The paper presented a new micomechanics load-transfer model for single-fibre fragmentation test. The interfacial shear streength and the crack will develop along the interface. The fibre stochastic strength distribution was modelled by a two-parameter Wibull distribution. The influence of the interfacial bonding strength and fibre axial-tensile strength on stress states in components of composites was discussed. The interfacial state during the fragmentation process may be one of following three states: 1) fully bonding; 2) partial bonding; 3) fully debonding; according to the fibre axialtensile strength and interfacial properties (including interfacial bounding shear strength, interfacial friction coefficient and matrix radial pressure) after elastic constants and geometrical parameters of composites phases are given. The necessary conditions for these three states were discussed- Finally, a suitable definition of the critical fibre length was given and the critical length was constrouted by two parts :debonding fibre length and bonding fibre length.