Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation

This chapter gives readers fundamental understandings of various nonlinear acoustical techniques. It briefly describes the nonlinear techniques that are popular today such as higher harmonic generation, subharmonic generation, nonlinear resonant acoustic spectroscopy, vibro-acoustics, wave modulation between two wave frequencies—pumping and probing frequencies—and sideband generation. Some examples are provided showing the applications of these techniques in nondestructive evaluation (NDE) of materials and structures. The difficulties associated with various nonlinear techniques and current challenges encountered by the scientists and engineers in implementing nonlinear guided wave-based techniques are discussed. Recent development (within last 5 years) of a new promising nonlinear technique called sideband peak count (or SPC) for NDE is also discussed. SPC overcomes many shortcomings of the existing frequency modulation techniques. The objective of this chapter is to present the readers, in simple words, a broad overview of nonlinear acoustical techniques starting with the fundamental equations of mechanics. This presentation does not go into great depth of every available technique but provides sufficient basic knowledge and exposure to the new developments in this field, such as SPC. SPC is described in detail in Sect. 1.10.2. Interested readers can read this section without going through the detailed derivations of the earlier sections and can still understand this new technique. Other techniques are discussed in greater detail in the subsequent chapters.

The term nonlinear resonant ultrasound spectroscopy (NRUS) was first coined in the 1990s and is one of the earliest nonlinear techniques used to quantify global damage in a sample. This chapter was written as an introduction and overview for the general reader, one interested in learning more about the technique, especially its origins. As rocks are highly nonlinear, it is perhaps not surprising that the study of the nonlinearity of a material full of cracks could be applied to nondestructive testing and applications. Thus, this chapter aims to show that link. The overview of resonance techniques presented in Chap. 1 is here expanded upon and placed in a historical context with an emphasis on the experimental side, including important measurement pitfalls of applying the technique. The fact that the technique was patented early on and that the measurements are complicated by rate effects likely contributed to its lack of general use in the NDE community. After reading this chapter, we think you may agree that the technique is ready for another, closer look.

Structural damage detection is frequently accomplished by interrogation with elastic waves.

This chapter provides examples of recent application developments in the field of nonlinear acoustics and damage detection, highlighting future trends and challenges. The major focus is on nondestructive testing of engineering components. Examples of damage detection methods based on the vibro-acoustic wave modulation technique are presented.

This chapter is devoted to theoretical concepts and models for wave propagation, vibrations, or other elastic deformations in solids containing internal contacts (cracks, delaminations, etc.). A direct problem of solid mechanics is solved by building up a solution for elastic fields in materials with known geometry and properties. This study is oriented to nondestructive testing and therefore focuses on the case where the material contains few cracks of known configuration, in contrast to microcracked solids in which a statistical ensemble of a large number of internal contacts is present. Our approach is based on finite element simulations and a frictional contact model assuming generic semi-analytical solutions. These solutions account for surface roughness, friction, and the evolution of stick and slip zones in the contact area. Finally, load–displacement relationships valid for arbitrary loading histories are produced which are used as boundary conditions imposed at internal boundaries (cracks) in the material. As a result, we have developed a numerical toolbox capable of modeling elastic waves and vibrations in damaged samples or structures. The access to all elastic fields together with their nonlinear components makes nondestructive testing fully transparent and offers an opportunity of purposeful optimization of the experimental techniques.

This chapter considers both the theoretical aspects of the nonlinear ultrasonic phenomena in elastic solids and their applications to materials characterization; it has been demonstrated that nonlinear ultrasound (NLU) measurements can provide quantitative inputs to determine the material state and measure damage in engineering components. It has recently been shown that NLU can be used to develop the framework for accurate life prediction of components under mechanical and thermo-mechanical loading. These NLU measurements are done at the material level, before the formation of macroscopic damage. The traditional NDE of damage of a material subject to, for example, fatigue starts from the time when a small crack initiates because there is no measurable macroscopic change in the material prior to the crack initiation. In most metallic materials, however, cracks of a measurable size appear late in the fatigue life (typically after 80%), while the material toughness and strength decreases gradually due to the microplasticity (dislocations) and associated change in the material’s microstructure. Starting from mechanics fundamentals, we first develop the theoretical equations of wave motion in an elastic solid with quadratic nonlinearity, covering bulk, surface, and guided waves. Various nonlinear acoustic phenomena occurring in the infinite and bounded elastic solids are described in a consistent mathematical framework. The next section considers measurement techniques for NLU, including examples of the assessment of fatigue and thermal damage in metals with NLU.

The second-harmonic generation at contacting interfaces between solid bodies is examined in this chapter from theoretical and experimental points of view. A nonlinear spring-type interface model is first laid down as a mathematical model of contacting interfaces. The second-harmonic generation at contacting interfaces is then analyzed using a perturbation approach for plane, time-harmonic waves at normal and oblique incidence. Both time-domain and frequency-domain formulations are presented. Some experimental aspects are discussed regarding the second-harmonic generation at a contacting interface of aluminum alloy blocks subjected to different levels of compressive loading, together with the quantitative comparison between the experimental results and the theoretical predictions.

Nonlinear acoustic material response, which is inherently related to the frequency changes of elastic waves, has long been identified as a sensitive instrument for material characterization and nondestructive evaluation (NDE). However, a bottleneck problem on the way of applications of nonlinear NDE is found to be a low efficiency of conversion from fundamental frequency to nonlinear frequency components. Fortunately, the situation changes for the better in the case of localized damaged areas, whose nonlinear acoustic response can be enhanced dramatically. The two major factors that contribute to the nonlinearity of cracked defects are concerned with specific type of acoustic nonlinearity of the damage fragments and a local mechanical resonance of the damaged area. The combination of these features turns the defect into a nonlinear oscillator that manifests peculiar nonlinear dynamics of local vibrations with efficient generation of higher harmonics and combination frequencies even at moderate excitation level. A frequency match to the damage resonance results in qualitatively new features characteristic of nonlinear and parametric resonances that provide an instable growth of local nonlinear vibrations. The resonant vibrations are strongly confined in the defect area that brings about an opportunity for high-resolution defect-selective imaging and proposes nonlinear resonant application as an extremely efficient means for nonlinear NDE and diagnostic imaging of damage. Due to the high efficiency of nonlinear frequency conversion, the resonant response of damage requires substantially lower input power to energize the defects that enables to avoid high-power instrumentation and even to realize for the first time noncontact nonlinear imaging via airborne sonic activation.

The first part of the chapter covers theoretical considerations and numerical modeling of higher-harmonic generation in elastic waves propagating in nonlinear prismatic waveguides, including plates, rods, and waveguides of arbitrary cross-sections and/or of inhomogeneous and anisotropic composition. The main purpose of these analyses is to identify suitable combinations of primary and secondary guided modes for the waveguide. The last part of the chapter examines the role of thermal stresses in higher-harmonic wave generation. The latter topic is relevant to the prevention of thermal buckling of slender structural components (e.g., rail tracks).

Crack depth is one of the important factors determining material strength. Hence, the accurate measurement of crack depth is essential to ensure the reliability of aged structures and manufactured products. If cracks are open, crack depth can be measured by ultrasonics because ultrasound is strongly scattered by the crack tip (Fig. 10.1a) [1]. However, if cracks are closed because of compression residual stress [2, 3] and/or oxide debris generated between the crack faces [4], ultrasonic testing can result in the underestimation (Fig. 10.1b) or nondetection (Fig. 10.1c) of cracks since ultrasound penetrates through closed cracks. Subharmonic phased array for crack evaluation (SPACE) is a novel imaging method for measuring closed-crack depths [5, 6]. SPACE uses the subharmonics generated by short-burst waves and a phased array algorithm with frequency filtering. It enables the precise measurement of closed-crack depths. This chapter starts from fundamental aspects of subharmonic generation at closed cracks. It then describes the principle of SPACE and its application to several types of closed crack.

This chapter introduces bases of nonlinear mesoscopic elasticity and presents a novel approach to model and numerically simulate the dynamical behavior of this class of material. Under dynamical solicitation, these so-called nonclassical materials exhibit two different time-dependent nonlinear mechanisms termed “fast” (nonlinear elasticity) and “slow” (loss of elastic properties and relaxation). A unified model of one-dimensional continuum is presented, which combines all of these phenomena as well as viscoelastic attenuation often neglected. The final set of partial differential equations is a system of conservation laws with relaxation described by a reduced number of parameters to account for all the effects. A numerical scheme based on finite-volume methods is presented which reproduces well the key experimental observations made in Dynamic Acousto Elasticity (DAE) and Nonlinear Resonant Ultrasound Spectroscopy (NRUS) type of experiments.

The durability of infrastructure materials, such as concrete, has direct impact on society because the productivity of many industries and safety of human beings depend on infrastructure condition, and further because maintenance of the infrastructure can represent a significant portion of a government’s budget. Thus the enhancement of concrete durability and improvement of infrastructure condition monitoring are significant concerns to the scientific community. The resonant frequency method has been traditionally used to assess the mechanical condition of concrete. Resonance frequencies of a solid body depend on test sample mass and dimensions, elastic properties, and boundary conditions. Resonance frequencies have been used to determine engineering properties such as the elastic moduli and material damping. The method is useful to assess the performance of materials within accelerated degradation durability test procedures, and to inspect quality of the products during manufacturing processes (pass/fail tests). Different testing standards and recommendations prescribe test configurations, and specific tests are recommended for different materials. A basic resonant frequency test requires a forced vibration system to set up mechanical resonances, and some system to sense the frequency content from the resonant vibration signals. For concrete-like materials, these specifications are given by ASTM C215 [1], wherein an impulsive impact event is applied to the test sample to excite the resonant frequencies and a small sensor is mounted on the surface of the test sample. From the impulsive impact vibration signals thus obtained, two standard parameters are usually derived: (1) the dynamic modulus, which depends on sample dimensions, mass, and the resonant frequency peak (f), and (2) the attenuation or damping capacity of the material. Figure 12.1a, b illustrates typical signals obtained from a single-impact vibration test, where the spectral (frequency domain) signal is computed from the time signal using a Fourier transform algorithm. The continuous reduction of the vibration signal amplitude with time during the signal “ring-down” is seen in the time domain signal. The resonant frequency and damping characteristics are extracted from the spectral signal in the region around the resonant frequency peak. The damping capacity of the material is determined from the quality factor (Q) (or inverse attenuation), which is defined as the ratio between the resonant frequency peak (f) and the bandwidth frequencies corresponding to a 50% reduction of vibration energy in the power frequency spectrum for a given vibration mode [2]. Meaningful application of the ASTM C215 test is found within other standard durability test methods [3, 4].

Pioneering measurements of elastic nonlinearity were static methods leading to the thermodynamic diagram that shows the relations between pressure, volume, and temperature (p-v-T diagram) [1]. The dependence of the bulk elastic modulus on the pressure, i.e., a measure of nonlinear elasticity, was deduced from this diagram. In the beginning of the twentieth century, resonance spectroscopy [2, 3] or methods based on interferometry [4] were proposed to measure the elastic moduli as functions of temperature and hydrostatic pressure. Finally, with the possibility of generating an ultrasonic short pulse [5, 6], acousto-elastic testing became an alternative way to assess elastic nonlinearity. Acousto-elastic testing consists in measuring changes of the speed of sound (by the determination of the travel time of an ultrasonic short pulse) induced by a hydrostatic or uniaxial stress (or strain). For metals and polymers, the relative variation in ultrasound wave-speed is found between 10⁻⁵ and 10⁻⁴ per MPa of the applied stress. In cracked or granular media, contacts between the two lips of cracks or contacts between grains can greatly increase the variation in ultrasound wave-speed up to about 10⁻² per MPa of applied stress, i.e., orders of magnitude larger than in metals and polymers [7].

Time reversal is a technique to focus wave energy to a selected point in space and time, localize and characterize a source of wave propagation, and/or communicate information between two points. This chapter will introduce the reader to the concept of time reversal and different implementations of this concept. The focus will then be directed to non-destructive evaluation applications using nonlinear elasto-dynamics together with time reversal.

Materials state awareness using conventional nondestructive evaluation (NDE) at the early stage of service life is extremely challenging because of the inherent material nonlinearity that initiates at the lower scales. Conventional NDE methods are limited by reporting location, size, and shape of the material discontinuities, e.g., cracks, voids, delamination, etc. In the past, several nonlinear ultrasonic methods are developed to detect the small discrete damages, whereas quantification of degraded material properties and detection of embryonic precursor damage in materials is currently challenging. Understanding the early stage of precursor damages using ultrasonic method inherently is to understand the material nonlinearity that arise from the bottom-up scales, which further requires to evaluate the ultrasonic signals with subtle nonlinearity in an innovative way that are essentially ignored in conventional ultrasonic NDE methods. Hence, in this chapter, it is hypothesized that such nonlinear effects at the early stage of damage at the lower scale are actually sensed by the ultrasonic NDE probes/sensors and hidden in the ultrasonic signals. Such hidden features are required to be extracted from the signals using innovative signal analysis method integrated with the microcontinuum physics. In this chapter defying the conventional nonlinear ultrasonic techniques, a newly formulated nonlocal approach is presented to quantify the damage precursor in materials at its early stage of the service life. Nonlocal parameter that carries information from the lower scale has a nonlinear dependency on the ultrasonic wave velocity at any particular frequency, which is assumed to be a constant in linear ultrasonics and no information could be extracted. Here, it should be noted that the nonlinear function of nonlocal parameter from a material that can be extracted from the material degradation state is not necessarily associated with the material discontinuities like cracks or delamination at the macroscale but due to distributed nonlocal effect of lower scale defects and damages. Thus, a new term called nonlocal damage entropy (NLDE) was coined by the authors in their recent publications to quantify the multiscale damage state in materials while exploiting the high-frequency ultrasonic (≥10 MHz) with microcontinuum field theory. In this chapter, first, a review of different “bottom-up” multiscale modeling approaches is discussed followed by the need of a “top-down” precursor quantification method is justified. Further, a review of the existing methods for quantifying damage precursor is presented followed by a mathematical and experimental derivation of NLDE is presented. To justify the findings with additional information from different scales, low-frequency (≤500 kHz) Guided wave ultrasonic NDE was performed. It is further hypothesized that the lower frequency ultrasonic guided wave signal that carries the nonlinear effect from the lower scale is essentially manifested but can only be extracted from the coda part of the signals and thus in this chapter the coda part of the signals were analyzed. Frequency transformation of the signals could result very low and almost undetectable higher harmonics due to the very early stage of damage and may not be useful for precursor quantification. Hence, a time domain analysis is required to find this information on the nonlinearity that could be manifested but are buried deep inside the signal. Thus, Guided coda wave interferometry (CWI) for composite is formulated for the first time using high-speed Taylor series expansion method. Precursor damage index is then formulated to quantify the damage state. Precursor damage index from Guided CWI and high-frequency NLDE are then correlated to evaluate the equivalency of information. To prove the positive indication of precursor damage from the newly coined NLDE, a set of benchmark studied are presented using optical microscopy and scanning electron microscopy (SEM). As metallic structures are well studied by many researchers, in this chapter the example study of precursor damage is restricted to the composite specimens under fatigue.

The historical background and the theoretical basis of the monitoring of stress and strain by acoustic waves is presented. Discussed are furthermore the results of digital simulations and the experimental developments and instrumental techniques needed to monitor the stress–strain relation present in the observed samples solely with the aid of traveling acoustic waves. The obtained experimental results are compared to conventional detection of the stress–strain relation performed synchronous to the developed ultrasonic monitoring for different metallic samples. Applications related to structural health monitoring of aircraft components by guided ultrasonic waves are exemplified to demonstrate the range of applications of the techniques developed for the presented monitoring scheme.

Fatigue crack is a progressive and localized structural damage that occurs when a structure is subjected to cyclic loading. It is a critical concern for in-service metallic structural components for the failures caused by fatigue crack, which constitute nearly 90% of the total failures in metallic structures. Additionally, a fatigue crack only becomes conspicuous after the crack approaches approximately 80% of the structural fatigue life. For laminated composite structural components, delamination is a critical failure mechanism in the form of separated layers caused by cyclic loading or impact because the composite laminates do not provide reinforcement through the thickness. Damages like fatigue crack and delamination are often invisible or barely visible but may compromise the integrity of structural components and cause catastrophic failures.

Current identification techniques towards small-scale damage (e.g., fatigue cracks) making use of nonlinear features of acousto-ultrasonic (AU) waves are confronted by two inherent bottlenecks: (1) the inefficiency in quantitatively pinpointing the location and severity of small-scale damage, though most approaches are able to infer its existence qualitatively; (2) the use of bulky probes, moving back and forth to generate and acquire AU waves. Bearing in mind the above twofold bottleneck, a damage characterization approach, in conjunction with the use of an active piezoelectric sensor network, is reported in this chapter, based on the authors’ intensive research in this connection over the years. The reported approach characterizes individual fatigue cracks quantitatively. From fundamental modeling to experimental verification, this study has achieved insight into generation of nonlinearity in AU waves induced by fatigue cracks. A diagnostic imaging algorithm is employed to facilitate an intuitive presentation of identification results in images. Experimental validation is carried out by quantitatively evaluating multiple cracks of small dimensions in a fatigued aluminum plate, showing satisfactory accuracy. This study has led to a characterization approach for fatigue cracks in a quantitative manner using embeddable piezoelectric sensor networks. This will be beneficial to implementation of structural health monitoring able to identify small-scale damage at an embryo stage and evaluating its growth. Compared with existing methods, the developed method (1) makes use of embedded sensor networks that is conducive to online structural health monitoring; (2) evaluates fatigue cracks quantitatively; (3) enables detection of multi-cracks; and (4) presents identification results in intuitive images.