It is well known that phase separation could severely intensify mechanical degradation and expedite capacity fading in lithium-ion battery electrodes during electrochemical cycling. Experiments have frequently revealed that such degradation effects could be substantially mitigated via reducing the electrode feature size to the nanoscale. The purpose of this work is to present a fracture mechanics study of the phase separating planar electrodes. To this end, a phase field model is utilized to predict how phase separation affects evolution of the solute distribution and stress profile in a planar electrode. Behavior of the preexisting flaws in the electrode in response to the diffusion induced stresses is then examined via computing the time dependent stress intensity factor arising at the tip of flaws during both the insertion and extraction half-cycles. Further, adopting a sharp-interphase approximation of the system, a critical electrode thickness is derived below which the phase separating electrode becomes flaw tolerant. Numerical results of the phase field model are also compared against analytical predictions of the sharp-interphase model. The results are further discussed with reference to the available experiments in the literature. Finally, some of the limitations of the model are cautioned.