Analytical computation of stress intensity factor for multi-physics problems

This work presents a methodology for the analytical calculation of the stress intensity factor when the stress distribution on the crack surfaces is non-homogeneous. At first, a polynomial function is used to express the non-homogenous stress distribution. Subsequently, the principle of superposition of effects is applied, and the stress intensity factor is computed by multiplying each polynomial term by its respective geometric factor. Finite element fracture model is used to compute the geometric factor of the single polynomial grade. To explain the method, a spherical body is considered, with central and superficial cracks. Each geometric factor depends on a normalized geometrical parameter (the ratio between the crack length and sphere radius). The proposed methodology is applied to determine the stress intensity factor in the case of a crack driving force caused by diffusive fields, such as the concentration gradient in particles of electrodes active material in lithium-ion batteries. The methodology allows to speed up the fracture computation, then it is used to give electrode design guidelines to limit the fracture likeliness and mechanical degradation in lithium-ion batteries, as well as it is the basis for the development of algorithms assessing the capacity loss and the remaining useful life of lithium-ion batteries in real-time.