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Flow instability is an intrinsic behavior of materials, especially during hot deformation, and it will be intensified and propagate internal defects, and finally lead to various damages in the significant perturbation. Some phenomenological models in the literature could present the flow instability behavior, but not available for describing the microstructure changes. To overcome this problem, we introduce a dissipation potential as a function of the plastic strain rate, the dislocation density rate, and the heat transfer rate, D(e˙p, ρ˙dis, q; e, ρdis, θ), coupled with strain, dislocation density, and temperature as the boundary condition to record the microstructure evolution and describe the flow instability. In this function, the stored energy rate marks the dislocation density evolution, i.e., the transient microstructure changes, and one parameter ηM, is introduced to evaluate the efficiency of metallurgy. And the flow instability criterion is derived from the principles of maximum dissipation (or maximum entropy production rate) and orthogonality proposed by HANS ZIEGLER. We obtain the necessary conditions of the flow instability are that the dissipation potential is with entirely positive values due to the large plasticity, and the dissipation potential D(e˙p, ρ˙dis, q; e, ρdis, θ) is convex, i.e., the associated Hessian matrix is semi-positive. In this work, the function was applied to describe the behavior of Ti6Al4V during hot deformation, and a Kocks-Mecking type model was used to describe the flow stresses as well.

7th International Conference on Recrystallization and Grain Growth, Ghent, Belgium, 4 Aug 2019 - 9 Aug 2019; Journal of physics / Conference Series 1270, 012049 (2019). doi:10.1088/1742-6596/1270/1/012049, Most commercial aluminum alloys are characterized by dynamic recrystallization at very large deformations in a continuous manner. The present study deals with the characterization and modeling of the evolution of the microstructure of an aluminum wrought alloy at large plastic deformations. Hot torsion tests of the AA6082 aluminum alloy are carried out using the thermomechanical simulator Gleeble®3800 in a wide range of temperatures and strain rates. The use of water quenching immediately after deformation avoids any static restoration during cooling. Microstructural investigations are carried out by means of electron back scattered diffraction using a scanning electron microscope to determine the grain and subgrain structures, as well as the misorientation distributions. In-situ synchrotron radiation tests during hot torsion are used to confirm the continuous dynamic recrystallization (CDRX) by the evidence of the conversion of low angle boundaries (LAGBs) into high-angle boundaries (HAGBs) and the formation of new texture. Experimental investigations show that CDRX starts with the formation of LAGBs at low strains (center of the sample). By subsequent straining (close to the surface of the sample), the accumulation of dislocations at the LAGBs causes an increase in their misorientation until a critical value is reached and LAGBs transforms into HAGBs. The developed model consists of a microstructural model, equation rates and constitutive equations. The microstructure is described by three internal variables. Their rates are evaluated using the Kocks-Mecking model. The modelled and experimental flow stresses show softening due to the consumption of dislocations and the continuous formation of new HAGBs., Published by IOP Publ., Bristol

A Fe-0.02 wt%C, containing cementite particles, and a pure α-iron are subjected to unconstrained high-pressure torsion and their microstructural refinement with strain are examined by electron backscatter diffraction (EBSD) and transmission Kikuchi diffraction EBSD (TKD-EBSD), based on which the influence of second-phase particles on grain refinement mechanisms is investigated. Both materials are refined rapidly by formation of subgrain boundaries and grain boundaries at low and medium strains. The single-phase iron generates a higher density of geometrically necessary dislocations and forms small grains in the deformation inhomogeneity regions. However, at a higher strain of ~12.3, the cementite particles facilitate to overcome the saturation microstructure that occurrs in the pure iron and promote further grain refinement. Continuous dynamic recrystallization (CDRX) by transforming subgrain boundaries to grain boundaries is the major grain refinement mechanism before evm~12–13. Geometric dynamic recrystallization (GDRX) is also operating during ultrahigh strains (evm~12–30), particularly prevalent in the cementite-containing specimen. Mechanical properties of the HPT-processed microstructures are examined by nanoindentation and micropillar compression.

International audience; The Nadai and Fields and Backofen expressions are widely used to convert the torque/twist data obtained during torsion testing into shear stress/shear strain curves as well as von Mises equivalent stress/ equivalent strain curves. However, when employed in the conventional manner using average values of the twist hardening exponent N, they overestimate the critical strains for the initiation of twinning, dynamic transformation and dynamic recrystallization by comparison with the values determined using compression testing. By contrast, when the local or instantaneous values of the exponent are employed, the torsion and compression results are in good agreement. Another feature of the corrected curves is that they indicate that considerably more dynamic softening takes place during the high temperature deformation of austenite than suggested by the average N flow curves. It is shown that, despite the lack of work conjugacy between the torque-twist and stress-strain curves, the above expressions always lead to the correct constitutive behavior at the external radius. (C) 2013 Elsevier B.V. All rights reserved.

Les alliages ferritiques Fe-8 %Al possedent des proprietes physiques et mecaniques prometteuses pour le developpement et la conception de nouveaux types d’aciers alleges. Ces alliages presentent cependant des defauts de surface appeles « roping », apparaissant apres l’etape d’emboutissage a froid. La formation de ces defauts est principalement attribuee a la distribution heterogene des orientations des grains. Dans cette etude, les effets de la quantite de deformation, de la vitesse de deformation et de la temperature ont ete examines en utilisant la torsion a chaud. Les essais ont ete realises a des temperatures comprises entre 900 °C et 1100 °C et des vitesses de deformation comprises entre 0,1 s-1 et 10 s-1 . Il a ete montre que deux types de recristallisation dynamique pouvaient intervenir durant la deformation a chaud : la recristallisation dynamique continue et la recristallisation dynamique discontinue.

International audience; A simple three-dimensional thermomechanical model for friction stir welding (FSW) is presented. It is developed from the model proposed by Heurtier et al. (2006) based on a combination of fluid mechanics numerical and analytical velocity fields. Those velocity fields are introduced in a steady state thermal calculation to compute the temperature field during welding. They allow partial sliding between the shoulder and the workpiece, the amount of which is provided as an additional result of the model. The thermal calculation accounts for conduction and convection effects by means of the particular derivative. The complete thermomechanical history of the material during the process can then be accessed by temperature and strain rate contours. The numerical results are compared with a set of experimental test cases carried out on an instrumented laboratory device. The choices for modeling assumptions, especially tribological aspects, are discussed according to agreements or deviations observed between experimental and numerical results. The amount of sliding appears to be significantly influenced by the welding conditions (welding and tool rotational velocities), and physical interpretations are proposed for its evolution.

International audience; The study was carried out to understand the mechanisms occurring during dynamic recrystallization of hot deformed 11 % chromium stabilized ferritic stainless steels and to compare the behaviour induced by various types of stabilization. The experimental temperatures ranged from 800 to 1150 °C and strain rates from 10-2 to 15 s-1. The development of the textures and microstructures was analysed using EBSD maps. It was observed that continuous dynamic recrystallization occurs in all materials starting at the onset of straining. Niobium has a more pronounced influence on hardening than titanium during hot deformation. The D2 component was found as the major texture component at the steady state for the torsion tests conducted along the negative shear direction. It was likely to be formed by the combination of straining and growth of the grains exhibiting both low stored energy and low rotation rate of the crystallographic axes. The texture evolution was the main reason for the flow stress behavior during the hot torsion tests. A complementary study was carried out to understand the texture formation occurring during the direct (negative shear direction) and reversed (positive shear direction) hot torsion. After reversion of the shear direction, i.e. during positive shear, the above major texture component is gradually changed into the D1 component. Using the method of Continuum Mechanics of Textured Polycrystals, the stress evolution is explained by the volume fraction changes of each component at various strains, associated with their respective Taylor factors. This simplified approach leads to a good agreement with experimental results.

Commercial 304 austenitic stainless steel was deformed in compression at high temperatures (800 to 1 280°C) and at strain rates from 0.001 to 1 s - 1 . The critical and peak strains associated with dynamic recrystallization were determined based on changes in the work hardening rate as a function of the flow stress. The effect of the deformation variables (T, e) on these values is analyzed; it is shown that over a range of temperature corrected strain rate (Z=10 1 4 to 10 1 6 s - 1 , Q d e f =405 kJ/mol), the initiation of dynamic recrystallization is delayed. This retardation is attributed to the segregation of substitutional impurity elements, principally phosphorus, to the sub-boundaries of the newly-forming DRX grains.

The elastic strain and stress fields between two bubbles of different sizes and different pressures were estimated by using the fundamental result of Eshelby. The equivalent inclusion method was extended to the case of two inclusions in an infinite elastic solid. This approach, which remains totally analytical, was compared successfully to finite element calculations. The mean stress provides information about gas diffusion between the bubbles: according to the results, the bubbles are likely to progressively equalize their sizes. Moreover, the derivation of the von Mises equivalent stress showed that its value, in the vicinity of the bubbles, is larger than the elasticity limit. Therefore, for a complete mechanical description of the problem, plasticity should be taken into account. In spite of its simplicity, this method nevertheless leads to results, which are very close to the prediction of numerical calculations.

Microstructural changes during high-temperature extrusion and torsion of an AZ91 alloy (Mg–9Al–1Zn, wt.%) were investigated. In the experimental domain studied, dynamic recrystallisation (DRX) occurs and the effect of temperature and strain rate on the resulting recrystallised grain size was investigated. Complete recrystallisation in torsion is associated with the development of a stress plateau after softening from the peak stress, which is systematically observed in the first steps of straining. The resulting grain size can be related to the value of the peak stress. It appears that the precipitation of the Mg 17 Al 12 phase does not affect significantly the torsion behaviour of the alloy in the experimental domain investigated here. This study supports the idea that very fine-scale microstructures (i.e. with a mean grain size smaller than 5 μm) can be easily produced by DRX during high-temperature extrusion of the AZ91 alloy.

A simple analytical model is proposed for predicting the plastic behaviour of orthotropic materials, considered as aggregates of cubic crystals. The behaviour of a single texture component is first described by a quadratic yield equation reduced to the case of cubic symmetry. A combination procedure of the components, using two different assumptions, is then presented. It turns out that the overall plasticity criterion is itself a Hill type quadratic equation, the associated orthotropy parameters of which are analytically derived. Comparison with experiment is carried out with results of the literature as well as direct measurements. Finally, the special case of axially symmetric materials is analyzed.

Five high purity base Fe-C grades, ranging from 0 to 500 ppm C, were prepared and submitted to hot compression and torsion tests. Addition of 50 ppm C induces a decrease of the apparent activation energy of the flow stress at low strains, but in contrast an increase of the latter at large strains. The compression stress-strain curves are analyzed using the Yoshie-Laasraoui-Jonas equation, which allows the dependence of strain hardening and dynamic recovery on the carbon content to be separately discussed. In the range over 200 ppm C, the carbide precipitation or the austenitic transformation occurs and additional hardening mechanisms are activated. This effect is one of the topics of the discussion.

In this paper, associated to a previous work, we present an experimental analysis of the channel die compression test. The channel die test occupies an important position within single crystal deformation studies and has been viewed as representing a first approximation to the constrain and loading condition for metal polycrystals. The latter is frequently found in plastic working operations such as rolling, deep drawing and wire flattening. In this test, where the walls of a channel supress lateral flow, the lateral stress developped at the walls varies with the crystal orientation and with the conditions of friction. We adress the conflict between ideal frictionless walls under the assumption of a uniform deformation of an anisotropic material. On the basis of prior results, three crystals of cubic structure to faces centered of various orientations were forced under conditions of extreme lubrifications. Such tests make it possible to confirm the previous theorical predictions by an analysis of the heterogeneous behaviour of the deformation.

A self-consistent model was applied to predict the plastic flow behavior during hot working of alpha/beta titanium alloys with wrought (equiaxed alpha) microstructures as a function of the flow behavior and volume fractions of the individual phases. For this purpose, constitutive relations that incorporated composition-dependent strength coefficients were determined for the alpha and beta phases. With these constitutive relations and measurements of the specific compositions and volume fractions of the two phases at hot-working temperatures, the flow stress dependence on temperature under nominally isothermal conditions and the (average) strain rates in the individual phases were predicted for Ti-6Al-4V. The effect of temperature transients during hot deformation on the flow stress under nonisothermal (conventional) forging conditions and under nominally isothermal, high strain-rate conditions was also established using the self-consistent modeling approach. In these instances, the effect of a rapid temperature drop or rise, respectively, on the retention of a metastable microstructure was quantified. The predicted flow behaviors showed good agreement with experimental measurements.

De nombreuses etudes ont deja ete consacrees a la recristallisation dynamique, mais la plupart des travaux ont porte jusqu'a present sur le cuivre et les aciers de construction microallies, et presque toujours sur des nuances industrielles riches en impuretes ou en elements d'addition. Nous avons donc decide d'elaborer un materiau modele de haute purete proche de la nuance 304L et sans element d'addition (C, N et S en particulier). Une serie d'essais interrompus a ete realisee a 850°C et 10 -3 s -1 . Dans ces conditions, la recristallisation dynamique provoque l'affinement des grains et la courbe contrainte-deformation presente un maximum unique. Nous observons une diminution d'un facteur 3 environ de la taille de grains moyenne entre l'etat initial (e = 0) et l'etat stationnaire (e = 1,5). Le phenomene classique de recristallisation en collier qui conduit a l'apparition de nombreux germes le long des joints de grains fortement ecrouis apparait pour une deformation de 0,4. La croissance des germes provoque alors un adoucissement observe sur la courbe contrainte-deformation. On verifie que les grains les plus jeunes (i.e. les germes) sont aussi les moins ecrouis. De plus, ce sont les seuls grains dans lesquels on detecte des joints de macles. Au regime stationnaire de la recristallisation dynamique, on constate que le degre d'ecrouissage des grains est tres variable. En particulier, les petits grains sont soit faiblement ecrouis (grains « jeunes »), soit au contraire fortement ecrouis (« grains vieux », sur le point de disparaitre). La distribution des tailles de grains semble proche de celle de l'etat recristallise initial.

Compression tests were carried out on two compositions of Cu–Sn bronze: Cu–9·2Sn and Cu–9·1Sn–0·26Zn (wt-%). The experiments were performed at temperatures from ambient up to 750°C and at nominal (initial) strain rates in the range 10-3 to 10-1 s-1. The measured data were converted into true stress–true strain curves; these displayed yield drops as well as single peaks (or maxima) at higher temperatures and lower strain rates. The mean rate sensitivity applicable to the curves was 0·25. Optical metallography indicated that dynamic recrystallisation of the ‘grain refinement’ type was taking place at the higher temperatures and proceeded by necklace formation. Electron backscattered diffraction measurements were also carried out; these revealed that twinning plays an important role in these materials. The present results show that the progress of recrystallisation is considerably slower than in OFHC copper and that the recrystallised grain size is appreciably finer. These observations, taken togethe...

In this paper, a generalized self-consistent method is proposed to predict the effective moduli of a material containing single-phase and randomly oriented spheroidal inclusions, with same aspect ratios. This is achieved by using an energy equivalence framework, associated with a generalization of the classical three phase model to spheroidal inclusions. The localization problem (spheroidal duplex inclusion problem) is formulated with the Papkovitch-Neuber approach; this requires expansion formulae for the spheroidal potentials, which are derived in the Appendix. Finally, the determination of the effective moduli is equivalent to solving a system of nonlinear equations. Effective moduli are presented for various types of inclusions, and comparisons are made with the estimations obtained from the self-consistent and Mori-Tanaka methods. Moreover, the effects of inclusion geometry and spatial distribution of inclusions on the effective moduli are investigated and compared to each other.

Un modele apparente aux automates cellulaires est utilise pour prevoir le comportement mecanique global et local d'agregats de deux phases viscoplastiques dans le domaine des grandes deformations. Les reponses de deux types de structures, uniforme et en amas (clusters), sont comparees en traction et en compression axisymetriques. Elles mettent en evidence un ecrouissage d'origine morphologique et topologique. Les histogrammes de deformation des grains montrent que les heterogeneites sont plus prononcees dans la phase dure que dans la phase molle.

Resume La methode des trois potentiels a ete utilisee pour traiter analytiquement deux configurations particulieres en elasticite lineaire: deux inclusions spheroidales allongees identiques, alignees suivant un axe de revolution commun, et une inclusion enrobee delimitee par deux interfaces spheroidales allongees de meme centre et de meme axe de revolution. Dans les deux cas, la matrice infinie est soumise a un chargement axisymetrique. La resolution du probleme exige d'etablir des relations mathematiques generales de translation et d'expansion des potentiels spheroidaux. Celles-ci ont ete obtenues analytiquement et la validite de la methode a ete verifiee par comparaison avec les resultats obtenus a partir d'une analyse par elements finis.

International audience; Iron-aluminium alloys display promising physical and mechanical properties. In this study, the effects of strain, strain rate and temperature on an Fe-8% Al were investigated. Hot torsion tests were performed in the temperature range 900-1100 degrees C and strain rate range 0.1-10 s(-1). In this alloy, two types of dynamic recrystallization may operate during hot deformation: at high temperature and high strain rate, this alloy undergoes discontinuous dynamic recrystallization, whereas at lower temperature and strain rate, continuous dynamic recrystallization occurs.

The theory of the invariant representation for tensor functions in first illustrated by providing a general form of the Hill (1948) orthotropic yield criterion. It is then applied to derive a quadratic yield equation for the case of prismatic monoclinic symmetry, which is induced by simple shear deformation. This new criterion can in turn be approximated by an orthotropic one by choosing the ‘best’ symmetry axes. The above equations are then used to derive the angular dependences of the uniaxial yield stress and strain rate ratio in the plane of a prismatic monoclinic sheet. Finally, it is shown on an example that they are able to predict the axial stresses occurring during torsion testing with a fairly good accuracy.

Les parametres microstructuraux, les contraintes residuelles initiales influent sur les caracteristiques mecaniques, la tenue en fatigue de l'acier a roulements cryotechnique EZ100CD17. Pour faire varier la microstructure, plusieurs traitements thermiques sont realises. Les fractions volumiques de phases, les caracteristiques mecaniques, par exemple, sont modifiees. Les influences des traitements thermiques, des conditions d'usinage sur l'etat de contraintes residuelles seront etudiees. Nous mettrons ensuite en evidence l'influence de la microstructure sur l'evolution des contraintes residuelles apres sollicitation mecanique en fatigue de contact, a la temperature de l'azote liquide. Les contraintes residuelles du premier ordre et du second ordre, mesurees en diffraction X pour les plans {211} de la martensite, seront considerees. Nous montrerons ainsi que les traitements thermiques et les essais mecaniques influencent a la fois les contraintes residuelles macroscopiques et microscopiques.

The deformation of two phase materials is analyzed and a mechanical model is derived for calculating the apparent activation energy of flow. The latter is expressed in terms of the individual activation energies of the two constituent phases. The model is used to account for the observation that the activation energy for two phase flow is generally much higher or much lower than the flow activation energies of the individual phases. This is because the apparent activation energy of the aggregate includes an additional term that depends on the rate of change with temperature of the volume fractions of the two phases. The predictions of the model are compared to experimental results and are shown to be in good agreement with them. The present mechanical approach demonstrates clearly that the apparent activation energy for the flow of a two phase material is not, in general, related to a specific mechanism since an additional mesoscopic term is involved.

The exact velocity, stress and strain rate fields around a spheroidal cavity in an infinite linear viscoplastic compressible matrix are derived analytically by the ‘three function approach’. The perturbation of the velocity field due to the cavity is the superposition of three independent modes, inducing homothetic growth, pure distortion and both volume and shape changes, respectively. This solution is then used to investigate the velocity field around a spheroidal cavity in a nonlinear viscous compressible material by means of a variational principle. The behaviour of such damaged linear and nonlinear materials will be discussed in a forthcoming companion paper. The importance of the reference strain, while studying void growth in a compressible material, is emphasized. If the axial strain is chosen as a reference, void growth is found to be enhanced at low triaxiality ratios, but lowered at high triaxiality ratios in a compressible matrix relative to an incompressible one. Finally, the transition from a power law to a linear law with intercept, at increasing strain rates, is shown to reduce damage growth rate.

A new mechanical model is proposed to predict the mechanical behavior of inhomogeneous materials. The simple case of an aggregate of two linearly viscous phases submitted to plane strain is addressed here. Calculations involve the Eshelby localization relationships associated with a Walpole-type averaging procedure. When the grains are equiaxed, derivations are entirely analytical, which allows the proposed method to be simply compared with the classical Hashin-Shtrikman lower and upper bounds and the self-consistent model. When large strains are considered, the model is used to predict numerically the overall stress-strain relationships. Significant morphological hardening or softening is shown to occur with increasing strain, depending on the initially equiaxed or elongated grain shapes. Finally, the local distributions of strains, and thus the development of strain inhomogeneities, are also predicted by the model.

Pour cerner les techniques metallurgiques des artisans protohistoriques, il est necessaire de connaitre les evolutions microstructurales obtenues selon les deformations imposees. La compression a chaud de deux bronzes industriels (contenant soit 0,026% soit 0,26% de zinc) et deux bronzes «archeologiques» (contenant soit 0,5% de soufre soit 0,5% de soufre et 0,5% de plomb) permet les observations suivantes : - Les comportements des bronzes «archeologiques» sont tres similaires : jusqu'a 600°C pour e = 0,1 on n'observe pas de recristallisation ; pour e = 1,2 on observe une recristallisation en collier le long des joints de grains. A 750°C la recristallisation semble homogene dans tout le materiau. - Pour les deux bronzes industriels, on observe a 750° C une recristallisation dynamique en collier. Pour le bronze contenant 0,26% de zinc, une deuxieme recristallisation a ensuite lieu dans les grains deja recristallises, d'ou un affinement de la taille des grains et un adoucissement de la contrainte. La purete du bronze semble donc etre un parametre determinant dans son comportement a chaud. Nous avons ainsi mis en evidence l'existence d'un phenomene d'affinement de grain qui ne semble pas jusqu'a present avoir ete decrit dans la litterature.

La recristallisation dynamique continue se manifeste par la transformation progressive des sous-grains en grains. Une etude microstructurale effectuee par diffraction des electrons retrodiffuses a permis de la mettre en evidence lors de la deformation par compression uniaxiale (0,7 T β , 10 -2 s -1 ) d'un aluminium 1200 (99,3 %).

International audience; An original analytical method is proposed for modeling asymmetric rolling (ASR) of metal sheet. It is based on a uniform strain field depending on a single optimization parameter, viz. the entry velocity of the sheet. The shear and normal strains associated with an ASR pass are derived analytically. Moreover, it is shown that the entry velocity almost coincides with the outer linear velocity of the slower roll, as far as ASR is sufficiently asymmetric. In that case, closed form formulae are available for the main rolling parameters such as the overall power dissipated and the two rolling torques. These results can be straighforwardly used for practical applications.

Le martelage artisanal comme procede de formage de certains objets en alliages a base de cuivre est d’abord replace parmi la problematique archeologique du 1er millenaire avant J.-C. en Europe temperee. Une discussion et un exemple montrent l’interet et les problemes souleves par ce theme de recherche. Une etude de metallurgie mecanique du martelage artisanal est ensuite developpee par modelisation et simulation experimentale. Des resultats sont obtenus pour differents parametres : effort et travail d’indentation, deformation et vitesse de deformation, ainsi que duree de l’impact.

Two complementary analytical approaches and the finite difference method are proposed for modeling asymmetric rolling (ASR) of metal sheet. The first analytical model is an upper bound method based on a uniform strain field depending on one single optimization parameter, viz. the entry velocity of the sheet. Its results can be straightforwardly used for practical applications. The second model uses a more refined analytical velocity field based on the classical parabolic estimation of the material flow lines in rolling. It involves an additional optimization parameter associated with the precise form of the velocity field. Local values of strain, strain rate and self‐heating temperature are easily calculated, as well as the rolling force. Finally, the finite difference method is applied to compute heat transfers between the rolls and the sheet. In conclusion, the respective advantages of the three methods are discussed.

The theory of the irreducible representation for tensor functions is used to derive an invariant formulation for anisotropic plastic behaviour. The case of cubic symmetry, applying to fcc or bcc strongly textured metals exhibiting any single ideal orientation, is investigated in detail. The plastic response of the material is described by a quadratic yield function and the flow rule associated by means of the normality rule. It is shown that the equations of the anisotropic plastic behaviour can be written in a vector form, so that they can be employed easily in any given reference system. Furthermore, the constitutive equation is deduced from the flow rule by simply taking the inverse of scalar coefficients.

Recrystallization is to a large extent responsible for their final mechanical properties. This article commences with a discussion on static recrystallization (SRX) and dynamic recrystallization (DRX). The DRX includes continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX). The article discusses the assumptions and simplifications for the Avrami analysis. It describes the effects of nucleation and growth rates on recrystallization kinetics and recrystallized grain size based on the Johnson-Mehl-Avrami-Kolmogorov model for static recrystallization. The article reviews the kinetics of DRX with the aid of the Avrami relations. It considers the basic framework of the mesoscale approach for DDRX, including the three basic equations for grain size changes, strain hardening and dynamic recovery, and nucleation. The article explains the mesoscale approach for CDRX to predict microstructural evolutions occurring during hot deformation, along with an illustration of the main features of the CDRX mesoscale model.

This article summarizes the general features of microstructure evolution during the thermomechanical processing (TMP) of nickel-base superalloys and the challenges posed by the modeling of such phenomena. It describes the fundamentals and implementations of various modeling methodologies. These include JMAK (Avrami) models, topological models, and mesoscale physics-based models.

As far as only volume changes are considered, the analysis of void growth during plastic straining of a material can be reduced to the two simple cases of (i) a cylindrical cavity submitted to axial and axisymmetric radial remote loads and (ii) a spherical cavity submitted to remote uniform mean stress. The latter are investigated for materials exhibiting either a power law or a linear stress-strain rate relationship. The influence of strain hardening is also considered in the case of spherical geometry. Finally, inertia effects are investigated. It is shown that both the linear strain rate dependence and inertia effects are likely to decrease void growth rate and thus to improve ductility at high strain rate.

The overall plastic response of a sheet can be simply calculated from the knowledge of its various texture components, the behavior of them being described by the equations of continuum plasticity. It is shown, however, that the classical assumptions used for combining the elementary components can lead to significantly different predictions of the sheet behavior.

International audience

International audience; A beta-quenched titanium alloy was studied by means of microtomography. This technique provides three dimensional (3D) representations of the microstructure. It appears that the colonies have non-convex shapes and form an intricate aggregate. An algorithm of 3D image segmentation based on the orientation of the lamellae is presented. Its results are in agreement with those derived from a manual segmentation method, and allow the colonies to be examined individually. Further perspectives on the basis of this experiment are outlined.

Basic knowledge regarding kinematics and dynamics of grain boundaries in metals is first reviewed. Typical effects of grain boundary migration during hot deformation, i.e. flow stress softening and grain coarsening, are illustrated by a simple one-dimensional model. The two mechanisms of continuous and discontinuous dynamic recrystallization are then introduced and compared from recent experimental data. Semi-analytical models involving mainly strain hardening, dynamic recovery, low and high angle boundary generation and migration are proposed. Finally, possible transitions between the two varieties of dynamic recrystallization are discussed.

Publication suite à la confèrence : 8th Int. Conf. on Mechanical and Physical Behaviour of Materials Under Dynamic Loading (Dijon 2006); International audience; A new experimental torsion test is developed to achieve intermediate strain rates. The gauge length of the classical torsion bar (27 mm) is reduced within the range 0 to 5 mm. Analytical predictions with simple constitutive equation show that strain rates achieve the magnitude of 250 s - 1. A finite difference analysis is proposed to simulate the test with more evolved constitutive equations. A comparison between experimental and numerical results shows a good agreement.

Dynamic recrystallization mechanisms in an austenitic stainless steel and a nickel base superalloy are compared. In the latter alloy, recrystallization may occur by “continuous nucleation”, but develops slowly due to more efficient dynamic recovery, and reduced grain boundary mobility.

International audience; The "Iso-W" approach recently proposed to generate simple flow rules for two phase materials is extended to nonlinear viscoplastic constituents and generalized, which produces three families of models. Comparison with the Hashin-Shtrikman bounds leads to select the variant assuming strain rate compatibility and stress equilibrium. The Iso-W assumption is in fairly well agreement with the Mori-Tanaka and self-consistent models for mixtures of both linear and nonlinear materials.