[en] Modern Li–ion batteries with LiFePO_4 cathodes have been shown to be low cost, non-toxic, have a high theoretical capacity, and high (dis)charging rates. Although LiFePO_4 has advantageous properties for electrical energy storage, it can lose some of its charging capacity when cycled. Researchers have found cracks that develop in LiFePO_4 cathode particles during cycling, and it has been suggested that this is the main cause of the capacity loss. The work presented here develops a multi-physics computational model to investigate the possible causes of fracture in single LiFePO_4 particles. The model combines the recently developed reaction-limited phase-field model for Li–ion intercalation with the phase-field model for brittle fracture. We use our numerical model to simulate single LiFePO_4 cathode particles during galvanostatic discharging as well as under no charging. It was found that because of the phase transformation and two-phase coexistence of LiFePO_4, cracks were able to grow due to large stresses at coherent phase boundaries. Phase nucleation at particle side facets was also examined and we show that pre-cracks grow that follow the high stresses at the coherent interface during charging. (paper)