Numerical simulation of sheet metal forming using anisotropic strain-rate potentials

For numerical simulation of sheet metal forming, more and more advanced phenomenological functions are used to model the anisotropic yielding. The latter can be described by an adjustment of the coefficients of the yield function or the strain rate potential to the polycrystalline yield surface determined using crystal plasticity and X-ray measurements. Several strain rate potentials were examined by the present authors and compared in order to analyse their ability to model the anisotropic behaviour of materials using the methods described above to determine the material parameters. Following that, a specific elastic-plastic time integration scheme was developed and the strain rate potentials were implemented in the FE code. Comparison of the previously investigated potentials is continued in this paper in terms of numerical predictions of cup drawing, for different bcc and fcc materials. The identification procedure is shown to have an important impact on the accuracy of the FE predictions.International audienceFor numerical simulation of sheet metal forming, more and more advanced phenomenological functions are used to model the anisotropic yielding. The latter can be described by an adjustment of the coefficients of the yield function or the strain rate potential to the polycrystalline yield surface determined using crystal plasticity and X-ray measurements. Several strain rate potentials were examined by the present authors and compared in order to analyse their ability to model the anisotropic behaviour of materials using the methods described above to determine the material parameters. Following that, a specific elastic-plastic time integration scheme was developed and the strain rate potentials were implemented in the FE code. Comparison of the previously investigated potentials is continued in this paper in terms of numerical predictions of cup drawing, for different bcc and fcc materials. The identification procedure is shown to have an important impact on the accuracy of the FE predictions

Time integration scheme for elastoplastic models based on anisotropic strain-rate potentials

Modelling of plastic anisotropy requires the definition of stress potentials (coinciding with the yield criteria in case of the associated flow rules) or, alternatively, plastic strain-rate potentials. The latter approach has several advantages whenever material parameters are determined by means of texture measurements and crystal plasticity simulations. This paper deals with a phenomenological description of anisotropy in elastoplastic rate-insensitive models, by using strain-rate potentials. A fully implicit time integration algorithm is developed in this framework and implemented in a static-implicit finite element code. Algorithmic details are discussed, including the derivation of the consistent (algorithmic) tangent modulus and the numerical treatment of the yield condition. Typical sheet-forming applications are simulated with the proposed implementation, using the recent non-quadratic strain-rate potential Srp2004-18p. Numerical simulations are carried out for materials that exhibit strong plastic anisotropy. The numerical results confirm that the presented algorithm exhibits the same generality, robustness, accuracy, and time-efficiency as state-of-the-art yield-criterion-based algorithms.International audienceModelling of plastic anisotropy requires the definition of stress potentials (coinciding with the yield criteria in case of the associated flow rules) or, alternatively, plastic strain-rate potentials. The latter approach has several advantages whenever material parameters are determined by means of texture measurements and crystal plasticity simulations. This paper deals with a phenomenological description of anisotropy in elastoplastic rate-insensitive models, by using strain-rate potentials. A fully implicit time integration algorithm is developed in this framework and implemented in a static-implicit finite element code. Algorithmic details are discussed, including the derivation of the consistent (algorithmic) tangent modulus and the numerical treatment of the yield condition. Typical sheet-forming applications are simulated with the proposed implementation, using the recent non-quadratic strain-rate potential Srp2004-18p. Numerical simulations are carried out for materials that exhibit strong plastic anisotropy. The numerical results confirm that the presented algorithm exhibits the same generality, robustness, accuracy, and time-efficiency as state-of-the-art yield-criterion-based algorithms

Caractérisation multi-échelle et analyse par essai d'indentation instrumentée de matériaux à gradient générés par procédés mécaniques et thermochimiques de traitement de surface

Cette thèse est un travail prospectif sur la caractérisation multi-échelle de matériaux à gradient de propriétés générés par des traitements de surface de type mécanique (grenaillage à air comprimé ou par ultrasons) ou thermochimique (nitruration, implantation ionique, cémentation basse température). Les apports de plusieurs techniques de caractérisation (microscopie électronique à balayage, spectrométrie, indentation instrumentée, microscopie interférométrique), à différentes échelles, et l existence possible d une signature des traitements de surface étudiés sur le matériau ont été examinés. Une analyse multi-échelle des échantillons grenaillés par ultrasons a permis d établir un lien entre les paramètres procédé et la rugosité du matériau. Une approche originale statistique a été proposée pour déterminer la dureté d un matériau modifié par un traitement de surface donné sans altérer la surface par une rectification. Elle a permis d établir un lien entre la rugosité des échantillons grenaillés par ultrasons et leur dureté. Une recherche bibliographique détaillée a été réalisée sur la simulation de l essai d indentation instrumentée par éléments finis en étudiant une centaine d articles afin d évaluer l influence des hypothèses des modèles sur leurs résultats. A l aide d un modèle éléments finis, la sensibilité des courbes d indentation à une variation des paramètres matériau a été examinée. Cela a permis de mettre en place une réflexion sur l identification des propriétés d un matériau à gradient à l aide de l essai d indentation.This thesis is a prospective work on the multiscale characterization of plastically graded materials obtained with mechanical (shot peening using air pressure or ultrasounds) or thermochemical (nitriding, ion implantation, low temperature carburizing) surface treatments. The benefits of several characterization techniques (scanning electron microscopy, spectrometry, instrumented indentation, interferometric microscopy), at different scales, and the possible existence of a signature of the studied surface treatments on the material were examined. A multiscale analysis of the ultrasonically shot-peened specimens linked the process conditions with the material roughness. A novel statistical approach was proposed to determine the treated material roughness without deteriorating the surface through resurfacing. The latter enabled to establish a link between the shot-peened specimen roughness and their hardness. A detailed literature review of a hundred articles examined the IV simulation of the instrumented indentation test with finite elements in order to assess the effect of different hypotheses on the simulation results. Using a finite element model, the sensitivity of indentation curves to a variation of material parameters was examined. The latter enabled to reflect on the identification of the properties of plastically grade materials using the instrumented indentation test.COMPIEGNE-BU (601592101) / SudocSudocFranceF

Quantitative approach to determine the mechanical properties by nanoindentation test: Application on sandblasted materials

A novel method is developed to improve the accuracy in determining the mechanical properties from nanoindentation curves. The key point of this method is the simultaneous statistical treatment of several loading curves to correct the zero point error and identify the material properties considering size effects. The method is applied to four sandblasted aluminum-based specimens with different surface roughness. A linear relationship is obtained between the standard deviation of the initial contact error and the roughness which highlights the effect of the surface roughness on the reproducibility of the indentation curves. Moreover, the smaller standard deviation of the hardness given by the method confirms the importance of considering the initial contact error for an accurate determination of the material properties

Application of a dislocation based model for Interstitial Free (IF) steels to typical stamping simulations

With a view to environmental, economic and safety concerns, car manufacturers need to design lighter and safer vehicles in ever shorter development times. In recent years, High Strength Steels (HSS) like Interstitial Free (IF) steels which have higher ratios of yield strength to elastic modulus, are increasingly used for sheet metal parts in automotive industry to meet the demands. Moreover, the application of sheet metal forming simulations has proven to be beneficial to reduce tool costs in the design stage and to optimize current processes. The Finite Element Method (FEM) is quite successful to simulate metal forming processes but accuracy largely depends on the quality of the material properties provided as input to the material model. Common phenomenological models roughly consist in the fitting of functions on experimental results and do not provide any predictive character for different metals from the same grade. Therefore, the use of accurate plasticity models based on physics would increase predictive capability, reduce parameter identification cost and allow for robust and time-effective finite element simulations. For this purpose, a 3D physically based model at large strain with dislocation density evolution approach was presented in IDDRG2009 by the authors [1]. This model allows the description of work-hardening's behavior for different loading paths (i.e. uni-axial tensile, simple shear and Bauschinger tests) taking into account several data from microstructure (i.e. grain size, texture, etc...). The originality of this model consists in the introduction of microstructure data in a classical phenomenological model in order to achieve work-hardening's predictive character for different metals from the same grade. Indeed, thanks to a microstructure parameter set for an Interstitial Free steel, it is possible to describe work-hardening behavior for different loading paths of other IF steels by only changing the mean grain size and the chemical composition. During sheet metal forming processes local material points may experience multi-axial and multi-path loadings. Before simulating actual industrial parts, automotive manufacturers use validation tools - e.g. the Cross-Die stamping test. Such typical stamping tests enable the evaluation of a complex distribution of strains. The work described is an implementation [2] of a 3D dislocation based model in ABAQUS/Explicit and its validation on a Finite Element (FE) Cross-Die model. In order to assess the performance and relevance of the 3D dislocation based model in the simulation of industrial forming applications, the results of thinning profiles predicted along several directions and the strain distribution were obtained and compared with experimental results for IF steels with grain sizes varying in the 8-22 μm value range.Cifre Renaul

Dislocation-based model for the prediction of the behavior of b.c.c. materials – grain size and strain path effects

Sheet metal forming processes involve multi-axial strain paths. For the numerical simulation of such processes, an appropriate constitutive model that properly describes material behavior at large strain is required. For accurate and time-effective simulations, it is crucial to use plasticity models based on physics, as material macroscopic behavior is closely related to the evolution of the associated microstructures. Accordingly, a large strain work-hardening phenomenological model that incorporates the intragranular microstructure evolution through a dislocation density approach is proposed. The model is defined by a yield criterion and hardening laws that are all grain-size dependent. The classical Hill criterion in which grain-size dependency was introduced is proposed. Hardening laws are given by a combination of kinematic and isotropic contributions that respectively take into account the evolution with strain of cell blocks formed by geometrically necessary boundaries (GNBs) and individual dislocation cells delineated by incidental dislocation boundaries within cell blocks (IDBs). On the one hand, IDBs evolution contribution is described by a modified Rauch et al. isotropic model, which is able to describe work-hardening stagnation and work-softening. On the other hand, GNBs evolution contribution is described by a grain-size dependent tensorial back-stress expression proposed by Aouafi et al. [2007] to describe the plastic anisotropy and Bauschinger effect. Moreover, the proposed model aims to accurately predict steel behavior through an innovative approach by only changing few “simply measurable” microstructure data (e.g. chemical composition, grain size…). The predictive capabilities of the model are assessed for interstitial free (IF) and dual phase (DP) steels with grain sizes varying respectively in the 8-40 µm and 1-10 µm value range. Different loading paths are analyzed, namely the uniaxial tensile test, reversal simple shear and orthogonal tests.CIFRE Renaul

Numerical investigation and experimental validation of a plasticity model for sheet steel forming

This paper investigates a recently developed elasto-plastic constitutive model. For this purpose, the model was implemented in a commercial finite element code and was used to simulate the cross-die deep drawing test. Deep drawing experiments and numerical simulations were conducted for five interstitial-free steels and seven dual-phase steels, each of them having a different thickness and strength. The main interest of the adopted model is a very efficient parameter identification procedure, due to the physical background of the model and the physical significance of some of its parameters and state variables. Indeed, the dislocation density, grain size, and martensite volume fraction explicitly enter the model’s formulation, although the overall approach is macroscopic. For the dual-phase steels, only the chemical composition and the average grain sizes were measured for the martensite and ferrite grains, as well as the martensite volume fraction. The mild steels required three additional tensile tests along three directions, in order to describe the plastic anisotropy. Information concerning the transient mechanical behavior after strain-path changes (reverse and orthogonal) was not collected for each material, but for only one material of each family of steels (IF, DP), based on previous works available in the literature. This minimalistic experimental base was used to feed the numerical simulations for the twelve materials that were confronted to deep drawing experiments in terms of thickness distributions. The results suggested that the accuracy of the numerical simulations is very satisfactory in spite of the scarce experimental input data. Additional investigations indicated that the modeling of the transient behavior due to strain-path changes may have a significant impact on the simulation results, and that the adopted approach provides a simple and efficient alternative in this regard.CIFRE Renaul

PARAMETER IDENTIFICATION OF ADVANCED PLASTIC POTENTIALS AND IMPACT ON PLASTIC ANISOTROPY PREDICTION

In the work presented in this paper, several strain rate potentials are examined in order to analyze their ability to model the initial stress and strain anisotropy of several orthotropic sheet materials. Classical quadratic and more advanced non-quadratic strain rate potentials are investigated in the case of FCC and BCC polycrystals. Different identifications procedures are proposed, which are taking into account the crystallographic texture and/or a set of mechanical test data in the determination of the material parameters.International audienceIn the work presented in this paper, several strain rate potentials are examined in order to analyze their ability to model the initial stress and strain anisotropy of several orthotropic sheet materials. Classical quadratic and more advanced non-quadratic strain rate potentials are investigated in the case of FCC and BCC polycrystals. Different identifications procedures are proposed, which are taking into account the crystallographic texture and/or a set of mechanical test data in the determination of the material parameters

Time integration scheme for elastoplastic models based on anisotropic strain-rate potentials

Modelling of plastic anisotropy requires the definition of stress potentials (coinciding with the yield criteria in case of the associated flow rules) or, alternatively, plastic strain-rate potentials. The latter approach has several advantages whenever material parameters are determined by means of texture measurements and crystal plasticity simulations. This paper deals with a phenomenological description of anisotropy in elastoplastic rate-insensitive models, by using strain-rate potentials. A fully implicit time integration algorithm is developed in this framework and implemented in a static-implicit finite element code. Algorithmic details are discussed, including the derivation of the consistent (algorithmic) tangent modulus and the numerical treatment of the yield condition. Typical sheet-forming applications are simulated with the proposed implementation, using the recent non-quadratic strain-rate potential Srp2004-18p. Numerical simulations are carried out for materials that exhibit strong plastic anisotropy. The numerical results confirm that the presented algorithm exhibits the same generality, robustness, accuracy, and time-efficiency as state-of-the-art yield-criterion-based algorithms.Financement Région Lorrain

Modelling the effect of microstructure evolution on the macroscopic behavior of single phase and dual phase steels. Application to sheet forming process

The aim of this work is to develop a dislocation density based model for IF and DP steels that incorporates details of the microstructure evolution at the grain-size scale. The model takes into account (i) the contribution of the chemical composition for the prediction of the initial yield stress, (ii) the description of initial texture anisotropy by incorporating grain-size dependent anisotropy coefficients in Hill’48 yield criterion, (iii) the contribution of three dislocation density “families” that are associated with forward, reverse and latent structures. It reproduces the macroscopic transient behaviors observed when strain-path changes occur. The model is implemented in FE code in order to assess its predictive capabilities in case of industrial applications