Automotive traction battery needs and the influence of mechanical degradation of insertion electrode particles

We derive and implement analytic solutions for the description of insertion particles subject to cyclic surface concentration variations consistent with a periodic voltage excitation source applied to an insertion electrode wherein the overall resistance is dominated by that of solid-state diffusion within the electrode particles. The form of the analytic solution allows for a direct analogy to cyclic fatigue phenomena that have been examined in detail for structural materials over the past two centuries. We utilize the strain energy density to assess the potential for crack nucleation, and we show that while the shear stress is independent of the surface tension and surface modulus, the strain energy density, which drives particle fracture, is sensitive to the surface mechanics and therefore the particle radii. Specifically, the analysis implies that smaller particles are more stable relative to diffusion-induced decrepitation and cracking, consistent with experimental observations.