Effects of concentration-dependent elastic modulus on diffusion-induced stresses for battery applications

Most lithium-ion battery electrodes experience large volume changes associated with Li concentration changes within the host particles during charging and discharging. Electrode failure, in the form of fracture or decrepitation, can occur as a result of repeated volume changes. It has been found recently that many electrode materials, such as graphite, Si, and LiFePO₄, change their elastic properties upon lithiation. However, previous diffusion-induced stress (DIS) models have not considered this relationship. In this paper, we developed a mathematical model, with the assumption of a homogeneous isotropic cylindrical electrode particle, to describe the effect of concentration-dependent Young's modulus on DIS in battery electrodes. The DIS model considers both increasing and decreasing Young's modulus with concentration. The model shows that the concentration dependence of Young's modulus has a significant effect on peak stress and stress evolution in the electrodes. Insertion and deinsertion are not symmetric in stress profiles. We conclude that Li stiffening is beneficial to avoid surface cracking during delithiation, and moderate Li softening is beneficial to avoid particle cracking from the center during lithiation.