Introduction

     The L_CR ultrasonic technique indicates stress through the acoustoelastic principle where small variations in strain affect the wave speed. By measuring the wave speed (or travel-time between known points) the change in stress can be calculated. Other material variations such as texture and temperature also affect the travel-time. The investigator using the L_CR method must be aware of these other effects so that the best data indicative of stress variation is obtained.

     The relationship of measured L_CR wave travel-time change and the corresponding uniaxial stress is given by:

        (1)

where  is change in stress, E is Young’s modulus, and L is the acoustoelastic constant for longitudinal waves propagating in the direction of the applied stress field, as given in Table 1. Travel-time change (D t) is the measured travel-time (t) minus the reference travel-time (t_o). The reference travel-time t₀ is a property of the probe sensor spacing for an assumed stress free material.

Table 1. Typical values for acoustoelastic constant (L)

Temperature Effects

     Temperature induced speed changes occur both in the material being investigated and in the probe material. The relationship of wave speed and temperature (dc/dT) is given by:

         (2)

where k_T is the constant for a particular material, as given in Table 2.

 

Table 2.	Temperature effects on
	wave speed.

     The effect of temperature on travel-time will be

where d is the travel distance in the material and D T is the measured temperature change. Obviously, the temperature effect for the PMMA wedge material is greater than that of the steel. Where data are collected under moderately uniform temperature conditions, the temperature effect, D t, can be ignored. For large temperature variations, the temperature of the wedge can be monitored with a thermocouple. The distance of wave travel in the wedge can be measured and a suitable correction in the travel-time can be made.
 

Texture Effects

     Texture as typically encountered in cold-rolled plates and other structural shapes can have a significant affect on the wave speed. While the affect of texture on the L_CR wave speed is less than that encountered by the shear waves often used in acoustic-birefringence stress measurements, there still is concern about the effects.

     Special data collection procedures may be used to minimize the effects of texture. In many items where stress is a concern, the texture may be uniform throughout. In these cases, L_CR travel-times taken with the probe always at the same orientation relative to the geometry of the item may be free of texture variation. In this case, the major effect may be stress. This has been found to be true for plates and welded plates. However, there is a need for more data on additional structures and shapes before this assumption may be more widely made.
 

Characteristics of the L_CR Pulse

     Ideally, the L_CR pulse is a true, nondispersive wave travelling at the longitudinal wave speed of the material. There are shape and material effects, however, that can cause dispersion of the wave. In many of these cases, the wave can still be used for stress measurement by the careful operator, and by choosing the proper probe.

     Wave-guide effects are one of the most serious causes of dispersion. These occur in plates and pipes when the wavelength of the wave approaches some fraction of the thickness. Typically, when the ratio of plate thickness to wavelength is ten or above, there is no risk of any waveguide effect. Satisfactory results have been obtained with rations of five, however. Texture effects, discussed above, and grain boundary scattering also affects the pulse shape. Waveguide effects are the easiest to eliminate due to knowledge of the geometry. Texture may be evaluated with a contact shear wave acting across the thickness. Grain boundary scattering may be evaluated with attenuation measurements also across the boundary. There are no data yet on acceptable ranges for L_CR stress measurement, however.

     Choosing the proper reference location within the L_CR pulse can enable the collection of reliable data. Typically, the second positive zero crossing at the first arrival of the pulse is used as this reference. In nondispersive conditions, this location is easy to identify at all pulse arrivals. Under dispersive conditions, however, identification may be more difficult. In difficult circumstances, identification can be aided by sliding a receiver probe along the travel path and observing the change of shape.
 

Experimental Procedure for L_CR Technique

     Typical stress induced travel-time changes are small, at approximately 0.01%. Thus, travel-time variations caused by the testing procedure must be reduced to at least one tenth of level for the desired stress resolution. Testing procedure variations can arise from the instrumentation and the repeatability of the ultrasonic probe system. Instrumentation capable of measuring arrival times of a least a nanosecond is needed for good resolution. Further, probe repeatability at a designated location should be in the 2 to 3 ns range.

     The nominal relationship of stress variation and travel-time for steel is shown in Fig. 1. The outer lines show the range for an expected measurement variation of ± 3 ns.

Setting up the Load Frame and Probe

     The load frame shown in Fig. 2 is designed to use magnets for force attraction to steel samples. Other devises such as vacuum and mechanical constraints can be used. A hydraulic ram is fitted on the top of the probe to provide a variable force at the couplant interface between the probe and the test sample. The force line of the ram is midway between the two receiving probes (R1 and R2), giving uniform pressure on these two interfaces. Pressure on the ram is indicated by the pressure gauge on the hydraulic pump.
 

     Obtaining the higher pressures required for achieving small travel-time variations is dependent on good magnetic coupling. This requires that the magnets be firmly placed on the plate, and that the frame be able to move freely on the posts. If this condition is not met, the magnets will pull loose from the plate when the piston force is applied. Some adjustment of the magnet position and the collar placement is often needed to achieve good quality data.

     To setup the load frame, follow the steps in Table 3.
 

Collecting L_CR Travel-Time using a High Speed Digitizing Card, Lab
View and a Tandem Receiver Probe – Dual Channel Mode

     Since the L_CR wave travels underneath the surface at bulk, longitudinal wave speed, it will be the first arriving wave at receivers along its path. The change in travel-time of the wave will be indicative of the stress change. The stress induced travel-time changes are small, however, and very accurate and precise methods are required to accomplish this measurement. The following is a description of a suitable data collection method using a high speed digitizing card and an appropriate interface program on a personal computer.

     A variety of measurement systems may be used for collecting L_CR data. Typical systems include a commercial ultrasonic pulser/receiver as well as an oscilloscope and the L_CR transducer, as shown in Fig. 3. The oscilloscope may be a stand-alone unit, such as LeCroy digital oscilloscope, or a high speed digitizing board (Gage Scope 265) inserted in a personal computer. If the high speed digitizing board is used, the computer must be fitted with suitable software, such as Lab View, so that the travel-time measurements can be made. The instrument must be able to resolve arrival-times in the 0.1 to 0.01 ns range. The pulse originates as the pulser/receiver emits a spike that excites the oblique sending transducer (T). The pulse travels as a L_CR wave through a short distance in the material, and is received by the two transducers (R1 and R2) which are arranged in tandem. In some cases, a preamplifier is inserted in the R2 line to increase the signal amplitude. For a probe spacing d (R2 – R1) of 152.4 mm (6 in.), the initial travel time in a stress-free state between the two tandem transducers is about 25.7 m s. With an instrumentation resolution of 0.1 ns, the system with the probe is capable of measuring travel-time changes of approximately 0.0004%.

     The time resolution (precision) of the high-speed digitizing card is a function of the sampling rate. Lab View enables the presentation of a typical oscilloscope screen on the computer monitor. While the presentation is similar to that of an oscilloscope, there are significant differences that need to be discussed.

     The parameter START on LabView is analogous to DELAY on a typical oscilloscope or ultrasonic flaw detector. NUMBER represents the expansion of the time base of the display. The larger the positive value in START, the later the start of the display after the trigger. The smaller the NUMBER value, the fewer points displayed, and the greater the time expansion of the time-base (i. e. smaller m s/div). The SAMPLING RATE represents the firing rate of the card, which is associated with the maximum time resolution of the system. Note that for dual channel operation, the ACTUAL SAMPLING RATE per channel is one-half of the maximum SAMPLE RATE. POINTS (lower, left corner of screen) describes the total number of points displayed on the screen.
 

Typical steps in collecting L_CR data are as follows:

1. Open the appropriate LabView file (e.g. LCR1.vi)
2. Turn display on by clicking the arrow at the top left corner.
3. Set parameters as shown in Fig 4. Typical settings are START 0, NUMBER 5376, EXTERNAL TRIGGER, TRIGGER LEVEL O.2 V (Adjusted by moving the trigger scale vertically to +20), DUAL CHANNEL, CHANNELS A&B, SAMPLE RATE 130 MHz, Sampling switch at CONTINUOUS. POINTS is set at the maximum value (999999), and does not usually change.
4. Click Power ON button at top right, and click CAPTURE.
5. Click the Right mouse button and set Auto Scale X and Y both ON. Note that the cursor must be within the blue screen face for this action to occur.

     The display (Fig. 4) shows the main bang at the left and both the channel A and channel B traces. The bottom trace is Channel A (receiver R1) and the top trace is Channel B (receiver R2). The L_CR wave is the earliest arrival in both traces.
 
 

 
For measuring arrival time at R1

     The purpose here is to adjust the START and NUMBER settings to expand the L_CR arrival at R1 so that the arrival time can be measured to its maximum precision. The necessary controls are ZOOM, identified by the magnifying glass located in the small menu box to the left, below the oscilloscope display, and the oscilloscope MOUSE which is the diamond to the right, at the bottom of the display.

     The steps are:

1. Increase START to 1600 (this can be entered directly).
2. Decrease NUMBER to 256 (this can be entered directly).
3. Set AUTO SCALE X and Y to OFF.

Note that the expanded display of the L_CR wave should be on the screen, and the cursor for Channel A should be aligned with the horizontal trace of the signal. This may be preset to the -30 V line. If the cursor is not correctly aligned, it can be reset in step 7 below.

1. If Sampling Switch is at CONTINUOUS switch it to SINGLE.
2. Click the CAPTURE button. If the screen goes blank set Auto Scale X and Y to ON and repeat from Step 3.
3. Bring the cursor lines to the center of the display if they are not shown on the screen. This is done by clicking the upper green square in the lower menu box.
4. Click the + in the left menu box so that you can move the cursor lines with the computer mouse. Set the horizontal cursor as described above, if needed, and move the vertical cursor line to the second positive zero crossing of the pulse, as shown in Fig. 5.

Fig. 5.	Expanded R1 arrival, with oscilloscope cursor line
	at second positive zero crossing.

1. Click ZOOM in lower left menu box.
2. In the ZOOM menu bar, click the square that sets the horizontal zoom boundaries (top, middle).
3. Next, click the square with outward pointed arrows (bottom middle).
4. Place the computer cursor at the intersection of the vertical and horizontal green oscilloscope lines, and hold down the left mouse button to expand the display. Continue this until the numbers on the horizontal axis differ by 0.02 m s, or less. Experience will dictate the resolution required for your application.
5. Use the oscilloscope cursor to align the vertical cursor line with the second positive zero crossing of the pulse. It might be convenient during the expansion to stop and align the vertical cursor with the second positive zero crossing so that it will not be lost.
6. Read the arrival time in the bottom menu square, to the right of the word Cursor. This will be a number like 26.XXXXXE-6 for R1.
7. When first running this system, you might have to turn Auto Scale X and Y ON and/or OFF to get the signal in the proper location on the screen. The wrong setting makes the signal behave erratically.

     In this case, the attention is directed to the second trace (Channel B). The amplification (V) for channel B should be adjusted so that the amplitudes of the L_CR wave in A and B is approximately the same. A typical arrival pulse is shown in Fig. 6.

1. Set Start to 3250.
2. Set Number to 256
3. Keep switch to SINGLE.
4. Click CAPTURE.
5. Return Auto Scale X and Y to ON, if needed to locate signal.
6. Proceed as for R1 at Step 3, using instead the upper trace, for R2. The horizontal cursor for Channel B should be along the oscilloscope trace. This may be the +30 V line. Keep Switch at SINGLE.
7. A typical arrival time for R2 might be 51.XXXXXE-6.

Single Channel Mode

     Higher precision will be achieved it all data are collected in single channel mode, using Channel A. This is due to the fact that in dual channel mode, the higher speed sampling rate is divided between the two channels so that the actual rate is one half of the peak. In single channel mode, the actual sampling rate is the maximum. A higher speed board than the one used here could give satisfactory performance in dual channel mode.
 

Bibliography

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