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Table of Contents
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The other methods will only be mentioned by name here:
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For example, the ultrasonic method can be applied to the following areas:
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Due to the fact that the state of developement for crack determination in metals is the most advanced, we will be concerning ourselves with this area of application in this overlook. Naturally the causes of crack creation, and therefore also the crack shape, are as varied as the materials.
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Cracks are cause by
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or a combination of these.
The different appearances of cracks, even in metals, can be seen in
Fig. 1.
The following physical phenomena can be observed depending on the crack size and shape:
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Information about the size of the crack must be evaluated from
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At the most, additional information can be obtained from the case history of the material or from the construction.
An echo pulse can only be evaluated in two different ranges:
In the time range; as it is presented on the screen of the ultrasonic instrument`s display, where the voltage amplitude superimposes over the time of flight or in the frequency range. For this, the echo pulse must undergo a Fourier transformation beforehand.
The following methods can be found in the time range for crack evaluation:
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The frequency range enables the following methods to be used for crack evaluation:
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With the introduction of application examples I would like to follow this pattern from simple to more complicated methods with the exception of time of flight related methods of measurement because they are, as opposed to image methods, also used with present day ultrasonic instruments and also used in the field of manual testing.
There is no proportional increase with the maximum echo amplitude especially with crack depth propagation, it is often not even a monotone behavior.
Drastically discouraging examples are shown in 
Fig. 2. In the upper diagram, according to (1), the true crack depths are plotted as well as certain crack depths via the echo height. The measurement points should be on the diagonals. In actual fact, the cracks are only determined with about one third of the real size.
The half amplitude method, as with all scanning methods with relative thresholds, uses the maximum echo amplitude. In the lower diagram of Fig. 2 are, according to (2), the results from extensive test series for the different methods of measurement. Once again with this method, the measurement points are not on the diagonals with the echo amplitudes but as before at one third of the true depth at the most.
In anticipation of the time of flight related methods one can see here that the utilizatzion of the signals from the crack peaks, as well as the individual probe method and the tandem method, produce good results.
Surface waves are influenced by surface cracks, independent of crack depth. Reflected and penetrated surface waves are proportional (3), as shown in the upper diagram of 
Fig. 3, up to a saturation limit which is dependent on the wavelength.
With scatter, the echo amplitude increases to a higher power, depending on the crack depth, as opposed to reflection. At the same time, the crack hardly shows any directional dependence at low frequencies (scatter). This method can be made use of according to (4) in order to determine the transition frequency fü between scatter and reflection via determination of the echo amplitude with a number of test frequencies. The wavelength of this transition frequency is approximately 3 to 5 times the crack depth.
The diagram for the vertical fatigue crack in the center of Fig. 3 shows the ideal behaviour.
The lower diagram in Fig. 3 shows, by the deviating curve, that the crack has no continuous area. A partial area (partial branch) of the complex crack formation is determined as crack depth.
Amplitude evaluation and scanning can be combined in order to improve the measurement results. This is shown in the upper diagram of 
Fig. 4 (5). By switching the receiver El - En one obtains the position of the crack peaks (when no reflected amplitude is received). This method can be carried out very well by a phased array probe.
The ALOK method is presented below, Fig. 4, which is generally a method for flaw classification and size determination (not only crack measurement method). Going from many positions, the echo times of flight to the reflector and the corresponding maximum echo amplitudes are captured, mathematically released from the noise signal and evaluated according to algorithms (6). For example one receives a display reconstruction of the reflector, e.g. a B-Scan of a crack (as shown) or as a C-Scan.
The COMSON system (7) also operates with data from the echo dynamic in the time range which is also a display giving a classification and size determination system for all weld flaws and can of course correspondingly also determine the crack depth propagation.
Fig. 5, the use of spectral data as an example on depth determination of surface cracks (through-transmission method according to (8)). Picture a) shows the pulse and the associated spectrum at a crack-free position.
Picture b) shows the typical display after passing a crack. The pulse clearly shows that the surface wave having a lower frequency is met earlier whilst in the remaining pulses there is an overlap of continuous surface waves on the crack. The corresponding spectrum shows a wavy curve.
Picture c) is produced if the lower frequencies are filtered out. The spectrum then corresponds to that of the non-interferred pulse. Therefore a trial was made to set the crack depth in correlation to the lower frequency parts as shown in Picture d). The maximum of the lower frequency spectrum part and especially the separation point (cut-off frequency) between the parts of the spectrums of the first pulse part and the second part have a good correlation to the crack depth as shown in the diagram in Fig. 5.
With this measurement method no effects of mechanical stresses were determined on the measurement result at the crack.
The sequence of steps for signal processing is shown from the top to the bottom on the lefthand side of 
Fig. 6.
The lower diagram in Fig. 6 shows classification in 4 classes in the time range with three features A, B, and C (9) as an example of evaluation by patern recognition on weld seam cracks. The upper diagram shows differentiation in two classes 1 and 2 having two features X1 and X5 according to (10).
The socalled focusing with synthetic aperture (SAFT) uses different positions of the receiving probe in order to evaluate the individual signals as if only a signal would be received from a very large focusing probe. As seen in the upper diagrams of 
Fig. 7, the crack indication cannot be recognized from the spacial distribution of the echoes (original data). The plot of a reflector indication is only possible after processing in a computer (diagram top right according to (11)). The acoustic holograph is another display method for reflector reconstruction in which nondestructive material testing is at least used with line scanning as linear holography.
The lower diagram in Fig. 7 shows the reconstruction of weld seam cracks using tandem probes according to (12). The diagram shows the good consistency between reconstructed and real reflector size with sizes above 2 wavelengths.
By diffraction of signals produced by the crack ends, there are slight dependencies on direction. However most of them are at least 12 dB smaller than the direct reflection signals. They can be measured with single probe methods as well as with tandem or delta arrangements. Together with the known probe positions (and the directional patern) the locations of the crack ends are determined via the time of flight (refer to (13)).
An example is given for the single probe technique in 
Fig. 8Fig. 8. The probe is moved away from the crack until the diffraction indicator displays the crack peak (14).
The lower diagram in Fig. 8 shows how well stress corrosion cracks can be determined with this method (15).
The diagrams in 
Fig. 9 (16) show examples for crack peak detection via the diffraction signal with a number of probes.
Rapid searching of the crack peak can also be achieved with phased array probes.
The diagram in Fig. 9 shows that this method of measurement achieves correct results with vertical surface cracks (0°) as well as with angled cracks (30°). The measurement was made with transverse waves at 45° (17).
Time of flight evaluation of surface waves for crack depth determination are shown as examples in the 4 diagrams in 
Fig. 10. On the upper left (18) the time of flight difference of the reflected surface waves are compared with the true depth (good results are achieved when the depth is greater than the wavelength).
The diagram on the upper right (19) shows the crack depth determination by time of flight differences with surface waves produced by laser.
As opposed to this, the lower left diagram (20) shows the results of surface wave through-transmission on cracks in fractured specimens. The crack depth is determined from the detour which the surface wave must travel around the crack. The right diagram shows the results of this technique on surface cracks in the running tread of railway wheels.
Via an internal crack and using the tandem probe arrangement according to Fig. 11, one obtains a direct wave on the surface between the probes, the diffracted waves from the crack ends and the backwall echo. With this tandem arrangement a reflection patern appears in the B-Scan as shown on the lower left of Fig. 11. If one corrects the different times of flight to the same crack end then one obtains an indication which is true to location as shown in the lower center. The shape of the reflectors cannot however be recognized. You are able to obtain a realistic reconstruction of true to location reflectors only after additional numerical processing corresponding to the algorithm of the synthetic aperture indication (lower right of Fig. 11).
The work in (23) is mentioned as a simple method for displaying cracks, which form under clading, using a multi-mode probe which receives diffracted signals after wave conversion.
In proportion to the very varied materials and constructions, there are also a number of specific testing techniques, methods of evaluation and indication applied for determination of the crack depth which depend on:
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Essentially, improvement of crack depth determination is achieved by eliminating the influence of the sound beam which unfortunately is nearly always greater than the crack depth propagation. For example, this can be obtained by focusing the sound beam or by the deconvolution method.
The many influences on the reflection amplitude can be eliminated by using the time of flight of the diffracted echoes for location of crack peaks.
These techniques will develop in two directions:
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The development of these measurement techniques is always advancing.
It is not possible to deal with all results in this field of work, many interresting publications must be mentioned, the profusion of materials is that great. Therefore I would like to ask the appreciation of this fact from all authors not mentioned here.
The Paper was presented on the UTonline Application Workshop in May '97
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