Ensayos

Techniques, such as ultrasonic pulse-echo or tandem, which have been used tradi-tionally for detection and sizing of cracks are based on specular reflection from the face of the crack. With point transducers and a perfectly smooth planar defect of infinite extent, a specular reflection would occur only at the unique angle where the angles of incidence and reflection at the defect are equal. In practice, because of the finite aperture and broad bandwidth of the transducers and the finite size and imper-fect smoothness of the deimper-fect, a ‘specular’ reflection will occur over a small range of angles, though still with a well defined central maximum. However, once the orien-tation of the crack is a few degrees away from the specular orienorien-tation the amplitude at the transducer will fall rapidly as the amount of misorientation increases.This is illustrated in Figure 3.2, taken from Toft [1987], which shows experimental values of signal strength in pulse-echo inspections of circular defects as a function of both tilt and skew of the defect. It can be seen that a misorientation of the defect of about 15^◦, of either tilt or skew, or a combination of the two giving a similar angle be-tween the normal to the defect and the transducer beam axis, gives a signal strength reduced by 6 dB from the perfect orientation. Time-of-Flight Diffraction signals, as

Fig. 3.1 Optimisation of transducer beam angles for Time-of-Flight Diffraction in steel using compression waves. The effects of beam angle on resolution are also shown. Atθ = 90^◦the transducers are infinitely far apart.

3.1. Time-of-Flight Diffraction signals from smooth flat cracks 55

Fig. 3.2 The effect of crack tilt and skew on signal amplitudes from a 25 mm diam-eter circular defect with pulse-echo inspection. The hatched region has a signal level of at least 36 dB above 10% DAC (distance-amplitude correc-tion). The other contours are relative to this level. [After Toft, 1987].

we shall see in Section 3.3, drop by 6 dB after only 45^◦– 60^◦of skew, and often increase rather than decrease with crack tilt. To ensure adequate sensitivity, using pulse-echo techniques, when inspecting a component which may contain defects at a range of angles, it is necessary to use several probes at different angles. This is the basis of the American Society of Mechanical Engineers (ASME) inspections which require inspection at 0^◦, 45^◦and 60^◦[ASME, 1974,1977,1983] and which are often supplemented by 70^◦probes.

In this section we calculate typical amplitudes for Time-of-Flight Diffraction signals and demonstrate the effect of crack orientation. The results are obtained from a mathematical model of the interaction of elastic wave energy in a transducer beam with an elliptical crack. These calculations relate the amplitude of the diffracted signals from the extremities of an elliptical, smooth, planar crack buried in a steel plate, to the signals from a flat-bottomed hole. The defect centre is taken to lie midway between a single transmitter and single receiver, as shown in Figure 3.3, and the amplitude of diffracted signals is calculated as a function of the tilt of the crack. This tiltε is measured away from the normal to the inspection surface so thatε = 0 corresponds to a crack in a vertical plane in Figure 3.3. The Time-of-Flight Diffraction signal amplitudes from this geometry are compared with those obtained when the same probes, with the same separation S, are positioned over a

Fig. 3.3 Geometry used in the mathematical model to predict Time-of-Flight Diffraction responses from elliptical, planar cracks.

3.1. Time-of-Flight Diffraction signals from smooth flat cracks 57

Fig. 3.4 Variation of Time-of-Flight Diffraction signals with tilt for an elliptical de-fect 24 mm by 60 mm, located 220 mm below the inspection surface. The calibration reflector is a flat-bottomed hole located midway between trans-mitter and receiver and 220 mm deep, with the flat end parallel to the in-spection surface.

flat-bottomed hole, as shown in the lower part of the figure. The flat-bottomed hole is assumed to have an axis which is normal to the inspection surface and the centre of the hole lies at the same position and depth from the surface as the centre of the elliptical crack. The particular geometry is chosen so that the maximum signal possible from the flat-bottomed hole is used in the comparison, i.e. the calibration signal is obtained by specular reflection at the flat-bottomed hole.

The transducer beam has a central maximum lying along a direction at angle θ_b to the normal to the inspection surface, and spreads out with the usual Bessel function form appropriate for a circular piston source (see Section A.3.2 of the Ap-pendix). Details of the calculations are given in Temple [1984a] and some typical results are presented in Figure 3.4. In this figure, the crack is taken to be a smooth, planar, elliptical crack with through-wall extent 2a= 24 mm and length, parallel to the inspection surface, of 2b= 60 mm, buried at a depth of 220 mm from the

inspec-Fig. 3.5 Comparison of experimentally determined Time-of-Flight Diffraction sig-nal amplitudes with theoretical predictions. The experimental results (from Silk [1979f]) are for narrow (0.5 mm) slits and for wide (2 mm) slits. The-oretical values for the wide slit are adjusted to have the same value as for the narrow slit for 60^◦incidence.

tion surface. The transducers have circular faces with diameter 24 mm and operate at a frequency of 5 MHz in such a way as to produce maximum amplitude travelling at 60^◦to the normal to the surface. The host material is taken to be isotropic steel and the two transducers are separated by 762 mm. The reference reflector is a 3 mm diameter flat-bottomed hole. Figure 3.4 [based on Temple, 1984a] shows how the diffracted signal varies as the tilt varies between−30^◦≤ ε ≤ +30^◦. Two things are important about this figure. First, the amplitudes of the diffracted signals are both comparable with that from a 3 mm diameter flat-bottomed hole at the same range,

3.1. Time-of-Flight Diffraction signals from smooth flat cracks 59

and, second the signal improves as the tilt of the defect increases. The reason for this latter point is, of course, that the signal is at a minimum value for a vertical crack and so must increase with tilt angle. It would become a specular reflection, like that from the flat-bottomed hole, asε → 90^◦and the ratio of the two signals would simply approach the ratio of their areas. For the particular crack chosen in this example, this would yield a maximum signal of 32 dB for a tilt of 90^◦. This result, for crack tilts of up to 30^◦, demonstrates how relatively insensitive the Time-of-Flight Diffraction technique is to crack orientation.

Temple [1983a,b] also showed how the signal varies as the crack position rela-tive to the two transducers changes. It was shown that the signals from the defect considered above, and shown in Figure 3.4, would only have fallen to 10 dB below those from a symmetrically placed 3 mm diameter flat-bottomed hole even if the crack were 30 mm off the symmetric position between the probes. This result also demonstrates the versatility and utility of the Time-of-Flight Diffraction technique.

Calculations similar to these but for different defect parameters have also been pre-sented [Temple, 1983b].

In the model, the crack is taken to be a cut in the material of zero width but with non- interacting faces on which the stress vanishes. This is an idealised model and it is obviously interesting to compare the predictions of the model with experimental evidence. To do this we use experimental results of Silk [1977, 1979b] on both saw cuts and real cracks. The saw cuts were of two widths, 0.5 mm and 2 mm. The results are given in Figure 3.5.

In the top part of the figure the experimental geometry is defined. Results for diffracted signal amplitudes from the two saw cuts are given in the lower part of the figure and the variation in signal amplitude averaged over four cracks is also shown.

The model is not valid at angles close to specular, that is near 90^◦, but gives fairly good agreement over the remaining range. The experimental signal amplitudes are higher than those predicted, over a good deal of the angular range, especially for diffraction by the top of a crack, and this may be a result of the blunt tips of the slit defects used. According to theory, the amplitude from the bottom of the defect should go to zero and the phase of the signal change byπ at an angle which depends on Poisson’s ratio for the material and would be about 38^◦for steel (see Section A.4).

However, neither a zero nor a minimum signal was observed experimentally and if any change of phase was present, it was not recorded. It has proved very difficult to detect this phenomenon, using conventional broad-band, finite size transducers and artificial defects. With a laser beam as the source of ultrasound and a capacitance transducer as receiver, however, Scruby and Newton [1986] were able to confirm the change of phase and hence the mathematical zero in amplitude.

Using the same laser technique, Ravenscroft et al. [1991] carried out a very de-tailed investigation of the diffraction response of both slots and cracks in steel blocks and were able to explain why previous experiments had usually not detected a mini-mum. Using an open fatigue crack, they obtained a very clear minimum amplitude at 38^◦, with a phase change of close to 180^◦, and excellent agreement with theoretical amplitudes at all angles in the ranges 20^◦– 80^◦and 120^◦– 160^◦. These results are

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Fig. 3.6 Comparison of theoretical predictions with measured signal amplitudes from an open fatigue crack, using a laser beam as the source of ultrasound and a capacitance transducer as a detector. Reprinted from Ultrasonics 29, F. A. Ravenscroft, K. Newton and C. B. Scruby, 29 – 37, Copyright 1991, with permission from Elsevier Science .

reproduced in Figure 3.6. They also showed that the phase change is obscured if the defect tip is blunt, which may explain why earlier attempts to confirm it failed.