Characterization of High Carbon Steel C68 at Elevated Temperatures and Different Strain Rates

This paper presents high-temperature tensile testing. This method is used to characterize the mechanical behaviour of a high-carbon steel C68 at temperatures up to 720°C. Samples are heated by an induction system controlled with a pyrometer. A high-speed camera (500 fps) is used to determine the displacement field with a digital image correlation software. For such tests a specific marking procedure of the sample is applied. Stress-strain curves are given from room temperature up to 720°C at strain rates ranging from 10-3/s to 10-1/s. Elastic parameters of the material are measured at room temperature using cyclic tests. Bridgman’s method is used to determine the equivalent stress-plastic strain curve during the necking phase

A Novel Constitutive Modelling for Spring Back Prediction in Sheet Metal Forming Processes

International audienc

Phase Transition and Mechanical Stability of InN Compound

International audienc

Characterization of elasto-plastic transition of sheet metal by using large-scale four-point bending test

International audienceAbstract The elastic properties of a material do play an important role in the spring back behaviour of sheet metal and have a dominant influence on the depth of where the bending tool has to go. In industry, the elastic behaviour is often approximated to a pure linear behaviour defined by two coefficients: Young’s modulus (E) and yield stress (Re). This modelling hypotheses result in geometrical errors in the angle and flange lengths of bended part. In order to better determine material behaviour at very small strains, a large-scale four-point bending test machine is presented in this study. Generating pure bending and measuring the residual radius allow observation of the transition between elastic and plastic deformation behaviour. By deforming the test beam in the supposed pure elastic area, it appears that the pure elasticity behaviour of the material is indeed non-existent. Plastic strains can be detected as soon as the very first bending of the sample, at very low equivalent stress well under usual accepted elastic yield stresses. Perspectives are addressed in order to solve this difficulty, which hinders the possibility of correctly simulating the bending process, particularly with regard to tight geometry requirements

Critère d’aptitude à l’emboutissage de tôles minces orthotropes

L’objet de cet article consiste en une présentation et une critique d’un critère en contraintes d’aptitude à l’emboutissage de tôles fines anisotropes. Le calcul est développé dans le cadre des grandes déformations et s’étend aux cas orthotropes visqueux en trajets de déformation plan quelconques (trajets brisés dans et hors axes d’orthotropie). Les récents travaux développés par R. Arrieux et coll. [1-6] sur le modèle de Marciniack et Kuczinsky (M-K) [7] nous ont amené à proposer un critère d’emboutissabilité en contrainte quasi indépendant des trajectoires de déformations. Le modèle de comportement actuellement utilisé est rigide visco-plastique à écrouissage isotrope associé au critère quadratique de Hill.Dans un premier temps, nous présenterons le modèle utilisé lorsque les directions principales des déformations ne sont pas confondues avec les directions d’orthotropie (laminage et transverse).Nous analyserons ensuite les résultats obtenus sur un matériau isotrope visqueux en chargement direct (trajectoire linéaire de déformation) puis en trajets brisés.Le critère d’emboutissabilité calculé sur un matériau orthotrope sera finalement comparé aux résultats expérimentaux obtenus sur un acier doux SEDDK A 151 en trajets directs et brisés

Experimental study with a Digital Image Correlation (DIC) method and numerical simulation of an anisotropic elastic-plastic commercially pure titanium

International audienc

Doświadczalne badania w zakresie sprężysto-plastycznym handlowo czystego tytanu za pomocą metody korelacji obrazu cyfrowego oraz symulacji numerycznej

International audienceIn this paper, the tensile behaviour of a commercially pure titanium is studied using a full-field strain measurement. A fine analysis of the measured strain fields is carried out in order to determine the intrinsic behaviour of the material. An elastic-plastic model taking material anisotropy into account is proposed. On the basis of experimental results, the parameters of this model are identified then introduced into a FEM code in order to simulate the behaviour of titanium. To assess the performance of the approach, the numerical results are finally analysed and compared with measurements coming from image processing. A quite satisfactory agreement between simulation and experiment is obtained.Podczas prób rozciągania blachy z handlowo czystego tytanu badano rozkład odkształceń za pomocą analizy obrazu i identyfikacji położenia przez korelację kontrastu. Metoda pozwoliła na wyznaczenie odkształceń podczas rozciągania na całej powierzchni próbki, łącznie ze strefą przewężenia, dla trzech kierunków rozciągania. Na podstawie pomiarów wyznaczono krzywe umocnienia, współczynniki anizotropii oraz przedstawiono równania konstytutywne badanego materiału, obejmujące izotropowy zakres sprężysty oraz anizotropowy zakres plastyczny. Do opisu właściwości anizotropowych zastosowano warunek Hilla z 1948 r. Poprawność modelu oceniono na podstawie modelowania MES próby rozciągania

Doświadczalne badania w zakresie sprężysto-plastycznym handlowo czystego tytanu za pomocą metody korelacji obrazu cyfrowego oraz symulacji numerycznej

International audienceIn this paper, the tensile behaviour of a commercially pure titanium is studied using a full-field strain measurement. A fine analysis of the measured strain fields is carried out in order to determine the intrinsic behaviour of the material. An elastic-plastic model taking material anisotropy into account is proposed. On the basis of experimental results, the parameters of this model are identified then introduced into a FEM code in order to simulate the behaviour of titanium. To assess the performance of the approach, the numerical results are finally analysed and compared with measurements coming from image processing. A quite satisfactory agreement between simulation and experiment is obtained.Podczas prób rozciągania blachy z handlowo czystego tytanu badano rozkład odkształceń za pomocą analizy obrazu i identyfikacji położenia przez korelację kontrastu. Metoda pozwoliła na wyznaczenie odkształceń podczas rozciągania na całej powierzchni próbki, łącznie ze strefą przewężenia, dla trzech kierunków rozciągania. Na podstawie pomiarów wyznaczono krzywe umocnienia, współczynniki anizotropii oraz przedstawiono równania konstytutywne badanego materiału, obejmujące izotropowy zakres sprężysty oraz anizotropowy zakres plastyczny. Do opisu właściwości anizotropowych zastosowano warunek Hilla z 1948 r. Poprawność modelu oceniono na podstawie modelowania MES próby rozciągania

Comparison of physically based constitutive laws used for numerical simulations of plasticity of single crystals

Various microstructural physical mechanisms involving mostly dislocation glides are responsible for plasticity of face centred cubic single crystals. These mechanisms have been pointed out experimentally using at least uniaxial tensile tests. Thus, many constitutive laws have been developed and integrated at the microstructural level to reproduce the experimental evolutions of various parameters (single glide, dislocation density...). More recently, general models have been written in a continuum mechanics framework for finite element simulations. Four main models of this kind are described and applied to the case of uniaxial tensile loading. The selected models present a similar formalism : a flow law plus a hardening law involving a hardening matrix describing the interaction between all the considered glide systems. Each model is integrated using a standard numerical procedure in order to simulate tensile tests. The simulation of a tensile test with a given orientation of the tensile axis is done for each model in order to compare them all together on the same basis. The suitability between the simulated results and experimental evidence is also commented. Finally, the evolution of the components of the hardening matrix is discussed

Identification through mesoscopic simulations of macroscopic parameters of physically based constitutive equations for the plastic behaviour of fcc single crystats

The objective of this work is to derive the parameters of macroscopic constitutive equations for the plasticity of fcc single crystals with the help of simulations performed at a dislocation level. The macroscopic model is based on the leading physical mechanisms which are involved in the plastic deformation. The three involved constitutive laws use the total dislocation densities on each glide system as fundamental variables. Those three expressions are derived from physical processes governing the behaviour of a single dislocation and adapted to be used at the macroscopic scale. Literature results could be widely used for the identification of the material parameters for different fcc materials but some of the parameters are mean values and must be seen as phenomenological parameters so that a good way to determine such values consists to use a numerical tool where each dislocation is individually simulated in a three dimensional network. Such a tool works at a mesoscopic scale (typically several microns) and deals with dislocations discretized into pure screw and edge segments. It includes all the well-known elementary events governing the dislocation motion such as the line tension effect, the Frank-Read multiplication mechanisms, the cross-slip events and the junction formations. The cross-analysis of several specific mesoscopic simulations allows to determinate the values of some macroscopic parameters and also to check the validity of both models