Homogenization of intergranular fracture towards a transient gradient damage model

This paper focuses on the intergranular fracture of polycrystalline materials, where a detailed model at the meso-scale is translated onto the macro-level through a proposed homogenization theory. The bottom-up strategy involves the introduction of an additional macro-kinematic field to characterize the average displacement jump within the unit cell. Together with the standard macro-strain field, the underlying processes are propagated onto the macro-scale by imposing the equivalence of power and energy at the two scales. The set of macro-governing equations and constitutive relations are next extracted naturally as per standard thermodynamics procedure. The resulting homogenized microforce balance recovers the so-called ‘implicit’ gradient expression with a transient nonlocal interaction. The homogenized gradient damage model is shown to fully regularize the softening behavior, i.e. the structural response is made mesh-independent, with the damage strain correctly localizing into a macroscopic crack, hence resolving the spurious damage growth observed in many conventional gradient damage models. Furthermore, the predictive capability of the homogenized model is demonstrated by benchmarking its solutions against reference meso-solutions, where a good match is obtained with minimal calibrations, for two different grain sizes.