Francis Wagner

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.

Evolution of recrystallisation texture and microstructure in low alloyed titanium sheets

The evolution of microstructure and crystallographic texture in low alloyed titanium sheets, initially deformed by 80% cold rolling, are investigated at different stages of the recrystallisation process. Optical and transmission electron microscopies, as well as X-ray diffraction and EBSD are used to provide information about recrystallisation mechanisms and kinetics. Orientation Density Function (ODF) differences are used to quantitatively compare recrystallised and deformed states. The main texture features of the deformed state evolve only slightly during the primary recrystallisation. The major changes in texture result from secondary recrystallisation or grain growth. Primary recrystallisation can be roughly separated into two stages. The first one is very fast and corresponds to the appearance of new grains in about 80% of the material volume. The second stage is more sluggish. It corresponds to the disappearance of the so-called “white grains”, which did not twin during deformation due to their stable orientation near {ϕ1=0°, φ=45°, ϕ2=0°}. Recovery is an important mechanism throughout the process and deformation heterogeneities must be taken into account for a good understanding of the recrystallisation in titanium.

Phase transformations and inherited lattice preferred orientations: implications for seismic properties

In phase transitions via either the martensitic (diffusionless shear) or nucleation and growth mechanism a specific orientation relationship may exist between the two phases. In cases where the orientation relationship is known, the lattice preferred orientation (LPO) inherited by the new phase may be calculated from the LPO of the old phase. The method of calculation is presented in a form suitable for the spherical harmonic method of texture analysis using the orientation distribution function (ODF). Examples are presented for the α-β-quartz, calcite-aragonite, orthopyroxene-clinopyroxene and olivine-spinel transformations. The seismic properties of the transformed and untransformed phases are calculated from the ODF and the single crystal elastic constants. In particular the α-β quartz transformation is considered in detail. The quartz polycrystal is very anisotropic in the alpha field (Vp anisotropy coefficient, A = 8.1%) and almost isotropic in the β-field (A = 2.1%). The transition is accompanied by Vp velocity increase of 0.6 km/s. In the other example discussed, olivine-β-spinel, there is also a decrease in Vp anisotropy coefficient from 11.1% (olivine) to 4.0% (β-spinel). The estimate of the volume fraction of olivine at the 400 km discontinuity (associated with this phase transition) is shown to depend on the direction of wave propagation.

Modelling of texture evolution for materials of hexagonal symmetry. I: Application to zinc alloys

Abstract This work describes the texture and microstructure evolution during cold rolling of zinc alloys. The choice of the Taylor model and its applicability to the ZnCuTi alloy are being discussed. The use of this kind of model in the case of ZnCuTi alloys permits to predict, with a good agreement, the texture evolution by cold rolling up to 80% reduction. The conditions of occurrence of various texture components are discussed. The authors compare their results with those published in the literature and compare also their results with those obtained according to different models (Sachs, Taylor..). They show, in particular, that the hypotheses of the model have to be in accordance with the evolution of the microstructure on the one hand and that the critical stresses of the deformation systems have to be well known on the other hand.

Quantification of dislocation structure heterogeneity in deformed polycrystals by EBSD

Plastic deformation in polycrystalline materials involves a complex interaction of dislocations with defects in the lattice. The geometrically necessary component of the dislocation density can be quantified to some extent using data obtained from automated electron backscatter diffraction scans over planar regions or volumes using the three-dimensional imaging techniques that are currently available. Reliable measurements require that the step size of the orientation data used in determination of geometrically necessary dislocation densities be on the scale of the microstructural information. Measurements were performed in deformed Cu, Al and steel specimens. Geometrically necessary dislocation density in Cu deformed 10% in compression was about 15–30% of the overall estimated dislocation density. Measurements in Al demonstrate that three-dimensional estimates are on the order of 1.2–2 times the values obtained from 2D measurements on the same structures. Analysis of interstitial free steel specimens shows an increase in average geometrically necessary dislocation density by an order of magnitude for specimens deformed to 12% tensile deformation elongation.

Development of preferred orientation in plane strain deformed limestone: Experiment and theory

Carbonate rocks deform preferentially by twin gliding on e={01¯18} and slip on r ={10¯14} and f={02¯21}. In polycrystalline aggregates strong textures develop. We report on experimentally produced textures in triaxial plane strain geometry with orthorhombic symmetry at 200° C and 400° C. Pole figure of the experimentally deformed specimens are compared quantitatively with theoretical simulations based on the Taylor theory using both slip and mechanical twinning as mechanisms. Agreement at low and high temperature is satisfactory and documents that models developed for f.c.c. metals can be applied to low symmetry minerals provided that deformation mechanisms are known and that mechanical twinning is properly accounted for. Comparison with experimental results indicates that strain was nearly homogeneous at the conditions considered and the same may apply to many geological textures. Three texture types are described which are differentiated mainly by the relative importance of e twinning.

Accuracy of orientation distribution function determination based on EBSD data‐A case study of a recrystallized low alloyed Zr sheet

The question of the statistical accuracy of EBSD data for global texture calculation was re‐explored on the basis of a very large grain population (83 000 grains measured on a recrystallized low‐alloyed Zr sheet). Previous works aimed mainly at identifying and quantifying the main texture components and were based on much smaller data sets. The present work attempts to quantify the accuracy of the complete texture, including low‐density regions of the orientation space. For that purpose, a new statistical parameter, VΔ, based on the calculation of texture difference functions is proposed. This parameter has two main advantages: it is equally sensitive to both high and low peaks of the orientation density function (ODF), and it has a physical interpretation because it is the material volume fraction corresponding to the difference between a given ODF and a reference ODF (considered, or known to be close to the truth). Two main variables were studied: the number of grains taken into account and the peak width ϕ0 of Bunges ‘Gaussian’ model density used as kernel for the actual analysis. The orientation distribution functions were computed by nonparametric kernel density estimation with harmonics up to the order of 34. Minimizing the value of VΔ serves as the objective function for optimizing the peak width ϕ0 as a function of the number of grains. The properties of the VΔ parameter also allows for the definition of a method for estimating the accuracy of a given texture that has been obtained from a limited number of grains, without knowing the true texture of the investigated material.

Optimization of the Positivity Method in Quantitative Texture Analysis

The direct calculation of the three-dimensional orientation density function (ODF), from its two-dimensional projections, the pole figures, yields only the reduced or even ODF, (g), which has usually negative values. The positivity method allows the determination of a physical acceptable positive ODF, f(g), best compatible with the experimental pole figures. The algorithm for the searching of the positive solution can be substantially improved in computing at each iteration step, the solution having the minimal distance to the set of positive functions.

Grain Growth Texture Evolution in Zirconium (Zr702) and Commercially Pure Titanium (T40)

Primary recrystallization of a 80% cold–rolled T40 or Zr702 sheets leads to equiaxed microstructures. Subsequently, only normal grain growth takes place in T40 while a few grains can grow abnormally after sufficient time at high annealing temperature (close to the transus) in Zr702. The grain sizes reached after extended grain growth at moderate temperatures in Zr702 are smaller than in T40. The presence of precipitates in Zr702 is probably responsible for this and also for the abnormal phenomena observed at high temperature in this material. The texture changes occurring in both materials under normal grain growth conditions (often roughly described as “30° rotation around c axes”) are due to the development of the largest grains produced by the primary recrystallization. These large grains are preferentially oriented around {j1=0°, F=30°, j2=30°} for T40 and around {j1=0°, F=25°, j2=30°} for Zr702, orientations which become predominant after extended grain growth.

Experimental Investigations of Recrystallization Texture Development in Zirconium (Zr702)

The microstructure and crystallographic texture in zirconium (Zr702) sheets, initially deformed by 80% cold rolling, are investigated at different stages of the primary recrystallization. Inhomogeneities were observed in the deformed microstructure at different scales down to the submicrometer range. The influence of these inhomogeneities on the local recrystallization mechanisms is discussed. The measurement of the orientation of the new grains shows that the nucleation is definitely not oriented. Since the global texture change is very slight, recrystallization by subgrain growth is probably one of the most important mechanism during the recrystallization process in zirconium.