Chapter 2: Literature Review and Theory
2.4. Micro X-ray Computed Tomography (Micro-XCT)
and without spalling, as well as those that exhibited partial spalling, were viewed optically with ultraviolet illumination: a non-spalled sample showed an increase in crack depth as the mid-point of the crack was approached as well as crack propagation laterally.
A spalled sample revealed that spalling had not arisen from the initial crack and was most likely initiated from branching of secondary surface cracks. Polishing through the partially spalled crack gave good insight in to the spalling mechanisms; a section which had not yet flaked off showed that the initial crack had propagated parallel to the surface and subsequent crack branching along this crack had started extending upwards but without intersecting the surface. Secondary surface cracks were also viewed to have propagated down in to the ball-bearing and connected with the branches from the initial crack leading to the formation of a crack network and resultant flaking. These investigations, along with complimentary computational analysis also by Zhao et al [59], lead to a mechanism of spalling from pre-existing cracks in silicon nitride bearings when put under rolling contact: Hertzian pressure in combination with bending pressure from the initial crack induce tensile stress in the surrounding region that causes the opening of secondary surface cracks which propagate downwards. Subsequent intersection with the primary crack, and its branching, that has extended laterally beneath the surface causes material removal via spalling [53]. Serial sectioning via incremental polishing can reveal useful information about sub-surface cracking; however it is a destructive method, meaning that samples investigated in this way are changed in the process. Therefore, investigation techniques with the ability to observe sub-surface cracking without inducing mechanical damage are highly desirable.
2.4. Micro X-ray Computed Tomography (Micro-XCT)
2.4.1. XCT Theory
X-ray computed tomography (XCT) is a non-destructive technique used for obtaining images and material property information from the interior of a sample. The most well-known application of XCT is in medical industry where it is commonly utilised to evaluate human bodily structures e.g. bone fracture [60]. In the area of material science, XCT is now widely used to view material microstructures for correlation with their macroscale properties. The basic principle, shown in Fig. 2.6, involves an x-ray source emitting high energy photons towards a sample which are then detected by a scintillator on the opposing
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side and used to form a grayscale image. The contrast in the image is a function of the x-ray attenuation: the decrease in intensity of the x-x-rays as they traverse the material. This is determined by the photon scattering and absorption mechanisms, which in turn are dependent on the materials density and composition [61], [62]. Therefore, materials with a high density will generally have higher x-ray attenuation and hence appear darker in a grayscale image. The intensity of radiation incident on the detector is related to Beer’s Law given in Eq. 2.2:
𝐼 = 𝐼
0𝑒
−𝑥µEquation 2.2: The relationship between x-ray intensity (I) at the detector, initial intensity (I0), and the material of interest.
where I0 and I are the initial and final intensity respectively, x is the x-ray path length and µ a material dependent attenuation coefficient [63]. This is a simplified situation for the actual intensity detected in practice because samples often contain more than one material as well as variations in density. In addition to this, Eq. 2.2 assumes a monochromatic x-ray source when for most devices the source emits across a range of energies meaning an integral over this range must be taken.
The usefulness of a single 2D plane image, called a radiograph, is limited because it only gives an average of x-ray absorption meaning that gauging three-dimensional positional information of features is not possible. For instance, if a porous region with low absorption was located behind a dense region of high absorption there would be no way of distinguishing these microstructures. In XCT scans this problem is overcome by rotating the sample (or rotating the source and detector combination whilst the sample remains static) around a single axis whilst taking images at set angle increments. These images are then used in conjunction with tomography algorithms to create a 3D reconstruction of the sample where each voxel (the equivalent of a pixel but in 3D space) is representative of the x-ray absorption and hence material density at any given location; allowing for the advanced 3D visualisation of the internal structure. The 3D reconstruction can then be digitally sectioned along any plane and converted to a stack of 2D images for further analysis. A schematic of this whole process is shown in Fig. 2.6 [60].
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Figure 2.6: A schematic showing the x-ray tomography process from the initial sample imaging to the tomographic reconstruction.
2.4.2. XCT for Fracture Investigations
The spatial resolution of an X-ray Computed Tomography (XCT) device is determined primarily by the x-ray source spot size, sample-detector position, and the detector attributes. The development of these devices over recent years has led to the emergence of microscale-XCT, and even nanoscale-XCT [60]. The increase in resolution has been key to XCT use in materials science as it has allowed for non-destructive internal investigations of materials approaching resolutions (~ 50 nm) previously only reserved for surface characterisation techniques (although nano-XCT is limited to samples < 15 µm in size) [64]. Typical lab-quality devices have a spatial resolution of ~ 0.5 µm. It is therefore clear to see why XCT is desirable in the study of sub-surface fracture, particularly at scales where other non-destructive methods become difficult to apply.
Even with the higher x-ray CT resolutions available, observing microscale cracks is not trivial because they must be within a block of material that encases the whole crack with representative stress state, and they also must be open, in order to be visible in a tomography scan. However, a crack with width less than the pixel size can still potentially be detected by the change in contrast of the pixel in comparison to an adjacent pixel due to the presence of the crack; cracks with opening displacements of < 1.8 µm have even
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been detected using this method where the crack width was one tenth of the pixel size (2 µm pixel size) [64]. It has been found that an alternative type of x-ray contrast, called phase contrast, is more suited to detecting cracks than the conventional absorption contrast dictated by Beer’s Law (Eq. 2.2) [65]–[67]. Absorption contrast is determined by the change in intensity of the x-rays as they permeate through different materials whereas phase contrast is a product of small changes in refractive index typically between low attenuation volumes that causes local changes in the x-ray path length causing a phase change. Phase contrast is particularly prominent for cracking where diffraction fringes increase the edge contrast, hence making them more detectable. A disadvantage of phase contrast is that it requires a coherent ray source, i.e. a source with a single x-ray wavelength and constant phase difference. This is only possible using advanced lab tomography devices or a synchrotron source in which the x-ray radiation is emitted from radially accelerated charged particles. Synchrotron sources are advantageous to lab sources in many ways: they offer significantly increased flux (<1000x that of lab tomography), a smaller source, and a parallel beam geometry allowing for higher resolution and faster scan times. However, the number of synchrotron facilities is limited as a particle accelerator is required for the x-ray emission [68].
Synchrotron x-ray tomography in conjunction with phase contrast imaging has been used to study sub-surface Vickers indentation damage in polycrystalline alumina [69].
Vertyagina et al [69], [70] performed in-situ indentation to measure crack opening displacement on loading and unloading for an applied load of 34 kg. Tomography scans were taken before, during, and after loading, with pores within the alumina being used as reference points in order to correlate the material displacement in a technique known as Digital Volume Correlation (DVC). Although not directly observed in the images, lateral cracking beneath the indentation was inferred by the upward displacement (~ 1 µm) of material on unloading, extending out to the radial crack tips. Radial cracks were visible via the phase contrast exhibited but not from attenuation contrast, and the cracks had an estimated width less than that of the voxel size (0.9 µm).
Although useful for the detection of cracks, phase contrast does have its limitations, for instance, when applied in lab-based tomography (i.e. not synchrotron) long acquisition times (> few hours) are required to get sufficient contrast [67]. In some cases, it may be beneficial to instead find ways of increasing crack visibility when using a lab x-ray source.
Such a study comparing various methods of crack imaging in XCT was carried out by Wu et al [71], [72] on glass-fibre composites. The three methods in addition to phase contrast
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investigated by Wu et al were: increasing image resolution (by decreasing the pixel size), using an applied load to open up the cracks hence making them more visible, and penetrating the cracks with a high attenuation dye to increase their contrast. Both increasing the resolution and crack opening via loading (although this can change the crack geometry) were found to be effective, in essence because they increase the pixel count associated with a crack. The most effective method was the use of zinc iodide penetrant as a contrast agent with cracks being detectable down to 1/10th of the spatial resolution (~ 0.2 µm) although the success of this method is based on the full saturation of cracks with the penetrant as well as the cracks intersecting with the surface in order for the penetrant to enter in the first place. It is also noted that crack opening is clearly not determinable when the width of the crack is less than that of the spatial resolution.
It is therefore apparent that a higher resolution method is required for observing sub-surface features on the micro and nanoscale.