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

Laue microdiffraction on polycrystalline samples above 1500 K achieved with the QMAX-µLaue furnace

X-ray Laue microdiffraction aims to characterize microstructural and mechanical fields in polycrystalline specimens at the sub-micrometre scale with a strain resolution of ∼10-4. Here, a new and unique Laue microdiffraction setup and alignment procedure is presented, allowing measurements at temperatures as high as 1500 K, with the objective to extend the technique for the study of crystalline phase transitions and associated strain-field evolution that occur at high temperatures. A method is provided to measure the real temperature encountered by the specimen, which can be critical for precise phase-transition studies, as well as a strategy to calibrate the setup geometry to account for the sample and furnace dilation using a standard α-alumina single crystal. A first application to phase transitions in a polycrystalline specimen of pure zirconia is provided as an illustrative example.

Processing Laue Microdiffraction Raster Scanning Patterns with Machine Learning Algorithms: A Case Study with a Fatigued Polycrystalline Sample

The massive amount of diffraction images collected in a raster scan of Laue microdiffraction calls for a fast treatment with little if any human intervention. The conventional method that has to index diffraction patterns one-by-one is laborious and can hardly give real-time feedback. In this work, a data mining protocol based on unsupervised machine learning algorithm was proposed to have a fast segmentation of the scanning grid from the diffraction patterns without indexation. The sole parameter that had to be set was the so-called “distance threshold” that determined the number of segments. A statistics-oriented criterion was proposed to set the “distance threshold”. The protocol was applied to the scanning images of a fatigued polycrystalline sample and identified several regions that deserved further study with, for instance, differential aperture X-ray microscopy. The proposed data mining protocol is promising to help economize the limited beamtime.

Using Powder Diffraction Patterns to Calibrate the Module Geometry of a Pixel Detector

The precision and accuracy of diffraction measurements with 2D area detectors depends on how well the experimental geometry is known. A method is described to measure the module geometry in order to obtain accurate strain data using a new Eiger2 4M CdTe detector. Smooth Debye–Scherrer powder diffraction rings with excellent signal to noise were collected by using a fine-grained sample of CeO2. From these powder patterns, the different components of the module alignment errors could be observed when the overall detector position was moved. A least squares fitting method was used to refine the detector module and scattering geometry for a series of powder patterns with different beam centers. A precision that is around 1/350 pixel for the module positions was obtained from the fit. This calibration was checked by free refinement of the unit cell of a silicon crystal that gave a maximum residual strain value of 2.1 × 10−5 as the deviation from cubic symmetry.

Digital Image Correlation of 2D X-ray Powder Diffraction Data for Lattice Strain Evaluation

High energy 2D X-ray powder diffraction experiments are widely used for lattice strain measurement. The 2D to 1D conversion of diffraction patterns is a necessary step used to prepare the data for full pattern refinement, but is inefficient when only peak centre position information is required for lattice strain evaluation. The multi-step conversion process is likely to lead to increased errors associated with the 'caking' (radial binning) or fitting procedures. A new method is proposed here that relies on direct Digital Image Correlation analysis of 2D X-ray powder diffraction patterns (XRD-DIC, for short). As an example of using XRD-DIC, residual strain values along the central line in a Mg AZ31B alloy bar after 3-point bending are calculated by using both XRD-DIC and the conventional 'caking' with fitting procedures. Comparison of the results for strain values in different azimuthal angles demonstrates excellent agreement between the two methods. The principal strains and directions are calculated using multiple direction strain data, leading to full in-plane strain evaluation. It is therefore concluded that XRD-DIC provides a reliable and robust method for strain evaluation from 2D powder diffraction data. The XRD-DIC approach simplifies the analysis process by skipping 2D to 1D conversion, and opens new possibilities for robust 2D powder diffraction data analysis for full in-plane strain evaluation.

EBSD-assisted Laue microdiffraction for microstrain analysis

The X-ray Laue microdiffraction (µLaue) technique has been establishing itself as a reliable means for microstrain analysis for the past few decades. One problem with this technique is that when the crystal size is significantly smaller than the probed volume and when the diffracting crystals are closely oriented, a large number of individual µLaue patterns are superimposed in a complex way on the recorded diffraction images. In that case, because of the difficulty of isolating unambiguously a single-grain µLaue pattern, a reliable analysis of strains is tedious manually and hardly achievable with current automated methods. This issue is even more severe for low-symmetry crystals or when high-energy X-rays are used, since each single-crystal µLaue pattern already contains a large number of spots. This paper proposes overcoming this challenge through the development of a combined approach coupling µLaue and electron backscatter diffraction (EBSD). The capabilities of this `EBSD-assisted µLaue' automated method are illustrated on a monoclinic zirconia-based specimen and µLaue diffraction patterns are analysed with the crystal orientation input from EBSD. The obtained results are statistically reliable, reproducible and provide a physical insight into the micromechanical characteristics of the material.

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.

Direct measurement of local constitutive relations, at the micrometre scale, in bulk metallic alloys

Multiscale models involving crystal plasticity are essential to predict the elastoplastic behavior of structural materials with respect to their microstructure. However, those models are often limited by a poor knowledge of the local constitutive behavior. This article reports a method to measure the mechanical behavior directly, at the micrometre scale, in bulk crystalline materials. Local strain and stress states were evaluated at the surface of a bent stainless steel crystal by combining total strain measurements – performed with the digital image correlation technique on optical images – with elastic strain measurements obtained by Laue microdiffraction. A local constitutive relation was measured, in an efficient nondestructive way, without the need for full-field simulations. The method was validated by a comparison between the measured local behavior and the macroscopic behavior of the single crystal.

Evaluation of intragranular strain and average dislocation density in single grains of a polycrystal using K-map scanning

Quick scanning X-ray microscopy combined with three-dimensional reciprocal space mapping was applied to characterize intragranular orientation and strain in a single grain of uniaxially deformed Al polycrystal. The strain component perpendicular to the direction of the applied tensile load was found to be very heterogeneous with high compressive and tensile values in the grain interior and near two grain boundaries, respectively. The distribution of the magnitude of diffraction vectors indicates that dislocations are the origin of the strain. The work opens new possibilities for analysing dislocation structures and intragranular residual stress/strain in single grains of polycrystalline materials.