Production of fatigue cracks by three-point bending (a). Top view and side view of the crack after removal of the notch (b).
(a) Top view of the crack in specimen 1 at 10× magnification and (b) side view of the crack mouth at 5× magnification.
Compliance of specimen 2 plotted vs back-face strain, as measured by the cross-crack (sensitive to crack breathing) and back-face strain gages.
Setups used for the estimate of the crack damping: (a) forced excitation and (b) high amplitude single mode (third flexural) excitation.
Loss factors as a function of frequency/mode shape measured using forced vibrations. The typical strain amplitude was in the range at all frequencies. The dotted line is the FEA simulation of the variation of the loss factor vs frequency for specimen 6, in the assumption constant with frequency. The strain measured here was low compared to the thermosonics experiments, but the assumption constant with frequency could be validated.
Loss factors as a function of strain in the third flexural mode of the beams. These values were used in the predictions of the thermosonics signal.
Block diagram representing the tasks involved in the prediction of the thermosonic signal.
(a) Thermosonics testing with camera pointing at the crack top. (b) Thermosonics testing with camera looking at the crack side to estimate the distribution of heat vs depth.
(a) Strain record for test number 5 on specimen 1; inserts a/1 and a/2 show different instantaneous vibration regimes within the pulse. (b) Average power generated at the crack plotted vs time during the excitation. (c) Prediction and measurement of the temperature rise on the top of the crack.
(a) Measured temperature distribution over the crack side in specimen 5 and its matching curve-fitted temperature distribution obtained by iterative FEA analysis (the y-axis origin is set to 0.02 °C as this was the general IR camera noise level). (b) Corresponding heat-release step function describing the crack in specimen 5 as three uniform-power rectangular heat sources located at different depths.
Examples of comparisons between measured and predicted thermosonic signals from different tests in different specimens: all significant cases are encompassed, from excellent agreement as in (a) (specimen 1, test 16) to the worst obtained correlation in (e) (specimen 2, test 18), including the case (f) of barely measurable temperature rise (specimen 4, test 7) and intermediate cases such as (b) overestimate (specimen 3, test 15), (c) underestimate (specimen 6, test 17) of the thermosonic signal from predictions, and (d) disagreement in the shape of the transient (specimen 7, test 9).
Average magnitude of the measured thermosonic signal vs average magnitude of the predicted thermosonic signal for all tests in all specimens. (a) specimen 1; (b) specimen 2; (c) specimen 3; (d) specimen 4; (e) specimen 5; (f) specimen 6; (g) specimen 7. The dotted line is the linear fit. The histogram (h) represents the distribution of the 116 tests in the six categories defined in Fig. 11.
(a) Measured average temperature rise per unit of strain squared plotted vs percentage of cracked cross section. (b) Crack loss factor vs percentage of cracked cross section. (c) Measured average temperature rise per unit strain squared plotted vs crack loss factor for each specimen. The dashed lines represent the linear fit.
Characteristics of the cracked beams.
Step functions used to describe the distribution of the heating over the crack depth.
Summary of the number of tests carried out for each specimen, the slope of the lines fitted to the predicted vs measured temperature rises and the average variability of the temperature across the width of each crack expressed as the standard deviation divided by the mean value.
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