Formulation and implementation of strain rate‐dependent fracture toughness in context of the phase‐field method.

Summary: The phase‐field approach is a promising technique for the realistic simulation of brittle fracture processes, both in quasi‐static and transient analysis. Considering fast loading, experimental evidence indicates a strong relationship between the rate of strain and the material's resistance against fracture, which can be considered by a dynamic increase factor for the strength of the material. The paper at hand presents a novel approach within the framework of phase‐field models for brittle fracture. A rate‐dependent fracture toughness is formulated as a function of the rate of crack driving strain components, which results in higher strength for faster loading. Beside the increased amount of energy necessary to evolve a crack at a high strain rate loading situation, the model incorporates quasi‐viscous stress‐type quantities that are not directly related to the formation of the crack and exist only in the phase‐field transition zone between broken and sound material. The governing strong form equations for a transient simulation are derived and the relevant information for an implementation of the model into a finite element code is outlined in detail. The performance of the model is demonstrated for static and dynamic benchmark simulations and for a comparison to experimental findings. [ABSTRACT FROM AUTHOR]