RESULTADOS

In order to simplify the discussion of calculating the depth from which the diffrac-tion signals originate, we shall assume that the ultrasonic wavefront can be treated as coming from a point source and converging on a point detector. Although this is clearly an approximation, it will be sufficiently accurate provided that two condi-tions are fulfilled. The first condition is that the diffraction sources are well into the far field of the transmitter and receiver probes, i.e. the range from each probe sub-stantially exceeds the near-field distance, defined as D²/4λ, where D is the effective diameter of the vibrating element of the probe, treated as a piston source andλ is the ultrasonic wavelength. For 10 mm diameter probes vibrating at 5 MHz in steel, the near-field distance would be about 21 mm. The second condition is that the diffrac-tion source lies reasonably close to the beam axes of the transmitter and receiver probes. The central lobe of the beam extends to an angle of approximatelyλ/D ra-dians from the beam axis and for the probe quoted above would be little more than 8^◦. If these conditions are fulfilled, we should be able to measure the time interval between signals following different paths to a small fraction of a period. In practice these condition are often not completely fulfilled but it is convenient to postpone discussion of the consequences until later in the chapter. The effects of working in the near field on the pattern of signals observed will be discussed in Section 2.3.4.

The effect of finite probe size and the consequent limited beam width on the

accu-2.3. Time-of-Flight Diffraction in Isotropic Media 23

racy with which signals can be timed will be discussed in Section 2.3.2.7. For the initial discussion, we shall also ignore the transit time of the ultrasound in the probe assemblies, probe shoes, coupling media etc., and assume that we can measure the travel times in the workpiece accurately, relative to the transmitter firing pulse. We shall return to a discussion of probe, shoe and coupling effects in Section 2.3.2.

To calculate the crack through-wall size and depth from the inspection surface requires nothing more than Pythagoras’s theorem. Suppose, at present, that the crack is oriented in a plane perpendicular to both the inspection surface and the line joining transmitter and receiver along the inspection surface. Suppose also that the crack is midway between the transmitter and receiver (i.e. the probe pair has been moved until the time-of-flight of the defect signal is at the minimum), with the extremity nearest the inspection surface at a depth d below it, and that the crack itself has through-wall extent a. Referring to Figure 2.1, if the separation between the centres of the transmitter Txand receiver Rxis taken to be 2S, and the speed of propagation of elastic waves is taken to be C, then the arrival times of the various signals are

t_L=2S times t₁and t₂are the arrival times of the signals diffracted by the extremities of the crack. The first signal to arrive, t_L, is due to the lateral wave and that marked t_bwis the time of arrival of a back-wall echo. C is taken to be either Cpor Cs, the speed of propagation of bulk compression or shear waves respectively.

Rearranging the above equations, we find the depth of the top of the crack from the inspection surface is d with

d=1 2



C²t₁²− 4S² (2.10)

and the through-wall extent a is given by a=1

2



C²t₂²− 4S²− d (2.11)

and the value of the separation of the probes need not be known, since we can sub-stitute

2S= C_Lt_L (2.12)

for this, where C_L is the speed of the lateral wave. On a flat plate this speed is identical to the bulk wave velocity Cpor Csof compression or shear waves respec-tively. This brings out an interesting question: which wave mode would be most advantageous to use? The shear wave has a wavelength roughly half that of com-pression waves and therefore offers an enhanced resolution but has the disadvantage that the speed of propagation is only half that of the compression waves. This slower speed means that in many cases the signals of interest from the defect will arrive in amongst other, possibly spurious, signals generated by mode converted compression waves which have travelled further, or by Rayleigh waves. Hence, in many cases, the shear wave signals will be more difficult to interpret than those from compres-sion waves. For this reason the normal choice is to use comprescompres-sion wave signals.

Although compression waves are usually preferable, because of their earlier arrival time than shear waves, there may be other considerations, such as the anisotropy of the material to be inspected, which might make the use of shear waves preferable in certain cases, and this will be discussed in Section 7.1.

If compression wave signals are to be used, we can choose the probe separation so that any signals which travel over their complete path as shear waves arrive after the compression wave back-wall echo. Referring to Figure 2.1, this will be the case if

t_L(shear) > t_bw(compression) (2.13)

or ex-clude the possibility of signals which travel part of their path as compression waves and part as shear waves, undergoing a mode conversion at a defect. Some such sig-nals appear in the lower part of Figure 2.2. Their main intensity arises where the shear wave beam from one transducer intersects the compression wave beam from the other. Since there are two such positions, a single defect gives rise to two sets of signals, compression wave converting to shear waves and vice versa.

Effects of this kind can be confusing in isolation, but a consideration of all the signals arriving and their relation to each other will normally make clear the origins of each; where any ambiguity remains, an additional scan with a different transducer separation will resolve it. In some circumstances these mode converted signals can be used to advantage. This is further discussed in Section 5.5.1.

2.3. Time-of-Flight Diffraction in Isotropic Media 25

RMS error 0.3mm

0 5 10 15

0 5 10 15 20

Distance across weld (cm)

Crackdepth(mm)

Fig. 2.3 Sizing a fatigue crack with Time-of-Flight Diffraction. The filled and open circles are TOFD measurements at beam angles of 10^◦and 20^◦to the nor-mal, from the surface from which the crack grew. The solid line gives the actual crack profile determined destructively.