Application of Hasselman's crack propagation model to insertion electrodes

Electrode failure, in the form of fracture or decrepitation, can occur as a result of repeated volume expansion and contraction in insertion electrodes used in lithium-ion batteries. Deleterious reactions with the electrolyte may also occur at the newly cracked surface, causing capacity fade. In this article, we derive an analytic expression for the total elastic energy stored within a spherical particle due to diffusion-induced stresses. Using this equation and taking an approach similar to that of Hasselman [J. Am. Ceram. Soc., 46, 535 (1963)], we establish a criterion for crack propagation within a spherical insertion electrode.