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Modern Li–ion batteries with LiFePO4 cathodes have been shown to be low cost, non-toxic, have a high theoretical capacity, and high (dis)charging rates. Although LiFePO4 has advantageous properties for electrical energy storage, it can lose some of its charging capacity when cycled. Researchers have found cracks that develop in LiFePO4 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 LiFePO4 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 LiFePO4 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 LiFePO4, 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. [ABSTRACT FROM AUTHOR]