Table of contents
1. Introduction Background
   
2. Comments on the Modelling Software
   
3. IOW Block Dimensions
   
4. D/ Effects on Refracted Angle Determination
   
5. Comments on Assessing Sound Fields in Solids
   Further Chapters on this page:
   
6. Charts and Graphs
   
7. Comments on Charts and Graphs Vertical Plane, Horizontal Plane
   
8. Trends
   
9. Comparison of Beam Spread Determination Using dB Drop from Maximum and dB Drop to DAC
   
10. Comparison of Theoretical with Actual Values
    
11. References

6. Charts and Graphs

Table 1 summarizes the probe parameters analyzed. These are some of the most common probes used in normal NDT work in North America. These element parameters were evaluated for nominal 0°, 45°, 60° and 70° refraction angles.

Table 1 Table of Modelled Probes
Probe Diameter	Frequency
6	2.25	5	7.5	10
9	2.25	5	7.5	10
10	2.25	5	7.5	10
12.5	2.25	5	7.5
19.5	2.25	5	7.5
25	2.25	5

Figure 2 Beam Plot of On Axis Amplitudes and Beam Dimensions Figure 2 shows the pressure along the axis for a 5 MHz 9mm diameter probe radiating into a medium having an acoustic velocity of 3230 m/s. under these conditions the peak would occur at 31mm and the 6dB spot diameter (in pulse echo) would be 2.4mm. The 6dB depth of field as measured along the axis would be 42mm long going from 21mm to 63mm

Figure 3 RF Beam Plot of a 5 MHz 12.5mm Diameter Probe Configured to Provide a Nominal 45° Refracted Beam The image displayed in Figure 3 shows the quasi-B-scan image and uses an auxiliary window above the B-scan to indicate the amplitude profile at the depth of 56.4mm. For this image the peak amplitude at this depth occurred at 93.8% and 56.5mm in front of the exit point. When the same element is put on a wedge to provide a 60° refracted beam the effect is seen in Figure 4.
Figure 4 RF Beam Plot of a 5 MHz 12.5mm Diameter Probe Configured to Provide a Nominal 60° Refracted Beam When the cursor is placed at the same depth the resulting amplitude profile shows a greater travel between the 6dB drop points. In the auxiliary window of Figure 4 the amplitude profile at the depth of 56.4mm has a peak amplitude of 74.6% and it occurs 98.7mm along the test surface in front of the exit point.
Figure 5 RF Beam Plot of a 5 MHz 12.5mm Diameter Probe Configured to Provide a Nominal 70° Refracted Beam When configured for a 70° refraction the peak for the 56mm depth is only 47.7% FSH and occurs 167mm from the exit point. In order to allow the profile to be seen at this depth for the 70° beam the scale was extended to 200mm.
Figure 6 Amplitude Profile Plot of a 2.25 MHz 12.5mm Diameter Probe Taken at 25mm Below the Refracting Interface for a Nominal 45° Refracted Beam From amplitude plots like that illustrated in Figure 6 measurements were made for X-displacements for the peak amplitude and -6dB and -12dB drop locations. By assembling all these values for the twenty probes modelled using the three angles refractions the effective beam angle and beam spreads could be evaluated.

Figure 7 Plotted Beam Spreads of a 2.25 MHz 12.5mm Diameter Probe Using Data Points Measured from Amplitude Plots Using Nominal 45°, 60° and 70° Beams


The following set of tables summarizes the results of the graphed refracted beam angles for the modelled options. Using a Best Fit Regression Curve on the centre of beam data points the refracted angle was determined for each condition modelled. Three angles are noted in each table; the nominal angle which would be the value marked on a wedge, Snell's angle which is the angle that should result based on the velocities of the two media used, and the tabulated angles which result from the best fit curves.

Table 2					Table 3					Table 4
Nominal 45°	Snell's Angle 44.8°				Nominal 60°	Snell's Angle 59.9°				Nominal 70°	Snell's Angle 71.2°
	Frequency MHz					Frequency MHz					Frequency MHz
Probe Diameter	2.25	5	7.5	10	Probe Diameter	2.25	5	7.5	10	Probe Diameter	2.25	5	7.5	10
6	44.1	44.9	44.7	45.0	6	58.5	59.6	60.2	60.4	6	66.4	69.7	70.7	71.0
9	44.8	44.7	44.8	45.1	9	59.1	60.0	60.1	60.2	9	68.4	70.6	70.9	71.1
10	44.5	45.2	45.1	44.7
12.5	44.5	45.2	45.0	45.0	12.5	59.9	60.3	60.2	60.1	12.5	69.5	71.1	71.1	71.2
19.5	45.1	44.3	45.4		19.5	60.4	60.2	59.6		19.5	70.7	71.1	71.3
25	46.2	46.4			25	60.2	59.3			25	71.1	71.4

7. Comments on Charts and Graphs

Models produced by the RF Beam software are displayed for the vertical and horizontal planes

Vertical Plane
This provides a pseudo B-scan showing relative pressure distributions in both the refracting "wedge" material and the second medium into which the beam is traveling. Media parameters used are similar to Lucite (PMMA) and steel which are commonly used in NDT applications.

V_L1 = 2760 m/s
V_L2 = 5850 m/s
V_S2 = 3230 m/s
₁ = 1.18 g/cm³
₂ = 7.8 cm³

To provide a characterisation like that obtained using manual techniques horizontal samples were taken for each probe modelled. Normally six to eight horizontal samples were used for each probe. These corresponded to depths in the second medium that are comparable to the holes found in the IOW Block used for beam profiling. At each sample depth the following values were recorded;

1. maximum amplitude of the highest peak
2. X- displacement at the maximum amplitude
3. the minimum X-displacement at the point the signal drops to -3dB from maximum amplitude
4. the minimum X-displacement at the point the signal drops to -6dB from maximum amplitude
5. the maximum X-displacement at the point the signal drops to -3dB from maximum amplitude
6. the maximum X-displacement at the point the signal drops to -6dB from maximum amplitude

Since the software calculates the pressure drop for the one way transit of a beam, the 3dB and 6dB drop points on the profiles can be interpreted to represent the -6dB and -12dB boundaries normally measured in pulse-echo methods using a point reflector.

The horizontal profile of amplitude versus horizontal displacement for a particular depth is equivalent to the amplitude locus that would be traced on the CRT if a probe was moved across a side drilled hole.

Horizontal Plane As with the vertical plane plots these too provide a pseudo B-scan showing relative pressure distributions in both the refracting "wedge". Files were generated for each horizontal profile made at the same depths as for the vertical plane but using a normal incidence from the refracting material. The Figure 8 shows accumulated beam amplitude plots for several cross sections out to 80mm from the interface for a 6mm diameter 7.5 MHz probe.

Figure 8 Example of Beam Spread in Horizontal Plane

8. Trends

Trends can be observed when the data is tabulated and graphed in this fashion.
• for small diameter lower frequency probes the average angle tends to be less than the Snell angle and the tendency increases with increasing angle
• the trendline for the centre of beam (linear regression extrapolated to zero) is about the same value as the average refracted angle when most data points fall in the far zone (better for 70° than for 45°)
• wide variation exists for individual refracted angles calculated from maximum amplitude for large diameter probes. The trend increases with decreasing angle (this variation occurs in the near zone and may be an artifact of no bandwidth)
• when data points fall in the far zone asymmetry of divergence is seen; i.e. front of beam to centre of beam has greater divergence than back of beam to centre of beam (this is more pronounced for smaller diameter lower frequency probes)
• graphing beam spreads by connecting 6dB and 12dB drop points indicates that divergence does not always occur in the working range of the probe
• graphs of the 6dB and 12dB drop points indicate that focal zones can be identified (contrary to constant divergence normally assumed in plotting- see 45° graph in Figure 7)

9. Comparison of Beam Spread Determination Using dB Drop from Maximum and dB Drop to DAC

Reference standards or specifications usually apply one of two techniques for determining beam spreads, either a dB drop from maximum amplitude response from a side drilled hole or a dB drop to a pre-drawn DAC determined by connecting the peak amplitudes from several side drilled holes. Beam spread diagrams as illustrated in Figure 7 use a specified dB drop from the maximum amplitude. This simplifies the beam spread construction as it becomes a one step procedure whereas the drop-to-DAC method requires each target to be maximized for the DAC construction then each target is returned to so that the drop positions to the DAC can be ascertained. A comparison of the two options was made using the modelled beams. This was done using the model for the 2.25 Mhz 12.5mm diameter probe nominally refracted to 60° (see Figure 9). By accumulating the amplitude profiles that would be achieved from the IOW block side drilled holes a DAC was drawn and another DAC was constructed usnig half these amplitudes. Recall that the modelling uses the transmission only, so the DAC at half maximum amplitude represents a -12dB DAC curve.

Figure 9 Accumulated Amplitude Profiles for 12.5mm Diameter 2.25 MHz Probe

Superimposing the -12dB DAC on the accumulated amplitude plots allows us to assess the difference between the two methods. This is shown in Figure 10. Dropping the signal to the predrawn DAC curve results in a shift to the right for the front and back of beam data points. Although this technique is designed to correct for soundpath differences, inconsistency of results can occur due to differences in the way the DAC is drawn; e.g. number of points used, and the method in which the points are connected - straight line, best guess-hand drawn curve or electronic DAC methods. With differences of 2 to 4mm between data points the perceived accurcay advantages of using the DAC may not be as significant as intended once DAC construction variability is a considered.

Figure 10 Comparison of Two Beam Spread Determination Methods

10. Comparison of Theoretical with Actual Values

To illustrate both the validity of the modelling concept and explain a practical problem in probe manufacturing, a comparison was made of actual beam angle readings from manual measurements and the model predicted values.

A probe manufacturer was given the task to manufacture an 80° refracted beam probe. The probe element was to be 2.25 MHz and 6mm (1/4") diameter. Calculations for machining the incident angle were made using Snell's Law. When the refracted angle was assessed using the standard method of a maximized peak off the 1.5mm diameter SDH in the IIW block the measured angle was around 68°. Several attempts were made to correct this by machining wedges at higher incident angles. The best that could be achieved was around 72° as determined by the peak off the 1.5mm SDH. When a 5 MHz element was used instead a slight improvement was seen but on the same series of wedges the range of measured refracted angles was 72° to 77°. [10]

A similar exercise was carried out using the RF Beam modelling for the nominal 80° refraction problem.Setup conditions for velocity and density were the same as used in the general modelling project mentioned above. Snell's Law was used to calculate several incident angles to produce refracted angles around 80° as listed below:

57° incident gives 78.96° refracted Snell angle
57.5° incident gives 80.76° refracted Snell angle
58° incident gives 82.96° refracted Snell angle
58.5° incident gives 86.23° refracted Snell angle


Modelling these angles using a 6mm diameter 2.25 MHz probe we measured the position of peak amplitude at 15mm depth just as one would do with the IIW block 1.5mm diameter hole at 15mm depth.

This was repeated with a 6mm diameter 5 MHz probe. Results are as follows;

Table 5 2.25 MHz			Table 6 5 MHz
Incident Angle	Snell's Refracted Angle	Max. Amp. Angle	Incident Angle	Snell's Refracted Angle	Max. Amp. Angle
57°	78.96°	70.5°	57°	78.96°	74.9°
57.5°	80.76°	70.5°	57.5°	80.76°	75.6°
58°	82.96°	71.6°	58°	82.96°	76.8°
58.5°	86.23°	72.3°	58.5°	86.23°	77.4°

The model accurately predicted the fact that an 80° refracted beam could never be measured using the traditional methods of determining refracted angle; no matter how high the incident angle was machined. Figure 11 shows the beam from a 2.25 MHz 6mm diameter probe with an incident angle sufficient to produce an 86° refracted angle but the actual angle an operator would determine using the peak off a SDH at 15mm from the test surface would be 72.3°. Figure 12 shows the beam from a 5 MHz 6mm diameter probe with an incident angle sufficient to produce an 86° refracted angle but the actual angle an operator would determine using the peak off a SDH at 15mm from the test surface would be 77.4°. This apparent breakdown of Snell's Law is merely a result of the way in which the assessment of refracted angle is made. This is again the D/ effects on refracted angle determination as predicted by Krautkramer [8]. The lobe effect is compounded by the echo transmittance whereby the return pressure from the 50°-60° components of the beam are more efficiently returned than the 75°-85° components. It was concluded that when manufacturing a probe wedge it should be ascertained the range the probe is intended for and the method by which the refracted angle will be determined. This information may affect the angle the manufacturer machines the wedge angle.

Figure 11: 2.25 MHz 6mm Diameter Probe Nominal 86° Actual 72.3° Figure 12: 5 MHz 6mm Diameter Probe Nominal 86° Actual 77.4°

References

1. British Standards, BS 4331 Part 3, British Standards Institution, 1987
2. DIN 25 450, Ultrasonic Test Equipment for Manual Testing, Deutsche Industrie Normen, 1990
3. ESI Standard 98-12, Calibration and Routine Performance Checks of Ultrasonic NDT Equipment, Electricity Supply Industry, 1989
4. ASTM E-1065, American Society for Testing and Materials, Annual Book of ASTM Standards, Vol. 03.03, 1996
5. Mair, D.H., Measurement of Hydrogen in Zr-2.5%Nb Using High Accuracy Velocity Ratio Measurements, Review of Progress in Quantitative NDE, Vol. 12, Plenum Press 1992
6. Duncan, D., Computer Simulation of Ultrasonic Testing, Proceedings of Ultrasonics International 85, London, UK, 1985
7. Wuestenberg, H., Erhard, A., Approximative Modeling for the Practical Application at Ultrasonic Inspections, UT Online Journal (../../../index.html) May 1997
8. Krautkramer, J. & H., Ultrasonic Testing of Materials, Third English edition (page 68) Springer-Verlag, 1983
9. Hall, K.G., Observing ultrasonic wave propogation by stroboscopic visualization methods, Ultrasonics, Butterworth Press, July 1982
10. Hotchkiss, F.H.C., personal notes, 1981

Author

Frederick H.C. Hotchkiss is product manager for Ultrasonic Transducer Products, Nondestructive Testing Division, Panametrics Inc. in Waltham, Massachusettes, USA. He received a B.Sc. from MIT in 1966, M.Phil. and Ph.D. from Yale in 1972 and 1974 respectively. He was a postdoctoral fellow at the Smithsonian Institution in 1975. Hotchkiss is responsible for the scientific and technical development of transducers at Panametrics. Panametrics Inc. Homepage www.panametrics-ndt.com

Ed Ginzel born 1952/04/04 in Kitchener, Ontario in Canada. Ed Ginzel is an independent consultant with the Materials Research Institute. Materials Research Institute provides training and consulting to the NDT industry. Consulting is provided to the nuclear and petrochemical industry to assist clients developing NDT techniques and to evaluate existing techniques and inspection systems. Email eginzel@mri.on.ca Homepage http://www.hookup.net/~ginzelea NDTnet Exhibition