Strain localization analysis using a multiscale model

In order to analyze the formability of steels in sheet metal forming, a ductility loss criterion is coupled with a multiscale model. The behavior at the mesoscopic (grain) scale is modeled by a large strain micromechanical constitutive law, which is then used in a self-consistent scale transition scheme. Hardening at the slip system level is taken into account through mean dislocation densities considered as internal variables. The determination of active slip systems and the calculation of plastic slip activity are achieved with help of a regularization technique drawn from viscoplastic formulations. The model is shown to be able to correctly simulate the macroscopic behavior for single-phase steels during both monotonic and sequential loading paths. Finally, Rice's localization criterion, based on the ellipticity loss of the elastic-plastic tangent modulus, is introduced and applied to determine forming limit diagrams (FLDs). The model allows us to obtain correct FLDs for monotonic as well as sequential loading paths. Pre-strain impact on FLDs is qualitatively reproduced as well.ArcelorMittal CNR

Impact of intragranular substructure parameters on the forming limit diagrams of single-phase B.C.C. steels

An advanced elastic-plastic self-consistent polycrystalline model, accounting for intragranular microstructure development and evolution, is coupled with a bifurcation-based localization criterion and applied to the numerical investigation of the impact of microstructural patterns on ductility of single-phase steels. The proposed multiscale model, taking into account essential microstructural aspects, such as initial and induced textures, dislocation densities, and softening mechanisms, allows us to emphasize the relationship between intragranular microstructure of B.C.C. steels and their ductility. A qualitative study in terms of forming limit diagrams for various dislocation networks, during monotonic loading tests, is conducted in order to analyze the impact of intragranular substructure parameters on the formability of single-phase B.C.C. steels

Ellipticity loss analysis for tangent moduli deduced from a large strain elastic–plastic self-consistent model

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 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).ArcelorMittal Researc

Impact of microstructural mechanisms on ductility limits

In order to investigate the effects of microstructure and deformation mechanisms on the ductility of multiphase steels, a formability criterion based on loss of ellipticity of the boundary value problem is coupled with an advanced multiscale model accounting for intragranular microstructure development and evolution. The resulting large strain elastic–plastic single crystal constitutive law (based on crystal plasticity) is incorporated into a self-consistent scale-transition scheme. The present contribution focuses on the relationship between the intragranular microstructure of B.C.C. steels and their ductility. The model allows interesting comparisons in terms of formability limits for different dislocation networks, during monotonic loading tests applied to polycrystalline aggregates.ArcelorMittal & CNR

Impact of intragranular microstructure development on ductility limits of multiphase steels

In this paper, the effects of microstructure and deformation mechanisms on the ductility of multiphase steels are investigated. To this end, a formability criterion based on loss of ellipticity of the boundary value problem is coupled with an advanced multiscale model accounting for intragranular microstructure development and evolution. The spatially heterogeneous distribution of dislocations inside the grain is represented by three types of local dislocation densities. The resulting large strain elastic-plastic single crystal constitutive law (based on crystal plasticity) is incorporated into a self-consistent scale-transition scheme. The present contribution focuses on the relationship between the intragranular microstructure of B.C.C. steels and their ductility. The model allows interesting comparisons in terms of formability limits for different dislocation networks, during monotonic loading tests applied to polycrystalline aggregates.ArcelorMitta

Strain localization analysis deduced from a large strain elastic-plastic self-consistent model for multiphase steels

In order to investigate the impact of microstructures and deformation mechanisms on the ductility of materials, the criterion based on bifurcation theory 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 scheme. This approach takes into account several microstructural aspects for polycrystalline aggregates: initial and induced textures, dislocation densities, softening mechanisms so that the behavior during complex loading paths can be accurately described. Based on this formulation, Forming Limit Diagrams (FLDs) are derived and compared with a reference model for multiphase steels involving linear and complex loading paths. Furthermore, the effect of various physical and microstructural parameters on the ductility limit of a single-phase steel is qualitatively studied with the aim of helping in the design of new materials.CNRS & ArcelorMitta

Role of intragranular microstructure development in the macroscopic behavior of multiphase steels in the context of changing strain paths

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.ArcelorMittal & CNR

Détermination des diagrammes de perte d’ellipticité par une approche micromécanique

La striction et la rupture au cours de l’opération d’emboutissage figurent parmi les principaux phénomènes limitant les déformations maximales admises par les métaux. Ces phénomènes sont liés à la microstructure des matériaux ainsi qu’aux conditions de sollicitation. Afin de caractériser l’aptitude au formage d’un matériau, et ce pour différents modes de déformations, Keeler (1965) et Goodwin (1968) ont introduit la notion de Courbe Limite de Formage (CLF). L'inconvénient de cette représentation est sa forte dépendance au chemin de déformation, ce qui suppose qu’elle doit être déterminée pour chaque type de trajet de déformation. L’idée d’Arrieux (1982) fut de rechercher une représentation indépendante du trajet de chargement, ce qui donna naissance aux courbes limites de formage en contraintes. Les diagrammes de perte d'ellipticité (PDE) représentés dans l’espace des déformations principales dans celui des contraintes principales à partir d’une approche micromécanique sont présentés dans ce poster. Ces diagrammes sont qualitativement similaires aux CLF mais beaucoup plus restrictifs. L’influence de certains paramètres sur le tracé de ces courbes est étudiée.CNRS & ArcelorMitta

Influence de la microstructure intragranulaire sur l'évolution des surfaces de charge d'un acier ferritique lors de trajets de déformation monotones et complexes

Deux modèles micromécaniques de comportement élastoplastique, développés en adoptant une formulation en transformations finies et couplés à une technique de transition d’échelle autocohérente, sont utilisés pour étudier l'évolution des surfaces de charge d'un acier ferritique polycristallin lors de changements de trajets de déformation. L'importance de l'impact de la microstructure intragranulaire sur l'anisotropie du comportement lors de trajets complexes est montrée par l'intégration de la modélisation de la microstructure intragranulaire dans l'un de ces modèles.Two micromechanical elastic-plastic behaviour models, developed within the framework of finite transformations and coupled with self consistent scale transition approach, are used to study the evolution of yield surfaces of polycrystalline ferritic steels during strain path changes. The importance of the impact of intragranular microstructure on behaviour anisotropy under complex loadings is shown thanks to the introduction of intragranular microstructure modelling in one of these models.CNRS & ArcelorMitta

Strain localization analysis using a large strain self-consistent approach

The development of a relevant constitutive model adapted to sheet metal forming simulations requires an accurate description of the most important sources of anisotropy, i.e. the slip processes, the intragranular substructure changes and the texture development. During plastic deformation of thin metallic sheets, strain-path changes often occur in the material resulting in macroscopic effects. These softening/hardening effects must be correctly predicted because they can significantly influence the strain distribution and may lead to flow localization, shear bands and even material failure. The main origin of these effects is related to the intragranular microstructure evolution. This implies that an accurate description of the dislocation patterning during monotonic or complex strain-paths is needed to lead to a reliable constitutive model. A crystal plasticity model coupled with an intragranular microstructure description, inspired by Peeters' works, is used to determine the single crystal behaviour and to describe the dislocation cells evolution. The scale transition between the local behaviour and the polycrystalline one is realized thanks to a large strain self-consistent approach. Moreover, the introduction of a ductility loss criterion, first introduced by Rice, based on the ellipticity loss of the elastic-plastic tangent modulus, is used to plot Ellipticity Loss Diagrams (ELD). Qualitative comparisons are made with experimental Forming Limit Diagrams (FLD) for ferritic steel for simple and complex loading paths. In particular, it is shown that numerical ELD have a shape close to experimental FLD and reproduce qualitatively the effects due to complex loading paths.CNRS & ArcelorMitta