Chemo-mechanical modeling of inter- and intra-granular fracture in heterogeneous cathode with polycrystalline particles for lithium-ion battery

Evolution of complex fracture patterns during electrochemical cycling for the polycrystalline particulate cathode of lithium-ion batteries is found to be a primary reason towards capacity fading. Such fracture of a particles involves inter- and intra-granular crack propagation and often with its debonding from the binder. Till date, a comprehensive understanding of these fracture mechanisms under chemo-mechanical environment towards overall electrochemical response is lacking. In that context, a thermodynamically consistent multi-physics modeling framework is developed to account for strongly coupled chemo-mechanical environments and the evolution of arbitrary fracture within polycrystalline cathode particles embedded in the matrix. Specifically, a regular phase-field fracture variable is introduced for initiation and propagation of the inter- and intra-granular crack within the particle and debonding of the particle-matrix interface. Adopting two additional phase-field descriptors, grain boundaries and particle-matrix interfaces are expressed as diffused regimes. Thus, fracture energies of the grains, grain boundaries, and particle-matrix interface are suitably incorporated within the mathematical framework. Employing a finite element-based numerical scheme, the coupled governing equations are solved for three state variables: concentration, displacement, and phase-field damage. Various parametric studies are performed to investigate the effect of grain sizes, charge rates, and elastic modulus of the matrix on the interplay between the chemo-mechanical behavior and evolution of fracture, and ultimately their collective influences on the electrochemical response. Finally, the present findings offer predictive insights towards engagement of key fracture mechanisms for mechanical degradation of the polycrystalline cathode at electrode level.