Path-independent axisymmetric J-integral for the chemo-mechanical fracture analysis of elastoplastic electrodes in lithium-ion batteries

The J-integral, which is commonly used to analyze the crack propagation under mechanical loading, loses path-independence in chemo-mechanical coupling problems. Research has been focused on the development of two-dimensional coupled chemo-mechanical integrals to address this issue. However, directly calculating the two-dimensional coupled chemo-mechanical integrals in axisymmetric plane does not provide the energy release rate. There is a need to develop path-independent integrals for axisymmetric chemo-mechanical coupling problems. This work introduces a path-independent axisymmetric J-integral for chemo-mechanical fracture problems, which is established by extending the three-dimensional surface integrals under chemo-mechanical loading to axisymmetric structure and loading. The path-independence of the proposed integral is demonstrated both theoretically and numerically. Using an axisymmetric elastoplastic incremental model, the fracture behavior of a silicon anode particle with pre-existing conical cracks is examined as a practical example. The impacts of crack size, crack inclination angle, and surface flux on the crack propagation are studied. Numerical results are presented in phase diagrams to illustrate the changes in the maximum value of the integral during lithiation.