Some Major Features in Texture and Anisotropy Field

This special issue of Advanced Engineering Materials is dedicated to Professor Richard Penelle, on the occasion of his official retirement after a fruitful career of more than half a century devoted to the study of texture and anisotropy and related topics. The editors thought that it might be interesting to compose a survey of the major developments that Professor Richard Penelle experienced when he was professionally active. This brief account below was established with the assistance of the dedicatee to make it even more personal. The description itself has no claim to be exhaustive and number of scientists cited has been restricted to a minimum, focusing on those who have been involved in this research area for a long time and whose activities had substantial crossovers with his own work. We apologize to all colleagues to whom all legitimate recognition has not been properly expressed. The notion of crystallographic texture or preferential orientations dates back to 1913 when Knipping attributed the appearance of a platinum diffraction pattern to the fact that the crystallites had a given orientation in relation to the sheet plane. From that time onwards, the “Texture” community proved to be very dynamic, as testified by the numerous technical and scientific developments that have appeared since the 1940s. Let us mention some of the major steps made in the field of texture, following a chronological order. At the end of the 1940s, the development of X-ray diffraction goniometers made it possible to characterize textures by measuring direct pole figures. The obtained pole figure is defined as the stereographic projection of the density of {hkl} plane poles in the reference frame of the sample. A crystallographic texture can also be represented by means of inverse pole figures representing the density of a specific sample direction (e.g. the Normal Direction) in the reference frame of the crystal. The two methods, on which the development of texture goniometry is based, are respectively Schulz's method in reflection and Decker, Asp & Harker's method in transmission. In the first one, the periphery of the pole figures cannot be measured, as opposed to the transmission method where this applies to the center. These limitations are mainly due to defocusing and a variation in diffracting volume. At a later stage, neutron diffraction was used to characterize textures, considering that neutrons offer the advantage of having a low absorption coefficient for most materials. Consequently, it is possible to use large specimens (1 cm3) with coarse grains and work in transmission without any defocusing corrections. However, the pole figures, be they measured by X-rays or neutrons, do not give direct access to the orientation density function f(g) and do not provide any information about the spatial distribution of the crystallites in the specimen. For this purpose, alternative techniques for the characterization of local orientation can be used. The continuous or harmonic method (H. M.) has been developed - simultaneously and independently - by Bunge and Roe. The discrete method was proposed first by R. O. Williams. The f(g) function represents a quantitative description of the crystallographic texture and makes it possible to derive some of the physical or mechanical properties of polycrystals from those of the single crystals. Later on - in the 1970s - the calculation of f(g) was further improved in France by three university research teams: a team in Orsay with Penelle as the leading scientist, working in Roe's formalism; another team with Esling, Humbert and Wagner in Metz who introduced the zero range method in Bunge's formalism, and finally the Baro, Ruer and Vadon team in Metz who developed the discrete vector method (V. M.). Knowing f(g), it became possible to calculate the physical properties of textured polycrystals, e.g. if a polycrystalline Fe-Si steel is considered as a superposition of single crystals, the value of the magneto-crystalline energy along a given direction is obtained as the mean value of single crystal values with f(g) as a weighting function. Two other examples can be provided: i) predicting the anisotropy of plastic deformation (normal and planar anisotropy) during deep drawing, which is a key parameter for sheet forming of low carbon steels in the automotive industry, and ii) simulating deformation textures. In the latter case, comparing the experimental and simulated textures enables to validate the relevance of polycrystal plasticity models. In both cases, in addition to the knowledge of f(g), it is also necessary to have a constitutive equation for the single crystal, including a plasticity criterion (e.g. Schmid law or the single crystal yield locus) and a grain interaction law. Moreover, it is also necessary to model the mechanical response, i.e. stress and strain states. Concerning the interaction law, two simple models have originally been used: Taylor and Sachs models. The Taylor model has been most widely used as it offers an appropriate and fast approach which offers a reasonable correspondence between experimentally measured and simulated deformation textures. In the late 1960s, Chin was one of the first to simulate deformation textures. Using the full-constraint Taylor model, Penelle's team predicted the position and the magnitude of the deep drawing ears in aluminum alloys, and later on the relaxed-constraint Taylor model was then introduced. In this approach it is suggested to relax certain shear components of the deformation tensor, when the deformed grains were very flat or elongated. However, we should bear in mind that the Sachs and Taylor models do not simultaneously satisfy the continuity conditions applying to strain and stress. Conversely, both conditions are satisfied with Kröner's model based on the interaction between an ellipsoidal inclusion (a grain) and its surrounding matrix or homogeneous equivalent medium (Eshelby model), the latter being assumed to represent the effective (usually isotropic) average properties of the polycrystal. This model is defined as self-consistent. However, we still come across flaws, in particular because of the anisotropy induced and/or the development of deformation inhomogeneities, such as shear bands. Even the Visco Plastic Self Consistent (VPSC) models do not offer the possibility of a complete and satisfactory solution of the plasticity of polycrystalline aggregates. The finite element method (F.E.M.) has been developed in more recent times as a complement to the plasticity theory of polycrystals to model non-uniform deformation. The n-point interaction models have been developed in the course of the past decade. In these models macroscopic deformation is imposed to the individual crystals in a polycrystalline aggregate, whereas the relaxation of shear strains along predefined sample planes and directions is made possible within a cluster of n grains in such a way that the relaxations cancel out each other over the entire volume of the cluster. These n-point interaction models proved to be quite successful, and are usually much faster than crystal plasticity FEM models. Other properties of industrial interest such as elastic properties, thermal expansion, internal stresses, magnetostriction, etc. have also been the subject of intensive investigation. The research on recrystallization and the formation of corresponding textures has fueled intense debating for several decades. As it can be assumed that the formation of the recrystallization texture depends on either the nucleation or the growth stage, Burgers submitted the concept of oriented nucleation, whereas Barrett and Beck that of oriented growth. Later, Cahn and Lücke have been fierce advocates of the two concepts, respectively. Interestingly, the debate has not abated up to the present, as both theories are acceptable, and the prevalence of which seems to depend on the experimental conditions. Parallel to the progress made in simulating deformation textures and the physical and mechanical properties of textured materials such as, for example, plastic deformation anisotropy during sheet forming, the emergence of new techniques, such as Transmission Electron Microscopy (TEM) and Electron Back Scatter Diffraction (EBSD) has made it possible to gain a better understanding of the evolution of the microstructure concurrently with texture. The EBSD detector mounted on a Scanning Electron Microscope by Dingley has been very successful since the 1980s in composing images of the microstructure based on local crystallographic contrast. There are two modes to record Kikuchi patterns, the manual and the automatic. In the latter, the sample is moved on a square or hexagonal grid via the microscope platform; an alternative method is by scanning the electron beam of the microscope with a fixed specimen. On the basis of the set of Kikuchi patterns recorded for the selected area of the specimen, it is possible to reconstruct a crystallographic orientation map of the microstructure. Therefore, it is also possible to identify the grain boundaries in relation to their characteristics, i.e. low angle, coincidence site lattice and high angle grain boundaries. This is known as orientation imaging microscopy (OIM®). The EBSD technique enables us to determine - over large areas - the surface crystalline orientation, the grain spatial distribution, the grain size and the grain shape. It also makes it possible to follow up the crystalline rotation field of each grain in a specimen during plastic deformation; this applies at least to small deformations. We are then able to check on the validity of the polycrystal plasticity models developed to simulate deformation textures. It is also possible to characterize the influence of the first neighbors surrounding a given grain on its plastic behavior. Moreover, the EBSD technique allows to study normal and abnormal grain growth. However, it is not possible to characterize the dislocation cells and subgrain growth during the early stages of primary recrystallization of severely cold-worked materials. This drawback has recently been eliminated in the wake of the recent developments concerning fully automated data collection and diffraction pattern indexing in the transmission electron microscope. Consequently, it is now possible to generate from the TEM, orientation imaging maps similar in nature to those obtained in SEM. Parallel to the progress made by experimental techniques, several teams have worked on the simulation of recrystallization and the grain growth phenomena, applying Potts' model, cellular automata or vertex models. As recrystallization and grain coarsening take place simultaneously, the evolution of the microstructure depends on the energy stored by dislocations and the interfacial energy. Thus, the energy stored by the dislocations of every texture component works as a driving force for recrystallization; it has been calculated from X-ray or neutron diffraction values of the broadening of diffraction lines and from TEM/SEM-EBSD measurements (cell size, cell misorientation) applying the Dillamore approach. It is worth emphasizing the benefit of using synchrotron radiation to perform in-situ experiments in relation to recrystallization or phase transformations. For several years the techniques of Severe Plastic Deformation such as Equal Channel Angular Extrusion (ECAE) or Accumulative Roll Bonding (ARB) have been used to produce bulk ultra-fine grained materials. ECAE allows in particular to produce simple shear as a unique industrial operation for microstructure and texture formation, opening new avenues for advanced materials. Bulk materials with ultra fine grains demonstrate outstanding high strength at room temperature (due to the Hall-Petch relationship), enhanced superplasticity at moderate temperatures and high corrosion resistance. Many works have been carried out during this period; an illustration of this is the wealth of contributions presented at the last ICOTOM Conference and the recent Texture and Anisotropy meetings held in Orsay, France in 2009 and in Dresden, Germany in 2010. However, one of the major problems posed by these materials is the lack of thermal stability of the ultra fine grained microstructure. Notwithstanding this progress, many research problems remain unresolved till now; including for instance, the substructure rearrangement during recovery and the influence of deformation inhomogeneities and material chemistry on the mobility of sub-boundaries and grain boundaries in the early stages of primary recrystallization or during abnormal growth. Another key issue is the influence of the gradient of the deformation energy stored at prior grain boundaries on the mechanisms of nucleation and subgrain growth. Efforts should be made in the field of simulation to include more physico-chemistry and micro-plasticity based approaches into the models used to describe the evolution of microstructure during plastic deformation of metals and alloys, and during static or dynamic recrystallization. All these issues of texture and anisotropy and their current development are being addressed during the annual meetings of the Belgian, Dutch, French and German “Texture and Anisotropy” communities organized under the aegis of the Société Française de Métallurgie et de Matériaux (SF2M) and the Deutsche Gesellschaft für Materialkunde (DGM). On April 03, 2009, Prof. C. Esling from Metz University and Dr. R. Penelle from the University of Paris-Sud 11 organized a “Texture and Anisotropy” symposium focusing on “Texture and Microstructure Control in Structural and Functional Materials” that was held at University of Paris-Sud 11. This symposium was preceded by a “Scientific day” organized by Dr. T. Baudin and Prof. C. Esling on April 02, 2009 with the focus on “Solid State Transformations – Consequences on Microstructures and Textures of Materials”. This meeting was dedicated to Dr. R. Penelle who was just retiring. Dr. R. Penelle has gained international recognition for his work in the field of textures, anisotropy and recrystallization (see the landatio by Prof. J. Philibert). About 80 scientists coming from 8 different countries attended this two-day symposium that witnessed a remarkable number of contributions including 14 invited lectures, 17 oral presentations and 9 posters. A selection of these presentations is published in the present special issue of AEM dedicated to Richard Penelle. The organizers would like to thank the President of the University of Paris Sud 11, the Division de la Recherche and the Institut de Chimie Moléculaire et des Matériaux d'Orsay for the financial support provided to hold this symposium.