Strain localization analysis for single crystals and polycrystals: Towards microstructure-ductility linkage

In this paper, we performed a strain localization analysis for single crystals and polycrystals, with the specific aim of establishing a link between the microstructure-related parameters and ductility. To this end, advanced large-strain elastic–plastic single crystal constitutive modeling is adopted, accounting for the key physical mechanisms that are relevant at the microscale, such as dislocation storage and annihilation. The self-consistent scale-transition scheme is then used to derive the overall constitutive response of polycrystalline aggregates, including the essential microstructural aspects (e.g., initial and induced textures, dislocation density evolution, and softening mechanisms). The resulting constitutive equations for single crystals and polycrystals are coupled with two strain localization criteria: bifurcation theory, which is also related to the loss of ellipticity in the associated boundary value problem, and the strong ellipticity condition, which is presented in full detail along with mathematical links allowing for hierarchical classification in terms of conservativeness. The application of the proposed coupling to single crystals and polycrystals allows the effect of physical microstructural parameters on material ductility to be investigated. Consistent results are found for both single crystals and polycrystals. In addition, forming limit diagrams (FLDs) are constructed for IF–Ti single-phase steels with comparison to the reference results, demonstrating the predictive capability of the proposed approach in investigations of sheet metal formability. The results of the self-consistent scheme are systematically compared to those of the more classical full-constraint Taylor model, both in terms of the impact of microstructural parameters on ductility and in terms of the predicted formability limits and the level of the associated limit strains. Finally, we investigated the impact of strain-path changes on formability through the analysis of the effect of prestrain on the FLDs.