Bragg's Law diffraction simulations for electron backscatter diffraction analysis

Kacher, Josh; Landon, Colin; Adams, Brent L.; Fullwood, David T.

doi:10.1016/j.ultramic.2009.04.007

Cited by 230 publications

(145 citation statements)

References 12 publications

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“…The elastic strain contribution to the GND density is often not addressed experimentally, especially in the absence of a quantitative assessment of the significance of the elastic strain contribution to the dislocation density tensor. However, it is significant that in addition to lattice rotation field measurements, advances in the EBSD technique (Wilkinson et al, 2006;Villert et al, 2009;Kacher et al, 2009) have enabled the detection of surface elastic strain fields and the determination of the Kröner dislocation density tensor at surfaces (Wilkinson and Randman, 2010;Britton et al, 2013;Wilkinson et al 2014). …”

Section: Introductionmentioning

confidence: 99%

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

Mohamed¹,

Larson²,

Tischler³

et al. 2015

Journal of the Mechanics and Physics of Solids

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CitationA statistical analysis of the elastic distortion and dislocation density fields in deformed crystals This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Abstract.The statistical properties of the elastic distortion fields of dislocations in deforming crystals are investigated using the method of discrete dislocation dynamics to simulate dislocation structures and dislocation density evolution under tensile loading. Probability distribution functions (PDF) and pair correlation functions (PCF) of the simulated internal elastic strains and lattice rotations are generated for tensile strain levels up to 0.85%. The PDFs of simulated lattice rotation are compared with sub-micrometer resolution three-dimensional X-ray microscopy measurements of rotation magnitudes and deformation length scales in 1.0% and 2.3% compression strained Cu single crystals to explore the linkage between experiment and the theoretical analysis. The statistical properties of the deformation simulations are analyzed through determinations of the Nye and Kröner dislocation density tensors. The significance of the magnitudes and the length scales of the elastic strain and the rotation parts of dislocation density tensors are demonstrated, and their relevance to understanding the fundamental aspects of deformation is discussed.

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Section: Introductionmentioning

confidence: 99%

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

Mohamed¹,

Larson²,

Tischler³

et al. 2015

Journal of the Mechanics and Physics of Solids

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“…A remaining challenge is to capture accurately the full details of microscopic strain, stress, lattice rotation, and GND density measured by experiments, and particularly with HR-EBSD [28]. The use of Bragg's law simulation patterns is a potential way to overcome this challenge [29], but the geometric configuration of EBSD camera and sample must be obtained with great accuracy. Common uncertainties in pattern centre lead to errors of about 10 -3 in strain measurement [30].…”

Section: Introductionmentioning

confidence: 99%

Crystal plasticity and high-resolution electron backscatter diffraction analysis of full-field polycrystal Ni superalloy strains and rotations under thermal loading

et al. 2014

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Electron back scattered diffraction (EBSD) has been employed to study a polycrystalline nickel superalloy containing a complex non-metallic agglomerate under thermal loading. Heterogeneous distributions of elastic strains are observed near the inclusion due to its complex geometry which have been quantified. Lattice rotations were also related to geometrically necessary dislocation (GND) density (~10 14 −2 ), indicating the development of localized plasticity arising from the mismatch in thermal expansivity between the Ni polycrystal and the inclusion. A crystal plasticity finite element (CPFE) model which explicitly represents the full detail of the complex microstructure was developed to interpret the experimental measurements, and good quantitative and qualitative agreement has been obtained. However, a limitation of the EBSD technique when investigating polycrystal systems is that full-field, trans-granular strain measurement remains difficult due to the necessity to reference a lattice spacing within a grain for strain calculation. An inverse reference shifting methodology has been developed using CPFE modelling to overcome this problem, thereby allowing like-for-like and grain-by-grain strain comparisons to be made. The method, in conjunction with high resolution-EBSD, shows promise for the determination of fullfield strains and rotations in polycrystalline materials, and provides key information for fatigue nucleation in these material systems.2

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“…The use of simulations to generate the reference patterns is an obvious approach to solving the 'reference pattern problem' and has been explored by several groups [8,9]. The simulations must have sufficient fidelity and while crude kinematic methods are unacceptable, dynamical simulation show promise [8,9,10]. Aberrations in the EBSD detector optics can lead to significant artifacts in the measured strains [9] and so need to be determined and accounted for using methods given for example by Day [11].…”

mentioning

confidence: 99%

“…However, the remaining barrier to successfully using simulations is the limited accuracy of currently available methods for determining the camera geometry. Errors in pattern centre position and specimen to screen distance are typically~0.5% of the screen width (or~5 pixels) and this has been shown [12,8,9] to induce errors of order 10 -3 which are generally too large. Iterative fitting, camera movement, and shadow casting methods are all under investigation as possible means of providing the required sub-pixel accuracy in the camera geometry.…”

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confidence: 99%

High Accuracy EBSD - A Review of Recent Applications, Innovations, and Remaining Challenges

Wilkinson

Jiang

Meaden³

et al. 2011

Microsc Microanal

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The implementation of cross-correlation analysis of EBSD patterns has allowed much improved angular sensitivity measurements to be achieved including the ability to determine the variations in elastic strains [1,2]. Cross-correlation functions between tests patterns and a reference pattern are calculated at selected sub-regions distributed across the patterns. A simple geometric analysis then allows the elastic strains and lattice rotations to be calculated from the shifts measured at these subregions. Sub-pixel resolution on the pattern shifts, typically to ±0.05 or better, leads to strain and rotation sensitivity of~±10 -4 . In many situations a convenient location on the sample can be used to generate a reference pattern for which the strain state is well known, and in most cases zero. This is the case when studying the flow fields and residual stresses near indents in single crystals. . Analysis of deformation fields near crack tips and particles are important situations where strains fall to negligible levels in the far field so that good reference patterns can be obtained from regions well away from the crack or particle [2,6,7]. In many more situations, such as a plastically deformed polycrystal, there is no obvious position on the sample from which to obtain a reference pattern corresponding to a known strain state. Fixing the absolute level of the strains in these situations remains the most significant challenge in continuing the development of the technique. One approach is to combine the local strain variations measured using the EBSD method with modeling at a longer length scale. A uniform strain state is then added to the measured EBSD strain variations to bring the average values into agreement with the model [6]. If characterizing the resulting deformation sub-structure is the main aim of the work then Nye's dislocation tensor analysis can be used to estimate the geometrically necessary dislocation (GND) density. This requires only gradients in the elastic strain and lattice rotation fields and so avoids the problem of assigning the absolute strain values. In all metal deformation studies we have made plastic flow results in rotations that are markedly larger than the elastic strains which can then be ignored when estimating the GND content. Indeed the lattice rotations can be sufficiently large so as to cause the cross-correlation analysis to give incorrect pattern shifts for parts of the pattern which change too much. We have recently implemented a robust fitting algorithm which identifies regions of the pattern for which the pattern shifts are suspect and down-weights their influence in an iterative scheme to determine the strain and rotation from the pattern shifts. This allows fuller coverage of the EBSD map as illustrated in FIG 2 (b) and (c) for a Cu sample deformed to 10% in tension. The use of simulations to generate the reference patterns is an obvious approach to solving the 'reference pattern problem' and has been explored by several groups [8,9]. The simulations must have sufficient ...

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Bragg's Law diffraction simulations for electron backscatter diffraction analysis

Cited by 230 publications

References 12 publications

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

Crystal plasticity and high-resolution electron backscatter diffraction analysis of full-field polycrystal Ni superalloy strains and rotations under thermal loading

High Accuracy EBSD - A Review of Recent Applications, Innovations, and Remaining Challenges

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