QUANTITATIVE ANALYSIS OF HETEROGENEITIES OF DEFORMATION WITH THE GRID METHOD

http://www.imim.pl/files/archiwum/Vol1_2009/7-18.pdfInternational audienceThe article deals with the measurement of heterogeneous deformations during the plastic flow of metals. To encode de surface of the test-pieces, transferable carbon grids were used. They proved a reliable technique in the conditions of the experiments (channel-die, step of 100 mu m), even for highly localized deformations. To calculate the displacement field, the grid method was chosen. Up to now it has been developed for elastic structures. It is extended here to large displacement situations. Results are analysed from a metrological point of view and the resolution is kept at 1/100(th) fringe, the final spatial resolution being at two fringes. The mean deformation is 15% between each loading step. Displacement maps, or better, principle shear strain maps, derived from the previous ones, show the presence of a preferential direction even at low deformation levels. They put forward the decisive role played in the development of heterogeneities by the corners of the test-piece, sensitive in channel-die compression because two of their faces are submitted to friction while the third is free. This first attempt of using the grid method for large displacements will be optimized in the future by automating the iterative procedure and reducing the calculation time

Traitements thermomécaniques des colonies de lamelles parallèles du Zircaloy-4 trempé-b.

Le Zircaloy-4 utilisé comme matériau de gainage des combustibles nucléaires est trempé b puis filé sur aiguille dans le haut domaine a. La microstructure de trempe, qui conditionne les opérations de mise en forme ultérieures, se présente sous deux formes : vannerie ou colonies de lamelles parallèles. Ces dernières se fragmentent difficilement lorsqu elles sont normales à l effort de compression. La thèse étudie trois aspects de ce phénomène. Le premier concerne les conditions de trempe : temps d homogénéisation dans le domaine b et vitesse de refroidissement. Une adaptation au Zircaloy-4 de l essai Jominy montre que ces deux paramètres ont une influence décisive sur la taille des colonies (par l intermédiaire de la taille des grains b) et sur l épaisseur des lamelles. Le second présente des essais de compression selon trois directions orthogonales. La troisième passe fragmente les colonies qui ont résisté aux deux autres et affine sensiblement la microstructure. A 750C en particulier, un cycle de trois passes permet d obtenir des grains de 30 m ; mais les meilleurs résultats sont obtenus à 650C (grains de 17 m) et à grande vitesse de déformation (grains de 10 m).Dans le troisième, un modèle de plasticité cristalline tridimensionnel implémenté dans le code d éléments finis ABAQUS simule le comportement des lamelles sous l effet de la contrainte. Il prend en compte leur orientation cristallographique en plus de leur morphologie. Dans la plupart des cas, les lamelles s incurvent dès le début de la déformation macroscopique du matériau, ce qui induit des localisations de la déformation.Zircaloy-4 used for fuel cladding in nuclear plants is quenched from the b range and then extruded and rolled in the upper a range. At the start of this mechanical process, the alloy possesses a lamellar, Widmanstätten microstructure. This one, which is critical for the subsequent forming process, appears under two forms: basket weave and colonies of parallel lamellas. These are difficult to break when they are normal to the compressive load. The thesis studies three aspects of this phenomenon. The first concerns the quenching conditions: homogenization time in the b range and cooling rate. An adaptation of the Jominy test to Zircaloy-4 shows that these two parameters have a decisive influence on the size of the colonies (via the b grain size) and the thickness of the lamellas. The second presents compression tests under three orthogonal directions. Results show that the third pass breaks the colonies that resisted to the previous attempts and refine noticeably the microstructure. In particular at 750C, three passes are sufficient to obtain grains of 30 m, but the best results are obtained at 650C (grains of 17 m) and at high strain rate (grains of 10 m). Thirdly, a three-dimensional crystal plasticity model is implemented in the finite elements code ABAQUS to simulate the behaviour of lamellas under stress. It takes into account their crystallographic orientation in addition to their morphology. In most cases, the lamellas bend at the onset of the macroscopic deformation, which induces localization phenomena.ST ETIENNE-ENS des Mines (422182304) / SudocSudocFranceF

Shear on the Flow Surface of Metallic Crystals

11p. Publié suite au congrès SHEAR07, Nancy 4-7 septembre 2007, dans n° spécial SHEAR BEHAVIOR AND RELATED MECHANISMS IN MATERIALS PLASTICITYInternational audienceThe present article addresses the following question: How is it that shears are so common in the plastic deformation of metallic alloys? An answer is sought in a geometric description of the shear flow when the deformation is produced by slip systems gliding according to the Schmid law. Such flows are represented schematically by what is called “simple shear” and a kinematic study is done of the way these shears can be produced by the joint activity of various slip systems. This implies specific conditions on the glide rates, which can be known analytically thanks to adequate parametrizations. All the possible shears have been calculated in the case of cubic metals deforming with identical critical resolved shear stresses (Bishop and Hill polyhedron). Three dimensional representations are given in the space of the Bunge angles associated with the principal directions of the shears. A special attention has been given to the number of slip systems involved. Most of the shears are not far from some combination of two or three systems. This is quantified by defining the misorientation omega between a shear taken at random and the set of shears produced by the glide on two or three octahedral slip systems. It is found that in most cases, omega<15 deg. The maximum value of omega (30.5 deg) is found for the orientations called Cube and U in rolled metals

Bifurcation into shear bands on the Bishop and Hill polyhedron. Part II: Case of the vertices

International audienc

Contribution à l'étude de l'instabilité de déformation plastique dans les cristaux cubiques à faces centrées

La thèse concerne des mono- et des polycristaux déformés en channel-die. Les hétérogénéités de déformation plastique sont étudiées à l échelle mésoscopique (longueur caractéristique : 100 micrométre ). Trois techniques spécifiques sont utilisées :des grilles de carbone transférables, qui sont appliquées sur le côté de l éprouvette et suivent sa surface jusqu à des déformations élevées: pour la de formation globale, beaucoup plus localement, - des microfoyers rayons X, technique lente mais fort efficace qui fonctionne sur les métaux légers, fortement écrouis et qui n oblige pas à repolir entre deux observations, - la méthode de grille pour l analyse des images numériques, dans une version initialement développée à Saint-Etienne et adaptée aux grandes déformations pour le présent travail.Une typologie de onze orientations cristallographiques est présentée. A l échelle mésoscopique, elle montre des hétérogénéités intrinsèques (dues au matériau lui-même) et d autres extrinsèques, provoquées par le contact avec l enclume et le poinçon. BeaucBeaucoup de ces hétérogénéités prennent la forme de bandes de déformation qui s initient aux coins de l éprouvette, et induisent des cisaillements dans le plan de compression. Les parts respectives prises dans la rotation de corps solide de l éprouvette par la rotation cristalline et par la rotation due à l activité des systèmes de glissement varient fortement selon les orientations. Les calculs théoriques comprennent un modèle de déformation phénoménologique du monocristal basé sur une approximation polynomiale de la surface d écoulement. Dans les limites de l analyse homogène de la déformation des éprouvettes, il rend compte de la rotation des monocristaux en compression par channel-die et il a été introduit dans un critère de bifurcation.The Ph. D. deals about single and poly-crystals of aluminium compressed in channel-die. The heterogeneities of the plastic deformation are studied at the mesoscopic scale (characteristic length: 100 micrometre). Three specific techniques are used:- fiducial carbon grids which are transferred on to the side of the test-piece and follow its surface up to high strains: global strain beyond , localized ones much higher, - microfocus X-ray analysis, a slow but most efficient technique which works on light, heavily strained metals and needs no polishing of the test-piece between two steps of deformation,- grid method for the analysis of digital images, in a version initially developed in Saint-Etienne for elasticity and extended to large strains for this study. A typology of the heterogeneities specific to each of 11 crystallographic orientations is presented. At the mesoscopic scale, it puts in evidence material instabilities along with extrinsic ones, due to the contact with the die and the indenter. Most heterogeneities take the form of deformation bands initiating at the corners of the sample, and cause shear in the plane of compression.The respective parts played by the crystal lattice rotation and by the rotation due to the glide of the slip systems in the global material rotation are found contrasted according to the orientations. Theoretical calculations include a phenomenological model of deformation of the single crystal based on a polynomial approximation of the flow surface. Within the limits of the homogeneous analysis of the deformation of the test-pieces, it captures the rotation of crystals in channel-die compression and has been introduced into a bifurcation criterion.ST ETIENNE-ENS des Mines (422182304) / SudocSudocFranceF

Homogeneity and heterogeneity of single crystals in channel-die compression; Representation of the yield locus

Publié suite à une conférence invitée au congrès : Symposium on Texture and Microstructure Analysis of Functionally Graded Materials, Cracow, POLAND, OCT 03-07, 2004 Pas de DOI : http://www.imim.pl/files/archiwum/Vol1_2005/art.nr.9.pdfInternational audienceA polynomial approximation of the flow surface of single crystals deforming plastically on various slip systems is considered. Because it involves an exponent n, it is known as the power law. It is shown that, by introducing deviations from the Schmid law (but deviations not discernible by measurement), an extension of the normality rule can be proposed: not only the flow direction, but also the rate of rotation due to the glide on the slip systems are obtained in a single algebraic formula. The validity of all this is assessed by comparing its predictions with the results of the. compression of single crystals in channel-die. The lateral reactions and the lattice rotations have been measured in typical rolling orientations and found in good agreement with the calculations

The occurrence of shear banding in a millimeter scale (¯1 ¯23)[634] grain of an Al-4.5% Mg alloy during plane strain compression

International audienc

Bifurcation into shear bands on the Bishop and Hill polyhedron - Part III: Case of the edges of dimension one

Pas de DOI : http://am.ippt.gov.pl/contents_pdf/1219334403.pdfInternational audienceTHE PRESENT PAPER ends a series of three papers devoted to the micro-mechanical conditions which render possible the appearance of shear bands in crystalline materials. It presents the results on the edges of dimension 1 (encompassing the states of the deviatoric stress applied between two vertices of the Bishop and Hill polyhedron). They show that bifurcation is possible with a relatively small number of active slip systems, in conditions of strain hardening which are of the same order of magnitude as those at the vertices. An application is given to the case of the C {112} oriented single crystal compressed in a channel die. The characteristic experimental feature: appearance of two successive sets of bands (111) [11-2] and (11-1) [112] is explained in terms of the most favoured bifurcation planes and the local rotation of the crystal. Though convincing to predict the onset of shear bands, the above calculations do not provide a description of their intergranular development, especially crossing of the grain boundaries, since at this stage the material has been too much affected by the intense shearing to be treated by a method of bifurcation