Analytical computation of stress intensity factor for active material particles of lithium ion batteries

The stress intensity factor is a widely used parameter in linear elastic fracture mechanics to assess the stress field near the crack tip, and it is usually defined as the product between the remote stress, the square root of the crack length, and a geometric factor depending on the geometry of the test specimen, the size and location of the crack. However, this well-established expression cannot be used in case of non-constant stress distribution on crack surfaces, typically resulting from diffusive field. This work presents an analytical procedure to compute the stress intensity factor due to any kind of stress distribution that can be expressed as a polynomial. Firstly, the non-constant stress distribution is expressed as a polynomial. Then, the stress intensity factor is computed according to the principle of superposition of effects, as the sum of the stress components of each single polynomial grade and the corresponding geometric factors. The geometric factors for sphere with central and superficial cracks are determined using a finite element model, and closed-form expressions for these geometric factors are provided as functions of a normalized geometric parameter. These functions can be used in case of any stress loading and spherical geometry. The analytical procedure is specifically applied to assess the stress intensity factor caused by stress resulting from lithium diffusion in active material particles of lithium ions batteries electrodes. The results are compared with those obtained using a multiphysics finite element fracture model, showing good agreement and demonstrating the accuracy of the proposed analytical procedure. Then, the procedure presented in this work enables avoiding expensive multiphysics simulations and can be used to develop fast, accurate, and computationally efficient lithium ion batteries degradation models for the online estimation of the capacity decay with charge/discharge cycles.