Jean-Jacques Fundenberger

Modelling and prediction of mechanical properties for materials with hexagonal symmetry (zinc, titanium and zirconium alloys)

Abstract In this work we have modelled various mechanical properties for hexagonal materials having various textures and/or deformation mechanisms. The main purpose of this work was to determine with great accuracy the active deformation mechanisms and to evaluate the corresponding CRSS ratios. This study—carried out by optical and electron microscopy—is based on the statistical data obtained for the deformation mechanisms (frequency of occurrence) applying to each alloy. Though more sophisticated models are available, we used—in a first approach—the relatively simple Taylor model (constrained and relaxed variants) with the fairly reliable CRSS ratios we had previously assessed (accuracy around 10%) and used earlier for the modelling of the texture evolution. With these values, we then modelled the variation in the sheet plane of the yield stress, the plastic strain ratio, and the yield loci. The predicted curves were then compared with the experimental ones that had been drawn, including the margin of experimental error. In the case of TA6V we made a distinction between pyramidal 〈c + a〉+ and 〈c + a〉2− slip directions. The predicted yield loci of TA6V show the same asymmetry in tension and compression as the experimental curves.

EP – a program for determination of crystallite orientations from TEM Kikuchi and CBED diffraction patterns

Orientations of individual crystallites are of interest in many areas of research on polycrystalline materials (see e.g., Kocks et al., 1998). Analysis of Kikuchi patterns is one of the oldest and best established techniques of orientation determination. Convergent beam electron diffraction (CBED) patterns have the same geometry as Kikuchi patterns and can be used for determining orientations if a suf®cient acquisition solid angle is available. The program EP is a user interface linked with KiKoCh ± an engine for pattern indexing and for determination of orientations. EP allows diffraction patterns to be loaded from bitmap ®les and the crystallite orientation to be obtained by marking lines with a mouse; in good quality patterns lines can be detected automatically. A similar system has been described recently by Zaefferer (2000).

Orientation density function-controlled pole probability density function measurements: automated adaptive control of texture goniometers

A novel control of a texture goniometer, which depends on the texture being measured itself, is suggested. In particular, it is suggested that the obsolete control with constant step sizes in both angles is replaced by an adaptive successive refinement of an initial coarse uniform grid to a locally refined grid, where the progressive refinement corresponds to the pattern of preferred crystallographic orientation. The prerequisites of this automated adaptive control is the fast inversion of pole intensities to orientation probabilities in the course of the measurements, and a mathematical method of inversion that does not require a raster of constant step sizes and applies to sharp textures.

Orientation mapping by transmission-SEM with an on-axis detector.

Conventional orientation mapping in a scanning electron microscope (SEM) is a valuable technique for characterizing crystalline materials, but its application to ultrafine or nano-grain materials is limited by its spatial resolution. The resolution can be increased by collecting transmission diffraction patterns in SEM. In previous works, such patterns were collected using off-axis detectors in nearly vertical position. To avoid some drawbacks of such arrangement, a new configuration was devised in which the scintillator is located underneath the thin foil on the optical axis of the microscope, and the light is reflected towards the camera by a mirror. This simple configuration gives intense patterns even at very low probe currents, and can be potentially used for collecting maps of relatively high spatial resolution. Example maps reveal details with dimensions of about 5nm. Because of its resolution and geometric simplicity, the proposed configuration will open new opportunities in SEM-based characterization of nanocrystalline materials.

Texture gradient in rolled zinc sheets

The bendability behavior of zinc-copper-titanium alloys at low temperature is an important problem for industrial application as far as the building industry is concerned. Microcracks appear in these alloys and grow when the deformation temperature decreases. This work aims at evaluating the texture gradient in the thickness of the sheet and understanding the reason of its development in this kind of alloys. In this way, some results of texture modelling are presented. These calculations were carried out in order to determine the influence of the introduction of shear and/or friction coefficients in the gradient tensor of deformation for modelling the rolling texture.

Texture Evolution in Commercially Pure Al during Equal Channel Angular Extrusion (ECAE) as a Function of Processing Routes

FCC metals with different stacking fault energy (SFE), namely Al, Cu and Ag have been investigated for the evolution of crystallographic texture during ECAE deformation using Route A. Different materials with different SFE result in their characteristic textures. The results have been analysed on the basis of microstructural features and related established concepts on texture evolution in FCC metals during other deformation modes.

Experiments and Modelling of ECAE Textures of f.c.c. Polycrystals

FCC metals with different stacking fault energy (SFE), namely Al, Ag and Cu have been investigated for the evolution of crystallographic texture during ECAE deformation using Route A. Different materials with different SFE result in their characteristic textures. The results have been analysed on the basis of microstructural features and related established concepts on texture evolution in FCC metals.

Textures and Anisotropy of Titanium Alloys

The present paper deals with the texture, deformation mechanisms and mechanical properties of α and near α alloys (i.e. with hexagonal symmetry matrix). For items related aspects are reviewed: 1) texture formation during thermomechanical treatments depending on the composition of the alloys 2) determination of active deformation mechanisms 3) mechanical properties depending on the texture and deformation mechanisms 4) modelling and prediction of mechanical properties. For all the alloys, the texture evolution during the whole process must be considered especially during the hot rolling taking into account phase transformations. In the same way, the texture evolutions observed during cold rolling will be explained in terms of the evolution of the microstructures and deformation mechanisms. Finally, a classification of the sheet textures is made as a function of the composition of the alloys. In titanium α or near α alloys, the deformation can be accommodated by both glide and twinning. The selection of the different mechanisms activated during plastic deformation depends of the alloying elements, the grain size, grain orientations and the condition of the test (T,e,e). We present a method to determine different types of glide (prismatic, basal, pyramidal slips) and twinning systems activated as well as their relative critical shear stress ratios. The initial textures of the sheets are generally sharp after thermomechanical treatments and many properties such as yield stress are anisotropic. In addition, yield stress and ductility can be directly correlated with the deformation mechanisms activated in the sample to accommodate the deformation. The present work demonstrates the qualitative correlations between textures, deformation mechanisms and mechanical properties for all the alloys studied. Using different approaches (Taylor or Self - Consistent models), it is possible to model the texture evolution during the deformation taking into account the initial texture and the deformation mechanisms actived, and also to predict the mechanical properties of the studied alloys. Predicted and experimental curves are compared and a discussion of the most important parameters emphasises the great importance of the behavior parameters (i.e. the deformation mechanisms for successful modelling. Insufficient knowledge of the critical resolved shear stresses remains the main obstacle and explains why some results may be questionable. In conclusion the review identifies the next steps which are necessary in order to make progress when establishing relationships between textures -microstructures - mechanical properties.

Texture Evolution in FCC Metals during Equal Channel Angular Extrusion (ECAE) as a Function of Stacking Fault Energy

FCC metals with different stacking fault energy (SFE), namely Al, Cu and Ag have been investigated for the evolution of crystallographic texture during ECAE deformation using Route A. Different materials with different SFE result in their characteristic textures. The results have been analysed on the basis of microstructural features and related established concepts on texture evolution in FCC metals during other deformation modes.

Local texture and microstructure in cube-oriented nickel single crystal deformed by equal channel angular extrusion

Local texture and microstructure was investigated to study the deformation mechanisms during equal channel angular extrusion of a high purity nickel single crystal of initial cube orientation. A detailed texture and microstructure analysis by various diffraction techniques revealed the complexity of the deformation patterns in different locations of the billet. A modeling approach, taking into account slip system activity, was used to interpret the development of this heterogeneous deformation.