Semi phenomenological modelling of the behavior of TRIP steels

The authors are grateful to ArcelorMittal R&D for supporting this research.A new semi-phenomenological model is developed based on a mean-field description of the TRIP behavior for the simulation of multiaxial loads. This model intends to reduce the number of internal variables of crystalline models that cannot be used for the moment in metal forming simulations. Starting from local and crystallographic approaches, the mean-field approach is obtained at the phase level with the concept of Mean Instantaneous Transformation Strain (MITS) accompanying martensitic transformation. Within the framework of the thermodynamics of irreversible processes, driving forces, martensitic volume fraction evolution and an expression of the TRIP effect are determined for this new model. A classical self-consistent scheme is used to model the behavior of multiphased TRIP steels. The model is tested for cooling at constant loads and for multiaxial loadings at constant temperatures. The predictions reproduce the increase in ductility, the dynamic softening effect and the multiaxial behavior of a multiphased TRIP stee

Semi phenomenological modelling of the behavior of TRIP steels

The authors are grateful to ArcelorMittal R&D for supporting this research.A new semi-phenomenological model is developed based on a mean-field description of the TRIP behavior for the simulation of multiaxial loads. This model intends to reduce the number of internal variables of crystalline models that cannot be used for the moment in metal forming simulations. Starting from local and crystallographic approaches, the mean-field approach is obtained at the phase level with the concept of Mean Instantaneous Transformation Strain (MITS) accompanying martensitic transformation. Within the framework of the thermodynamics of irreversible processes, driving forces, martensitic volume fraction evolution and an expression of the TRIP effect are determined for this new model. A classical self-consistent scheme is used to model the behavior of multiphased TRIP steels. The model is tested for cooling at constant loads and for multiaxial loadings at constant temperatures. The predictions reproduce the increase in ductility, the dynamic softening effect and the multiaxial behavior of a multiphased TRIP stee

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

Stress distribution in the 16MND5 bainitic steel. Experimental analysis and polycrystalline modeling

La nature biphasée de l’acier bainitique 16MND5 (ferrite/cémentite) fait de la Diffraction des Rayons X (DRX) l’outil privilégié pour déterminer les états de contrainte dans la phase ferritique (méthode des sin2 ψ). Couplés aux observations réalisées lors d’essais de traction (surface des éprouvettes et faciès de rupture), ces derniers ont permis d’établir des critères décrivant le comportement et l’endommagement du matériau à l’échelle cristallographique, aux points bas de la transition fragile-ductile ainsi qu’aux basses températures [−196 ◦C;−60 ◦C]. Au cours du chargement, l’endommagement est observé au Microscope Electronique à Balayage, tandis que les contraintes internes sont déterminées par DRX : l’état de contrainte dans la ferrite est inférieur à celui de la bainite (contrainte macroscopique), l’écart n’excédant pas 150 MPa. Un modèle polycristallin à plusieurs échelles est développé parallèlement aux mesures expérimentales : une formulation de type Mori–Tanaka est utilisée pour décrire le comportement élastoplastique d’un monocristal ferritique renforcé par des précipités de cémentite, le passage au polycristal étant réalisé par une approche autocohérente. La modélisation développée prend en compte l’influence de la température sur les états de contrainte dans chaque phase et inclut un critère de clivage (valeur critique de la contraite normale aux plans {100}), qui traduit l’endommagement du matériau : elle permet ainsi de prédire le comportement réel de l’acier 16MND5 en fonction de la température, et de prendre en compte le mode de rupture qui est fragile à partir de −120 ◦C. En outre, il est également possible de calculer les déformations des plans diffractants εϕψ, qui peuvent être comparées à celles mesurées par DRX : cela permet d’évaluer les déformations par orientation cristallographique.The 16MND5 bainitic steel being a two-phase material (ferrite/cementite), the X-Ray Diffraction (XRD) is the most efficient tool to determine the stress states into the ferritic phase (sin2 ψ method). The latter, coupled to the observations realized during tensile tests (specimen surface and facies), have permitted to establish criteria to describe the behavior and the damaging processes of the material on a crystallographic scale, in the lower part of the ductile-to-brittle transition region and at lower temperatures [−196 ◦C;−60 ◦C]. During the loading, the damage is observed with a Scanning Electron Microscope, while the internal stresses are determined by XRD: the stress states are less important in ferrite than in bainite (macroscopic stress), the difference not exceeding 150 MPa. A multi-scale polycrystalline model is developed concurrently with the experimental measurements: a Mori–Tanaka formulation is used to describe the elastoplastic behavior of a ferritic single crystal reinforced by cementite precipitates, while the transition to the polycrystal is achieved by a self-consistent approach. The developed modeling takes into account the temperature effects on the stress states in each phase and includes a cleavage criterion (critical value of the stress normal to {100} planes), which expresses the damage of the material: thus, it enables to predict the actual experimental behavior of the 16MND5 steel in relation to temperature, and to take into account the failure process which is fragile from −120 ◦C. Besides, it is also possible to calculate the strains of the diffracting planes εϕψ, which can be compared to those measured by XRD: this enables to evaluate the heterogeneity of the strains for each crystallographic orientation

Internal Stress Analysis for the Damage Study of a 16MND5 Bainitic Steel

The behavior and the fracture mechanisms of the 16MND5 bainitic pressure vessel steel are studied using a local approach of fracture on a crystallographic scale. A series of tensile tests are performed on the material at various temperatures ranging from - 96°C to -60°C: the damage is observed with a Scanning Electron Microscope (SEM) while the residual stresses in the ferritic phase are determined by using the X-Ray Diffraction (XRD), never exceeding -150 MPa in compression. Thanks to these measurements, each stress value can be associated with a microscopie observation in order to couple the behavior of the material with the damage at various temperatures

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

Role of discrete intra-granular slip bands on the strain-hardening of polycrystals

This work investigates a new micromechanical modeling of polycrystal plasticity, accounting slip bands for physical plastic heterogeneities considered as periodically distributed within grains. These intra-granular plastic heterogeneities are modeled by parallel flat ellipsoidal sub-domains, each of them may have a distinct uniform plastic slip. To capture the morphology of slip bands occurring in plastically deforming polycrystals, these interacting sub-domains are considered as oblate spheroids periodically distributed and constrained by spherical grain boundaries. In this paper, we focus the study on the influences of internal length scale parameters related to grain size, spatial period and thickness of slip bands on the overall material's behavior. In a first part, the Gibbs free energy accounting for elastic interactions between plastic heterogeneities is calculated thanks to the Green function's method in the case of an isolated spherical grain with plastic strain occurring only in slip bands embedded in an infinite elastic matrix. In a second part, the influence of discrete periodic distributions of intra-granular slip bands on the polycrystal's behavior is investigated considering an aggregate with random crystallographic orientations. When the spatial period of slip bands is on the same order as the grain radius, the polycrystal's mechanical behavior is found strongly dependent on the ratio between the spatial period of slip bands and the grain size, as well as the ratio between the slip band thickness and the grain size, which cannot be captured by classic length scale independent Eshelby-based micromechanics

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