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# Applied Research in Nonlinear Studies

### Materials World, the Journal of the Institute of Materials for publication in the September 1999 issue.

##### NonDestructive Testing of Materials By Nonlinear Elastic Wave Spectroscopy (NEWS)

Summary - Nonlinear wave methods for examination of damage in materials are the new frontier of acoustical nondestructive testing. NEWS offers previously unimagined sensitivity, speed of application, and ease of interpretation.

Strike a bell, and the bell rings at its resonance modes. Strike it harder and the bell rings at the same tone, only louder. Now imagine a small crack in the bell, perhaps invisible to the eye. We strike the bell gently and it rings normally. Striking it harder we find, to our surprise, that the tone drops in frequency ever so slightly. Striking it even harder, the tone drops farther down in frequency. The frequency shift is a manifestation ofnonlinearity due to the presence of the crack. Figure 1 illustrates how the bell responds elastically linearly when undamaged, but elastically nonlinearly when damaged.

We take this example a step further in Figure 2 for the sake of illustrating additional manifestations of nonlinearity. For instance, we input 440 and 8000 cycles per second (Hz) into the undamaged bell using an audio speaker (these are arbitrarily chosen frequencies and are not crucial to the general result). Not surprisingly, the bell will ring at the two input frequencies (Figure 2a). If we input the two tones into the bell when a small crack is present, interesting things happen again. We find that, not only does the bell ring at 440 and 8000 Hz, but other frequencies abound, as illustrated in Figure 2b. We also detect two times, three times and four times each input frequency (880, 1320, and 1740 Hz; and 16000, 24000, and 32000 Hz, respectively). In addition, we detect the sum and difference frequencies between the 440 and 8000 Hz: 8000+/-440 Hz (These frequencies are called sidebands.). The resonance peak change with amplitude noted in Figure 1, and the appearance of new frequencies inside the material, are not expected results! They are the result of nonlinear interaction of the sound in the damaged bell.

The nonlinearity due to the presence of the crack(s) is (are) an extremely sensitive indicator of the presence of damage. The undamaged portion of the sample produces nearly zero nonlinear effect. The damaged portion of the material acts as a nonlinear mixer (multiplier). It is a localized effect. Using a frequency spectrum analysis, we can easily tell the difference between an undamaged and damaged object. In fact, I am not aware of a more sensitive, more rapid, easy-to-apply method for detecting and examining material damage.

In our studies we have found that the nonlinear response of a sample provides a quick, qualitative test of pass/fail (go/no go) in numerous metal components such as alternator housings, engine bearing caps, various gears, Plexiglas, synthetic slates, weapons components, etc., where damage is localized; however, the elastic nonlinear response is also useful in examining the physical state of volumetrically damaged materials, such as concrete, rock core and other porous materials (including the effects of fluid saturation) and is being applied to characterize dislocations in metals, and to study progressive damage in these materials. Some of the materials that we have tested are shown in Figure 3.

The general concept of nonlinearity, what we call nonlinear mesoscopic elasticity, can be stated as follows: as a material fatigues or is damaged, dislocations, cracks and flaws may be introduced resulting in a significant change in the material nonlinear elastic wave behavior. This behavior is manifest in two primary manners when sound is applied to the object. First, (1) Under resonance conditions (such as the bell), the resonance tone changes as the applied volume is increased. Second, (2) under resonance, continuous wave, or pulse-wave excitation, frequency-mixing spectral components such as wave harmonics appear. These effects are enormous in damaged material but nearly unmeasurable in undamaged materials. They are the signatures of damage. Linear methods in acoustical nondestructive testing rely on either reflected wave energy from a crack, wave speed changes and/or amplitude changes. None of these linear wave characteristics is as sensitive as the nonlinear response of the material.

In volumetrically damaged materials, micro-features such as dislocations are responsible for the nonlinear behavior. It is very interesting that volumetric and local damage over several orders of magnitude in scale (~10-9 - 10-1), provide very similar nonlinear characteristics (e.g., Guyer and Johnson, 1999)! That is, there are close similarities between the nonlinear response from the presence of dislocations in a sample and a single macrocrack in a sample. The similarities are currently under intense scrutiny in order to determine why this is so. Figure 4 illustrates the type of features, large and small, that lead to a large nonlinear wave response under wave excitation. Dislocations, soft grain contacts in rock and concrete, microcracks and macrocracks can all lead to a large and complex nonlinear wave response.

As a practical example we show wave mixing experiments in undamaged and damaged automobile engine bearing caps used to discern whether or not damage is present. In these tests, one high frequency wave and several low frequency waves were used simultaneously as input. Thus we would expect mixing of all waves with each other, leading to the creation of many harmonics and sidebands when damage is present. Figure 5a and 5b show the frequency wave spectrum of the undamaged and damaged samples, respectively, only around the sideband frequencies. The damaged sample is one of those shown in Figure 4. It contains a crack several mm deep and a cm long, approximately. The sample in Figure 5b clearly failed the go/no go test. We call this technique Nonlinear Wave Modulation Spectroscopy (NWMS), a subset of NEWS. Note that we observed no change in linear wavespeed or wave dissipation between the two samples, despite the fact that the nonlinear response is very different. (Due to space limitations, we cannot illustrate a NRUS experiment here, but one can refer to the references below for such examples.).

NEWS is ideal for monitoring progressive damage in materials as well. Figure 6 illustrates such a test (courtesy of Peter Nagy). It is clear from the figure that nonlinear means are far superior to linear means in progressive damage detection.

We have not mentioned other, extremely interesting, and complex nonlinear effects such as the slow dynamical response often observed. Nor have we addressed the very different nature of the nonlinearity described here compared with that of classical media (water, gas, intact materials), which have a much smaller nonlinear response and one which arises from atomic anharmonicity as opposed to the presence of damage. Nor have we mentioned the elaborate theory developed by Guyer and McCall for predicting the behaviors illustrated here. The topics just mentioned can be found in the suggested further reading section. For our purposes, the instantaneous nonlinear response illustrated in this paper is of most interest to the NonDestructive Testing community. Of significance is that we are currently developing a method by which to not only diagnose damage, but to locate damage as well.

In summary, NEWS represents the new frontier in acoustical nondestructive testing of materials for damage. The sensitivity of nonlinear wave methods to the appearance and progression of damage in materials is orders of magnitude larger than that of conventional acoustical methods of nondestructive testing. In fact, measurement of nonlinear behavior may well be the most sensitive method available for study and early detection and the progression of damage. There are potentially a huge number of applications of enormous economic and safety impact that will evolve from nonlinear applications. Applications and spin-off research have and will affect a broad category of problems, from aiding design in earthquake resistant structures, to eliminating bad components fabricated on an assembly line, to monitoring long term aging in infrastructure. Further, application to structures after an earthquake may well provide valuable information regarding damage to that structure. We also believe that application of nonlinear methods, this one and others, will revolutionize nondestructive testing by providing a sensitivity to damage never before imagined. Moreover, the work may well lead to aiding in developing better, longer lasting concrete, the foundation of all building materials. We anticipate that within 10 years nonlinear methods may be routinely used in applications as diverse as quality control in manufacturing processes, quality control of concrete curing, monitoring reactor containment walls for damage, inspecting aircraft and spacecraft for damage, observing fatigue damage in buildings, bridges, tunnels, gas and oil pipe lines.

### Acknowledgments

Thanks to my colleagues in this work, A. Sutin, R. Guyer, K. Van Den Abeele, J. TenCate, E. Smith, and T. Shankland. Thanks to J. Browning for photography, and to T. Mitchell, and Y-M. Liu for photos. This work was funded by the the US DOE Defense Programs and OBES through LANL.

Guyer, R. A., and P. A. Johnson, The astonishing case of mesoscopic elastic nonlinearity, Physics Today, 52, 30-35, 1999.

Van Den Abeele, K., P. Johnson, and A. Sutin, Nonlinear Elastic Wave Spectroscopy (NEWS) techniques to discern material damage. Part I: Nonlinear Wave Modulation Spectroscopy (NWMS), Research on Nondestructive Evaluation, in press, 1999.

Van Den Abeele, K. J. Carmeliet, J. A. TenCate and P. A. Johnson, Single Mode Nonlinear Resonant Acoustic Spectroscopy (SIMONRAS) for damage detection in quasi-brittle materials Part II. Nonlinear Wave Modulation Spectroscopy, Research on Nondestructive Evaluation, in press, 1999.

Guyer, R. A., P. A. Johnson, and J. N. TenCate, Hysteresis and the Dynamic Elasticity of Consolidated Granular Materials Physical Review Letters, 82, 3280-3283, 1999.

Korotkov, A. and A. Sutin, Modulation of ultrasound by vibrations in metal constructions with cracks, Acoustical Letters 18, 59-62, 1994.

Nazarov, V., L. Ostrovsky, I Soustova and A. Sutin, Nonlinear acoustics of microinhomogeneous media, Physics of the Earth and Planetary Interiors 50, 65-73, 1988.

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