Silicon nano-wires (Si-NWs) are attractive candidates for electrodes in Li-ion batteries because they provide less constraint on the volume changes during Li charging. Recent experiments show that crystalline Si anodes expand highly anisotropically during lithiation, and a sharp phase boundary between the crystalline silicon and the amorphous lithiated silicon exists. In the present study, we developed a microscopic model to explain size-dependent fracture in crystalline Si-NW anodes. Adopting a void growth model, we derived a simple traction-separation law for a cohesive zone model. Taking anisotropic expansion and the sharp phase boundary into account, the deformation and fracture behavior of Si-NW anodes were explored. In an effort to make the model conform to recent experiments that showed the critical diameter of Si-NW anodes to be 300~400nm, the fracture toughness of lithiated amorphous Si were computed. With this analysis, our simple model may shed light on the mechanics of failure of crystalline Si-NWs during Li-ion battery cycling.