Use of Ultrasonic Waves for Stress Analysis

1. Introduction

Since it was proposed that ultrasound could be used to identify flaws in metals using transmission techniques, non-destructive examination methods involving ultrasound has made tremendous progress. Later, certain properties of the ultrasonic waves were used to evaluate elastic constants and their change with load and temperature.

Subsequent progress and discoveries in associated fields such as the discovery of birefringent phenomenon of acoustic waves have empowered the advancement of the usage of ultrasonic waves to analyze stresses within a material. This document attempts to describe theory behind the usage of ultrasonic waves for stress analysis, it’s applications and finally advantages & disadvantages of the technique.

2. Theory

It was discovered that the velocity of acoustic waves within a material changes if it subjected to a stress field. This phenomenon was called the acoustoelastic effect and forms the principle behind the usage of ultrasonic waves for stress analysis. Therefore it was inferred that the measurement of acoustic wave speed can provide quantitative information regarding the stresses present in a material. Stress measurements using ultrasonic waves is carried out primarily by one of the two modes described here.

Mode I – Using the critically refracted longitudinal LCR wave

The LCR wave travels parallel to the surface of the specimen, and also has its particles in motion in a direction parallel to the surface. The velocity with which LCR travels is designated to be V11. The LCR waves have the maximum sensitivity to stress. The critically refracted longitudinal wave LCR is typically excited just underneath the surface in plates and bars, at approximately the first critical angle as defined by Snell’s Law (angle of refraction is 90° making LCR parallel to the surface).

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Fig. 2 illustrates a typical arrangement where an incident longitudinal wave ‘T’ in material ‘A’at angle ‘θ’strikes the interface with material ‘B’. The LCR longitudinal wave travels at a bulk longitudinal wave speed in the test piece, parallel to the surface, and is received by probes at ‘R1‘ and ‘R2‘ that are inclined at an angle equal to the first critical angle of the transmitter wedge. The distance between ‘R1‘ and ‘R2‘ is ‘d’.

Generally, the material used for the wedge is of low impedance (density*wave speed) while the material being inspected would have higher impedance. In such situations, couplants such as motor oils, glycerin-based gels or grease may be used for impedance matching between two dissimilar materials. Change in travel time from ‘R1‘ to ‘R2‘ in Fig. 3 is the indicator of stress related velocity change.

Based on the principle of acoustoelastic effect, the relation between the velocity change ΔV11 induced by the stress change Δσ is given by the following equation where ‘E’ is Young’s Modulus, ‘L11’ is the acoustoelastic coefficient, ‘to’ is the travel time in stress free conditions and ‘Δt’ is the measured travel time change after having made the correction for time in the couplant and wedge.

$\mathrm{\Delta \sigma }=\frac{\mathrm{E}\left(\frac{\mathrm{\Delta }\mathrm{V}11}{\mathrm{V}11}\right)}{\mathrm{L}11}=(\mathrm{E}*\mathrm{\Delta }\mathrm{t})/(\mathrm{L}*\mathrm{t}\mathrm{o})$

Mode II – Using the shear wave in birefringence mode

Shear wave birefringence uses two contact shear probes acting across the thickness of the part. Shear waves are polarized so that the particle motion is perpendicular to the direction of propagation. The velocities of these two mutually perpendicular waves are measured to enable analysis.

On Fig. 1b, the velocities of the two shear waves are shown as V21 and V23. The wave with the velocity V21, being parallel to the applied stress field is more sensitive to the same. For a homogenous isotropic material, the stress effect would be demonstrated by the wave with velocity V21, and the material zero stress travel time by V23.

In homogeneous, isotropic plates, a shear wave is launched across the thickness of the plate using a normally incident contact probes, as shown in
Fig. 5. Here the shear wave probe is contained in the upper vertical tubular member of the apparatus and the plate is held fixed to the rear. Particle motion polarization is typically along the direction of the cable connection to the probe and as the probe is rotated on the surface, the particle motion moves with the rotating probe. For the arrangement shown in Fig. 5, shear waves are propagated across the thickness of the specimen with the angle of polarization ‘θ’ relative to a reference angle ‘R’. The angles can be read from the scale marked on the base plate. ‘R’defines the orientation of the coordinate system relative to some characteristic of the plate or bar. Thereafter, the arrival time and orientation angle of the fastest wave is noted. Following that, the probe will be rotated typically 90° to find the opposite component and the arrival time and angle recorded. This technique requires a very viscous couplant and care must be taken to ensure that the couplant has stabilized at the interface to eliminate error.

The stress difference in the two perpendicular direction is given by the following equation

$\mathrm{\sigma }\mathrm{\theta }–\mathrm{ \sigma R}=(\mathrm{B}–\mathrm{Bo})/\mathrm{ C}$

A

where :-
σθ = stress in the direction of θ
σR = stress in the direction R
CA = acoustoelastic constant for the material
Bo = birefringence in unstressed state
B = 2*(tR – tθ) / tR + tθ ; tR & tθ are times of flight in R & θ directions respectively.

3. Applications

1. Weld stresses

An early application of ultrasonic stress measurement was for stresses in welds and the region surrounding the weld seam for both hot rolled and cold rolled plates. Upon completion of welding, if a travel time peak was observed in the weld zone, this would be indicative of residual stress existing within the material.

2. Uniaxial stress states, (eg. stress in a screw / bolt)

The longitudinal time-of-flight is measured before and after the screw has been tightened. The simultaneous use of a radially polarized shear wave, propagating the length of the screw allows the strain and / or stress analysis even if the original length or time-of-flight in the unstrained case is not known.

3. Determination of principal axis of strain and stress in isotropic materials

Ultrasonic birefringence of linear polarized shear waves is used for that purpose. This also assumes that the thickness direction coincides with one of the principal axes. A linear polarized shear wave, propagating the thickness is reflected at the opposite surface of the plate and a backwall echo is received. Multiple back and forth reflections yield a backwall echo sequence. Turning the probe, that is also turning the direction of vibration with respect to the two principal directions of the plane, the backwall echo sequence shown in Fig. 6 can be seen if the direction of polarization coincides with a principal axis. In the case of coincidences of both directions, the linear polarized shear wave keeps its polarization. The amplitudes decrease due to attenuation effects. In case of no coincidence of both directions, the shear wave vibrates elliptically.

4. Stresses in ductile cast iron

Ductile cast iron structures may be complex in shape and susceptible to warpage and breakage due to unfavorable residual stresses. Residual stresses may be evaluated in these materials using the LCR technique. With knowledge of these conditions, the foundry can adjust the process to reduce the residual stresses.

5. Measuring stress gradient

Since material properties often vary with depth, there is a need for a technique to evaluate the stress gradient. The effective penetration depth of the LCR wave has been demonstrated by several researchers, to be approximately equal to one wavelength. Varying frequency, and therefore the wavelength, leads to the possibility of evaluating the gradient. However, the ability of the technique to do this is limited by the fact that it interrogates an average from the surface to the wavelength depth.

6. Detecting reversible hydrogen attack

In many chemical and petroleum operations there is serious risk of the small hydrogen atom creeping between the grain boundaries, creating a stress buildup at the surface and initiating a crack which could lead to failure if undetected. Experimental data was produced to show that both the velocity and the spectrum of the LCR wave are affected by hydrogen in the metal. While the velocity changes are very small, they are measurable.

4. Advantages

• Ultrasonic method of stress evaluation is a non-destructive technique which permits evaluation of surface and bulk stress of states.
• It is characterized by its high resolution and high penetration.
• It is not harmful to the human body and so does not require a controlled / secured space for its application.
• Since LCR wave travels beneath the surface, the LCR method for stress measurement is largely unaffected by surface roughness arising from manufacturing. Therefor this method calls for relatively simple and easy surface preparation. However, large gouges and other major surface irregularities can adversely affect probe placement and couplant thickness.
• Ultrasonic techniques offer fast data acquisition, possibility of locus or time continuous measurements and low costs per measuring point.
• A test can be rather easily carried out at the same location multiple times, enabling better understanding of the effects of service loading or effectiveness of processes like post weld heat treatment that is meant for stress relieving.

5. Limitations and Disadvantages

• Accuracy and repeatability of the ultrasonic stress measurements depend a great deal on the couplant thickness.
• Material variations such as grain size and orientation, as occurring in ordinary rolling and cooling, greatly affect travel-times obtained for LCR stress measurement. Therefore, for the LCR technique, probe placement assuring uniform material conditions has been found to have a significant effect on repeatability.
• The wave speed is significantly affected by temperature changes (especially in PMMA) so either the setup must be in a constant temperature environment, or the temperature must be constantly monitored and accounted for in the wave speeds to maintain the accuracy of the calculated values for stress.
• Increased dependency on the education and experience of the technician.
• Acoustoelastic constants have not yet been established for a wide range of materials.
• Material anisotropy can have a serious effect on the observed travel times and users of this technique must be aware of this occurrence.

6. Conclusion

Ultrasonic stress measurement has its basis in the acoustoelastic effect. However, other than stress, material parameters / characteristics such as temperature and texture may also affect wave speeds, so these factors affects the results obtained from experiments. Another major source of error is the couplant thickness. Methods have been devised to combat these error sources and over the years, repeatability has been proven with the ultrasonic method of stress analysis. The effectiveness of this technique does depend on the experience and education of personnel performing it and good knowledge on the expected stress field and material variations is needed. Apart from that, acoustoelastic constants for a wide range of materials are yet to be established. Considering the opportunity offered by this method, and the possibility of further enhancing the efficiency of the technique by increase automation, it is quite likely that ultrasonic stress measurement will continue to progress in the coming years.

7. References / Bibliography

1. CRECRAFT, D. I. (1967). The Measurement of Applied and Residual Stress in metals using Ultrasonic Waves. F Sound Vb, 173-192.
2. Crecraft, D. I. (1968). Ultrasonic Measurement of stresses. ULTRASON1C.S FOR INDUSTRY 1967, (pp. 117-121).
3. Current directions of Ultrasonic Stress Measurement Techniques. (2018, November 09). Retrieved from NDT.NET: https://www.ndt.net/article/wcndt00/papers/idn647/idn647.htm
4. Hauk, V. (1997). Structural and Residual Stress Analysis by Nondestructive Methods. Amsterdam: Elsevier Science B.V.
5. Schajer, G. S. (2013). Practical Residual Stress Measurement Methods. West Sussex: John Wiley & Sons Ltd.
6. William N. Sharpe, J. (2008). Springer Handbook of Experimental Solid Mechanics. New York: Springer Science+Business Media, LLC.
7. Xu, C. (2015). Nondestructive Testing Residual Stress Using Ultrasonic Critical Refracted Longitudanal Wave. 2015 International Congress on Ultrasonics, 2015 ICU Metz (pp. 594-598). Physics Procedia.