Accuracy of stress measurement by Laue microdiffraction (Laue-DIC method): the influence of image noise, calibration errors and spot number

Laue microdiffraction, available at several synchrotron radiation facilities, is well suited for measuring the intragranular stress field in deformed materials thanks to the achievable submicrometer beam size. The traditional method for extracting elastic strain (and hence stress) and lattice orientation from a microdiffraction image relies on fitting each Laue spot with an analytical function to estimate the peak position on the detector screen. The method is thus limited to spots exhibiting ellipsoidal shapes, thereby impeding the study of specimens plastically deformed. To overcome this difficulty, the so-called Laue-DIC method introduces digital image correlation (DIC) for the evaluation of the relative positions of spots, which can thus be of any shape. This paper is dedicated to evaluating the accuracy of this Laue-DIC method. First, a simple image noise model is established and verified on the data acquired at beamline BM32 of the European Synchrotron Radiation Facility. Then, the effect of image noise on errors on spot displacement measured by DIC is evaluated by Monte Carlo simulation. Finally, the combined effect of the image noise, calibration errors and the number of Laue spots used for data treatment is investigated. Results in terms of the uncertainty of stress measurement are provided, and various error regimes are identified.

Tomography and imaging at the PSICHE beam line of the SOLEIL synchrotron

PSICHE (Pressure, Structure and Imaging by Contrast at High Energy) is the high-energy beam line of the SOLEIL synchrotron. The beam line is designed to study samples at extreme pressures, using diffraction, and to perform imaging and tomography for materials science and other diverse applications. This paper presents the tomograph and the use of the beam line for imaging, with emphasis on developments made with respect to existing instruments. Of particular note are the high load capacity rotation stage with free central aperture for installing large or complex samples and sample environments, x-ray mirror and filter optics for pink beam imaging, and multiple options for combining imaging and diffraction measurement. We describe how x-ray imaging techniques have been integrated into high-pressure experiments. The design and the specifications of the beam line are described, and several case studies drawn from the first user experiments are presented.

Determination of deviatoric elastic strain and lattice orientation by applying digital image correlation to Laue microdiffraction images: the enhanced Laue-DIC method

A new method of determining the deviatoric elastic strain and lattice orientation from Laue microdiffraction images is presented. Standard data treatment methods can suffer from the difficulty of precisely pinpointing the positions of diffraction peaks on two-dimensional Laue images. In a previous article, digital image correlation (DIC) was introduced for the treatment of Laue images, leading to the so-called Laue-DIC method. This performed better than the standard method in terms of the deviatoric elastic strain increment and relative rotation from one lattice to another, particularly when the shape of the Laue spots departs from regular ellipsoids. The present work intends to push forward the Laue-DIC method, aiming to determine the deviatoric elastic strain and lattice orientation, as well as the calibration parameters. The performance of this new method, named enhanced Laue-DIC, is assessed by modeling the spot displacements and accounting for random fluctuations relevant for typical experimental conditions. When the enhanced Laue-DIC method is applied to the case of anin situdeformed Si crystal, the obtained standard deviation of local stress is of the order of 1–2 MPa, while the calibration parameters are optimized to high accuracy.

Laue-DIC: a new method for improved stress field measurements at the micrometer scale

A better understanding of the effective mechanical behavior of polycrystalline materials requires an accurate knowledge of the behavior at a scale smaller than the grain size. The X-ray Laue microdiffraction technique available at beamline BM32 at the European Synchrotron Radiation Facility is ideally suited for probing elastic strains (and associated stresses) in deformed polycrystalline materials with a spatial resolution smaller than a micrometer. However, the standard technique used to evaluate local stresses from the distortion of Laue patterns lacks accuracy for many micromechanical applications, mostly due to (i) the fitting of Laue spots by analytical functions, and (ii) the necessary comparison of the measured pattern with the theoretical one from an unstrained reference specimen. In the present paper, a new method for the analysis of Laue images is presented. A Digital Image Correlation (DIC) technique, which is essentially insensitive to the shape of Laue spots, is applied to measure the relative distortion of Laue patterns acquired at two different positions on the specimen. The new method is tested on an in situ deformed Si single-crystal, for which the prescribed stress distribution has been calculated by finite-element analysis. It is shown that the new Laue-DIC method allows determination of local stresses with a strain resolution of the order of 10(-5).

Laue pattern analysis for two-dimensional strain mapping in light-ion-implanted polycrystals

In polycrystals implanted by light ions, a thin layer close to the surface is deformed. X-ray microdiffraction in Laue mode is used to measure the induced strain. In the resulting Laue patterns, the diffraction spots are observed to split, forming double spots, one corresponding to the nondeformed substrate and the other to the deformed layer. A specific image analysis, using bi-Gaussian shape functions, has been developed to improve diffraction spot detection. This is used in association with several numerical tools (conditioning, goodness-of-fit, hat matrixetc.), based on least-squares techniques and statistics, for detecting incorrect data and estimating the accuracy of the result. The use of these tools is not restricted to the study of ion-implanted polycrystals but should find a systematic application for strain analysis from Laue patterns.