Problems Using Flat Reference Blocks for
Calibrating Ultrasonic Systems for Testing
Cylindrical Material

by Kenneth H. Beck*

It is a common industrial practice to use flat reference blocks for testing cylindrical materials. This article points out a number of problems with this approach and provides an analytical explanation for the inadequacy of this practice. This article also demonstrates the importance of selecting proper transducers and reference blocks. It should be of interest to anyone involved in the ultrasonic testing of cylindrical materials. G.P.  Singh Associate Technical Editor

Figures 1-2

Introduction
It has been the practice for many years in some industries to use the response from flat reference blocks to standardize the sensitivity and focal conditions for the testing of cylindrical material. Some specifications and procedures such as MIL-STD-2154 (US Department of Defense, 1982) indicate that this is at least acceptable when applied to material over 100 mm (4 in.) in radius. This practice may be justified where years of essentially empirical experience have demonstrated that all important discontinuities are discovered in a given product by its employment. However, there are a number of problems to this approach which should preclude its incorporation in a document intended to prescribe a general practice for such tests. Some have been discussed elsewhere (Beck, 1999) and others are listed below.

• Most specifications for testing materials for critical end use specify that reference standards be made from material of the same composition, surface finish and heat treatment as the parts to be tested. There is a very small likelihood of these conditions being met by a flat reference standard when test material is cylindrical.

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This represents a compromise with good practice that should be used only in special circumstances.

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• To ensure reliable test results, most specifications for other than manual contact tests require that the rejection sensitivity be verified by initial and periodic checking of the reference standard at the full scanning speed used for the test. Depending upon the nature of the scanning system employed for the cylindrical material, this requirement may be difficult or impossible to meet with flat reference blocks
  
• Most importantly, dimensions and focal conditions of a transducer selected to optimize response from a target at a certain depth in a flat reference block bear no relation to those needed by a transducer for testing of cylindrical material at the same depth. This point is demonstrated by the following analysis. Furthermore, transducer selection based on the use of a flat reference block would obviate transducer dimensional selection procedures such as are described in Beck (2003).

 

Analysis
An example of the inadequacy of transducer selection for cylindrical materials testing at a given depth, based on optimization of its characteristics to maximize response from a target at the same depth in a flat reference standard, is demonstrated by the following analysis.

Refer to Figure 1, which shows, in simplified form, the beam from a transducer focused for maximum response from a target at a depth d in a block with a flat surface.

The focus of the refracted beam as shown in this figure may be achieved by a lens, by a phased array or may be due to the natural near field convergence of the beam from a flat transducer. As shown, it is an approximation of actual focal conditions because the wave front from transducers is never "flat" in the optical sense and because the ratio of transducer element size to wavelength is so much smaller than is required for this pseudooptical representation (Krautkramer and Krautkramer, 1990). However, the use of short pulse lengths smoothes amplitude variations in the near field (Singh and Rose, 1982) and allows this representation to adequately demonstrate the conditions to be described.

Equation 1 expresses the depth d from the top surface of a flat block to the approximate location of the refracted beam focus point in terms of the focal length L_f of the transducer (which may be the Y₀⁺ [last near field maximum] distance of a flat transducer), the water path length L_w and the ratio K of the sound wave velocity in the material to the velocity in the couplant. Since greatest beam intensity is achieved at this point, it is assumed that d represents the center of the depth range to be examined.

(1)

The water path must be selected to place the first water path multiple beyond the back surface of the block. Since a cylindrical bar of radius R is to be tested, the minimum water path length is given by Equation 2.

(2)

Substituting this in Equation 1 yields for the flat block:

 

(3)

Solving this for the proper transducer focal length for maximum intensity at depth d results in Equation 4.

(4)

The expression equivalent to Equation 1 for the depth of focus in a cylinder (Beck, 1991) with the Equation 2 substitution is:

(5)

The equation for minimum focal length required to obtain normalized focus at any depth d in a solid cylinder may be obtained from Beck (1991), with the substitution for water path given in Equation 2 above as:

(6)

Example
If it is desired to have maximum beam intensity at the center of a cylinder of 127 mm (5 in.) radius (d = R = 127 mm [5 in.]) and the velocity ratio K is assumed to be 4, the required minimum water path length is found from Equation 2 to be:

If the calibration is based on optimizing on a flat block, the focal length (or Y₀⁺) of the transducer is found from Equation 4 to be:

If this focal length is substituted in Equation 5, the actual depth for maximum beam intensity is found to be:

The minus sign indicates that the focus is really a virtual one above the top surface. This condition is shown in Figure 2. This obviously does not produce the desired maximum intensity at the center of the bar.

The proper focal length for center focus in a bar of 127 mm (5 in.) radius is obtained from Equation 6 by substituting d = R. This yields:

This is seen to equal the water path length plus the material radius (L_w = R), which is obviously correct for a transducer focused at the center of a round since all incident rays enter the surface perpendicular to it (that is, along radii) and so have zero incidence angle and are therefore not refracted.

The disparity between focal length determined by optimization on a flat block and that determined by a round one becomes even worse at smaller diameters and is not negligible until very large diameters are considered. For instance, to optimize at a depth of 254 mm (10 in.) in a flat bar L_f = 1143 mm (45 in.) while the L_f for focus at the center of a 508 mm (20 in.) diameter bar is 381 mm (15 in.).

Large transducer elements are needed to produce the long focal lengths required for optimization at long distances in a flat block. (For example, element diameter = 39 mm [1.45 in.] for Y₀⁺ = 1143 mm [45 in.] at 5 MHz and 55 mm [2.16 in.] for operation at 2.25 MHz.) If available, elements of these diameters would produce poor signal to noise ratios for operation on round bars.

It might be argued that, after using a transducer with a large focal length to optimize the response from a target such as a flat bottom hole at a given depth in a flat block, the water path length could be changed to produce optimum focus at the same depth in round material to be tested. There are two problems with this approach in addition to those mentioned in the introduction. First, the extra long water path required during actual testing would increase the opportunity for spurious signals from small bubbles and other possible contaminants in the couplant. Second, and probably more important, at long water path lengths the stability of the transducer position and angulation with respect to the material surface becomes more difficult to maintain. This could lead to degradation of the test reliability.

 

Conclusions
The practice of allowing the use of flat blocks for material over 100 mm (4 in.) should not be permitted in general specifications or recommended practices except as a special case sanctioned by written permission from the procuring agency. Such permission might best be obtained in cases where years of empirical evidence has shown satisfactory results based on a specifically defined system standardization technique with flat blocks for cylindrical material testing. Even so, this represents a compromise with good practice that should be used only in special circumstances.

 

References
Beck, K.H., "Ultrasonic Transducer Focusing for Inspection of Cylindrical Material," Materials Evaluation, Vol. 49, 1991, pp. 875-882.

Beck, K.H., "Limitations to the Use of Reference Blocks for Periodic and Preinspection Calibration of Ultrasonic Inspection Instruments and Systems," Materials Evaluation, Vol. 57, 1999, pp. 323-326.

Beck, K.H., "Ultrasonic Transducer Selection for Fixed Water Path Scanning of a Range of Bar Sizes," Materials Evaluation, Vol. 61, 2003, pp. 517-522.

Krautkramer, J., and H. Krautkramer, Ultrasonic Testing of Materials, fourth edition, New York, Springer-Verlag, 1990.

Singh, G.P. and J.L. Rose, "A Simple Model for Computing Ultrasonic Beam Behavior of Broad Band Transducers," Materials Evaluation, Vol. 40, 1982, pp. 880-885.

US Department of Defense, Military Standard, MIL-STD-2154, Inspection, Ultrasonic, Wrought Metals, Process For, 1982.

 

* TAC Technical Instrument Corporation, 152 Mercer County Airport, Trenton, NJ 08628; (609) 882-2894; fax (609) 882-3147; e-mail <tactictest@aol.com>.

 

Copyright © 2004 by the American Society for Nondestructive Testing, Inc. All rights reserved.

 

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