Investigating inhomogeneity effects on the crack driving force in two-phase electrode particles using a planar composite core-shell model

Abstract

It is well known that phase separation occurs in many intercalation materials as a result of solute intercalation. In lithium storage materials, phase separation induced by electrochemical cycling is known to intensify mechanical stresses in the host, and results in the emergence of a variety of defects causing mechanical degradation of the electrode particles. Treating two-phase electrode particles as a homogeneous material, fracture mechanics models have been previously developed for studying fracture of two-phase electrode particles. Recent theoretical and experimental studies, however, reveal that the elastic properties of the coexisting phases in the material could significantly differ due to their markedly different solute contents. This work aims to present a fracture mechanics study of the two-phase electrode particles accounting for the different elastic moduli of the phases. To this end, a planar composite core-shell model is utilized to examine how different elastic moduli of the phases could impact the stress intensity factors and the energy release rates associated with the pre-existing cracks in the particle. Our results reveal that although softening of the material as a result of phase change could result in stress relief in the electrode particle, however, it could still raise the energy release rate for pre-existing cracks, since a softened material behaves like a weakened deformational constraint ahead of a pre-existing crack. The model presented is also applied to the material systems exhibiting modulus change as a result of phase separation, and implications of the modulus change on the energy release rate for crack growth are also discussed. It is shown that although significant changes in the toughness of the material could arise due to the phase transformation, however, changes in elastic moduli could still raise the energy release rate for a crack whose tip is embedded in the phase with the lower toughness.