Determining grain resolved stresses in polycrystalline materials using three-dimensional X-ray diffraction

2010 ◽  
Vol 43 (3) ◽  
pp. 539-549 ◽  
Author(s):  
Jette Oddershede ◽  
Søren Schmidt ◽  
Henning Friis Poulsen ◽  
Henning Osholm Sørensen ◽  
Jonathan Wright ◽  
...  
Keyword(s):  
Near Field ◽  
Three Dimensional ◽  
Polycrystalline Sample ◽  
Polycrystalline Materials ◽  
Interstitial Free ◽  
Outlier Rejection ◽  
X Ray Diffraction ◽  
Positional Accuracy ◽  
X Ray ◽  
Elastic Loading

An algorithm is presented for characterization of the grain resolved (type II) stress states in a polycrystalline sample based on monochromatic X-ray diffraction data. The algorithm is a robust 12-parameter-per-grain fit of the centre-of-mass grain positions, orientations and stress tensors including error estimation and outlier rejection. The algorithm is validated by simulations and by two experiments on interstitial free steel. In the first experiment, using only a far-field detector and a rotation range of 2 × 110°, 96 grains in one layer were monitored during elastic loading and unloading. Very consistent results were obtained, with mean resolutions for each grain of approximately 10 µm in position, 0.05° in orientation, and 8, 20 and 13 × 10−5in the axial, normal and shear components of the strain, respectively. The corresponding mean deviations in stress are 30, 50 and 15 MPa in the axial, normal and shear components, respectively, though some grains may have larger errors. In the second experiment, where a near-field detector was added, ∼2000 grains were characterized with a positional accuracy of 3 µm.

scholarly journals Comparison between a near-field and a far-field indexing approach for characterization of a polycrystalline sample volume containing more than 1500 grains

2014 ◽  
Vol 47 (4) ◽  
pp. 1402-1416 ◽  
Author(s):  
Laura Nervo ◽  
Andrew King ◽  
Jonathan P. Wright ◽  
Wolfgang Ludwig ◽  
Péter Reischig ◽  
...  
Keyword(s):  
Diffraction Data ◽  
Near Field ◽  
Three Dimensional ◽  
Pure Titanium ◽  
Polycrystalline Sample ◽  
Sample Volume ◽  
Polycrystalline Materials ◽  
Far Field ◽  
X Ray Diffraction ◽  
X Ray

A comparison of the performance of X-ray diffraction tomography, a near-field diffraction technique, and a far-field diffraction technique for indexing X-ray diffraction data of polycrystalline materials has been carried out by acquiring two sets of diffraction data from the same polycrystalline sample volume. Both approaches used in this study are variants of the three-dimensional X-ray diffraction (3DXRD) methodology, but they rely on different data-collection and analysis strategies. Previous attempts to assess the quality of 3DXRD indexing results from polycrystalline materials have been restricted to comparisons with two-dimensional electron backscatter diffraction cross sections containing a limited number of grains. In the current work, the relative performance of two frequently used polycrystalline-material indexing algorithms is assessed, comparing the indexing results obtained from a three-dimensional sample volume containing more than 1500 grains. The currently achievable accuracy of three-dimensional grain maps produced with these algorithms has been assessed using a statistical analysis of the measurement of the size, position and orientation of the grains in the sample. The material used for this comparison was a polycrystalline commercially pure titanium grade 2 sample, which has a hexagonal close-packed crystal structure. The comparison of the two techniques shows good agreement for the measurements of the grain position, size and orientation. Cross-validation between the indexing results shows that about 99% of the sample volume has been indexed correctly by either of these indexing approaches. The remaining discrepancies have been analysed and the strengths and limitations of both approaches are discussed.

Measuring Type II Stresses Using 3DXRD

2010 ◽  
Vol 652 ◽  
pp. 63-69 ◽  
Author(s):  
Jette Oddershede ◽  
Søren Schmidt ◽  
Henning Friis Poulsen ◽  
Walter Reimers
Keyword(s):  
Polycrystalline Sample ◽  
Interstitial Free ◽  
Type Ii ◽  
If Steel ◽  
Outlier Rejection ◽  
X Ray Diffraction ◽  
Elastic Loading ◽  
Loading And Unloading ◽  
Stress States

An algorithm is presented for characterization of the grain resolved (type II) stress states in a polycrystalline sample based on monochromatic X-ray diffraction data. The algorithm is a robust 12-parameter-per-grain fit of the centre-of-mass grain positions, orientations and stress tensors including error estimation and outlier rejection. As examples of use results from two experiments – one on interstitial free (IF) steel and one on copper – will be presented. In the first experiment 96 grains in one layer of IF steel were monitored during elastic loading and unloading. Very consistent results were obtained, with resolutions for each grain of approximately 10 μm in position, 0.05˚ in orientation and 80 μstrain. When averaging over all grains a resolution of 10 μstrain was obtained. In the second experiment it was demonstrated that the strain states of more than 1000 grains in a plastically deformed Cu specimen could be determined to an accuracy of 100 μstrain.

High Resolution Synchrotron X-Ray Diffraction Tomography Of Large-Grained Samples

1996 ◽  
Vol 437 ◽  
Author(s):  
D.P. Piotrowski ◽  
S.R. Stock ◽  
A. Guvenilir ◽  
J.D. Haase ◽  
Z.U. Rek
Keyword(s):  
Spatial Distribution ◽  
High Resolution ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Diffraction Tomography ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Image Storage ◽  
X Ray ◽  
Dimensional Distribution

AbstractIn order to understand the macroscopic response of polycrystalline structural materials to loading, it is frequently essential to know the spatial distribution of strain as well as the variation of micro-texture on the scale of 100 μm. The methods must be nondestructive, however, if the three-dimensional evolution of strain is to be studied. This paper describes an approach to high resolution synchrotron x-ray diffraction tomography of polycrystalline materials. Results from model samples of randomly-packed, millimeter-sized pieces of Si wafers and of similarly sized single-crystal Al blocks have been obtained which indicate that polychromatic beams collimated to 30 μm diameter can be used to determine the depth of diffracting volume elements within ± 70 μm. The variation in the two-dimensional distribution of diffracted intensity with changing sample to detector separation is recorded on image storage plates and used to infer the depth of diffracting volume elements.

scholarly journals Maximum a posteriori estimation of crystallographic phases in X-ray diffraction tomography

2015 ◽  
Vol 373 (2043) ◽  
pp. 20140392 ◽  
Author(s):  
Doĝa Gürsoy ◽  
Tekin Biçer ◽  
Jonathan D. Almer ◽  
Raj Kettimuthu ◽  
Stuart R. Stock ◽  
...  
Keyword(s):  
National Laboratory ◽  
Spinous Process ◽  
Argonne National Laboratory ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Reconstruction Method ◽  
Diffraction Tomography ◽  
A Posteriori ◽  
X Ray Diffraction ◽  
X Ray

A maximum a posteriori approach is proposed for X-ray diffraction tomography for reconstructing three-dimensional spatial distribution of crystallographic phases and orientations of polycrystalline materials. The approach maximizes the a posteriori density which includes a Poisson log-likelihood and an a priori term that reinforces expected solution properties such as smoothness or local continuity. The reconstruction method is validated with experimental data acquired from a section of the spinous process of a porcine vertebra collected at the 1-ID-C beamline of the Advanced Photon Source, at Argonne National Laboratory. The reconstruction results show significant improvement in the reduction of aliasing and streaking artefacts, and improved robustness to noise and undersampling compared to conventional analytical inversion approaches. The approach has the potential to reduce data acquisition times, and significantly improve beamtime efficiency.

High Resolution Synchrotron X-Ray Diffraction Tomography of Polycrystalline Samples

1994 ◽  
Vol 375 ◽  
Author(s):  
S. R. Stock ◽  
A. Guvenilir ◽  
D. P. Piotrowski ◽  
Z. U. Rek
Keyword(s):  
Spatial Distribution ◽  
High Resolution ◽  
Three Dimensional ◽  
Compact Tension ◽  
Polycrystalline Materials ◽  
Diffraction Tomography ◽  
X Ray Diffraction ◽  
Image Storage ◽  
X Ray ◽  
Nondestructive Measurements

AbstractThe macroscopic response of polycrystalline materials to loading depends on both the spatial distribution of strain and the variation of microtexture on the scale of 100 μm. Nondestructive measurements are needed if the three-dimensional evolution of strain is to be studied. This paper describes approaches for high resolution synchrotron polychromatic x-ray diffraction tomography of polycrystalline materials. Preliminary experiments are reported on partially cracked compact tension samples of Al-Li 2090 and on model samples of randomly-packed, millimeter-sized pieces of Si wafers. Polychromatic beams collimated to 100 μm diameter have been used, and the distribution of diffracted intensity has been collected on high resolution x-ray film as well as on image storage plates. The depths of diffracting volume elements are determined from the changes in the spatial distribution of diffracted intensity with varying sample to detector separation.

scholarly journals Three-dimensional α colony characterization and prior-β grain reconstruction of a lamellar Ti–6Al–4V specimen using near-field high-energy X-ray diffraction microscopy

2015 ◽  
Vol 48 (4) ◽  
pp. 1165-1171 ◽  
Author(s):  
E. Wielewski ◽  
D. B. Menasche ◽  
P. G. Callahan ◽  
R. M. Suter
Keyword(s):  
Near Field ◽  
Three Dimensional ◽  
High Energy ◽  
Grain Structure ◽  
X Ray Diffraction ◽  
Orientation Field ◽  
X Ray ◽  
Hexagonal Close Packed ◽  
Flood Fill ◽  
Diffraction Microscopy

Near-field high-energy X-ray diffraction microscopy has been used to characterize the three-dimensional (3-D) crystallographic orientation field of the hexagonal close-packed α phase in a bulk Ti–6Al–4V specimen with a lamellar (β-annealed) microstructure. These data have been segmented using a 3-D misorientation-based grain finding algorithm, providing unprecedented information about the complex 3-D morphologies and spatial misorientation distributions of the transformed α lamella colonies. A 3-D Burgers orientation relationship-based flood-fill algorithm has been implemented to reconstruct the morphologies and crystallographic orientations of the high-temperature body-centered cubic prior-β grains. The combination of these data has been used to gain an understanding of the role of the prior-β grain structure in the formation of specific morphologies and spatial misorientation distributions observed in the transformed α colony structures. It is hoped that this understanding can be used to develop transformation structures optimized for specific applications and to produce more physically realistic synthetic microstructures for use in simulations.

Three-dimensional grain resolved strain mapping using laboratory X-ray diffraction contrast tomography: theoretical analysis

2022 ◽  
Vol 55 (1) ◽  
Author(s):  
Adam Lindkvist ◽  
Yubin Zhang
Keyword(s):  
Near Field ◽  
Three Dimensional ◽  
Simulated Data ◽  
Three Dimensions ◽  
X Ray Diffraction ◽  
Strain Mapping ◽  
X Ray ◽  
Microstructural Parameters ◽  
Diffraction Contrast ◽  
Sample Distance

Laboratory diffraction contrast tomography (LabDCT) is a recently developed technique to map crystallographic orientations of polycrystalline samples in three dimensions non-destructively using a laboratory X-ray source. In this work, a new theoretical procedure, named LabXRS, expanding LabDCT to include mapping of the deviatoric strain tensors on the grain scale, is proposed and validated using simulated data. For the validation, the geometries investigated include a typical near-field LabDCT setup utilizing Laue focusing with equal source-to-sample and sample-to-detector distances of 14 mm, a magnified setup where the sample-to-detector distance is increased to 200 mm, a far-field Laue focusing setup where the source-to-sample distance is also increased to 200 mm, and a near-field setup with a source-to-sample distance of 200 mm. The strain resolution is found to be in the range of 1–5 × 10−4, depending on the geometry of the experiment. The effects of other experimental parameters, including pixel binning, number of projections and imaging noise, as well as microstructural parameters, including grain position, grain size and grain orientation, on the strain resolution are examined. The dependencies of these parameters, as well as the implications for practical experiments, are discussed.

scholarly journals Formation and annihilation of stressed deformation twins in magnesium

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Karim Louca ◽  
Hamidreza Abdolvand ◽  
Charles Mareau ◽  
Marta Majkut ◽  
Jonathan Wright
Keyword(s):  
Mechanical Response ◽  
Axial Stress ◽  
Three Dimensional ◽  
Service Performance ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
Sign Reversal ◽  
X Ray ◽  
Hexagonal Close Packed

AbstractThe mechanical response of polycrystalline materials to an externally applied load and their in-service performance depend on the local load partitioning among the constituent crystals. In hexagonal close-packed polycrystals such load partitioning is significantly affected by deformation twinning. Here we report in-situ compression-tension experiments conducted on magnesium specimens to measure the evolution of grain resolved tensorial stresses and formation and annihilation of twins. More than 13000 grains and 1300 twin-parent pairs are studied individually using three-dimensional synchrotron X-ray diffraction. It is shown that at the early stages of plasticity, the axial stress in twins is higher than that of parents, yet twins relax with further loading. While a sign reversal is observed for the resolved shear stress (RSS) acting on the twin habit plane in the parent, the sign of RSS within the majority of twins stays unchanged until twin annihilation during the load reversal. The variations of measured average stresses across parents and twins are also investigated.

Reconstruction of Grains in Polycrystalline Materials From Incomplete Data Using Laguerre Tessellations

2019 ◽  
Vol 25 (3) ◽  
pp. 743-752 ◽  
Author(s):  
Lukas Petrich ◽  
Jakub Staněk ◽  
Mingyan Wang ◽  
Daniel Westhoff ◽  
Luděk Heller ◽  
...  
Keyword(s):  
Polycrystalline Material ◽  
Three Dimensional ◽  
Morphological Data ◽  
Polycrystalline Materials ◽  
Internal Stresses ◽  
X Ray Diffraction ◽  
X Ray ◽  
Quick Measurement ◽  
Centers Of Mass ◽  
Diffraction Microscopy

AbstractFar-field three-dimensional X-ray diffraction microscopy allows for quick measurement of the centers of mass and volumes of a large number of grains in a polycrystalline material, along with their crystal lattice orientations and internal stresses. However, the grain boundaries—and, therefore, individual grain shapes—are not observed directly. The present paper aims to overcome this shortcoming by reconstructing grain shapes based only on the incomplete morphological data described above. To this end, cross-entropy (CE) optimization is employed to find a Laguerre tessellation that minimizes the discrepancy between its centers of mass and cell sizes and those of the measured grain data. The proposed algorithm is highly parallel and is thus capable of handling many grains (>8,000). The validity and stability of the CE approach are verified on simulated and experimental datasets.

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