Strain gradient enhanced chemo-mechanical modeling of fracture in cathode materials for lithium-ion batteries

Abstract

Next generation lithium-ion batteries (LIBs) cathodes are composed of polycrystalline microstructures where spatial heterogeneity such as grain size is often comparable to the geometric dimension of the cathodes. Incorporating the influence of the aforementioned heterogeneity in a chemo-mechanical continuum description is necessary to address the diffusion induced stress field during electrochemical cycling. Therefore, in the present study, the micro-structural size-dependent characteristic length of the cathode is embedded through a non-classical continuum mechanics approach known as the strain gradient elasticity (SGE) theory. Accordingly, a thermodynamically consistent multi-physics framework is developed where nonlinear diffusion kinetics is included along with the energetic interaction between the lithium-ions and host lattice of the electrode. The coupled governing equations are derived for the spherical cathode, and the generalized differential quadrature (GDQ) method is utilized to build the numerical procedure. The role of material heterogeneity length scale is addressed for strongly coupled chemo-mechanical process. Subsequently, the growth of potential surface flaws is examined under multiple length scales, particle size, and charge rate conditions. Ultimately, a comprehensive fracture map is established to illustrate the regime of flaw insensitivity, partial breakage and complete disintegration. Thus, the present findings can provide a suitable design perspective for fail-safe particulate type composite cathodes.