11. Qualitative and Quantitative X-ray Tomography of Filter Macrostructures and Functional Components

The tomographic methods provide non-destructive 3D insights into the microstructure of materials whereby a variety of radiation, e.g. light [1], Gamma-rays [2] and X-rays [3, 4], as well as particle radiation, e.g. electrons [5], and neutrons [6], can be used as source for tomographic imaging depending on the scale of the samples to be investigated, the desired spatial resolution and the scope of the imaging. Each type of radiation has its own characteristics and interacts on a different way with the matter [7]. When a high resolution on atomic or low nanoscopic scale is required, only destructive methods such as 3D atom probe tomography, TEM and FIB-SEM, respectively, are suitable [7].

The X-rays can basically be generated by industrial/laboratory X-ray tubes or synchrotron light sources. Due to the electrons with a relativistic speed passing through magnetic fields, the synchrotron light sources feature very high photon flux density, high brilliance and monochromatic, almost parallel beam with coherent properties [8]. However, since there is only a restricted number of synchrotron light sources operating imaging facilities, the beamtime is limited and allocated according to the ranking of submitted proposals. The X-ray tomographic imaging can be performed by different contrast modes such as absorption, phase contrast, diffraction, fluorescence, spectroscopy and small angle scattering [7, 8].

In this chapter, specific applications of laboratory, attenuation-based X-ray computed tomography to questions focusing on the research and development of porous ceramic materials and functional components are discussed. The details on the technology, composition of the investigated samples as well as the applied measuring parameters can be found in the respective reference.

The tomographic investigations presented in this chapter have been performed by means of a conventional attenuation-based X-ray computed tomograph CT ALPHA (ProCon X-Ray, Sarstedt, Germany) using a microfocus X-ray transmission tube FXE-160 (Feinfocus, Garbsen, Germany), a motorized, precision rotation stage M-062.PD (Physik Instrumente, Karlsruhe, Germany) as well as a flat panel detector 79425 K-05 (Hamamatsu, Japan) with a pixel pitch of 50 µm and an photodiode are of 120 ×  120 mm², a CMOS flat panel X-ray detector Dexela 1512 (Perkin Elmer Inc. Europe, Walluf, Germany) with a pixel pitch of 75 µm and an active area of 150 × 120 mm² for small samples as well as a large X-ray detector (Perkin Elmer Inc. Europe, Walluf, Germany) with a pixel pitch of 200 µm and a photodiode area of 410 × 410 mm² for large samples. During each X-ray tomographic scan, 1200 radiographs within 360° were acquired with different exposure time as shown in Fig. 11.1.

3 radiographic images of the ceramic foam structure at 0, 45, 67.5, and 90 degrees. The morphology of the sample has a porous structure.

From the finite number of radiographs, i.e. projections of the analyzed object on the detector, a volume data was reconstructed using the measurement and reconstruction software Volex 6.0 (Fraunhofer EZRT, Fürth, Germany). The reconstructed volume data were visualized and evaluated using the software VG Studio MAX 2.2 (Volume Graphics, Heidelberg, Germany).

Since more than 30 years, the X-ray computed tomography is widely used for 3D imaging of highly porous solids [9], such as polymeric [10, 11], metallic [12, 13], glass [14] and ceramic [15, 16] foams due to their low density and thus favourable X-ray transmission properties.

Therefore, a qualitative X-ray computed tomography shall exemplarily be demonstrated on the open-porous alumina foam structures. The commercially available Al₂O₃ filters with three different ppi (pores per inch) numbers, i.e. 10 ppi, 30 ppi and 60 ppi were investigated using µCT, see Figs. 11.2, 11.3 and 11.4, respectively. The foam geometry and the pore density have a significant impact on the determination of elastic properties by both static and dynamic methods [17] as well as on the determination of compressive and 3-point bending strength [18].

Left. A 3 D rendering image of the ceramic foam has uniform pore density. Right. A magnified view of the specific site of the foam at 15 millimeters. The morphology of the foam has a highly porous surface.

Left. A 3 D rendering image of the ceramic foam has a uniform pore density of 30 pixels per inch. Right. A magnified view of the specific site of the foam at 15 millimeters. The morphology of the foam has an open porous surface.

Left. A 3 D rendering image of the ceramic foam has a uniform pore density of 60 pixels per inch. Right. A magnified view of the specific site of the foam at 15 millimeters. The morphology of the foam has an open porous surface.

Furthermore, the reticulated ceramic foam structures can be functionalized with different coating methods. Moritz et al. carried out a feasibility study of electrophoretic deposition of alumina on foam ceramics by varying the voltage and deposition time. Al₂O₃-C foams (20 × 15 × 15 mm³) were used as deposition electrode due to their sufficient electrical conductivity. The formation of channel-like pores, the quality of the coating and its adhesion after sintering as well as after thermal shock loading by immersion in molten aluminium were evaluated by means of X-ray computed tomography. It has been proven that the electrophoretic deposition can be successfully applied for coating of Al₂O₃-C foam structures, see Fig. 11.5. The electrophoretic coatings are mainly formed on the outer surface of the substrate foams, but even the outer surface poses the most impacted zone during the metal melt filtration process [19].

Left. A 3 D rendering image of the ceramic foam has a uniform pore density. Right. A magnified view of the specific site of the foam at 5 millimeters. The morphology of the foam has a uniform porous channel.

Besides electrophoretic deposition also a cold spraying technique or conventional slip casting can be used for coating of foam [20] and dense ceramics by alumina slurry, respectively. Aneziris et al. tested slip casted carbon bonded nozzles with and without active alumina coating regarding their clogging behavior in a steel casting simulator consisting of an inductive heated melting unit and an inductive heated tundish unit with two nozzles in the bottom part [21]. The Fig. 11.6 shows the configuration of the nozzle setup comprising the adapter made of coarse-grained spinel-bonded alumina castable with inserted test nozzle made of fine-grained carbon bonded alumina without reactive alumina coating. The CT scans of test nozzle with reactive alumina coating can be found elsewhere [21].

Left. A 3 D model of the nozzle. Right. A 2 D model of the nozzle at 20 millimeters. The top and bottom regions of the nozzle are represented as bright, while the center region is represented as dark.

The qualitative X-ray computed tomography is often used for quality control purposes. Moreover, the reconstructed volume images can serve as a reference for target-actual performance comparison to estimate the variance between the computer-aided design and the CT scan of the fabricated object based upon the model. Herdering et al. generated an open cell foam model, printed polyamide (PA) foams thereupon by selective laser sintering (SLS) technique and compared the foam model with the reconstructed isosurface of the printed foam. The SLS additive manufacturing could well reproduce the macrostructure of the computer-aided model, however the strut thickness and the relative density was significantly higher for the printed foams [22].

The Fig. 11.7 shows hybrid manufactured porous alumina ceramics (cubes with an edge length of 25 mm) with a Kelvin structure based on templates 3D printed by SLS method and subsequently flame sprayed with alumina. Instead of usually applied polymeric materials (polyamide, polyurethane, polycarbonate) which have to be burned-out, environmentally friendly raw materials were introduced such as saccharide or salt. The new hybrid manufacturing approach overcomes difficulties connected with the thermal treatment of the polymeric materials by solving the template material in water.

Two 2 D models of the ceramic cube at 20 millimeters. The left model has a Kelvin structure, and the right model has a structure sprayed with alumina.

The qualitative X-ray computed tomography is very well suited for the investigation of fracture mechanisms as presented in Fig. 11.8. In order to increase the ultimate fracture strain of Al₂O₃-C materials a new approach has been developed and evaluated. An aqueous suspension of graphene oxide (GO) was reinforced with sapphire nanosheets, slip casted to strip-like samples with a size of 25 × 8 × 0.2 mm³ and subjected to 3-point bending loading. An extreme deflection without failure and a delamination as a determining fracture mechanism are clearly visible. The resulting voxel size after reconstruction was 8.6 µm.

A 2 D model of the sample strip at 2000 micrometers. The morphology of the sample has a thread-like structure with a bend.

In addition to the visualisation, a quantification of the microstructure in 3D [23, 24] or even in 4D [23] is of major significance. The quantitative analysis of the reconstructed volume data was performed by the software Modular Algorithm for Volume Images MAVI 1.5.3 (Fraunhofer ITWM, Kaiserslautern, Germany).

The quantitative X-ray computed tomography can provide essential 3D structural features and statistical characteristics useful for the development of new technologies and the optimal choice of processing steps, e.g. for the manufacturing of reticulated foam filters [25]. Based on alumina [26] or carbon-bonded alumina [27]. In order to evaluate the homogeneity of the ceramic foam structure, the global and local features were analyzed using the whole filter (50 × 50 × 25 mm³) and several ROIs, respectively. Voigt et al. divided the manufactured alumina foam filters virtually in 6 layers along the filters [26] while Luchini et. al constituted five distinct ROIs, one in the center and four in the edges of the foam filter samples [27]. Thus, the homogeneity of the strut thickness distribution, the porosity and the macropore sizes at several filter production steps can be statistically analyzed and used for a direct comparison of conventional rolling/spraying and centrifugation technique.

But not only the relationship between the processing route and the macro and macrostructure but also the correlation between the measurement parameters and the mechanical properties of foam materials, e.g. the influence of the loading plate size, the sample dimensions and the application of a compliant pad on the crushing strength can be evaluated by µCT [28]. The experimental results were validated by mechanical simulations of a crushing strength measurement based on minimum principal stress distribution calculated with FEM.

Moreover, the understanding of the experimental results of the compressive strength measurement can be supported by numerical simulations decoding the crucial determinants. In compliance with the real foam filters, artificial foam geometries were modelled by combination of different relative densities and strut shape factors [29]. A good correlation between the real and virtual strength was obtained and two distinct failure mechanisms depending on the strut shape factor were detected. An advanced experimental–numerical approach taking besides the strut shape and the relative density also pore stretching and polydispersity into account can be used for the prediction of creep deformations of carbon-bonded alumina foams at high temperatures [30]. In order to achieve a high creep resistance and the dimensional stability of a foam filters at high temperature, the stretching direction of the foam should be parallel to the loading direction.

In the run-up to the quantification, the reconstructed volume images must be post-processed in order to extract desired quantitative characteristics, cp. [15]. After the reconstruction of the volume image with a resulting voxel size of 18.9 µm, a region of interest ROI avoiding the edge errors has to be selected, as shown in Fig. 11.9 exemplarily for uncoated carbon bonded alumina foam filters of a cylindrical geometry with a diameter and a height of 20 mm. In the presented case, the volume image was cropped to a size of 300 × 300 × 300 voxels.

A reconstructed model of the carbon foam. The coated and uncoated regions are represented by different shades. The center region of the model is cropped and has a rough surface.

After the binarization step using Otsu´s threshold automatically separating voxels in foreground (white) and background (black) [31], field features were determined, see Fig. 11.10. Subsequently, all pores inside the struts (PU pores, material´s micropores) were eliminated using the morphological closing procedure in order to be able to quantify the strut system as a whole as well as the functional macropores. By complementing the binarization, the background voxels representing the functional macropores can easily be inverted into the foreground voxels and quantified as well.

Afterwards, the morphological procedure called spherical granulometry can be performed on the binarized volume image by successive morphological openings with structuring elements (balls) of increasing size until all foreground voxels disappeared, see Fig. 11.11. As a result, each voxel is assigned to the diameter of the ball belonging to the step where this voxel disappeared for the first time [24].

Left. A reconstructed model of the carbon foam. The morphology of the sample has a Y-shaped region with different patterns on a dark background. Right. The Y-shaped region is cropped.

Left. A reconstructed model of the carbon foam. The morphology of the sample has a Y-shaped region with different circular patterns on a dark background. Right. The Y-shaped region is cropped, and the circular pattern is drawn in the background region.

Thus, by means of the spherical granulometry cumulative distribution functions of both struts and macropores can be established. The spherical granulometry revealed for struts a d₅₀-value of 1.33 mm and a d₉₀-value of 1.82 mm whereas for macropores a d₅₀-value of 2.44 mm and a d₉₀-value of 4.56 mm.

Ex-situ tomographic investigations require neither implementation of the testing equipment inside the µCT device nor restrictions regarding the acquisition time. Therefore, they are widely used for gathering of 3D tomographic data prior and posterior of thermal [32], mechanical [33, 34] or chemical [35] loading events. For ex-situ loading, the investigated sample must be removed from the µCT device and repositioned on the sample rotation stage upon loading completion [36]. Obviously, the relocation of the sample involves an extrinsic shift of the acquired image data which has to be distinguished from the inherent displacement or alteration induced by intended loading.

The ex-situ tomographic investigations are well suited for localising and identifying the prime cause of failure under extreme loading and environmental conditions not implementable into µCT devices, such as creep experiments at high temperature under inert atmosphere or corrosion experiments in a steel casting simulator.

Figure 11.12 compares two different states of a cylindrical, carbon-bonded alumina sample manufactured by the replica technique using a cylindrically shaped polyurethane foam with a diameter of 20 mm and a height of 25 mm [30]. The Al₂O₃-C foam sample was coked at 1400 °C under reducing atmosphere representing the initial state. The initial state was scanned by µCT. The finished, coked foam sample was evacuated and subjected to a creep experiment in an induction heated high temperature testing machine at 1350 °C under argon atmosphere. After cooling, the thermo-mechanically loaded sample was analyzed using the µCT again with the same acquisition parameters. The voxel size after reconstruction was 19.8 µm. The direct comparison of both states at the same position (virtual cross section through the middle of the sample) revealed two cracks originating from the sharp triangular strut pores left by decomposition of the polyurethane foam template.

Left. A 2 D reconstructed model of the cylindrical slice at 5 millimeters that is bonded to carbon foam. Right. A model has a cylindrical slice at 5 millimeters, and the bond between carbon and foam is broken down.

Figure 11.13 demonstrates another ex-situ investigation of foam filters. Wetzig et al. produced cylindrical carbon-bonded alumina foam filters (10 ppi) with a diameter and a height of 200 mm by replica technique [37]. The polyurethane foam templates were provided with one central and eight circularly arranged macro-channels with a diameter of 40 mm each, allowing flow conditioning during continuous casting of steel. The templates were twice coated with an alumina-carbon slurry, dried and cooked at 800 °C under reducing atmosphere.

2 radiographic images of the carbon bonded foam with and without testing. Left. The foam before testing has a uniform pore distribution. Right. The foam after testing has dark patches of varying sizes.

The microstructure of the final foam filter was analyzed by µCT using the large PerkinElmer X-ray detector in order to visualize possible radial density and strut thickness gradients and inhomogeneities. The resulting voxel size was 262 µm. Afterwards, the foam filter was tested in a steel casting simulator regarding its thermo-mechanical behavior. The steel melt was cast through the foam filter being placed in a tundish vessel into the copper molds positioned below the tundish vessels. After cooling and opening the steel casting simulator, the removed foam filter with steel residues was analyzed by µCT again. As can be seen from Figs. 11.13 and 11.14, the macrostructure of the foam filter remained undamaged but numerous steel residues in the form of spheres and a rim stuck on the surface of the foam filter.

Two 3 D reconstructed models of the carbon bonded foam with and without testing. Left. The foam before testing has a uniform pore distribution. Right. The foam after testing has dark patches of varying sizes.

In contrast, for in-situ loading the sample remains in the same position while the whole loading equipment is placed on the rotation stage thus the arising microstructural changes can primarily be attributed to the applied loading. A distinction needs to be drawn between so called interrupted and true in-situ µCT investigations. The interrupted in-situ µCT investigations are carried out discontinuously, i.e. the loading must be interrupted in order to perform a CT scan while maintaining the loading level at a constant value. Obviously, such assumption does not necessary reflect the reality since all launched processes are being continued even during the CT scan. In comparison, the true in-situ CT investigations are performed continuously, i.e. the scan time is substantially shorter than the time frame of the unfolding events.

Interrupted in-situ investigations of metallic (316L steel) scaffolds and metal-ceramic (TRIP-steel/Mg-PSZ) foams and honeycombs under compressive load were successfully performed using lab-based X-ray µCT equipment providing detailed insights into the deformation mechanisms of architectures metallic structures [38] and metal-ceramic composite structures [39].

However, the interrupted in-situ tomographic investigations of brittle foam materials present a particular challenge as a consequence of its sudden failure of a stochastic nature. Therefore, extensive preliminary investigations are necessary.

In the presented study, the interrupted in-situ investigations of white and black glass foams under quasi-static strain-controlled compression loading were performed. The white and black foam glass samples were prepared by foaming of a powdered recycling float glass while adding neutralization foaming agent resp. redox foaming agent at a temperature of 800 °C. The foamed glass samples were cut to cubes with an edge length of 20 mm and underwent in-situ tomographic scans at different compressive strains based on preliminary investigations. After reaching of the intended compressive strain level and subsequent awaiting of force balance, tomographic scans taking approx. 15 min were carried out. The details of the experimental procedure and in-situ µCT parameters can be found elsewhere [40]. For the interrupted in-situ compressive testing, a specially designed in-situ load frame was used [39].

Figure 11.15 shows the reconstructed volume rendering of white foam glass at compressive strains of 0, 1, 3.8 and 5.1%. The tomographic scans underlined that the failure of the white foam glass takes place in a mere brittle mode. At a compressive strain of 1%, no visible changes of the microstructure could be detected, only an elastic compression can be traced by the movement of the lower loading plate against the upper loading plate. Already at a compressive strain of 3.8%, several cell walls in a shear direction failed, i.e. a shear deformation band was formed. The force-displacement curve showed a clear peak with a consequent drop of the force.

Four 2 D models of the black foam slice at 5.5 millimeters with different compressive strains. The first two models have a slice with a uniform pore structure. The next two models have a damaged slice with a uniform pore.

The compressive behaviour of the black glass foam differs distinctly from the white glass foam. As can be seen from the Fig. 11.16, either a successive local failure nor a formation of a global crack could be identified. A deformation band close to the upper compressive plate perpendicular to the loading direction unfolded. Such quasi-ductile behaviour of the black glass foams can be attributed to the nature of the pores. In contrast to the white foam glass, the pores of the black foam glass are predominantly closed.

Four 2 D models of the black foam slice at 5 millimeters with different compressive strains. The morphology of the models has a slice with a uniform pore distribution.

The black foam glass exhibited an extraordinary compressive behaviour, i.e. no pronounced force peak could be identified. The force–displacement curve of black foam glass shows a linear increase up to a displacement of approx. 2%. Afterwards, a force plateau arises and the force–displacement curve proceeds constantly up to the last compressive strain of 15%.

By means of DVC (Digital Volume Correlation) software DaVis 10 (LaVision, Göttingen, Germany) the full 3D strain and displacement maps were exemplary calculated for the black foam glass at a compressive strain of 10% comparing the volume image of the black foam glass in unloaded state (0%) as a reference and in the deformed state. The deformation band was excluded from the DVC calculation due to the extreme alteration (Fig. 11.17).

2 contour plots of 1y versus x. Left. The black foam slice has a porous surface shaded with different color gradients. Right. The slice has a pore surface with displacement represented by the arrows.

Nevertheless, the true in-situ X-ray µCT experiments for fast progressing processes, especially for dynamic loading [41, 42], are currently feasible only using synchrotron sources. Recently, dynamic processes during foaming of liquid aluminium such as nucleation, growth and coalescence of the bubbles at high temperatures have been investigated by applying of a continuous X-ray tomoscopy [43]. Otherwise, an automatic tracking algorithm was developed enabling follow up the damage evolution, particularly void nucleation, growth and coalescence during in-situ tensile loading of pure iron material by microtomography [44].

The conventional, attenuation-based X-ray computed tomography has been shown to be a useful tool for assessing of 3D structures as well as detecting of microstructural defects, inhomogeneities, pores and pore size distribution, cracks etc. [45]. The advantages are undoubtedly its non-destructive matter, good availability and possibility to scan real components with large dimensions. However, some limitations still remain. First of all, the spatial resolution is rather limited since X-rays are divergent and the control of the magnification is achieved by adjusting the source to sample distance or by implication the source to detector distance, i.e. the magnification is merely of geometrical nature.

The X-ray computed tomography of large components features a tightrope walk between a sufficient transmittance, achievable resolution and incidence of artefacts impairing the reliability and quality of the tomographic images since the X-ray beam leaving the target represents by no means a point source. In fact, a focal spot of a non-negligible size forms on the target resulting in the blurring effects in the acquired radiographs. The spot size is directly proportional to the applied accelerating voltage and current. However, the maximizing spot size along with minimizing the number of projections on the condition that no notable increase of blurriness arises could be beneficial, particularly for high-speed imaging [46].

Furthermore, the conventional, attenuation based X-ray computed tomography is just an imaging technique without any possibility to obtain additional information on chemical or phase composition and distribution. In recent past, novel techniques not only for synchrotron microtomography [47] but also for laboratory X-ray microscopy [48] have been developed.

Nevertheless, the acquired attenuation-based X-ray CT imaging data and extracted 3D/4D quantities can be used as input for a virtual laboratory in order to set realistic boundary conditions, to validate simulation outputs and to establish new, reality-based models of material microstructure as a function of environmental conditions. The steps towards future would comprise the implementation of machine-learning algorithms not only on the acquisition side, e.g. for significant reducing of the acquisition time at required resolution, but also on the image processing side, e.g. for automatizing of binarization and particularly segmentation of structural parts to be evaluated [49].

The findings of the performed µCT measurements indicate that the attenuation-based, laboratory X-ray microcomputed tomography is a valuable tool for non-destructive analysis of macro and micro structures of different materials and components taking some constraints into account. Obviously, there are some technical (size and resolution of the detector, source-to-detector distance, max. accelerating voltage, max. target power) and physical limitations (polychromatic and cone X-ray beam, focal point on the target) so that the spatial and temporal resolution are constrained while maintaining a reasonable signal-to-noise ratio. Therefore, the size and composition of the objects to be investigated should be chosen with respect to the sufficient penetrability, achievability of expected results and timescale of the processes that unfold during loading.