Fracture in solid solutions, such as electrodes for lithium-ion batteries and fuel cells, is mediated by intricate interactions between solid-state diffusion and crack propagation. In this work, we developed a composition-dependent cohesive zone model and integrated it with a chemo-mechanical coupling constitutive model to study the fracture mechanisms of solid solutions. The computational framework was used to investigate the effective fracture properties of chemo-mechanically coupled solid solutions over a wide range of crack growth velocities and compositional dependence of intrinsic fracture energy. The results revealed an important characteristic crack velocity, which is set by the ratio of the diffusivity to the intrinsic fracture energy and dictates the effective fracture resistance of the material. We also applied the model to study the fracture behavior of two-phase lithiated silicon (Si) and germanium (Ge) nanostructures as candidate high-capacity anodes for next-generation lithium-ion batteries, and showed that Ge nanostructures are more fracture resistant than their Si counterparts. The computational study presented here provides important insights for the rational design, operation, and mechanical testing of chemo-mechanically active material systems for their use in energy storage and conversion.