ABSTRACT

Table of contents
1. Introduction
2. An approximative model for the ultrasonic inspection
3. The model on a separat page!
4. Practical applications and experimental veriffication of the model
   • 4.1 Inclined notches
   • 4.2 Inner crack
   • 4.3 Crack within a Turbine shaft
5. Summary
6. References

1. Introduction

Endorsed by the wide spread availability of powerful computer technology the manual ultrasonic inspection e. g. on welds is to an increasing amount replaced by mechanized automatic inspections. The standard presentation of a result from an automatic inspection is a picture of indications either in a direct presentation of the basic datas received by the ultrasonic inspection device (e.g. C-Scans or B-Scans produced by combining A-scan- and probe position data) or derived from the primary datas with more or less sophisticated transformation procedures (SAFT, Holography etc.). Due to the imagelike presentation of the results, the operator has to apply special acceptance criteria which are not only derived from the echo amplitude. They should ruthermore be based on typical patterns corresponding to special defect situations. Theoretical modeling of such patterns represents therefore a stringent need for a reliable automatic ultrasonic inspection and for the training of operators. This contribution tries to describe a kind of approximative modeling for the practical application at ultrasonic inspections for some typical cases. Figure 1 shows a schematic of a procedure for the developement of solutions for a new inspection task for an NDT method. The selection of the best method for the inspection, the optimization of the method, the qualification and the evaluation of the results can successfully be executed and accellerated by the appropriate use of theoretical modeling. But the practical use of modeling requires the on line availability of results and the possibility to change rapidly the interesting parameters of a modeled situation, that means e.g. to play with different hypothesis of possible defects etc. This leads at present to a certain preference for approximative methods, because they are the only ones being fast enough on the basis of the mainly applied personal computers. Powerfull workstations will in future also be present in many laboratories and service companies, but they certainly require higher qualified personal, which is usually not available on site. Some problems with the approximations and their limitations will be discussed at the end of this contribution.

The simulation of an NDT situation by computers can contribute to the training of operators and to the solution of different problems: e.g. it seems to be possible to predict the reliability of certain inspection methods, the direction of optimization procedures can be defined and the comparison of a given result with a theoretically calculated defect image can enhance the qualitative and quantitative evaluation of the results.

2. An approximative model for the ultrasonic inspection

Despite the positive esteem of the important quality improvements by the ultrasonic inspection at the early fiftees e.g. on forged and rolled steel products, the application of a theoretical modeling of this inspection method had been limited to the description of the most important parameters using simplified idealisations of the wave propagation and of the interaction between the waves and the surface of a defect, see also the theoretical argumentation for the DGS-diagram of J.Krautkrämer [2] (1959). A look into the classical book "Materials Testing with Ultrasound" by Joseph and Herbert Krautkrämer [1] shows on the first 120 pages a lot of elementary physical thoughts introducing into the theory of the ultrasonic inspection. Today even the most powerful finite element programming tools like EFIT and others, [14, 15] offering a reliable reference with a modeling very close to the reality are not ready to be used on an inspection site due to the time needed for the calculations. Such a finite element code is a very useful tool for single experiments, but it is very time consuming, if used for the simulation of a fairly detailed problem on site and on line. This underlines the strong interest on approximative calculation models. At the BAM we have therefore started to work again on some simplified modeling coming back to experiences from the late seventees.

3.The model:

On a separat page.

4. Practical applications and experimental veriffication of the model The results of this approximative model had been compared with test-block measurements for three special cases: (Figure 8) inclined notches detected by the corner effect within half a skip distance a perpendicular crack in the center of a planar and parallel test-object and a crack in a turbine shaft with an inner bore

Fig 8: Three cases for the Modelling of Crack detection with Ultrasound

4.1 Inclined notches

Figure 9 demonstrates the different rays or soundpathes of the partial echos to be considered for inclined notches. The 30mm thick test blocks contained 10 mm notches with a 2mm gap and inclinations between 0° and 20°. There are simple shearwaves soundpathes, shear-longitudinal soundpathes with mode conversion at the defect or mode conversion at the bottom surface of the test object. There are echos produced by interactions between the defect and the bottom surface and there are echo indications from the roof of the notch with its 2 mm gap. Figure 10 and 11 compare typical TD-scans from measurement and model calculations on notches. The pictures give an impression of the complexity of interactions to be considered in this case. ( see also [12, 13]). There are beneath the tip diffraction indications also echos from long wave contributions (to be recognized by the slightly deviating slope) and direct interactions with the bottom surface. In order to check the amplitude behaviour of the model, several experiments have been carried out. Fig 12 shows the comparison of A-scans for a notch oftenly used during UT-inspections in german nuclear power plants (the so called "KTA-notch") and a 3 mm Flat bottom hole. There is a fairly good agreement between the measurement (16 dB) and the theory (18 dB). Fig. 12: Comparison of calculated A-Scan: 3mm FBH and 3x20mm perpendicular notch. Difference in Echoamplitude: dH=62-44=18 dB (16 dB measured) Figure 13 demonstrates another important behaviour of an ultrasonic indication from notches. The echo amplitude dynamic range (That means the increase of the echo amplitude with the notch depth) for two different probes is described by the model with sufficient experimental agreement. Even the orientation dependency can be predicted by our model (Fig 13 below).	Fig 9: Rays and partial waves at the model for crack detection with the corner
	Fig 10: Comparison of measured and calculated B- Scans from inclined corner reflectors	Fig 11: Comparison of measured and calculated B- Scans from inclined corner reflectors

4.2 Inner crack

The case of a crack in the inner medium of a planar and parallel test object is demonstrated in figure 15. The different rays of this model are shown in figures 14 and 14a. Using a 45° angle beam probe for shear waves with a small transducer size (8 x 9 mm) enables the probe to receive not only crack-tip indications produced by shear waves but also some mode converted signals for longitudinal waves between the crack and the bottom surface generated at about 35°-38° angle of incidence at the defect surface. Figure 15 shows a typical TD-scan received by this arrangement. See also a downloadable demonstration program [17] (hf-bild.exe in : ut_sim.zip). The same downloadable demonstration program contains also the case of an inclined and perpendicular notch.

Figures 14 and 14a

Fig 15: Comparison of measured and calculated B-Scans at internal Crack

4.3 Crack within a Turbine shaft

In order to take into account curved surfaces we have modified the three dimensional planar geometry and have adapted it to the curvature influences. The soundfield of probes coupled to a curved surface must take into account an additional focussing which results in a modified distance law and a differentiation of the soundfield description within the model between the focal spot area and the farfield of the probe. If the focal area determined by the curvature is greater then the nearfield length of the transducer size the focussing effects are neglected. Figure 16 demonstrates the typical interactions regarded for the model of a crack in a turbine shaft. The figures 17 and 18 show the time-of-flight displacement scans with defects at different distances from the inner surface and at different orientations.

Figure 16

5. Summary

The examples of a simplified modeling of the indication pattern at different inspection cases are demonstrating the possibility to predict with a standard Personal Computer the patterns of typical defect situations and thus to enhance the planification of a NDT inspection and the interpretation of its result.
The application of program codes based on approximations requires, that the user possess sufficient physical background knowledge of the applied inspection approach. The greater computer expenses for more exact approaches with finite element programs is replaced at the approximative modeling by simplifying descriptions which mostly are based on expert knowledge. The very fast calculations and the possibility to adapt the parameters to a given situation with an interactive variation justify this procedure. The approximations used for the presented model are physically well based and are describing the most essential interactions qualitatively and to a satisfying degree also quantitatively in a sufficient agreement with experimental results. But for the time being the simplicity of the approach is limiting its application to well defined classes of geometry (rectangular or trapezoidal blocks and concentric cylindrical bodies with abritrarly oriented defects). It seems not to be a useful task to extend this approach to general geometries, because this would need a very detailed individual ray tracing study for each case. The real gain in time and plausible understanding of the physics may then vanish and at the end one has to decide upon the option to apply a more generally valid program like the one using the EFIT-Code of Prof.Langenberg in Kassel/Germany. Therefore we would recommand the use of our approximative model only together with a geometrically idealized description of the practical problem fitted to the capability of the modeling software. The model requires the classification of the considered inspection case depending on the geometrical difficulties.

7. References

1. Krautkrämer, J.; Krautkrämer, H.: "Werkstoffprüfung mit Ultraschall". Springer Verlag Berlin, Heidelberg, New York 1980
2. Krautkrämer, J.: "Fehlergrößenermittlung mit Ultraschall". Archiv für das Eisenhüttenwesen 30 (1959), S. 693-703
3. Miller, G.F.; Pursey, H.: The field and radiation impedance of mechanical radiators on the free surface of a semi-infinite isotropic solid. Proc. Roy. Soc. London, A 223 (1954), S. 521/542
4. Schlengermann, U.: "Schallfeldausbildung bei ebenen Ultraschallquellen mit fokussierenden Linsen". Acustica 30 (1974) Nr. 6, S. 291-294
5. Wüstenberg, H.; Kutzner, J.: "Empfindlichkeitseinstellung beim Einsatz fokussierender Prüfköpfe in der Ultraschallprüfung an ebenen und gekrümmten Bauteilen". Materialprüfung 19 (1977) Nr. 10, Oktober
6. Wüstenberg, H.: Untersuchungen zum Schallfeld von Winkelprüfköpfen für die Materialprüfung mit Ultraschall. Dissertation, TU Berlin (1973). BAM-Berichte Nr. 27 (1974)
7. H. Wüstenberg: Improvements in the Design of Focussed Angle Probe; Nondestructive Testing Communications, 1985, Vol. 2, pp. 55-64
8. H. Wüstenberg, W. Möhrle, BAM Berlin Erfahrungen mit theoretischen Modellen für Schallfeld- und Impulsverhalten beim Bau von Sonderprüfköpfen für die Ultraschallprüfung Berichtsheft der Deutschen Gesellschaft für ZfP e.V. zur DACH-Tagung 6.-8. Mai 1991 Luzern/Schweiz
9. Krimholtz, R.; Leedom, D.A.; Mattaei, G.L.: New Equivalent Circuits for Elementary Piezoelectric Transducers. Electron. Lett. 6 (1970), p. 398-399
10. K. J. Langenberg, T. Kreutter, P. Fellinger Physikalische Elastodynamik statt Punktquellensynthese Gesamthochschule Kassel, Dezember 1987
11. F. Walte, W. Gebhard, S. Ekinci, Z. Jaszczuk, Saarbrücken Ultraschallprüfung unter Benutzung der Wellenumwandlung, Teil II: Auslegung von Ultraschallprüfköpfen für die LLT-Technik Materialprüfung 30 (1988) 10
12. R. Werneyer, U. Schlengermann Über die Reflexion von Ultraschallwellen an Oberflächenrissen und nutförmigen Testfehlern Materialprüfung Bd. 13 (1971) Nr. 7, S. 213/218 und Nr. 9, S. 298/300
13. H. Wüstenberg, U. Völkel, J. Kutzner Reflexionsverhalten von flächigen Trennungen in festen Körpern bei der Ultraschallprüfung, Materialprüfung 16 (1974) Nr. 10 Oktober, S. 323 f
14. F. Walte, K.J. Langenberg, P. Fellinger, R. Marklein "Die Reflexion von Ultraschallwellen an Rißspitzen-Vergleich von Simulationen" DGZfP Tagungsband 37.2 der Jubiläumstagung in Garmisch-Partenkirchen, Mai 1993, S. 684 - 690
15. R. Marklein, P. Fellinger, K.J. Langenberg "Die Ultraschall-Modellierungscodes AFIT und EFIT als Werkzeuge zur quantitativen Fehlerbewertung" DGZfP Tagungsband 33.2 der Jahrestagung in Fulda, April 1992, S. 823 - 833
16. Christophe Bellon (Ecole Nationale des Mines de Saint-Etienne) "Modélisation de la réflexion d´une onde sur un défaut. Vérification de l´approximation de l´élastodynamique physique" Travail de fin d´études BAM - Berlin 1997
17. H. Wuestenberg, R. Boehm Simulation of an Ultrasonic Inspection
    http://www.ndt.net/article/wuesten/wuesten.htm Copyright 1. Nov 1996

Author

Hermann Wüstenberg, Anton Erhard
Bundesanstalt für Materialprüfung BAM
ZfP Ultrasonic Laboratory VIII.4, D-12205 Berlin
Tel. + 49 (0) 8104-0, Fax + 49 (0) 8112029
E-mail: Hermann.Wuestenberg@bam-berlin.de
Home Page: http://trappist.kb.bam-berlin.de/dept8.html

Presented on the Application Workshop in May '97