tablishes the usability of the phase-retrieval procedure in multiple purposes, and suggests the implementation of this methodology aiming at practical use in advanced laboratory systems.
7.3 Tomography of composite materials
In this section, persuasive employment of X-ray microscopic imaging in the investigation of composite materials is discussed. The benefit of phase contrast and phase retrieval for the characterization of these materials is highlighted.
7.3.1 Motivation
An accurate knowledge of the orientations of fibrous rigid materials included in polymer matrixes is important in material science, in order to improve their physical and mechan-ical properties. These matrixes include multiple additives like resins and fillers aiming to reduce the weight (non functional fillers) or to fulfil a specific task (functional fillers) [Kia, 1993]. As an example, sheet molding compounds (SMC) have gained importance mainly in lightweight construction due to their flexibility and cost efficiency [Orgéas and Dumont, 2012, Palmer et al., 2010]. Besides mechanical testing, which can predict some material properties, three-dimensional imaging of samples is required to determine the relative dis-tribution and local orientation of fibers [Czabaj et al., 2014, Whitacre and Czabaj, 2015].
Hence, a net contrast between the fibers and components of the investigated sub-volume is indispensable.
With a non-commercial device, single-distance phase-contrast imaging was demonstrated to be promising for the evaluation of structural materials with the aid of epoxy and alu-minium alloys [Zoofan et al., 2006]. In this perspective, several material composites such as carbon fibers, aluminium composite materials were also characterized by using commercial machines [Kastner et al., 2012a,Kastner et al., 2012b], and the edge enhancement resulting from phase shift was proven to emphasize the contrast for effective segmentation. Beyond its use in the characterization of materials, this effect is also applied for testing segmentation al-gorithms through comparisons between computational results and those that are experimen-tally observed [Czabaj et al., 2014]. Nevertheless, using SMC as an example of a composite sample containing fibers and granular fillers, the contrast could remain low despite the edge enhancement. The phase-retrieval method is demonstrated here to considerably increase the contrast in composite material specimens.
7.3.2 Sheet molding compound
Description of the sample and experiment
The sheet molding compound is the best example of reinforced and filled polymers and finds frequent usage in transportation, construction and appliances [Kia, 1993]. The sample investigated in this work has a dimension of≈1 cm in diameter and is built of resin, glass fibers and alumina trihydrate also designated as aluminium hydroxide–Al(OH)3. The latter is a filler that aims to reduce the weight of the compound but has a functional property as a flame retardant.
Experiment and data analysis
The scan was performed at a tube voltage of 60 kV, and with apseff = 0.96µm. The sample dimension is obviously large above the FOV of almost 1 mm (1024 × 0.96µm). Accord-ingly, the sample was scanned in a zoomed modality, commonly known as local tomography.
The phase retrieval procedures presented in the following are restrained to the SM and the MBA, which have been performed respectively with a βδ-ratio = 199 and the regularization termα= 8.e-03.
Results and discussion
The transverse slice of the transmission data (Fig. 7.8(a)) shows a low contrast. The re-sults obtained by applying the SM and MBA phase-retrieval operation display visually in Figs. 7.8(b) and (c) an improvement in the contrast, which is concretely witnessed to the well-structured histograms in Figs.7.8(e) and (f) compared to Fig.7.8(d).
The sagittal layer, exposed in Fig. 7.9(a), gives a little overview of the positioning of fibers in the composite material. In comparison, the corresponding slice derived from the reconstruction through phase retrieval in Fig. 7.9(b) raised the discrimination between the fibers and the additives, particularly in the selected region. These regions selected from Fig. 7.9(a) and (b) are enlarged in Fig.7.9(c) and (d), and are used to express in an explicit manner the role played here by the phase retrieval. The horizontal line profiles (left to right) and the vertical (up to down) in the latter figures in the graphs of Figs. 7.9(e) and (f) in-dicate that the granular fillers and the fibrous structures are clearly defined in a less noisy environment, when the data is processed via a phase retrieval algorithm.
The production process of SMC requires several characteristics of each component to be procured. Fillers may then have a certain size and distribution [Kia, 1993]. The fibers may rather need to form a strand or bundle and keep this orientation after compounding, in order to ensure a dimensional stability. This state is however complicated to maintain, so that the 3D rendering shown in Fig.7.10(a) represents a satisfactory achievement with the process-ing performed in this work. The directions as well as the bondprocess-ing of the filaments have been ideally detected by simple thresholding (Figs.7.10(b)–(d)).
Though the choice of this kind of specimen is only based on its mixed composition, the type of its constituents matters with regard to the contrast achieved in order to track the orientation of the fibers. Considering chalk–CaCO3 of density 2.71 g.cm−3 as a prevalent filler in SMC, its contrast to glass fibers i.e., SiO2 of density 2.65 g.cm−3 is low in X-ray attenuation imaging. With reference to the index of refraction from [Henke et al., 1993], this outcome is quite conceivable, and an advisable solution is phase-contrast microtomography [Le et al., 2008]. While still referring to the index of refraction of the fillers, Al(OH)3 of density 2.42 g.cm−3might reveal better contrast to SiO2with increasing photon beam energy in attenuation imaging. Consequently, the contrast formation based on attenuation imaging may not be optimal for the specimen studied in this section, which has been scanned with an average energy ofEav= 13.15 keV. Hence, a low contrast is issued in the transverse slice of the transmission data (Fig.7.8(a))
7.3 Tomography of composite materials 101
100 µm
T RANSMISSION SM MBA
a b c
d
Figure 7.8: 3D reconstructed slices from transmission and phase of the sheet molding com-pound (SMC). (a) Transverse slice from a simple reconstruction with the FBP. (b) and (c) Corresponding slices reconstructed using a phase map calculation with the SM and MBA, respectively. (d) Histograms of the data shown in (a)–(c).
7.3.3 Conclusion
The use of phase-contrast imaging and tomography at research laboratory systems in order to produce solely edge-enhanced images has procured benefits in the study of a variety of materials [Mayo et al., 2012, Kastner et al., 2006,Zoofan et al., 2004]. Phase retrieval has increasingly gained importance by improving the results of tomographic reconstructions and
T RANSMISSION SM
100 µm
a b
c d
e f
Figure 7.9: Explicit comparison between the transmission data (a) and the data derived from phase retrieval (b). The regions selected in previous images are highlighted in (c) and (d). Focus is set on the horizontal and vertical lines in both images. The horizontal plot profiles are displayed in (e), while the vertical profiles are shown in (f). In the latter graphs the contrast is shown as emphasized in the phase-retrieved data, where the fibers are clearly higher than the additives.
7.3 Tomography of composite materials 103
100 μm
a b
c d
Figure 7.10: 3D rendering of the data processed using the phase retrieval. (a) A segmen-tation by simple thresholding has permitted the visualization of the oriensegmen-tation of the fibers (orange and yellow) included in the granular mass of fillers (grey). (b)–(d) show the state of the fibers basically meant to form a bound.
procuring extensive contrast [Mayo et al., 2003]. It has been proven in this section with the case study of a sheet molding compound, that this procedure is effectively an asset. Although these results have been reproduced on several samples such as carbon fibers composites and aluminium compounds (AlSi12,Al2O4), this SMC sample is shown here as an example.
Hence in our opinion, this methodology is worth being incorporated in the development of future laboratory systems optimized for phase-contrast imaging.