The imaging of failure in structural materials by synchrotron radiation X-ray microtomography

Engineering Fracture Mechanics 182 (2017) 127–156

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The imaging of failure in structural materials by synchrotron radiation X-ray microtomography S.C. Wu a,⇑, T.Q. Xiao b, P.J. Withers c,d a

State Key Lab. of Traction Power, Southwest Jiaotong University, Chengdu 610031, China Shanghai Synchrotron Radiation Facility (SSRF), Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201204, China c School of Materials, The University of Manchester, Manchester M13 9PL, United Kingdom d Research Complex at Harwell, Didcot, Oxfordshire OX11 0FA, United Kingdom b

a r t i c l e

i n f o

Article history: Received 12 May 2017 Received in revised form 19 July 2017 Accepted 19 July 2017 Available online 21 July 2017 Keywords: Stress intensity factor Fatigue crack growth Crack opening displacement (COD) Damage tolerance approach Linear elastic fracture mechanics (LEFM) Crack closure

a b s t r a c t The initiation and propagation of short cracks are critical to the detailed understanding of the failure mechanisms of engineering materials and structures. Therefore, for a safety critical component, it is beneficial to be able to follow the progress of cracks in loaded structures and real environments ideally at sub-micron spatial resolution and/or sub-second time resolution. Here we review the great progress that has been made in the application of synchrotron radiation X-ray computed microtomography (SR-lCT) to the study of internal damage accumulation and evolution in structural materials including cast irons and steel, nickel superalloys, lightweight titanium and aluminum alloys as well as metallic, ceramic and polymer composite materials together with additatively manufactured or three-dimensional (3D) printed metallic materials. SR-lCT is shedding light on the complex interactions of cracks with intrinsic porosity, precipitates and intermetallic inclusions and grain structure, as well as macroscopic features such as holes and joints. Furthermore it is enabling qualitative and quantitative relations between the microstructural features and engineering performance to be established and validated under realistic service loading and environmental conditions. Here we introduce the basic 3D and time-lapse (4D) tomographic methods and discuss their strengths and limitations across a range of the applications, as well as identify opportunities for the future. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Understanding the initiation and evolution of damage is a critical aspect in the design and safe operation of engineering components [1–4]. To evaluate the lifetime as precisely as possible, surface-based optical microscopy (OM), scanning electron microscopy (SEM) and post-mortem fractography are frequently employed to establish the empirical relationships between fatigue crack growth rate and the applied stress intensity factor range (DK) within an engineering fracture mechanics framework. This macroscopic view of fracture and fatigue has achieved a great deal, but neglects the crack-shielding mechanisms that can confer increased fatigue crack resistance [5,6]. Furthermore, these surface-based two-dimensional (2D) approaches provide little insight into microstructural effects within the short crack regime that occur within the

⇑ Corresponding author. E-mail address: [email protected] (S.C. Wu). http://dx.doi.org/10.1016/j.engfracmech.2017.07.027 0013-7944/Ó 2017 Elsevier Ltd. All rights reserved.

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interior in three dimensions. This is important because the nucleation and growth of short fatigue cracks can represent a significant fraction of the exploitable service life [6–8]. Industrial X-ray computed tomography (CT) is able to inspect whole components but at a resolution (>100 lm) only sufficient to identify long cracks or relatively large sized defects [5,6,9–13]. For many high performance components, this resolution would impose too large a smallest detectable critical-defect size resulting in over conservative design, if used to predict minimum remnant life from a damage tolerance viewpoint. Equally importantly, the crack path of short fatigue cracks can be influenced by grain orientations and grain boundaries, defects, precipitates, second phases and inclusions which can therefore play a significant role in determining the fatigue resistance properties of a material [6,14–18]. Consequently, a better understanding of the effect of microstructural factors- and features-induced damage accumulation on fatigue crack growth behaviour is required so that we can improve the fatigue performance of engineering structures and predicted safe life [19–21]. With a resolution of the order of a micron micro-computed tomography (lCT) is being increasingly applied to investigate the damage and presence of short cracks and other life-limiting defects in three dimensional (3D) bodies non-destructively [22–29]. It offers sufficient resolution to study microstructural interactions, but has sufficient field of view to study samples large enough to be of engineering interest (2–20 mm). Both lab. and synchrotron X-ray sources can achieve such resolutions, and thus provide insights into the study of fatigue and damage evolution inside engineering materials as reviewed by Withers and Preuss [30] in 2012. However the high brightness associated with synchrotron radiation micro CT (SR-lCT) enables the rapid acquisition of successive high spatial resolution 3D images to create 3D movies, for example to track crack propagation or damage accumulation under monotonic, or cyclic, loads using time-lapse 3D imaging (sometimes called 4D imaging). Consequently, in this paper, we focus on the unique characteristics of SR-lCT to study the damage and degradation mechanisms in structural materials such as monolithic materials, composites, and multiphase materials as well as additively manufactured materials. Initially, we introduce the basic principles of the underlying SR-lCT before looking at the use of in situ environments for time resolved imaging. We then outline the special qualitative and quantitative insights that SR-lCT can provide into the damage accumulation behaviour of monolithic and multiphase/composite materials through a consideration of selected examples. Finally we consider the future opportunities of SR-lCT in studying fatigue damage and degradation mechanisms, including the potential use of new generation X-ray sources.

2. Computed microtomography with synchrotron X-rays High energy X-rays are radiated whenever a charged particle is accelerated or decelerated. Consequently, the centripetal accelerations that occur when bending magnets maintain the circular trajectory of a ‘bunch’ of electrons around the storage ring at a synchrotron creates an X-ray beam tangential to the curved electron path. At a 3rd generation synchrotron light source, much higher brilliance can be achieved by more drastically bending the electron beam using insertion devices such as wigglers and undulators [31], as illustrated in Fig. 1. Insertion device performance is sometimes quoted in terms of flux, which is the number of photons per second passing through a defined aperture, and is the appropriate measure for experiments that use the entire, unfocused X-ray beam. More commonly the beam intensity is expressed in terms of brilliance (expressed as the flux per unit area of the radiation source per unit solid angle of the radiation cone per unit spectral bandwidth), which is a measure of the intensity and divergence of an X-ray beam.

Fig. 1. The spectral brilliance of a SPring-8 bending magnet, wiggler and undulator; the solid curve for the undulator shows the output at a fixed gap between top and bottom poles, the dashed lines the variation in the harmonic peaks as the gap is varied from 25 to 8 mm [31].

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2.1. Penetrating capability of synchrotron X-rays Critical to imaging deep inside engineering components is the distance through which synchrotron X-rays are transmitted because this places a limit on the size of sample from which a radiograph can be collected. The transmitted intensity, I(x) on penetrating a ray distance x is given in terms of the incident intensity I0 by I(x) = I0e
lx where l is the local linear attenuation coefficient depending on photoelectric effect, incoherent scattering, coherent scattering and pair production. The attenuation capability is often represented by the attenuation length l0, which is the distance through which 37% (e
1) of the photons will pass. Generally, penetration increases approximately as the 3rd power of the X-ray energy (keV) and so hard (high energy) X-rays are best suited to large samples or high atomic number materials. If the energy is too high there is little attenuation contrast, if the energy is too low then too few X-rays are recorded on the detector. Grodzins has calculated that an image can be reconstructed in the minimum time when the incident energy is such that the linear attenuation coefficient l0 = 2/D where D is the specimen diameter [32–34]. Considering Fig. 2 [41] this translates to 20 keV for a 100 lm sample of iron but 100 keV for a 6mm sample. As a comparison, 50 keV is suitable for imaging a 20 mm Al sample. Characteristically, for a synchrotron, the X-ray source is usually a long way from the sample (often 30 m or more) giving an effectively parallel beam geometry. The spatial coherence of X-rays from a 3rd generation SR facility is high enough and applicable for phase contrast imaging [35]. With synchrotron X-rays, it is normal to use a monochromatic beam which avoids beam hardening artefacts. One of the disadvantages is that, because synchrotron beams diverge quite slowly with increasing distance from the source, and are characteristically wider than they are tall, synchrotron beams are often best suited to high resolution imaging of medium to small sized objects (<10 mm). Further, the high brilliance of the synchrotron beam means that synchrotron imaging is especially well suited to imaging events that occur over short timescales. While laboratory imaging can often achieve similar resolutions (currently down to 50 nm [36–40]), much longer time periods are required to acquire all the projections for a lab-source lCT scan. In order to follow the failure process within a lCT scanner it is necessary to be able to accommodate special environmental or mechanical loading stages within the scanner. Synchrotron radiation based lCT lends itself to such studies partly because the acquisition time is short so that many time-lapse images can be acquired, even over sub-second timescales. Furthermore, synchrotron beamlines usually afford the users a significant amount of space on the sample stage to accommodate environmental/loading stages. To date the behaviour of materials have been studied under many environments by time lapse lCT and a comprehensive review is given by Buffière et al. [42]. When choosing between laboratory and synchrotron source lCT it should be borne in mind that as user facilities, access to synchrotron beamlines is limited with most experiments lasting a few days. This makes longer period experiments difficult logistically and precludes studies that require the examination of many samples. 2.2. Capabilities of SR-lCT All 3rd generation sources have imaging beamlines, with resolutions ranging from tens of nanometres to micron scales (see Fig. 3). Among the synchrotron sources in operation, ESRF, SPring-8, APS and Petra-III are the four largest high energy synchrotron radiation sources of which Petra-III and ESRF can also undertake nanotomography (resolutions <0.2 lm). Currently, the majority of synchrotron source imaging beamlines exploit a parallel beam and so the maximum illuminated area is characteristically small being tens of millimetres or smaller in most cases [43–74]. Consequently they are best suited for high resolution of small or short cracking rather than imaging of long or macro cracks in large-sized metallic components. Some of the key concerns when considering lCT for tracking damage nucleation and growth of metallic materials include:

Fig. 2. The X-ray attenuation length (37% transmission) through various metals as a function of photon energy [41].

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Fig. 3. A summary of the capabilities of a selection of imaging beamlines at current high resolution synchrotron sources used for the study of damage in metallic materials [43–74].

(1) Spatial resolution. The imaging capability of state-of-the-art SR-lCT can be quantified in terms of the spatial and temporal resolution. In contrast to industrial CT scanners, modern SR-lCT facilities achieve spatial resolutions better than 1 lm (typically 2–3 times the pixel size), suitable for imaging short cracks and micron-sized defects [75]. The time resolution of modern SR-lCT varies according to the spatial resolution, but micron resolution can be achieved at a time scale of about 0.1 s per 1000–2000 projection dataset (see Fig. 4 [74–81]). This requires a fast rotation stage. (2) Defect detectivity. It is recognized that both laboratory and synchrotron lCT are well suited to detecting round defects. They have difficulty in resolving sharp cracks or cracks of large aspect ratio due to the unequal transmission and uneven contrast at different projection angles, especially when the crack opening displacement (COD) is small. (3) Specimen size. Computed tomography conventionally requires the whole width of the sample to be within the field of view for all projections. This means that the size of specimen that can be accommodated depends intrinsically on the spatial resolution. The higher the spatial resolution, the smaller the field of view (sample width). (4) Sample types. While it is possible to undertake SR-lCT at high energies most systems currently operate between 10 and 40 keV. For this energy range, SR-lCT is well suited, in terms of penetration, to the study of 1–10 mm sized lightweight metal materials (such as aluminum alloys, titanium alloys or other relatively low density homogeneous materials, see Fig. 2). (5) Sample shape. From the viewpoint of optimal imaging conditions, it is better to image approximately cylindrical samples rather than extended plate samples of high aspect ratio so as to ensure a relatively uniform transmissivity across all the projections;

Fig. 4. A plot showing the historical development of X-ray tomography [74]. It is clear that while lab. sources can compare well with sycnhrtron ones in terms of resolution, synchrotron sources open up much shorter timescales. In many cases the spatial resolution is not cited and a resolution twice the pixel size has been assumed. Open symbols denote commercial synchrotron sources, while filled ones represent laboratory sources, red squares denote white beam and black circles monochromatic beam scanners [74–81]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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(6) Rendering software. A range of commercial and free software is available for the segmentation, analysis and visualization of 3D volume images including VGstudio, Avizo, Drishti and ImageJ, Mimics, etc. [5,43,76,82–86]. Furthermore, segmented images can be used to generate conformal finite element meshes to enable high spatial resolution image-based finite element models containing initial, or evolving defects from 3D measurements, during external loading [87].

2.3. In situ testing for time lapse imaging Nowadays, the majority of synchrotron beamlines can accommodate in situ rigs for time-lapse experiments. These include rigs for tensile loading at ambient temperatures [88–90], low temperatures [91,92] and elevated temperatures [93–98], as illustrated in Figs. 5–7. A typical ambient in situ fatigue test can be performed with a 49 N servo fatigue testing machine developed by Shimadzu Corporation (see Fig. 5a) [90,99]. There are a variety of designs to enable room temperature loading in situ. These rigs generally satisfy the following conditions: (1) their size and total weight should be as small as possible consistent with the load required such that they can be accommodated on the SR-lCT stage; (2) the level of vibration due to monotonic loading or fatigue loading must be as low as possible in order to avoid damaging the tomography stage or causing undue vibrations and sample movements; (3) the environment needs to be contained to prevent the heating up of beamline components or the escape of hazardous materials. For fatigue studies, the loading frequency should be ideally not be less than 10 Hz in order to enable the completion of high cycle fatigue tests within the timescale of allocated synchrotron beamtime periods (usually 1–2 days). The great majority of rigs have been designed to be essentially transparent to X-rays so as to allow unobstructed 360° viewing (see for example Fig. 5a) and of a weight and size that they can be accommodated directly on the rotation stage of the beamline. A range of rig designs have been developed to allow mechanical testing at sub-zero temperatures, moderate and extreme high temperatures (see Fig. 6). These are extensions of the basic loading rig shown in Fig. 5.

Fig. 5. Ambient loading rig: Crack initiation and growth SR-lCT results based on in situ fatigue testing rig at the beamline BL47XU and BL20XU of the SPring-8 [90,100,101]: (a) in situ fatigue test rig for cyclic loading and in situ lCT observation; (b) 3D volume rendering (0.5 lm/pixel) of a fatigue crack after 120000 cycles under a frequency of 10 Hz for a cast Al-Mg-Si single-edge specimen (top) virtual section showing the crack morphology (bottom).

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Fig. 6. SR-lCT based environmental testing rigs (leftmost image in all panels) for damage studies[91–97]: (a) A crack (circled) formed in the ice between two particles of sand at
8 °C. (b) Hot tearing in an Al-8 wt% Cu alloy deformed at a strain rate of 2  10–4 s–1 at 540 °C, (c), SiC–SiC single-tow failure at very high temperature (1750 °C) showing the pull-out of fibres as a matrix micro-crack opens upon increased loading.

In certain cases it is either infeasible or undesirable to develop rigs with unobstructed views over the full range of projection angles. In Fig. 7a a rig is shown where most of the rig does not rotate at all – instead only the jaws holding the sample rotate. This has certain operational advantages, for example rigs with greater weight than the normal load of the rotation stage can be used, although this means the rotation of the sample cannot be controlled in the normal manner since the beamline data acquisition system must now be adapted to control the rotation of the sample jaws directly. In other cases it is difficult to design rigs without pillars which come into view as the stage is rotated preventing an unobstructed view (see for example Fig. 7b). As a result an angular wedge of projection data cannot be collected. While such rigs do give non-ideal datasets in that some projections are missing, provided the angular range over which there are missing projections is small (missing ‘wedge’ less than 40°) then good image quality can be obtained without using special reconstruction algorithms [76,98]. Iterative reconstructions [97,102] can be employed to reduce the level of artefacts that would otherwise arise for larger missing wedges. While good results can be obtained with incomplete sets of projections the reconstruction algorithms currently available at synchrotron sources are not generally optimised for missing wedge data [86].

3. Failure of monolithic materials 3.1. Imaging and analysis of monotonic fracture behaviour Ductile failure studies have been carried out, both in a time lapse manner through stepwise increases in straining with intermittent imaging, or through continuous straining [104,105]. In the latter case the fast imaging capability of synchrotron sources is critical. The ductile fracture behaviour of Al alloys has been studied by in situ tensile SR-lCT (see Fig. 8) by Toda et al. using fast tomography and continuously increasing loading [100,101,106–111]. Local crack driving force analyses based on tracking the particles by digital image correlation (DIC) in the alloy was used to analyse crack-tip stress/strain singularities in an aluminum alloy. Gradual crack-tip blunting was clearly observed fol-

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Fig. 7. Alternative in situ rig designs (photo in the left most panel along with representative tomographic slices); (a) a rotating sample design capable of high temperature testing used to measure the cracking and crack healing of self-healing max phase ceramic at 1050 °C; (b) a nanotomography rig for tension, bending and indentation. In this case the rig obstructs the field of view for certain projection angles (the missing wedge) here the missing wedge extends over 40° shown here indenting a piece of elephant dentin [103]

Fig. 8. Virtual tomographic slice from ‘fast’ (22 s per tomograph) tomography during continuous loading of an 2024-T351 aluminum alloy showing the typical crack-tip morphology and its growth during tension [106–111]: (a) tomography slice (x = 59 lm) showing progressive crack-tip blunting; (b) tomography slice (x = 577 lm) showing the interaction of a sharp crack regions of the crack with a damaged particle.

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lowed by subsequent initiation of a sharped crack from the blunted crack tip [112,113]. Crack opening displacement measurements also corroborated periods of stationary (blunt) and growing (sharp) crack behaviour. Such observations of short crack effects have helped to establish a theoretical fatigue crack growth rate model [114,115]. Research on 3D imaging of fatigue damage and cracking has mainly centred on small samples, either of square cross section, or round cross section to achieve good spatial resolution (given current CCD cameras the field of view is usually around 2–4000 times the pixel size). This geometrical constraint presents a problem when attempting to look at high spatial resolution at a crack, or other region of interest, in extended plate-like samples such as compact tension samples. This challenge has been met in laboratory lCT through laminography in which the source and detector move in synchrony either side of the plate-like sample to optimise the reconstruction. Clearly it is not possible to move a synchrotron source, but recently, a Synchrotron Radiation Computed Laminography (SR-lCL) set-up has been developed by the ESRF [116–119]. This has been used to explore the ductile crack initiation and growth for laterally extended sheet AA6061 specimens, as shown in Fig. 9. Alongside these experiments the Gurson-Tvergaard-Needleman (GTN) damage model and Voce hardening law were introduced to reveal the fracture mechanism based on finite element simulation. By combining SRlCL data and the tensile loading curve from the servo-hydraulic machine, critical parameters for a GTN micromechanical damage model were extracted experimentally and validated. This work shows that coarse Mg2Si precipitates in AA6061 have a predominant influence on the void nucleation. Moreover, these prerequisite GTN parameters are identified experimentally without the use of adjustment parameters. The coupling of X-ray lCT to micromechanics damage model has the potential to markedly improve our understanding and prediction of damage processes and hence to predict safe regimes from a structural integrity viewpoint [120–123].

3.2. Characteristics of short fatigue crack behaviour It is well-known that fatigue crack morphology strongly affects short fatigue crack behaviors. Further, at this length scale the local microstructure plays a very important role in determining crack shape [124–136]. Short cracks are able to grow below the threshold for long crack growth at the same cyclic DK [137–139]. For most critical safety components, short crack fatigue growth represents 90% of the lifetime. Some of the first SR-lCT studies of short crack behaviour looked at the nucleation of short cracks from graphite nodules in ductile cast iron [22]. Here both nucleation and growth rate were explored over the early stages of fatigue life. Subsequently, Buffière et al. [87,123,140] successfully studied the fatigue cracking process inside ultrafine-grained Al-Li alloys subjected to cyclic loading on the beam line ID19 of the ESRF using an in situ rig similar to that in Fig. 5a. They observed classical short crack growth devoid of microstructural features or heterogeneities (see Fig. 10a). In contrast, fractographic evidence for coarse grain material is consistent with the idea that in this case the grain boundaries present a strong barrier to crack growth giving rise to an irregular crack front shape [23,141,142], and consequently very uneven growth characterised by significant crack deflection at the scale of the grain size, as illustrated in Fig. 10b. It is generally believed that the irregular fatigue crack shape is due to frequent acceleration and arrest in the presence of grain boundaries or other microstructural barriers. From the viewpoint of elastoplastic fracture mechanics, such microstructurally short cracks can be closely correlated with variations in the plastic region near the crack tip [93,114,144].

Fig. 9. (a) Synchrotron radiation computed laminography based loading test set-up at ID 19 at the ESRF and damage evolution process ahead of the fatigue pre-crack tip in AA6061. A fiducial-tracking method was used to record the relative displacement (d5) of two markers (in the main picture) positioned on the surface (b) d5 = 0 lm, (c) d5 = 23 lm, (d) d5 = 83 lm and (e) d5 = 153 lm [116].

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Fig. 10. Short fatigue cracking behaviour from the SR-lCT and post-mortem fractography: (a) 3D rending of a corner fatigue crack in ultrafine grain AA5091 (the crack length is 500 lm) [141]; (b) fractographic evidence of a nonplanar crack in coarse grain (300 lm in diameter) AS7G03 cast alloy [143].

Conventional absorption lCT is not sensitive to the grain boundaries, or the orientation of the grains, meaning that one cannot normally unambiguously infer the interaction between short cracks and these features from absorption lCT alone. Some alloys however do have sufficient natural grain boundary contrast to be detected by lCT or phase contrast lCT. Examples include beta titanium alloy (Tib21S) in which an alpha phase is precipitated on the grain boundaries [145] and Ti-6Al2Sn-4Zr-6Mo [146]. For example Babout et al. [147] examined the short fatigue cracking path within the lamellar microstructure of Ti-6246, as illustrated in Fig. 11a. In other cases it is possible to decorate the grain boundaries; Ludwig et al. [141] used Ga to decorate the boundaries in Al after crack growth to reveal the location of the grain boundaries as illustrated in Fig. 11b and c. Diffraction contrast tomography (DCT) is capable not just of locating grain boundaries, but also of identifying the grain orientations in 3D, as illustrated in Fig. 12 [148]. The physical colour coding shown in Fig. 12a reveals correlations between crack deflection and grain boundaries while the crystallographic colour coding as shown in Fig. 12b highlights the correlations between crystallographic slip planes and fracture surface orientation. Furthermore using time lapse methods they were able to correlate grain orientation and the presence of grain boundaries with local crack growth rates [149].

3.3. Fatigue crack nucleation and growth Pores are known to be a site of stress concentration from which fatigue cracks can nucleate. Time-lapse synchrotron lCT can provide unique insights into the propensity for cracks to form at such defects and the rate and shape they take up as they propagate (see for example the growth of cracks from pores in additively manufacture material in Section 3.5). As well as individual defects it is important to understand the tendency for clusters of pores to initiate fatigue cracks. Investigations

Fig. 11. (a) Phase contrast tomographic slice showing the interaction of a short fatigue crack after 27,000 cycles with the underlying microstructure [147]; (b) a tomographic slice before and (c) after the application of Ga showing the influence of the grain boundaries [141].

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Fig. 12. Two views of a fatigue crack from a 150  40  2 lm3 notch in Tib21S: (a) the inclination of the crack to the z axis using the stereographic projection from a standard lCT image; (b) the crystallographic orientation of the crack from DCT[148], where black and white lines in (a) and (b) respectively indicate intersections of the crack with the grain boundaries.

Fig. 13. (a) Magnified 3D views of fatigue crack initiation in cast Al alloy samples acquired on beamline 47XU of the SPring-8 [90,99]. Note that multiple fatigue cracks initiate from pairs or clusters of large pores (coloured red) located sub-surface in the specimen [99]; (b) 3D view of the fatigue crack initiation from red micropores in the rectangular cuboid; (c) schematics showing crack growth from an isolated pore and a fatigue crack growth from a pair of pores. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

have revealed that fatigue cracks are initiated from porosity situated at, or near the free surfaces. For about 92–100% of specimens in Al-Si alloys produced by gravity casting [150–152], low-pressure permanent-mold die casting [153] and high-pressure die casting [154]. In casting Al alloy samples it has been found through the multiple regression analysis of high resolution time lapse SR-lCT images that the pairs or clusters of micro-pores larger than 5.4 lm in average diameter can preferentially nucleate fatigue cracks near the specimen surface (see Fig. 13a).

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It was found that pairs or clusters of micro-pores can nucleate cracks when their separation is less than a pore diameter apart and the mean distance of gas pore’s gravity to the casting free specimen surface studied, are predominant in fatigue crack initiation and propagation, as shown schematically in Fig. 13b [99]. Note here a paired micro-pore is defined when the mutual distance between gravity centers is less than 9.7 lm. Classically, a notch-like defect can induce a crack when the stress field intensity near the notch root penetrates the fatigue process zone [142]. In Fig. 14 in situ fatigued SR-lCT under the loading ratio of R = 0.1 and a frequency of 20 Hz is used to delineate how multiple surface breaking defects inside a hybrid laser welded AA7020-T651 sample may coalesce once the stress fields around the defects interact with each other [76]. In this case, these defects defined by regularized crack length a and regularized crack depth c can be dealt with an equivalent primary crack for quantitative analysis, as illustrated in Fig. 15. Such regularization results are in good agreement with the analytical solution in terms of Newman formula for a semielliptical surface crack [18,155,156]. Based on standard Paris equation within the framework of linear elastic fracture mechanics, fatigue crack growth rate da/dN can be linearly expressed by the DK together with fitted material parameters of C and n in logarithm coordinates. Pores do not just cause fatigue crack nucleation, but they can also affect the propagation of a fatigue crack and advanced lCT is well suited to observing such effects. In Fig. 16 we can see a fatigue crack that is nucleated at the corner of a tensile fatigue specimen growing as a quarter elliptical crack through a hybrid laser welded AA7020-T651 specimen containing a

Fig. 14. SR-lCT observations of the fatigue cracking process from multiple surface breaking pores under a loading ratio of 0.1 acquired on the ID19 of ESRF [18,156] for a hybrid laser welded AA7020-T651 joint with a 1  1 mm2 cross section.

Fig. 15. The regularization process based on Newman formula where A and B are the deepest point and intersection point with the surface: (a) projected images of fatigue cracks; (b) characterization results of fatigue crack shape based on Newman formula [18,156].

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Fig. 16. Corner fatigue cracking at the corner of hybrid laser welded AA7020-T651 specimen [18]: (a) irregularly advancing shape of the corner crack indicated by different colours; (b) 3D rendering of the corner fatigue crack and pore locations. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

large number of solidification gas pores. It is clearly observed that many pores become entrained (see Fig. 16b) and that the crack growth significantly increases as the crack breaks into each pore [18], as illustrated in Fig. 16a. Solidification cracking, which occurs in both welding and casting processes, leads to premature failure under reversed cyclic loading and offers favourable sites for hydrogen assisted cracking and stress corrosion cracking [157]. Furthermore, understanding the failure mechanism during high-cooling-rate process is necessary to control or predict the fatigue resistance. Recently, the damage initiation and growth kinetics of EN1A mild steel weld pool has been investigated and an evolution mechanism controlled by the advancing columnar dendrites elucidated at the ID19 of ESRF, as shown in Fig. 17. It is found that cracking initiates at a relatively low true strain of about 3.1% in the form of micro-cavities at the weld subsurface where peak volumetric strain and triaxiality are localised. The growth of micro-cavities is physically driven by increasing strain imposed on the solidifying steel. Cavities grow through the coalescence of micro-cavities to form microcracks first and then through the propagation of these micro-cracks. 3.4. Characterization of crack closure It has been widely recognized that during fatigue the crack faces can close well before the minimum load is reached, this closure effect can shield the crack from the full loading range [142,158], thus decreasing fatigue crack growth rates especially for negative loading ratios or lower nominal stress [159–161]. The well-known closure mechanisms of oxide-induced closure, plasticity-induced closure and roughness-induced closure are usually correlated with fatigue short crack growth, which

Fig. 17. Solidification crack initiation and growth of a TIG welded EA1N steel conducted at the ID19 of the ESRF [157]: (a) the early crack initiation from the micro-cavities with average sizes of 18  10
6 m in the weld sub-surface directly underneath the weld pool; (b) 3D tomographic reconstruction of fracture initiation sites in which the yellow broken square highlights the fracture initiation sites and the white broken lines highlights a series of isolated and coalesced micro-cavities. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 18. Views of fatigue cracks and grain boundaries in a single-edge notched AA2024-T351 specimen (1  1  25 mm3) under a load ratio of 0.1 and frequency of 50 Hz: (a) 3D rendition without Ga wetting to show the closure; (b) 3D rendition with Ga wetting to show the grain/crack behaviors [165].

leads to longer fatigue crack initiation life (see Fig. 18a). Unfortunately, standard serial sectioning is time consuming and can destroy the specimen due to physical changes in constraint that occur on removing material. Some of the very earliest synchrotron lCT images (6.2 lm/pixel) of crack behaviors were used to observe crack closure of an Al-Li 2090 alloy at the SRlCT setting of Lawrence Livermore National Laboratory [162–164]. More recently improvements in spatial resolution have meant that it is possible to observe the crack closure in greater detail, for example Khor and Toda [165–168] used 0.7 lm pixel SR-lCT to study the closure in a 2024-type Al alloy (AlCu-Mg-Mn) along with Ga grain boundary decoration to elucidate the interactions between the crack closure and microstructure by combining electron backscattering diffraction. As illustrated in Fig. 18, a conventional roughnessinduced crack closure event is clearly seen at a deflection in the crack wake and is linked with crack ridges in the crack growth direction. Subsequently, the locations of micro-pores distributed within a commercial high strength Al alloy were used as a displacement gauge to quantify the fatigue crack closure [27]. Actually, Toda has confirmed his observation on local fatigue crack opening and closure as described in Section 2.3. Despite remarkable progress in detecting closed cracks, additional contrast enhancement, for example phase contrast, is necessary to delineate the crack as precisely as possible by calibrating the grey value of the closed and opened crack region [5,36,148,165,169,170]. 3.5. Additively manufactured materials Additive (layer) manufacturing (ALM, or 3D Printing), namely the incremental build-up of high performance metal components layer-by-layer, has attracted much attention for making metallic materials and structures. To date several promising ALM technologies have emerged such as Laser Beam Melting (LBM), Electron Beam Melting (EBM), Laser Metal Deposition (LMD), Plasma Deposition Melting (PDM) and etc. [171–177]. However, these processes are not well understood, especially with respect to the various shrinkage defects and pores generated during the rapid solidification and their effect on the fracture and fatigue resistance. Furthermore, the in-service performance of these 3D Printed parts has become the most important issue on its application into industries. For example during additive manufacturing processes the entrainment of voids during solidification is a key issue and high spatial and time resolution SR-lCT is proving an effective way of identifying their size and location [178]. While Hot Isostatic Pressing (HIpping) [179] can significantly reduce the voids, they can regrow at elevated temperature indicating that they have not been completely removed [180]. Consequently it is critical to understand the propensity for crack growth from internal and external defects under fatigue conditions for additively manufactured components. Time-lapse imaging enables one to follow the nucleation and growth of fatigue cracks from defects introduced by additive manufacture processes [178,180]. This work suggests that surface breaking defects are more likely to initiate fatigue cracks than pores in the interior providing the same stress intensity driving force (see Fig. 19). Recently, high resolution SR-lCT has been used to quantify the porosity-induced damage evolution of both selective laser melted and wrought 316L stainless steels during in situ mechanical tests developed at the ALS [181–187]. In this work, the specimens with a gauge diameter of 6.35 mm were loaded using displacement control at a quasi-static rate. To image the

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Fig. 19. Crack growth measured by X-ray lCT projected onto the x-y plane for additively manufactured Ti-6Al-4 V tensile samples for different numbers of fatigued cycles. Pores within 0.5 mm of the crack plane are shown in red. The sample designation and number of 1000 fatigue cycles were: (a) IH-600c after 100, 101 and 102 cycles; (b) IH-600d after 70, 71, 72, 73, 74, 75, 76 and 77 cycles; (c) V-500 after 100, 103 and 104 cycles; and (d) V-600c after 100 and 101 cycles [178,180]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 20. SR-lCT based in situ tensile tested failure mechanism of selected laser melted 316L stainless steel conducted at beamline 8.3.2 of the ALS: (a) 3D rendition of the segmented porosity of initial 2.2% at zero loading stress; (b) captured at 350 MPa loading stress, in which the crack bridging is observed between existing 5.3% porosity as pointed out with the white arrows [186].

damage as accurately as possible, all specimens were held at the specified loads for about 3–5 min duration. The typical void evolution (the initial average porosity was 2.2%) during in situ tensile test was depicted for a high porosity additively manufactured stainless steel in Fig. 20.

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It is clearly observed that the failure of additively manufactured AM 304 L specimen is highly defect driven. Moreover, crack bridging and bifurcation occur in the presence of near-spherical pores or cavities during the necking. Emerging results demonstrate the use of X-ray tomography to better understand the relationship between additively manufacturing parameters, scan patterns and post manufacture consolidation so that the defect density and location is better controlled. Laboratory source based lCT has been used as the post mortem to map the geometrical distribution of included voids as a function of ALM scan procedures [188–192].

4. Failure of composite and multiphase materials Composites derive their excellent properties in part from their heterogeneous nature which enables them to achieve multiple or combined functions [193–199]. Perhaps surprisingly given their 2D and 3D architectures, the propensity for complex patterns of damage and the competition between different damage mechanisms, lCT studies of composite fatigue damage and cracking mechanism are relatively scarce. The high photon flux and high-speed cameras available at third generation synchrotron radiation X-ray source mean that synchrotron X-ray lCT can play a key role in elucidating fatigue and fracture mechanisms in composites for a crucial reference to structural integrity assessment.

4.1. Polymer composites Polymer composites and carbon fibre reinforced composites in particular (CFRPs) present some challenges to X-ray CT [200]. Firstly the contrast is typically low between the damage, the polymer matrix and the carbon fibres. Approaches have been explored to increase the detection of damage in composites including the effect of using finer pixel sizes, staining with heavy elements, phase contrast and holding cracks upon under superimposed loading [201]. They found that in common with previous researchers [202] both high spatial resolution and phase contrast are helpful as is holding the cracks open by in situ loading, phase contrast staining, where appropriate, is the best means of increasing the detectability of cracks. Polymer composites are often manufactured in the form of plates or panels (>200 mm), in the case of woven structures the repeat distances (repeating unit cell) can be extensive (20 mm say) while the fibres are characteristically fine (6 lm is typical). These requirements place conflicting demands (i.e. large volumes and high spatial resolution) on X-ray tomography. SR-lCL has been used to examine damage in large composite plates [203–205]. To clearly identify the damage progression under different lifetime proportion for 3D woven glass-fibre reinforced composites, in situ lCT has been applied to quantify the evolution of different failure mechanisms as a function of the number of fatigue cycles [206]. For the automatic classification of fatigue damage, an innovative algorithm was proposed. In view of elaborate microstructures, complex interactions are found between the different modes of damage. These modes can be basically aggregated into three types, namely the interactions between transverse cracks and weft-binder debonds, the interactions between weft-binder debonds and binder-binder debonds and the interactions between longitudinal cracks and weft-binder debonds [206]. This work confirms that fatigue damage inside woven composites can start very early during fatigue partly due to the crimp, but that the periodic through thickness constraint means that load is redistributed around damaging sites, thus providing a highly damage tolerant structure. Fast, in situ synchrotron X-ray computed tomography has been used to capture the evolution of fibre failure and the final moments (within 99.9% of the failure stress) before final fracture in [90/0]s carbon fibre/epoxy coupons under monotonic slow strain rate tensile loading [207]. The majority of fibre breaks appear as isolated events (Fig. 21). While, some clusters of fibre failures occur at intermediate and high stress levels, contrary to conventional wisdom, the fractures in a cluster

Fig. 21. Fast imaging (1 tomography/s) of a 2D slice parallel to the loading direction for C-fibre epoxy composite acquired during continuous straining to catch the state immediately prior (within 0.1% of UTS) to failure showing the development of multiple fractures along a single C fibre [207].

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formed simultaneously, at least at the frame rates used (1 s/tomography). Further such clusters were never seen to accumulate additional broken fibres as the load increased further. To better assess the impact damage of carbon fibre reinforced polymer toughened materials subjected to low velocity impact, SR-lCT and SR-lCL were combined on ID19 at the ESRF to provide a novel, multi-scale imaging approach [208]. The lower resolution images indicate that the particle-toughening system suppresses delamination with very little effect on intraluminal damage. While the higher resolution images reveal that the particles contribute to toughening by crack deflection and bridging. This highlights the potential for the use of complementary, multi-scale, 3D X-ray imaging to correlate the micromechanical damage response to the macroscopic mechanical performance of composite materials and structures. Less attention has so far been directed towards short fibre polymer composite systems. The underlying micro-damage mechanisms of randomly oriented short fibre-reinforced composites were recently investigated, for the first time, on the basis of real internal microstructure characteristics obtained by the high-resolution (0.7 lm/pixel) SR-lCT experiments conducted on the 13W1 of SSRF [209]. The special ‘‘pore dominant micro-damage mode” was successfully observed and further validated for the composites used in current testing. Fig. 22 demonstrates the fibre-end aggregation-induced pore connection mode of crack initiation. In addition to directly observing the evolution of damage, two important microstructural parameters, namely, the distance between neighbouring fibres ends le and the number of neighbouring fibre ends Ne, have been used to consider quantitatively the effect of the real microstructure on failure for randomly oriented short fibre-reinforced composites. Ne

Fig. 22. 3D renderings and mechanism of the planar crack, the fibre arrangement around the planar crack and the ultimate fracture surface (marked blue, yellow and red, respectively) for randomly oriented short fibre-reinforced composites [209]. (a) the ultimate fracture situation and the planar crack from pores; (b) and (c) location of the planar crack relative to the surrounding fibre ends; (d) two representative cracking modes of fibre-end aggregationinduced pore connection and fibre-bridging crack; (f) critical value le in the composite with certain properties and external loading; (g) region with maximum number Ne of neighbouring fibre ends and the cracking site; (h) region with the width l and the distance between neighbouring fibre ends (in red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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indicates the region with maximum number of neighbouring fibre ends was the weakest area inside the sample, thus causing the planar crack initiation [209]. 4.2. Ceramic matrix composites Relatively little work has yet been undertaken on damage propagation in ceramic matrix composites [210–214]. The safe operation of applications physically depends on how short cracks initiated inside the material are restrained by a tailored microstructure. One notable study of note is that by Bale et al. who have compared the tensile failure behaviors of two SiC matrix-SiC ceramic matric composites at both room and elevated temperature (1750 °C) as shown in Fig. 23 [93] using the rig shown in Fig. 6 mounted at the ALS. Note that for high temperature testing, a non-oxidizing environment is maintained by admitting a low flow of high-purity nitrogen while pumping to 10
3 torr. For the single-tow specimens (see Fig. 6), cracks detected using 0.65 lm/voxel over a 5 mm tested length were found to initiate and propagate inside the matrix, so that the entire load is carried by intact fibres bridging these cracks. Similarly, cracks are also generated inside a C-SiC textile matrix during initial loading. With increasing load (40–70 N), the cracks stably propagate through the transverse tows until they meet an underlying axial tow, where they are deflected exhibiting different cracking behaviors at room and elevated temperatures (see Fig. 23). SR-lCT is well suited to the study of failure under such extreme environments. 4.3. Metal matrix composites Damage micromechanics is critical to understanding the behaviour of long fibre and discontinuous metal matrix composites. One of the first studies looked at the propensity of particulate metal composite systems for particle cracking and matrix-reinforcement decohesion as a function of tensile straining for soft (commercially pure) and hard (2124-T6) Al alloy matrix systems containing 4% spherical ceramic balls comprising a mixture of zirconia (70 wt%) and silica (30 wt%) [215,216]. It is evident from both Figs. 24 and 25 that particle matrix decohesion is the important failure mechanisms for the soft matrix system whilst particle crack the key damage mechanisms for the harder.

Fig. 23. In situ tensile loaded SR-lCT (1.3 lm/voxel) of C-SiC textile composites at 25 °C and 1750 °C [93]: (a) and (b) show the development of damage in specimens tested at room temperature and high temperature, respectively. The higher magnification slices at the right, from Section 1 and 2, represent different cracking mechanisms (indicated by arrows) in the later stages of failure: at room temperature, splitting cracks grow within the axial fibre tows; at high temperature, cracks grow along the boundary between the axial fibre tows and the matrix.

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Fig. 24. Reconstructed images of the same internal section of commercially pure Al + 4%ZS at five different relevant plastic deformation states: (a) initial state; (b) ep = 0.13; (c) ep = 0.28; (d) ep = 0.42 (necking); (e) ep = 0.60 (necking)[216].

Fig. 25. Reconstructed images of the same internal section of commercially pure Al + 4%ZS at five different relevant plastic deformation states: (a) initial state; (b) ep = 0.13; (c) ep = 0.28; (d) ep = 0.42 (necking); (e) ep = 0.60 (necking) [216].

In a series of experiments Withers et al. have examined the propagation of failure in Ti-SiC fibre metal matrix composites for example to calculate the extent to which SiC fibres bridge a fatigue crack conferring fatigue cracking resistance by minimising the crack opening displacement (COD) via the high resolution SR-lCT [213]. Furthermore it was possible to study fatigue crack growth by time-lapse lCT. For a layered Ti-Al composite (layer thickness of 100 lm) fabricated by hot pressing and hot rolling, it was observed using a combined DIC and SR-lCT that strain delocalization and a constrained crack distribution are responsible for extraordinary tensile ductility [217,218]. Fig. 26 shows the 3D renderings of cracks under the accumulated damage, which can be characterized via equivalent strain eeq in terms of the change gauge section [219]. It is found that the cracks propagated along the Ti-Al interface by generating subsequent damage elsewhere before interface delamination. Once the constraint effect disappears, the layer quickly necked under a rapidly increased eeq, leading to the sudden fracture. 5. Quantifying crack driving force In the preceding sections high resolution lCT imaging has largely been used qualitatively to identify key damage mechanisms and to understand the sequence of events leading up to failure of the material. In addition, SR-lCT can also be used to provide quantitative information about key fracture mechanics parameters [4,5,220,221].

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Fig. 26. Reconstructed crack images of the fractured Ti-Al composite sample [217]: (a) the damage progression under increased equivalent strain; (b) the rapid initiation and propagation of cracks near the necking region along a 45° shear direction inside an abstracted Ti layer.

5.1. Quantifying the stress intensity factor Using an image-based extended finite element method (XFEM) [222,223], it is possible to infer the local DK which can be correlated with the measured local crack growth rate. Due to relatively fine grains of Al-Li alloys, a microstructurally long crack with semi-elliptical morphology can be considered, as presented in Fig. 27 [123,140]. It is also found that such fatigue long cracks shows a regular 3D shape, which is consistent with the assumptions of elastic fracture mechanics. By using a general crack-tip interaction integral, the values of the mixed-mode stress intensity factors (Kmix in MPam1/2) along curved cracks were calculated in terms of linear elastic fracture mechanics. It was found that calculated crack growth rate is faster in the bulk than at the surface under the same nominal value of DK. This phenomenon can be rationalised in terms of a larger plastic zone size at the free surface which produces a higher closure stress, thus indicating a lower crack growth rate (see Fig. 28 [224]). This is the first work to extract the crack growth driving for fatigue long crack inside a homogeneous deformed material by coupling X-ray microtomography to XFEM. Another means of calculating the DK has also been proposed and has been validated for the curved front of a growing crack. Here an artificial defect was introduced at the free surface of a small nodular cast iron (grain size 50 lm) sample from which a short (<500 lm) fatigue crack initiated and propagated under constant amplitude cyclic loading whilst monitored in situ by laboratory X-ray tomography. The nodular graphite cast iron contains a homogeneous dispersion of graphite nodules which act as natural markers to extract displacement fields by digital volume correlation (DVC). For this case of a

Fig. 27. 3D X-ray rendering (a) and simulated crack (b) of the semi-elliptical crack inside ultrafine-grained Al-Li alloy after 16,000 cycles under loading ration R = 0.1, where the rectangle in black dotted line indicates the notch in the crack plane, the iso-zero surface represents the crack surface and the curved surface normal to the X-Y plane represents the crack front that corresponds to the interaction of two iso-zero surfaces [140].

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Fig. 28. Evolved KI values along the curved semi-elliptical crack front based on XFEM predictions and analytical calculations for a powder metallurgy Al-Li alloy with grain size of 1 lm [224].

Fig. 29. Superposition of the detected curved crack front and the microstructure. The colour map indicates the estimated distance to the crack front (in microns) by the Williams’ series and the black line shows the initial crack front. The laser notch from which the short fatigue crack was initiated is also given as well as the graphite nodules and a pore [225]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

small curvilinear crack (see Fig. 29 [225]) an improved Williams’ series [226] was used to evaluate the stress intensity factors and crack tip position. The predicted stress intensity factors coincide well with analytical values. The results also reveal show the crack to be affected by the local microstructure, as is characteristic of short crack behaviour. Due to higher levels of plasticityinduced crack closure near surface due to the state of plane stress there in contrast to the bulk, a smaller DK was observed very close to the free surface (plane strain status).

5.2. Quantifying the crack opening displacement Exploiting an in situ fatigue testing rig, Toda et al. [90] used SR-lCT to observe damage evolution and fatigue crack behaviour in a ductile cast aluminum alloy at the ID19 of ESRF and XU47 of Spring-8. Compared with traditional surface-based and post-mortem fractography approaches, the centroid locations of densely distributed micro-pores have been used as displacement gauges to quantify the complex local fatigue crack opening and closure behaviour in the interior, as shown in Fig. 30 [27,227]. The crack opening has been quantified for 2.48  1.08 mm2 Ti-SiC metal matrix composite specimens as an indicator of the local crack driving as a function of fatigue crack growth undertaken using a 2 kN BOSE fatigue test rig [228] on Beamline ID15 of the ESRF. This beamline provides the ability to switch quickly between the white beam mode used for fast tomography and the monochromatic mode used for strain mapping during the fatigue loading [5]. The COD profiles at

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Fig. 30. Centroids location of gas pores based displacement to identify the crack front and to compute internal local crack driving forces in a commercial high strength Al alloy: (a) 3D rendering of a propagating crack along with dispersed pores; (b) illustration of the bipolar separation of local K calibrated at each micro-pore [27,227].

Fig. 31. (a) crack opening displacements for a W = 2.4 mm Ti-SiC wide fibre composite sample measured by synchrotron tomography at Kmax (darker shade) p and Kmin (lighter shade) as it grows through the sample alongside the r best fit curves for Kmax (solid lines) and Kmin (dashed lines); (b) increase in local crack-tip driving force inferred from the local crack opening displacements with crack length, a, compared with that nominally applied (red squares) [227,228]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the maximum (Kmax) and minimum (Kmin) stress intensity factor are shown in Fig. 31a at various stages of crack growth (Fs0, Fs1, Fs3 and Fs7). It is clear that the compressive thermal residual stresses in the fibres bridging the crack hold it open at Kmin while the fibres hold it closed at Kmax such that the change in COD is relatively small for all crack lengths. This reduced the range of stress experienced at the crack-tip and the crack-tip shielding effect DKeff inferred from the COD results is shown in Fig. 31b. It is evident that the crack grows at a relatively constant level of DKeff despite the rapidly increasing nominal DK that must be applied to propagate the crack as more and more fibres bridge the crack. It was found that the calculated is in relatively good agreement with level of crack tip shielding derived from the crack bridging [194], although the COD at is Kmin much larger than one would expect. This can be thought to be complex hysteretic response of the fibre sliding and local plasticity taking place in the crack zone. 6. Discussion and future opportunities The high flux, the wide range of energies, imaging modalities and spatial resolutions available with good time resolution at synchrotron X-ray sources, mean that SR-lCT has much to offer for the 3D imaging of damage accumulation and the time lapse imaging of damage evolution for many environmental and mechanical loading regimes. It is expected that there will be increasing focus on exploiting its ability for very fast imaging of damage evolution [229–233]. Currently it is possible to col-

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lect more than 10 tomographs per second at micron resolutions [105,234] (see Fig. 4) and this is likely to be improved further. There will also be increasing focus on combining X-ray CT with other techniques (DCT, diffraction, fluorescence, small angle scattering, etc.) to build up a multifaceted picture of materials in 3D. This has been coined correlative tomography [ 120,235,236,208,237–239]. For an example, multi-scale X-ray imaging has allowed damage to be assessed in 3D at both the macroscopic and microscopic levels on the same sample [201,240–248]. It is expected that further improvements in both the temporal and spatial resolution will be achieved with current thirdgeneration X-ray sources. Looking forward it is possible that X-ray free-electron lasers (XFELs) will give us for the first time the possibility to explore unknown structures and dynamics of matter in unprecedented detail at the nanometer spatial scale or over femtosecond time scales. Continued development and upgrades to existing XFEL sources, together with the upcoming commissioning of several new sources, will rapidly expand the possibilities they present for materials science [249–254]. Finally the range of environmental and mechanical loading stages available are increasing all the time, enabling the degradation behaviour of the materials and structures under a plethora of complex in operando conditions [255–257]. One of the most important issues is to visualize damage initiation and growth in materials and components under very/super high (giga) cycle fatigue (VHCF). It has been well-recognized that the giga-cycle fatigue damage and failure behaviors are quite different from those of traditional high (tens of millions of cycles) cycle fatigue loads. The fatigue cracks in the case of VHCF are mainly initiated from internal defects rather than surface or sub-surface defects (which if present would cause the sample to fail at lower cycles) [258,260]. These tend to give rise to the characteristic fisheye features on the fracture surfaces (see Fig. 32a). In practice it is presumed that the time needed to nucleate the fisheye represents a significant fraction of the total life [262–264]. To the authors’ knowledge, there are still only a few papers to have investigated such failure behaviors under very high fatigue cycled loads, mainly due to limited beamtime periods [265–267]. Perhaps the first such study is the study of Ti-6Al-4V alloy subjected to VHCF loading (1.96  107 cycles) which was recently investigated at the SPring-8 (see Fig. 32b) demonstrating damage nucleation from an internal defect under VCHF [261]. While the capability of laboratory sources are rapidly improving there is little doubt that the on-going development of instrumentation, the higher flux and monochromatic nature of SR-lCT will ensure that it will continue to provide unique 3D and 4D non-destructive information shedding new light on failure mechanisms across a range of materials with high density and systems that cannot be obtained in any other way [79,97,102,134,268]. In this context it is noteworthy that the X-ray imaging of cracks can be complemented by mapping of the local crack-tip stress field using synchrotron highenergy X-ray diffraction or neutron diffraction. The seamless integration of evolved crack and stress field is strongly expected to calibrate the damage and then extract the DK of a crack [269–280]. Taken together diffraction and imaging can provide a detailed picture of the local fracture mechanics [5]. In this context a few synchrotron sources world-wide allow diffraction and imaging on the same beamline (e.g. ID15 at the ESRF, I12 at DLS). A practical challenge remains, how to bridge gap between the microstructural behaviour that can be studied on smallsized specimens via the lCT and real in-service behaviour of full-scale engineering components via standard specimens needs to be further investigated in both systematic theory and extensive experiments. Nevertheless, An effective solution to characterize the fatigue performance of the material is to simultaneously extract the stress field evolved around the cracking front, which helps to correlate the fatigue strength obtained by standard specimens [281,282]. This problem is well defined as the influence of specimen geometry or so-called constraint effect due to scaling effect [283–285]. Finally as the capabilities of X-ray imaging increase in terms of spatial resolution and field of view (aided by cameras with increasing numbers of pixels), by increases in flux which mean more frames per second and by complementary techniques such as X-ray diffraction and digital image correlation it seems inevitable that datasets will increase exponentially in size.

Fig. 32. Representative defect morphorlogy of a GCF fatigued specimen with a characteristic fisheye: (a) the fisheye morphology inside a high strength 4240 steel [258–261]; (b) the inner cracking image inside a (a + b) dual phase Ti alloy [261].

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Consequently there is an urgent need to develop in tandem with instrumental advances more automated data analysis workflows if the full potential of this data is to be realised and so that the experimenter can follow the outcomes of the experiment in real time rather than simply carry out experiments blind. This is critical in the area of crack and damage accumulation because real materials behave unpredictably. Without real-time appreciation of the events being captured, it is likely that really interesting phenomena will either missed, or if they are captured, never properly analysed, nor the data fully archived for others to benefit from. While this is appreciated by synchrotron sources worldwide there is still a preference to invest in new hardware in preference to software which in many cases exacerbates this problem. Only by facilities teaming up to make a concerted effort to develop new analysis workflows will we be able to move to a more effective and full use of the data that is collected. As a possible solution, to speed up the data processing for dynamic lCT, parallel GPU based lCT image reconstruction and other data processing strategies should been urgently developed [286,287,82,288,289]. Methods for the quantitative analyses with high efficient and high accuracy to large-scale complex microstructures have been conducted [290,291]. Though developed for biomedical applications, these methods can be easily transplanted to the investigation of failure in structural materials.

Acknowledgements The authors give sincere thanks to the National Natural Science Foundation of China (11572267), the Science and Technology Research & Development Application Project of Sichuan Province (2017JY0216) and the Open Foundation of the State Key Laboratory for Strength and Vibration of Mechanical Structures (SV2016-KF-21). Prof. PJ Withers is grateful to the European Research Council Funding (CORREL-CT grant No. 695638) and for EPSRC Funding for under the following grants EP/M010619, EP/K004530, EP/F007906, EP/F028431 and EP/I02249X/1 through which access to the Research Complex at Harwell is provided alongside the Diamond-Manchester collaboration.

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