoretical cylinder model is utilized to predict the stress distributions in radial, hoop and axial directions for fiber, interface and matrix. The results are in good agreements with finite element method (FEM) results. Especially, we discuss the effects of the fiber shape on the mechanical behavior. Classic shear-lag theories are compared to modify the axial stress distributions. For the fragmentation test, two basic failure modes are studied in the proposed model. Based on accurate stress distributions, the energy-balance scheme takes into account all strain energies, the failure consumption, the friction consumption and the applied load work to calculate interface fracture energy release rate, results of which is consistent with other models. Furthermore, we study the effects of friction coefficients and radial debonded locations. Using the softening and failure model of the interface, the debonding process is simulated for zero-thickness and thick interfaces, respectively. [GRAPHICS] .