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Simulation-Assisted Augmentation of Missing Wedge and Region-of-Interest Computed Tomography Data
(2024)
This study reports a strategy to use sophisticated, realistic X-ray Computed Tomography (CT) simulations to reduce Missing Wedge (MW) and Region-of-Interest (RoI) artifacts in FBP (Filtered Back-Projection) reconstructions. A 3D model of the object is used to simulate the projections that include the missing information inside the MW and outside the RoI. Such information augments the experimental projections, thereby drastically improving the reconstruction results. An X-ray CT dataset of a selected object is modified to mimic various degrees of RoI and MW problems. The results are evaluated in comparison to a standard FBP reconstruction of the complete dataset. In all cases, the reconstruction quality is significantly improved. Small inclusions present in the scanned object are better localized and quantified. The proposed method has the potential to improve the results of any CT reconstruction algorithm.
The combination of tomographic, microstructural data with other experimental techniques and with modeling is paramount, if we want to extract the maximum amount of information on material and component properties. In particular, quantitative image analysis, statistical approaches, direct discretization of tomographic reconstructions represent concrete possibilities to extend the power of the tomographic 3D representation to insights into the material and component performance. This logic thread holds equally for industrial and academic research, and valorizes expensive experiments such as those carried out at synchrotron sources, which cannot be daily repeated. We shall show a few examples of possible use of X-ray tomographic data for quantitative assessment of damage evolution and microstructural properties, as well as for non-destructive testing. We will also show how X-ray refraction computed tomography (CT) can be highly complementary to classic absorption CT, being sensitive to internal interfaces.
Alternative to conventional transmission-based radiography and computed tomography, X-ray refraction techniques are being increasingly used to detect damage in light materials. In fact, their range of application has been recently extended even to metals. The big advantage of X-ray refraction techniques is that they are able to detect nanometric defects, whose size would lie below the resolution of even state-of-the-art synchrotron-based X-ray computed tomography (SXCT). The superiority of synchrotron X-ray refraction radiography and tomography (SXRR and SXRCT) has been shown in the case of light materials, in particular composites. X-ray refraction techniques also yield a quantitifaction of the amount of damage (the so-called relative internal specific surface) and can well be compared with damage models. At the same time, it is impossible for SXRR and SXRCT to image single defects. We show that the combination of refraction- and transmission-based imaging techniques yields an impressive amount of additional information about the type and amount of defects in microstructured materials such as additively manufactured metals or metal matrix composites. We also show that the use of data fusion techniques allows the classification of defects in statistically significant representative volume elements.
X-ray refraction is analogous to visible light deflection by matter; it occurs at boundaries between different media. The main difference between visible light and X-rays is that in the latter case deflection angles are very small, from a few seconds to a few minutes of arc (i.e., the refraction index n is near to 1). Trivially but importantly, deflection of X-rays is also sensitive to the orientation of the object boundaries. These features make X-ray refraction techniques extremely suitable to a) detect defects such as pores and microcracks and quantify their densities in bulk (not too heavy) materials, and b) evaluate porosity and particle properties such as orientation, size, and spatial distribution (by mapping). While X-ray refraction techniques cannot in general image single defects, their detectability is simply limited by the wavelength of the radiation.
We thereby show the application of X-ray refraction 2D mapping (topography) and tomography to different sorts of problems in materials science and technology: 1) Sintering of SiC green bodies; 2) Porosity analysis in additively manufactured alloys; 3) Fiber de-bonding in metal and polymer matrix composites.
Such techniques, especially at the Synchrotron BESSY II, Berlin, Germany, can be used in-situ, i.e. when the specimen is subjected to temperatures or external loads. Applications of in-situ X-ray refraction radiography on aluminum alloys and composites are also shown.
The use of X-ray refraction analysis yields quantitative information, which can be directly input in kinetics, mechanical and damage models.
High-density polyethylene becomes optically transparent during tensile drawing when previously saturated with diesel fuel. This unusual phenomenon is investigated as it might allow conclusions with respect to the material behavior. Microscopy, differential scanning calorimetry, density measurements are applied together with two scanning X-ray scattering techniques: wide angle X-ray scattering (WAXS) and X-ray refraction, able to extract the spatially resolved crystal orientation and internal surface, respectively. The sorbed diesel softens the material and significantly alters the yielding characteristics. Although the crystallinity among stretched regions is similar, a virgin reference sample exhibits strain whitening during stretching, while the diesel-saturated sample becomes transparent. The WAXS results reveal a pronounced fiber texture in the tensile direction in the stretched region and an isotropic orientation in the unstretched region. This texture implies the formation of fibrils in the stretched region, while spherulites remain intact in the unstretched parts of the specimens. X-ray refraction reveals a preferred orientation of internal surfaces along the tensile direction in the stretched region of virgin samples, while the sample stretched in the diesel-saturated state shows no internal surfaces at all. Besides from stretching saturated samples, optical transparency is also obtained from sorbing samples in diesel after stretching.
For the first time we present direct 2D imaging of refracted X-rays without any discrimination of the Primary radiation. X-refraction works in analogy to visible light optics: X-rays are entirely deflected at interfaces where discontinuities of (electron) density occur. This is demonstrated at the example of inner and outer surfaces of model samples of well-defined geometry (fibres, capillaries, and monodisperse micro particles). The samples are scanned through a 50 μm monochromatic (20 keV) pencil beam. In order to warrant a sufficient angular resolution a 2D detector (pixel size 7 μm) is placed 3 m downstream of the sample. Scanning the sample in micron steps allows for detecting local changes of interface / surface orientation directly in two dimensions. At the actual angular resolution of about 3 seconds of arc (scattering vector increments Δk = 10-3 nm-1) and 50 μm spatial resolution (scanning) the material’s inner surfaces (with nanometer separation) can be characterized even at sampling rates below 1 second per frame. Moreover, our technique is suited to directly determine particle diameters of up to 250 nm by means of diffraction fringes. Some potential applications to technical submicron structures are discussed.
Evaluating porosity in cordierite diesel particulate filter materials, part 1 X-ray refraction
(2013)
Bi-continuous porous ceramics for filtration applications possess a particularly complicated microstructure, with porosity and solid matter being intermingled. Mechanical, thermal, and filtration properties can only be precisely estimated if the morphology of both solid matter and porosity can be quantitatively determined. Using x-ray absorption and refraction, we quantitatively evaluate porosity and pore orientation in cordierite diesel particulate filter ceramics. Porosity values turn out to agree with mercury intrusion measurements, while pore orientation factors agree with published crystallographic texture data.
Bi-continuous porous ceramics for filtration applications possess a particularly complicated microstructure, whereby porosity and solid matter are intermingled. Mechanical, thermal, and filtration properties can only be precisely estimated if the morphology of both solid matter and porosity can be quantitatively determined. Using 3D computed tomography (CT) at different resolutions, and several X-ray refraction-based techniques, we quantitatively evaluated porosity and pore orientation in cordierite diesel particulate filter ceramics.Moreover, applying both Fast Fourier Transform (FFT) and a newly developed image analysis algorithm (directional interface variance analysis, DIVA), we quantitatively evaluated porosity and pore orientation. Both the experimental techniques and the statistical approach allow extraction of spatially resolved or average values.Porosity values from synchrotron computed tomography used turn out to agree with mercury intrusion measurements, while pore orientation factors agree with published crystallographic texture data. This latter point also implies that the study of the pore/matter interface is sufficient to describe the morphological properties of these materials.
While structural ceramics usually display a brittle mechanical behavior, their composites may show nonlinearities, mostly due to microcracking. Herein, the stiffness evolution of a sandwich-like laminate of an Al2O3 15%vol. ZrO2 matrix reinforced with Nextel 610 fibers is studied as a function of number of cycles N in tension. The stiffness of the composite degrades with increasing N, indicating microcracking. However, synchrotron X-ray refraction radiography shows that the internal specific surface of such cracks varies differently. A modeling strategy is developed for the calculation of the equivalent stiffness of mixtures (first the matrix and then the sandwich), based on the Voigt and Reuß schemes. The Bruno–Kachanov model is then used to estimate the initial microcrack density in the matrix (due to the thermal expansion mismatch) and the amount of microcracking increase upon cyclic loading. The stiffness in the composite degrades dramatically already after 20 000 cycles but then remains nearly constant. The combination of mechanical testing, quantitative imaging analysis, and modeling provides insights into the damage mechanisms acting: microcrack propagation is more active than microcrack initiation upon cyclic loading, but the second also occurs. This scenario is similar but not equal to previous results on porous and microcracked ceramics.
The most substantial innovations in radiographic imaging techniques of the last two decades aim at enhanced image contrast of weakly absorbing micro and nano structures by taking advantage of X-ray refraction effects occurring at outer and inner surfaces. The applications range from fibre reinforced plastics to biological tissues. These techniques comprise, among others, X-ray refraction topography, diffraction enhanced imaging, phase contrast imaging, Talbot-Lau grating interferometry, and refraction enhanced imaging. They all make use of selective beam deflections up to a few minutes of arc: the X-ray refraction effect. In contrast to diffraction, this type of interaction has a 100 % scattering cross section, as shown experimentally. Since X-ray refraction is very sensitive to the orientation of interfaces, it is additionally a tool to detect, e.g., fibre or pore orientation. If the detector resolution exceeds the size of (small) individual features, one detects the integral information (of inner surfaces) within the gauge volume. We describe the above-mentioned techniques, and show their experimental implementation in the lab and at a synchrotron source. We also show strategies for data processing and quantitative analysis.
3D imaging techniques are very fashionable nowadays, and allow enormous progress in understanding ceramic microstructure, its evolution, and its link to mechanical, thermal, and transport properties. In this feature article, we report the use of a powerful, yet not so wide-spread, set of X-ray techniques based on refraction effects. X-ray refraction allows determining internal specific surface (surface per unit volume) in a non-destructive fashion, position and orientation sensitive, and with a nanometric detectability. While the techniques are limited by the X-ray absorption of the material under investigation, we demonstrate showcases of ceramics and composite materials, where understanding of process parameter influence or simply of microstructural parameters could be achieved in a way unrivalled even by high-resolution techniques such as electron microscopy or computed tomography.
Modern air-liners and wind turbine rotor blades are made up primarily of fiber reinforced plastics. Failure of these materials heavily impairs the serviceability and the operational safety. Consequently, knowledge of the failure behavior under static and cyclic loads is of great interest to estimate the operational strength and to compare the performance of different materials. Ideally, the damage evolution under operational load is determined with in situ non-destructive testing techniques. Here, we report in-situ synchrotron X-ray imaging of tensile stress induced cracks in carbon fiber reinforced plastics due to inter-fiber failure. An inhouse designed compact tensile testing machine with a load range up to 15 kN was integrated into the beamline. Since conventional radiographs do not reveal sufficient contrast to distinguish cracks due to inter-fiber failure and micro cracking from fiber bundles, the Diffraction Enhanced Imaging (DEI) technique is applied in order to separate primary and scattered (refracted) radiation by means of an analyzer crystal. This technique allows fast measurements over large fields-of-view and is ideal for in-situ investigations. Imaging and the tensile test are run at the highest possible frame rate (0.7 s-1 ) and the lowest possible strain rate (5.5∙10-4 s -1 ). For 0°/90° non-crimp fabrics, the first inter-fiber cracks occur at 380 MPa (strain 0.8 %). Prior to failure at about 760 MPa (strain 2.0 %), we observe the evolution of nearly equidistant (1 mm distance) cracks running across the entire sample in the fully damaged state.
3D structural investigations are described by X-ray laminography studies of sandwich shell segments, made of a PVC foam core, covered by non-crimp fabric glass fibre composite lay-ups processed by vacuum assisted resin infusion of epoxy. The specific scope of this study is to image transversal flaws within the foam core (joints) and of single ply overlaps. Test flaws were purposely implemented in order to simulate typical failure under cyclic load. In a dedicated test rig for shell structures, the flaw evolution/propagation is monitored by thermography and optical 3D inspection of deformation. Due to the unfavourable preconditions for classical computed tomography as of large aspect ratio, the samples were investigated by coplanar translational laminography. Its limited range of observation angles of ± 45°, results in anisotropic artefacts about the normal to the sample surface, but the typical flaws are well visualized in the as-prepared state, in a state of early damage, and in the repaired state.
Using SXRR to Probe the Nature of Discontinuities in SLM Additive Manufactured Inconel 718 Specimens
(2020)
The utilization of additive manufacturing (AM) to fabricate robust structural components relies on understanding the nature of internal anomalies or discontinuities, which can compromise the structural integrity. While some discontinuities in AM microstructures stem from similar mechanisms as observed in more traditional processes such as casting, others are unique to the AM process. Discontinuities in AM are challenging to detect, due to their submicron size and orientation dependency. Toward the goal of improving structural integrity, minimizing discontinuities in an AM build requires an understanding of the mechanisms of formation to mitigate their occurrence. This study utilizes various techniques to evaluate the shape, size, nature and distribution of discontinuities in AM Inconel 718, in a non-hot isostatic pressed (HIPed) as-built, non-HIPed and direct age, and HIPed with two step age samples. Non-destructive synchrotron radiation refraction and transmission radiography (SXRR) provides additional information beyond that obtained with destructive optical microscopy. SXRR was able to distinguish between voids, cracks and lack of melt in, due to its sensitivity to the orientation of the discontinuity.
While the problem of the identification of mechanisms of hydrogen assisted damage has and is being thoroughly studied, the quantitative analysis of such damage still lacks suitable tools. In fact, while, for instance, electron microscopy yields excellent characterization, the quantitative analysis of damage requires at the same time large field-of-views and high spatial resolution. Synchrotron X-ray refraction techniques do possess both features. In this work, we show how synchrotron X-ray refraction computed tomography (SXRCT) can quantify damage induced by hydrogen embrittlement in a lean duplex steel, yielding results that overperform even those achievable by synchrotron X-ray absorption computed tomography. As already reported in literature, but this time using a non-destructive technique, we show that the hydrogen charge does not penetrate to the center of tensile specimens. By the comparison between virgin and hydrogen-charged specimens, we deduce that cracks in the specimen bulk are due to the rolling process rather than hydrogen-assisted. We show that (micro)cracks propagate from the surface of tensile specimens to the interior with increasing applied strain, and we deduce that a significant crack propagation can only be observed short before rupture.
3D Crack analysis in hydrogen charged lean duplex stainless steel with synchrotron refraction CT
(2016)
Hydrogen in metals can cause a degradation of the mechanical properties, the so-called hydrogen embrittlement. In combination with internal stresses, hydrogen assisted cracking (HAC) can occur. This phenomenon is not completely understood yet. To better characterise the cracking behaviour, it is important to gain information about the evolution of the 3D crack network. For this purpose samples of lean duplex stainless steel were loaded with hydrogen by means of electrochemical charging and investigated by means of synchrotron refraction CT and SEM fractography after uniaxial tensile loading. Synchrotron refraction CT is an analyser-based imaging (ABI) technique. It uses a Si (111) single crystal as analyser, which is placed into the beam path between sample and detector. According to Bragg’s law only incident x-rays within a narrow range around the Bragg-angle are diffracted from the analyser into the detector. Hence, the analyser acts as an angular filter for the transmitted beam. This filtering allows to turn the refraction and scattering of x-rays into image contrast. Refraction occurs at all interfaces, where the density of the material changes and is more sensitive to density changes than the attenuation. Therefore, it is possible to detect smaller cracks than with classical x-ray imaging techniques, like CT, with comparable spacial resolution. It also visualises the 3D structure of the cracks and gains quantitative information about their morphology and distribution. Since cracks introduced by HAC are usually very small and have a small opening displacement, synchrotron refraction CT is expected to be well suited for imaging this cracking mechanism and can be a valuable tool to characterise the formation and the evolution of a 3D crack network.
The determination of the anisotropy of materials’ microstructure and morphology (pore space) in diesel particulate filter (DPF) materials is an important problem to solve, since such anisotropy determines the mechanical, thermal, and filtration properties of such materials. Through the use of a dedicated (and simple) segmentation algorithm, it is shown how to exploit the information yielded by 3D X-ray computed tomography data to quantify the morphological anisotropy. It is also correlated that such anisotropy of the pore space Such anisotropy of the pore space is also correlated with the microstructure and crystallographic anisotropy of the material in several showcases: a microstructurally isotropic material, such as SiC, and some morphologically and microstructurally anisotropic cordierite materials. In the later case, the finer the grain size, the more isotropic the microstructure.
The reconstruction of cone-beam computed tomography data using filtered back-projection algorithms unavoidably results in severe artefacts. We describe how the Direct Iterative Reconstruction of Computed Tomography Trajectories (DIRECTT) algorithm can be combined with a model of the artefacts for the reconstruction of such data. The implementation of DIRECTT results in reconstructed volumes of superior quality compared to the conventional algorithms.
X-ray computed tomography has many applications in materials science and non-destructive testing. While the standard filtered back-projection reconstruction of the radiographic data sets is fast and simple, it typically fails in returning accurate results from missing or inconsistent projections. Among the alternative techniques that have been proposed to handle such data is the Direct Iterative REconstruction of Computed Tomography Trajectories (DIRECTT) algorithm. We describe a new approach to the algorithm, which significantly decreases the computational time, while achieving a better reconstruction quality than that of other established algorithms.