Diffusion Induced Stress in a Phase Transforming Spherical and Cylindrical Insertion Electrodes for Lithium Ion Batteries

In lithium ion batteries, insertion and de-insertion of lithium in and out of the battery electrodes result in diffusion induced stresses (DISs). Diffusion induced stress may be one of the main reasons for mechanical degradation of electrode . Recently, several mathematical models have been proposed that attempt to understand DISs in battery electrodes. It is well known that some of the electrode materials undergo formation of two or more phases during lithium insertion and de-insertion. This phase transformation during lithiation or de-lithiation in an electrode particle may be assumed to form a core shell structure with a moving phase boundary. In this work, we mathematically model such a system to study DISs in phase transforming electrodes. We find that the concentration jump at phase boundaries can result in stress discontinuities at interfaces. We believe that this stress discontinuity is one of causes for electrode cracking. We are able to quantify the effect of concentration jump at the interface on the stress discontinuity. We can also investigate the effects of mechanical properties of the two phases on stress behavior and stress discontinuity. Our model can be used to help select electrode material properties to minimize the stress discontinuity at the interface to possibly enhance battery life.