Un modèle continue pour le transfert de glissement aux joints de grains

International audienceUsing a continuous representation of dislocations in elastoplastic polycrystals, we investigate slip transfer at grain boundaries by assessing the compatibility of the slip system shear rates with tangential continuity of the plastic distortion rate tensor at these interfaces. Fulfillment of this tangential continuity condition is needed for consistency of the continuous description of dislocations in polycrystals. We show that, in f.c.c. materials at moderate temperatures, this condition unequivocally translates into constraints on the slip rates on both sides of grain boundaries. Appended to the elastoplastic boundary value problem, it allows a complete determination of the slip system shear rates. An algorithm enabling the implementation of compatible slip transfer in both the finite element methods and the spectral methods based on Fast Fourier Transforms is provided in both standard crystal plasticity and the mechanics of dislocations fields.En utilisant une représentation continue des dislocations dans les polycristaux élastoplastiques, nous étudions le transfert de glissement aux joints de grains en évaluant la compatibilité des taux de cisaillement du système de glissement avec la continuité tangentielle du tenseur de taux de distorsion plastique à ces interfaces. La réalisation de cette condition de continuité tangentielle est nécessaire pour la cohérence de la description continue des dislocations dans les polycristaux. Nous montrons que, dans des matériaux c.f.c. à des températures modérées, cette condition se traduit sans équivoque par des contraintes sur les taux de glissement des deux côtés des joints de grains. Associé au problème de la valeur limite élastoplastique, il permet une détermination complète des taux de cisaillement du système de glissement. Un algorithme permettant la mise en œuvre d'un transfert de glissement compatible dans les méthodes par éléments finis et les méthodes spectrales basées sur la transformation de Fourier rapide est fourni à la fois dans la plasticité cristalline standard et dans la mécanique des champs de dislocations

Geometrically Nonlinear Field Fracture Mechanics and Crack Nucleation, Application to Strain Localization Fields in Al-Cu-Li Aerospace Alloys

International audienceThe displacement discontinuity arising between crack surfaces is assigned to smooth densities of crystal defects referred to as disconnections, through the incompatibility of the distortion tensor. In a dual way, the disconnections are defined as line defects terminating surfaces where the displacement encounters a discontinuity. A conservation statement for the crack opening displacement provides a framework for disconnection dynamics in the form of transport laws. A similar methodology applied to the discontinuity of the plastic displacement due to dislocations results in the concurrent involvement of dislocation densities in the analysis. Non-linearity of the geometrical setting is assumed for defining the elastic distortion incompatibility in the presence of both dislocations and disconnections, as well as for their transport. Crack nucleation in the presence of thermally-activated fluctuations of the atomic order is shown to derive from this nonlinearity in elastic brittle materials, without any algorithmic rule or ad hoc material parameter. Digital image correlation techniques applied to the analysis of tensile tests on ductile Al-Cu-Li samples further demonstrate the ability of the disconnection density concept to capture crack nucleation and relate strain localization bands to consistent disconnection fields and to the eventual occurrence of complex and combined crack modes in these alloys

Crystal plasticity modeling of the effects of crystal orientation and grain-to-grain interactions on DSA-induced strain localization in Al–Li alloys

International audienceWe develop a crystal plasticity model to investigate the coupled actions of crystal orientation, grain neighborhood and grain-to-grain elasto-plastic interactions on dynamic strain aging (DSA) and the onset and development of associated plastic strain localization in Al-Li alloys. Considering simple model multilayered microstructures with preferred orientations representative of rolled alloys, the aim is to identify grain orientation couples that can limit dynamic strain aging induced strain localization without compromising the flow stress and strain hardening properties. To this end, a slip system-based formulation of dynamic strain aging is implemented in a crystal plasticity finite element framework. The model validity is first checked with the simulation of a tensile specimen loaded at quasi-static applied strain rate. The introduction of dynamic strain aging allows predicting complex propagation of intense plastic localization bands. We further investigate the influence of crystal orientations on early strain localization in Al-Cu-Li-Mg alloys, by performing simulations representative of the early stage of a Kahn Tear test for single crystals and layered polycrystals. Using experimentally reported crystal orientations for rolled microstructures, the simulation results show that in both single and multilayered crystals, there is a strong influence of dynamic strain aging on localization patterns, as well as a significant orientation dependence. In multilayered crystals, the nature of strain localization can be remarkably modified when stand-alone crystals of a certain orientation are coupled with other orientations: strain localization may intensify or fade away depending on the coupling with neighboring orientations

A Fast Fourier Transform-based approach for Generalized Disclination Mechanics within a Couple Stress theory

International audienceRecently, a small-distortion theory of coupled plasticity and phase transformation accounting for the kinematics and thermodynamics of generalized defects called generalized disclinations (abbreviated g- disclinations) has been proposed. Then, a first numerical spectral approach has been developed to solve the elasto-static equations of field dislocation and g-disclination mechanics set out in this theory for periodic media and for linear elastic media using the classic Hooke’s law. Here, given a spatial distribution of generalized disclination density tensors in a homogenous linear higher order elastic media described, a couple stress theory with elastic incompatibilities of first and second orders is developed. The incompatible and compatible elastic second and first distortions are obtained from the solution of Poisson and Navier-type equations in the Fourier space. The efficient Fast Fourier Transform (FFT) algorithm is used based on intrinsic Discrete Fourier Transforms (DFT) that are well adapted to the discrete grid to compute higher order partial derivatives in the Fourier space. Therefore, stress and couple stress fields can be calculated using the inverse FFT. The numerical examples are given for straight wedge disclinations and associated wedge disclination dipoles which are of importance to geometrically describe tilt grain boundaries at fine scales in polycrystalline solids

Continuous description of the atomic structure of grain boundaries using dislocation and generalized-disclination density fields

AbstractAn atomistic-to-continuum method is developed to derive dislocation, generalized-disclination density fields and the associated elastic strain, rotation, curvature and second-distortion fields from the atomic structure of grain boundaries. From the relaxed and un-relaxed atomic positions, calculation of the transformation gradient feeds a mechanical framework, where discontinuities of the lattice elastic displacement and distortion (rotation and strain) are captured by smooth incompatible strain and second-distortion fields associated with the dislocation and generalized-disclination density fields, respectively. The method is applied to a copper symmetrical tilt boundary as obtained from molecular dynamics simulations. The core structure of the boundary is found to contain edge dislocations and dipoles of generalized-disclinations, including standard wedge-disclination dipoles. The latter reflect in particular localized shear and stretch discontinuities across the interface, in addition to the overall rotation discontinuity

Surface Damage and Treatment by Impact of a Low Temperature Nitrogen Jet

International audienceNitrogen jets under high pressure and low temperature have been introduced recently. The process consists in projecting onto a surface a low temperature jet obtained from releasing the liquid nitrogen stored in a high pressure tank (e.g. 3000 bars) through a nozzle. It can be used in a range of industrial applications, including surface treatment or material removal through cutting, drilling, striping and cleaning. The process does not generate waste other than the removed matter, and it only releases neutral gas into the atmosphere. This work is aimed at understanding the mechanisms of the interaction between the jet and the material surface. Depending on the impacted material, the thermo-mechanical shock and blast effect induced by the jet can activate a wide range of damage mechanisms, including cleavage, crack nucleation and spalling, as well as void expansion and localized ductile failure. The test parameters (standoff distance, dwell time, operating pressure) play a role in selecting the dominant damage mechanism, but combinations of these various modes are usually present. Surface treatment through phase transformation or grain fragmentation in a layer below the surface can also be obtained by adequate tuning of the process parameters. In the current study, work is undertaken to map the damage mechanisms in metallic materials as well as the influence of the test parameters on damage, along with measurements of the thermo-mechanical conditions (impact force, temperature) in the impacted area

Effects of the impact of a low temperature nitrogen jet on metallic surfaces

Lien vers la version éditeur: http://rspa.royalsocietypublishing.org/content/468/2147/3601.abstractThe technology of nitrogen jets impacting surfaces at low temperature has recently been introduced for surface cleaning/stripping. Under the impact of the jet, the material surface undergoes a thermomechanical shock inducing complex transformation mechanisms. Depending on the material and test parameters such as standoff distance, dwell time, upstream pressure, the latter include cleavage, cracking, spalling, blistering, grain fragmentation, phase transformation and ductile deformation. Quite often, these modes are superimposed in the same test, or even in the same material area. In this study, an overview of these mechanisms is proposed for metallic materials. Measurements of thermomechanical variables in the impacted area are presented and the influence of the test parameters on surface transformation is investigated. Grain fragmentation and ultrafast transport of nitrogen in a deep layer below the surface are explored

Vers une approche à champs moyens à longueurs internes validée par dynamique des champs de dislocations : application aux effets de taille de particules dures dans un matériau de type ferrite / carbures

Une approche à champs moyens à longueurs internes rend compte des effets de taille d’inclusions dures noyées dans une matrice ferritique. Une couche intermédiaire entre l’inclusion et la matrice reflète la présence de GND dues aux gradients de distorsion plastique. L’épaisseur de cette couche et ses effets sur l’écrouissage sont obtenus à l’aide d’une théorie mécanique des champs de dislocations basée sur l’incompatibilité de réseau et l’équation de transport des dislocations de Mura

Analyse de la stabilité des milieux élastiques et méthodes numériques

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Instabilités thermo-viscoplastiques aux grandes vitesses de déformation

The instability of plastic deformation is widely observed in most materials. It often results in a localization of plastic flow which acts as a precursor of failure. In order to investigate these phenomena, constitutive laws suited to large strains and to high strain rates have to be proposed. Kinematic hardening models are presented which are based upon different objective derivatives and exhibit shading memory effects. Next, an approach of textural softening of metals at high strain rates is given where the crystallographic slips are assumed to obey a linear viscous law. The implications of such laws on plastic instability are discussed. The competition for localization between stabilizing mechanisms (strain and strain rate hardening, inertia and thermal conductivity) and destabilizing ones (thermal and geometrical softening) is shown in simple tension. Inertia and thermal effects are emphasized since they can play a major part at high strain rates. The linearization methods are discussed; linear results are compared to nonlinear closed form or numerical calculations. The comparison with available experimental data shows that the observed dynamic increase and adiabatic decrease of materials ductility may be well described by these models. It is shown that instability and localization of deformation are different concepts, and that shear band formation is generally predicted by a localization (not instability) analysis. This is done by means of a relative perturbation method; such a method accounts for the unsteadiness of plastic flow. Instability criteria and localization is discussed. Closed form and numerical nonlinear instability and localization results, related to shear band formation in non-strain hardening materials, are presented. Under isothermal boundary conditions, a critical shear stress is show to exist, beyond which plastic deformation is unstable. For adiabatic boundary conditions, a nonlinear relative perturbation method provides approximate critical shear strain for localization. This result is compared to nonlinear numerical calculationsL'instabilité de la déformation plastique des matériaux est couramment observée lors de processus à grande vitesse. La localisation de la déformation qui en résulte peut provoquer la rupture. Son étude nécessite des lois de comportement adaptées aux grandes déformations et aux grandes vitesses de déformations et aux grandes vitesses de déformation. Nous présentons des modèles d'écrouissage cinématique en grande déformation, basés sur différentes dérivées objectives et pourvus d'effets de mémoire. Puis une approche de l'adoucissement textural des métaux aux grandes vitesses est proposée, où l'on considère que les glissements sur les plans cristallographiques suivent une loi visqueuse. Les conséquences sur l'instabilité de la déformation plastique sont discutées. Les influences des facteurs stabilisants : écrouissage, sensibilité à la vitesse, inertie, conduction thermique, et des facteurs déstabilisants : adoucissement thermique et géométrique, sur la ductilité sont illustrés en traction. L'accent est porté sur les effets d'inertie et les effets thermiques qui peuvent être prépondérants aux grandes vitesses. Les méthodes de linéarisation sont discutées. Des analyses non linéaires sont présentées, qui permettent de décrire l'accroissement dynamique de la ductilité, et son affaiblissement adiabatique. Les résultats sont comparés aux résultats expérimentaux disponibles. On montre que les concepts d'instabilité et de localisation de l'écoulement sont différents, et que la formation des bandes de cisaillement n'est pas en général correctement prédite par le concept d'instabilité, mais par celui de localisation. Une méthode de perturbations relatives est présentée qui prend en compte le caractère instationnaire de la déformation homogène, et permet d'étudier la localisation. Les critères d'instabilité et les critères de localisation fournis par la méthode relative sont comparés; tous sont confrontés aux données expérimentales. L'influence des défauts et de l'adiabaticité de la déformation sur l'instabilité et la localisation sont discutées. On présente des résultats non linéaires relatifs à la formation de bandes de cisaillement dans les matériaux sans écrouissage. Pour des conditions à la limite isothermes, on met en évidence une contrainte critique au-delà de laquelle la déformation plastique est instable. Pour des conditions adiabatiques, une méthode de perturbations non linéaires relative fournit une approximation de la déformation critique de localisation, qui est comparée à la valeur calculée numériquemen