In order to investigate the impact of microstructures and deformation mechanisms on the ductility of materials, the criterion first proposed by Rice is applied to elastic-plastic tangent moduli derived from a large strain micromechanical model combined with a self-consistent scale transition technique. This approach takes into account several microstructural aspects for polycrystalline aggregates: initial and induced textures, dislocation densities as well as softening mechanisms such that the behavior during complex loading paths can be accurately described. In order to significantly reduce the computing time, a new method drawn from viscoplastic formulations is introduced so that the slip system activity can be efficiently determined. The different aspects of the single crystal hardening (self and latent ACCEPTED MANUSCRIPT 2 hardening, dislocation storage and annihilation, mean free path, etc…) are taken into account both by the introduction of dislocation densities per slip system as internal variables and the corresponding evolution equations. Comparisons are made with experimental results for single and dual-phase steels involving linear and complex loading paths. Rice's criterion is then coupled and applied to this constitutive model in order to determine the ellipticity loss of the polycrystalline tangent modulus. This criterion, which does not need any additional "fitting" parameter, is used to build Ellipticity Limit Diagrams (ELDs).
Sheet metal forming processes are commonly associated with strain-path changes in the material. Macroscopic softening/hardening transient effects can appear due to the plastic anisotropy induced by these deformation stages. Such characteristic effects can mainly be ascribed to the intragranular microstructure development and its evolution. It subsequently becomes necessary to accurately describe the dislocation patterning during monotonic and sequential loading paths in order to obtain a relevant constitutive model. In the present work, three types of local dislocation densities are taken to represent the spatially heterogeneous distributions of dislocations inside the grain. The resulting large strain single crystal constitutive law, based on crystal plasticity, is incorporated into a self-consistent scale-transition scheme. With the help of a rate-independent regularization technique, this new extended multiscale model is able to calculate plastic slip activity for each grain, and it can also characterize the evolution of the dislocation microstructure. We show that our model successfully reproduces several mechanisms of intragranular substructure development that have been observed in TEM micrographs in the context of various loading conditions. Our approach is also capable of quantitatively predicting the macroscopic behavior of both single-phase and dual-phase polycrystalline steels in the context of changing strain paths.
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