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Probing the strain locally and throughout the bulk of various materials has long been of interest in Materials Science. This article presents a general methodology for assessing the plastic strain in terms of the displacement gradient tensor throughout the bulk of opaque samples. The method relies on a homogenous distribution of marker particles throughout the bulk of a sample, markers which are detected through the application of synchrotron X-ray tomography. Making use of the morphology of individual markers, motion of individual markers is tracked during deformation allowing the local displacement field to be determined throughout the bulk. The local displacement gradient tensor is derived from the displacement field. Spatial resolution is directly related to marker particle density in the sample, here 30 μm. The accuracy of the displacement gradient tensor calculation is dependent on the accuracy with which each marker position is determined and is shown to be in the range from 0.005 to 0.012.

Three-dimensional X-ray diffraction (3DXRD) is used to characterize the nucleation and early growth of individual bulk nuclei in situ during recrystallization of 92% cold-rolled copper. It is found that some cube nuclei, but not all, have a significantly faster initial growth than the average growth kinetics. These results are discussed and compared to previous 3DXRD results for recrystallization of aluminum alloys, and implications of the results on modeling of recrystallization are considered. Finally, a new 3DXRD technique suitable for non-destructive 3D characterization is outlined and its potential for recrystallization studies is discussed.

The three-dimensional X-ray diffraction (3DXRD) microscope has become a mature tool to investigate the microstructure in the bulk of polycrystalline materials. The present paper describes the 3DXRD method together with two applications. The first application presented is a study of grain rotations during plastic tensile deformation of polycrystalline aluminium. The second is the acquisition of a video revealing the 3D growth of an embedded nuclei during recrystallization of a deformed aluminium sample.

Summary By combining a synchrotron X-ray source and the microtomography technique, the displacement gradient tensor components can be measured directly throughout the volume of a metal sample containing highly absorbing marker particles to detect material flow. The present article describes application of these techniques to compression of a rectangular Al–W specimen with a central hole. The results show that the externally imposed axial displacement gradient is accommodated mainly in two 45° shear bands passing through the hole. A simple deformation analysis provides insight into shear band formation.

Newly developed experimental methods allow the extension of surface strain measurements into three dimensions throughout the bulk of opaque materials. By comparing two specimens with different geometries but consisting of similar materials under compression deformation, the ability of one of these new methods to distinguish between homogeneous and heterogeneous response to identical macroscopic boundary conditions is illustrated. Extending a previous study of a specimen deforming homogeneously to the entire specimen volume rather than a small subvolume, the effect of the marker particles on the material properties is discussed.

By diffraction of high-energy synchrotron X-rays, the variance of the axial lattice strains of individual grains is measured during tensile loading of a weakly textured copper polycrystal. Peak profiles are measured for {4 4 0} reflections arising from 20 bulk grains, all of which are at least one average grain diameter below the surfaces within a 0.2-mm thick specimen. The reflecting lattice planes are all perpendicular to the tensile axis. The variance in lattice strain between grains can therefore be attributed to differences in the boundary conditions imposed by the different sets of neighboring grains. The results are compared to finite-element modelling (FEM). Up to the highest applied strain of 2%, the experimental and FEM values are in fair agreement and the standard deviations may be roughly approximated as 6% of the average axial lattice strains.

We observed the in situ growth of a grain during recrystallization in the bulk of a deformed sample. We used the three-dimensional x-ray diffraction microscope located at the European Synchrotron Radiation Facility in Grenoble, France. The results showed a very heterogeneous growth pattern, contradicting the classical assumption of smooth and spherical growth of new grains during recrystallization. This type of in situ bulk measurement opens up the possibility of obtaining experimental data on scientific topics that before could only be analyzed theoretically on the basis of the statistical characterization of microstructures. For recrystallization, the in situ method includes direct measurements of nucleation and boundary migration through a deformed matrix.

A reconstruction method is presented for generation of three-dimensional maps of the grain boundaries within powders or polycrystals. The grains are assumed to have a mosaic spread below 1°. They are mapped by diffraction with a wide beam of hard X-rays, using a setup similar to that of parallel-beam absorption contrast tomography. First the diffraction spots are sorted with respect to grain of origin. Next, for each grain the reconstruction is performed by an algebraic algorithm known as three-dimensional ART. From simulations it is found that reconstructions with a spatial accuracy better than the pixel size of the detector can be obtained from as few as five diffraction spots. The results are superior to three-dimensional reconstructions based on the same data using a variant of the filtered back-projection algorithm. In comparison with layer-by-layer type reconstructions based on the two-dimensional ART algorithm, as introduced by Poulsen & Fu [J. Appl. Cryst.(2003),36, 1062–1068], the quality of the maps is found to be similar, provided that five to ten spots are available for analysis, while data acquisition with the three-dimensional method is much faster. The three-dimensional ART methodology is validated on experimental data. With state-of-the-art detectors, the spatial accuracy is estimated to be 5 µm.

A 3D map of an interior grain and its crystallographic orientation in a single-phase bulk sample has been obtained non-destructively, for the first time, by 3DXRD microscopy using an algebraic reconstruction method. The method is new and has potentials for in situ 3D mapping of structural changes during for example annealing.

The recrystallization kinetics of a 90% cold-rolled commercial aluminium alloy AA1050 annealed at 270 °C has been investigated by use of 3-dimensional X-ray diffraction (3DXRD) microscopy. For the first time growth curves of a large number of individual bulk grains have been measured in situ during recrystallization providing unique information on the nucleation and growth behaviour of the individual grains. From observations of 244 individual growth curves, it is found that each grain has its own growth kinetics. The orientation dependencies of the recrystallization kinetics are investigated by grouping the measured growth curves into cube, rolling and other orientation classes. Based on analysis of the growth curves, distributions of nucleation time, grain size and growth rate has been derived, and are used for a discussion of the recrystallization kinetics of aluminium AA1050.

A universal method is presented for characterising the three-dimensional (3D) plastic displacement gradient field in bulk materials that contain particles or voids observable by X-ray tomography. Millimetre sized samples are investigated by absorption contrast microtomography using high intensity X-rays from a synchrotron source. The positions of dispersed marker particles are determined as a function of imposed strain. The particle diameter can be in the micrometre range, and the volume fraction can be less than 1%. The method is demonstrated by evaluation of compression deformation of a cylindrical Al specimen containing W marker particles. By interpolating the displacement gradient components determined at each particle on a 30×30×30 μm 3 grid, 3D maps of the displacement gradient components are obtained with a resolution of 10 −2 in each component. Limitations of the method are discussed, and the potential for application in materials science is outlined.

Three-Dimensional X-Ray Diffraction (3DXRD) microscopy, an emerging characterisation tool based on high energy synchrotron radiation is presented. The 3DXRD microscope located at the Materials Science beam line at ESRF is dedicated to local μm scale structural characterisation within bulk materials. It is capable of providing information on position, volume, crystallographic orientation, and stress-state of hundreds of embedded grains simultaneously. Furthermore for recrystallized materials three-dimensional maps of the grain boundary morphology can be produced with a spatial resolution of 5 μm. The capabilities of the method is illustrated with a number of applications from the field of metallurgy, but the technique applies equally well to a wider range of materials science problems.

A fast and non-destructive method for generating three-dimensional maps of the grain boundaries in undeformed polycrystals is presented. The method relies on tracking of micro-focused high-energy X-rays. It is verified by comparing an electron microscopy map of the orientations on the 2.5 × 2.5 mm surface of an aluminium polycrystal with tracking data produced at the 3DXRD microscope at the European Synchrotron Radiation Facility. The average difference in grain boundary position between the two techniques is 26 µm, comparable with the spatial resolution of the 3DXRD microscope. As another extension of the tracking concept, algorithms for determining the stress state of the individual grains are derived. As a case study, 3DXRD results are presented for the tensile deformation of a copper specimen. The strain tensor for one embedded grain is determined as a function of load. The accuracy on the strain is Δ∊ ≃ 10−4.

A method for non-destructive characterization of plastic deformation in bulk materials is presented. The method is based on X-ray absorption contrast micro-tomography using X-rays from a synchrotron radiation source. The method can be applied to materials that contain marker particles, which have an atomic number significantly different from that of the matrix material. The size of the marker particles can be 1–2 μm and their positions ( x , y , z ) are determined as a function of strain. The use of the method is demonstrated by a compression study of an aluminium specimen containing tungsten marker particles.

Good dispersion of modified laponite clay was achieved in polybenzimidazole (PBI) solutions which, when cast and allowed to dry, resulted in homogeneous and transparent composite membranes containing up to 20wt% clay in the polymer. The clay was organically modified using a series of ammonium and pyridinium salts with varying polarity and hydrogen-bonding capacity. Clay modification by ion-exchange reactions involving replacement of interlayer inorganic cations was confirmed using X-ray photoelectron and infrared spectroscopy techniques. The cast PBI membranes were characterized by their water uptake, acid doping and swelling, tensile strength, conductivity and hydrogen permeability as well as by fuel cell tests. For the composite membranes, high acid doping levels were achieved with sufficient mechanical strength and improved dimensional stability or reduced membrane swelling. At an acid doping level of 12mol H 3PO 4 per monomer unit, proton conductivity as high as 0.12Scm -1 was obtained at 150°C and 12% relative humidity. The composite membranes exhibited hydrogen permeability ranging from 0.6 to 1.2×10 -10molcm -1s -1bar -1 from 100 to 200°C, which was five times lower than that of acid-doped pristine PBI membranes. In accordance with the hydrogen permeability measurements, fuel cell tests exhibited high open circuit voltages (i.e., 1.02V) at room temperature as well as high I-V performance compared with normal PBI membranes. © 2011 Elsevier B.V.

A recently developed marker-based technique for mapping of the displacement gradient tensor and the strain throughout the bulk of optically opaque specimens is presented and applied to an aluminium alloy multicrystal. Through investigations at 4%, 10% and 14% axial strains, the internal strain field is observed to be non-homogenous with the observed patterns present throughout the range of strains investigated. The morphology of the strain field is visualized with a resolution better than 50μm and variations are tentatively associated with the grain structure as recorded by EBSD. Future applications of the technique in combination with other 3-dimensional approaches are discussed with respect to comparison with Finite Element modelling approaches.

Understanding the distributions of strain within solid bodies undergoing plastic deformations has been of interest for many years in a wide range of disciplines, ranging from basic materials science to biology. However, the desire to investigate these strain fields has been frustrated by the inaccessibility of the interior of most samples to detailed investigation without destroying the sample in the process. To some extent, this has been remedied by the development of advanced surface measurement techniques as well as computer models based on Finite Element methods. Over the last decade, this situation has changed by the introduction of a range of tomographic methods based both on advances in computer technology and in instrumentation, advances which have opened up the interior of optically opaque samples for detailed investigations. We present a general method for assessing the strain in the interior of marker-containing specimens undergoing various types of deformation. The results are compared with Finite Element modelling.

The dislocations in the extended planar dislocation boundaries formed during deformation are generated by the active slip systems. Investigation of the boundaries is therefore a tool to obtain information on the active slip systems. Here, the orientation of the dislocation boundaries in uniaxially deformed aluminum poly- and single crystals are compared. It is found that the single crystal boundary planes are consistent with those found in polycrystals, indicating that the active slip systems in single and polycrystals are the same. However, boundaries are closer to the slip planes in the single crystals. This is taken as an indication that the secondary slip systems are more active in the polycrystal. The orientation of the boundary plane varies with the crystal orientation in a way that is consistent with activation of the five most stressed slip systems.

By Three Dimensional X-ray Diffraction (3DXRD) microscopy it is possible to characterize microstructures non-destructively in 3 dimensions. The measurements are furthermore typically so fast that dynamics may be monitored in-situ, giving also the 4th dimension, namely the time. The 3DXRD technique is based on diffraction of high energy x-rays from third generation synchrotron sources. In the present paper the 3DXRD technique is described and it’s potentials are illustrated by examples relating to elastic and plastic strains, recovery, recrystallization and grain growth.Copyright © 2004 by ASME

The growth of individual grains in commercial aluminium (AA5182) was measured in situ during a recrystallization heat treatment at 543 K including an intermediate cycle to room temperature and back on the three dimensional X-ray diffraction microscope at the European Synchrotron Radiation Facility. It is shown that the growth kinetics of the individual grains were not affected by the intermediate cycle to room temperature.

The microstructure in polycrystalline materials has mostly been studied in planar sections by microscopy techniques. Now the high penetration power of hard X-ray synchrotron radiation makes three-dimensional (3-D) observations possible in bulk material by back tracing the diffracted beam. The three-dimensional X-ray diffraction (3DXRD) microscope installed at the European Synchrotron Radiation Facility in Grenoble provides a fast and non-destructive technique for mapping the embedded grains within thick samples in three dimensions. All essential features like the position, volume, orientation, stress-state of the grains can be determined, including the morphology of the grain boundaries. The accuracy of this novel tracking technique is compared with electron microscopy (EBSP), and its 3-D capacity is demonstrated.

A newly developed synchrotron instrument – the so-called 3D X-ray microscope – is presented. The instrument is placed at the Materials Science beamline at ESRF and dedicated to local μm scale structural characterization within bulk materials. In this paper, emphasis is on in situ studies of thermomechanical processing. The potential of the instrument for characterization of single nuclei and grains is described and discussed based on both first results and planned experiments.

Traditionally, depth resolution in diffraction experiments is obtained by inserting pinholes in both the incoming and diffracted beam. For materials science investigations of local strain and texture properties this leads to very slow data-acquisition rates, especially when characterization is performed on the level of the individual grains. To circumvent this problem a conical slit has been manufactured by wire-electrodischarge machining. The conical slit has six 25 microm-thick conically shaped openings matching six of the Debye-Scherrer cones from a face-centred-cubic powder. By combining the slit with a microfocused incoming beam of hard X-rays, an embedded gauge volume is defined. Using a two-dimensional detector, fast and complete information can be obtained regarding the texture and strain properties of the material within this particular gauge volume. The average machining and assemblage errors of the conical slit are found both to be of the order of 5 microm. An algorithm for alignment of the slit is established, and the potential of the technique is illustrated with an example of grain mapping in a 4.5 mm-thick Cu sample.

International audience; Experimental investigations in STO ceramics revealed a grain growth anomaly, that pre- sumably originates in the interface anisotropy of these materials. However, the influence of anisotropic grain boundary (GB) properties on grain growth behaviour is to a large extent unknown. The present paper presents 3D grain growth simulations as a possible approach to understand the influence of anisotropic GB properties on the collective behaviour of the GBs in a polycrystal during grain growth. Possibilities to compare 3D growth simulations with experimental 2D sections are discussed and a first reconstructed x-ray diffraction contrast tomography image of a SrTiOspecimen is presented.

International audience; The growth of a single grain during recrystallisation into a mildly deformed {001}100 oriented single crystal has been monitored by synchrotron radiation using the topotomo technique. The formation and migration of individual facets is analysed using a new method which measures distances between grain boundary segments at different time steps along parallel lines normal to the facet plane. One facet is shown to move with a constant rate, while it remains planar and keeps the same boundary plane orientation. The formation of another facet, which is analysed in detail, reveals that first a planar boundary with a different orientation forms before it changes its boundary plane orientation into that of the final facet. It is argued that the local microstructural configuration in front of moving grain boundaries has a considerable influence on the kinetics of individual boundary segments and facets.

International audience; So far, 3D X-ray diffraction microscopy (3DXRD) and X-ray diffraction contrast tomography (DCT) experiments have typically been performed in forward scattering geometry, the detector intercepting diffraction cones up to limited opening angles below 30°. The extension of the current synchrotron–based methodology towards 3D orientation mapping of deformed microstructures with down to (sub-)micrometer spatial resolution will require a reduction of the pixel and hence sample size by one order of magnitude. This in turn relaxes the need for high energy beams and opens interesting possibilities for new acquisition geometries, taking advantage of improved spatial resolution and strain sensitivity at high diffraction angles. First results obtained in this acquisition geometry will be discussed and a comparison to polychromatic micro-diffraction experiments is drawn.

International audience; Large scale finite element simulations of the elastoviscoplastic behaviour of polycrystalline aggregates have become a standard technique to study the stress-strain heterogeneities that develop in grains during deformation. For a long time, comparison between continuum crystal plasticity and experimental field measurements was confined to the observation of surface behaviour. As for example the study of the development of intense deformation bands at the free surface of a polycrystal. Recent 3D experimental techniques open new perspectives in computational crystal plasticity. After reviewing how to define a representative volume element for polycrystal properties and showing that actual 3D computations, including grain shapes and orientations, are really needed to accurately determine the stress and strains distributions, two examples of applications of large scale simulations are described in this paper. First the simulation of 3D coherent X-ray diffraction in a polycrystalline gold sample is detailed. Based on the real geometry of the grains and their columnar nature, a 3D avatar is reconstructed. FE computations are then carried out to evaluate the effect of mechanical and thermal strain of the diffraction pattern resolved in the reciprocal space by complex FFT. Qualitative comparison with the experimental diffraction patterns shows that such computations can help understand the true nature of strain heterogeneities within the material. The second example of application deals with short fatigue crack propagation in polycrystals. One fundamental problem caused by short fatigue cracks is that despite decades of research, so far no reliable prediction of the crack propagation rates, comparable to the well-known Paris law in the long crack regime, could be established. This ``anomalous'' behaviour of short cracks is commonly attributed to factors like their complex three dimensional shapes and the influence of the local crystallographic environment affecting their propagation behaviour via a combination of physical mechanisms. Crystal plasticity computations based on the real grain shapes and orientations obtained thanks to diffraction contrast tomography are carried out using an ideal crack shape. The stress concentration at the crack tip is analysed with respect to possible crack growth directions.