The use of TSA for determining the stress intensity factor associated with cracks, by fitting equations describing the stress field around the crack tip to the measured TSA data, is well established [19,20]. The coordinates of the crack tip can be treated as unknowns in some of these methods and hence the crack tip can be accurately located. Alternatively, the map of the phase difference between the loading signal and temperature response can be used to identify the location of the crack tip, as a point of inflexion between the non-zero phase differences associated with the crack tip plastic zone and the crack wake [21]. Non-zero phase differences occur when adiabatic conditions do not prevail, for instance, due to energy released by dislocation movement in the crack tip plastic zone and frictional heating in the crack wake [22]. However, these techniques assume that the crack tip stress field can be accurately described by linear elastic fracture mechanics and are computationally intensive, require appropriate seeding and high-resolution data obtained using constant amplitude and frequency loading. These drawbacks render these techniques of limited value when using low-cost sensors, with relatively low spatial, temporal and temperature resolution, or in industrial applications where the loading might be of variable amplitude and frequency, such as during flight cycles.
Ancona et al. [23] have used TSA to track the propagation of fatigue cracks in martensitic and austenitic steels assuming a prior knowledge of the initial crack. While in 2017, Rajic & Brooks [24] combined a TSA system and an X-Y movement stage to track the propagation of cracks in real time. More recently, Hwang et al. [25] have combined passive thermography to identify cracks and active thermography to track fatigue cracks with an accuracy of 99.43% compared with microscopy; however, this system requires a scanning laser which makes its industrial deployment complicated due to safety considerations. Our previous work has introduced the concept of tracking the initiation and propagation of cracks (see for example figure 1) with a method based on the concept of optical flow [10]. This method works well with spatially and thermally high-resolution TSA data, such as collected with a photovoltaic effect detector, and under controlled conditions. However, since the optical flow method is based on identifying apparent movement in a series of images, it is susceptible to errors when applied to data collected using lower resolution sensors or flight cycle loading with varying amplitude and frequency, because the differences between consecutive datasets are too large relative to the differences in the stress magnitudes caused by crack initiation and propagation.
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Uncalibrated data (normalized using the mean of the field of view) from TSA (left) of a hole in plate specimen after initiation of a fatigue crack, illustrating the TSA patterns indicative of the presence of a crack tip in which the colours are proportional to the amplitude of the temperature ΔT in equation (2.1); and large magnification image (right) taken with a visual spectrum camera showing the same crack.
Normalized Euclidean distance between the feature vectors representing the initial and current TSA data fields (S in equation (2.1)) collected by the photovoltaic effect detector during constant amplitude and frequency loading as a function of load cycle (blue diamonds; left axis) compared with crack length (right axis) from the optical flow method (black squares) due to Middleton et al. [10] and with the crack length calculated from crack tip positions evaluated from the phase difference between the load and temperature signals using the method due to Diaz et al. [21]. Insets show the TSA data fields at indicated cycle values. Optical flow data for this specimen were previously presented in [10].
In figure 6, the results are compared with the crack lengths determined (i) using the optical flow method [10], and (ii) from examination of the phase data to identify the position of the crack tip using the method developed by Diaz et al. [21]. Individual TSA data fields are also shown at selected cycle numbers, illustrating that changes in the measured optical flow crack length, crack length based on phase information, and the Euclidean distance between feature vectors representing the initial and current state, correspond to qualitative changes in the data fields. The Euclidean distance calculated using both the whole field of view and the defined ROI is approximately zero from 98 000 to 120 000 cycles, i.e. there is no significant change in the shape of the TSA data fields (S in equation (2.1)) and, hence, there is no damage in the specimen sufficient to change the strain field. After 120 000 cycles, there is an increase in Euclidean distance, indicating the initiation of damage sufficient to change the elastic strain field. The Euclidean distance between the feature vectors describing the initial and current state begins to increase gradually and then the rate of increase accelerates until 140 000 cycles, which corresponds to just prior to complete failure of the specimen. The optical flow method indicates crack initiation and propagation slightly later, at 124 000 cycles, than the change in Euclidean distance that occurred at 122 000 cycles.
The equivalent data in figure 7 from the microbolometer detector show similar trends, with the Euclidean distance between the feature vectors representing the initial and current state starting to increase from zero at 55 000 cycles; and then increasing at an accelerating rate towards complete failure. A comparison with the TSA data fields in the inset figures shows that the increase in Euclidean distance corresponds to movement in the stress concentrations associated, initially with the hole, and subsequently with the crack tips. The lower resolution of the data fields from the microbolometer detector was inadequate for the optical flow algorithm and no meaningful results were obtained.
Euclidean distances calculated using the defined ROI following detection of the crack appear to be less noisy than those based on the whole field of view; however, the difference is not significant and does not influence the capability to identify crack initiation. We have shown in previous work [10] that the optical flow method can indicate the initiation of cracks at sub-millimetre lengths; and as can be seen in figure 6, a change in the Euclidean distance occurs before the equivalent change in crack length indicated by the optical flow method. This suggests that the differential feature vector method, based on Euclidean distance, is more sensitive than the optical flow method, and therefore that it would indicate crack initiation earlier.
The constant amplitude and frequency loading experiments were designed to induce crack initiation and propagation to failure in a relatively short time period; so that the TSA data could be recorded for the entire event in a single session in the laboratory. However, the flight cycle loading was substantially less aggressive, and it was necessary to pre-crack the specimens using constant amplitude and frequency loading to initiate a crack. Hence, it was impractical to demonstrate the initiation of a crack due to flight cycle loading; but, it is anticipated that the sensitivity of the differential feature vector method to crack initiation due to flight cycle loading would be similar to that demonstrated for constant amplitude and frequency loading.
It was found that the optical flow method did not work for the flight cycle data and thus would be unlikely to work for random loading. The optical flow method [10] relies on the only significant change in the stress field between two successive data fields resulting from the initiation or propagation of a crack, which is not the case when the applied loads vary, depending on the relative position of the TSA integration window within the flight cycle. However, because the differential feature vector method exploits the shape of the data and is largely independent of the magnitude of the applied load, it is therefore more robust in a wider range of conditions.
In the data presented here, crack initiation is only indicated by Euclidean distance in the constant amplitude data, where the Euclidean distance increases from approximately zero to a positive number. It is not possible to see an equivalent increase in the flight cycle data, as the initiation stage of the crack development occurred during pre-cracking which was necessary due to time limitations. However, given unlimited time, observation of initiation should be possible, but would probably not be as clear as in the constant amplitude case, due to the oscillations in the Euclidean distance caused by the flight cycle.
One disadvantage of the differential feature vector method compared with the optical flow method is that it does not indicate the position of the crack tip, so does not directly determine the location or length of a crack, rather it gives the relative progression of damage. However, the location of a crack and a quantitative measure of crack length could be important in some industrial contexts; and hence, this information could be provided by dividing the ROI into tiles. The TSA data from each tile could be decomposed and the difference feature vector method applied on a tile-by-tile basis. When one tile indicated a change before others, it would show the position of crack initiation and indications appearing in successive tiles would provide information on crack length at the resolution of the tiles. This approach has been used in applying image decomposition to the validation of computational models of structural mechanics to indicate zones in a model where its predictions do not correlate with measurements [38]. A limitation of using tiles to survey an ROI is the spatial resolution of the detectors, which would limit the number of tiles and, thus, the resolution at which cracks could be located and their length monitored. However, the low cost and small size of an OEM microbolometer detector would enable an array of detectors to be deployed; thus, allowing data to be acquired from a large number of relatively small tiles. 2ff7e9595c
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