INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 10, No. 1, pp. 123-135 JANUARY 2009 / 123 10.1007/s12541-009-0019-y
1. Introduction
The evaluation of structural changes of materials and constructions and monitoring their ultimate strength and endurance in operation is required for many industrial structural integrity problems. Especially the evaluation of accumulated damage or degradation in the material properties at the early stage of fracture is important in refinery plants, nuclear power plants, or aircraft parts in order to ensure their structural safety.
The most powerful nondestructive way of evaluating material degradation is the ultrasonic method since the characteristics of ultrasonic wave propagation are directly related to the properties of the material. Traditional ultrasonic NDE is bad on linear theory and normally relies on measuring some particular parameter (sound velocity, attenuation, transmission and reflection coefficients) of the propagating signal to determine the elastic properties of a material or to detect defects.1 The prence of defects changes the pha and/or amplitude of the output signal, but the frequency of the input and output signals is the same.
However, the conventional ultrasonic technique is nsitive to gross defects or opens cracks, where there is an effective barrier to transmission, whereas it is less nsitive to evenly distributed micro-cracks or degradation. An alternative technique to overcome this limitation is nonlinear ultrasonics. The principal difference between linear and non-linear ultrasound NDE is that in the latter the existence and characteristics of defects are often related to an acoustic signal who frequency differs from that of the input signal. This is related to the radiation and propagation of finite amplitude (especially high power) ultrasound and its interaction with discontinuities, such as cracks, interfaces and voids. Since material failure or degradation is usually preceded by some kind of non-linear mechanical behavior before significant plastic deformation or material damage occurs, considerable attention has recently been focud on the application of nonlinear ultrasonics.2,3
Linear acoustics deals with propagation of vibrations through medium. Deviations from the equilibrium state of a medium that are caud by the vibrations are assumed to be small; that is, the propagating wave is assumed to have small amplitude or a low intensity. The propagation of finite-amplitude (or high-intensity) ultrasonic waves is accompanied by a number of effects, who magnitudes depend on the vibration amplitude.
Investigation of the propagation of finite-amplitude elastic waves in gas, liquids, and solids has be
en of continuing interest. It was pointed out by L. Rayleigh4 that the prence of nonlinear terms in the wave equation caus inten acoustic waves to generate new waves at frequencies which are multiples of the initial sound-wave frequency. Subquently, many authors, most notably Brillouin5 and Murnaghan,6 have contributed to the theoretical treatment of nonlinear elasticity. Acoustic harmonic generation was first verified experimentally in air by Thuras et al.7 and subquently obrved in
Nonlinear Ultrasonic Techniques for Non-destructive Asssment of Micro Damage in Material: A Review
Kyung-Young Jhang1,#
1 School of Mechanical Engineering, Hanyang University, 17, Haengdang-dong, Seongdong-gu, Seoul, South Korea, 133-791
# Corresponding Author / E-mail: kyjhang@hanyang.ac.kr, TEL: +82-2-2220-0434, FAX: +82-2-2299-7207
KEYWORDS: Nonlinear Acoustic Effect, Ultrasound, Material Characterization, NDE (Nondestructive Evaluation), Micro Damage
The nondestructive asssment of the damage that occurs in components during rvice plays a key role for
condition monitoring and residual life estimation of in-rvice components/structures. Ultrasound has been widely
utilized for this; however most of the conventional methods using ultrasonic characteristics in the linear elastic
region are only nsitive to gross defects but much less nsitive to micro-damage. Recently, the nonlinear
ultrasonic technique, which us nonlinear ultrasonic behavior such as higher-harmonic generation, sub-
harmonic generation, nonlinear resonance, or mixed frequency respon, has been studied as a positive method
for overcoming this limitation. In this paper, overall progress in this technique is reviewed with the brief
三字经注释及译文
introduction of basic principle in the application of each nonlinear ultrasonic phenomenon.
Manuscript received: December 1, 2008 / Accepted: December 11, 2008 © KSPE and Springer 2009
liquids by veral investigators. The nonlinear third-order elastic constants of solids were first measured in the early 1960’s and harmonic generation of bulk waves was soon reported by a number of authors.8,9 This resurgence of interest let to more convenient formulations of nonlinear acoustic propagation by Thurston and Brugger10 and by Wallace.11 Thereafter, it was found in a solid expod to a strong ultrasonic field that there occur such nonlinear effects as sub-harmonic generation, shift of resonance frequency, or mixed frequency respon as well, besides the higher harmonic generation.
Fig. 1 Detectable defect size of various nondestructive and destructive methods for material characterization
All the phenomena can exert a strong effect on the structure and interaction of solids, making inten ultrasound applicable in material characterization. Moreover, the effects are enormous in damaged material but nearly un-measurable in undamaged materials, hence the interest in applying nonlinear ultrasonics. Tho are expected to be much more nsitive to micro-damage than the conventional linear characteristics of ultrasonic wave, as shown in Fig. 1 where the ability of veral nondestructive and destructive methods is summarized in the detectable defect size.
This review covers tho nonlinear acoustic phenomena induced in solids, which are categorized as follows:
•Higher harmonic generation
•Sub-harmonic generation
•Shift of resonance frequency
•Mixed frequency respon
The basic physical mechanism of each phenomenon is introduced with applications to evaluation of micro damage such as fatigue, aging, or clod-crack, etc.
2. Higher Harmonic Generation
Higher harmonic generation is the most classical phenomenon that the waveform of incident wave is distorted by the nonlinear elastic respon of medium to the incident wave, and so that higher harmonic waves are generated in the transmitted wave as shown in Fig. 2.
This phenomenon can be understood simply by considering the nonlinear system. Let’s consider a 2nd order nonlinear system as shown in Fig. 3, and a sine wave is given as input. Then the output of this system will have 2nd order higher harmonic wave component. When we consider 3rd or higher order nonlinearity, then the system
output will have 3rd or higher harmonics also. However, usually the
nonlinear effect of 3rd or higher orders is much smaller than 2nd order,
therefore we ud to consider up to 2nd order nonlinearity.
Then, how about the physical mechanism? There are two kinds of
physics in the generation of harmonic generation. One is the
nonlinear elasticity and the other is contact nonlinearity. In this paper,
their basic principles and applications are parately introduced.
2.1 Nonlinear Elasticity
2.1.1 Principles
Physically the phenomenon of higher harmonic generation is
related with the nonlinearity in the elastic behavior of material, as
shown in Fig. 4. That is, the relationship between stress σ and strain ε哪里好玩的景点推荐
is nonlinear, which is called the nonlinear version of Hooke’s law as
shown in Eq. 1 for the simple one-dimensional ca.2,3,12-14
(1)
E
σεβε
=++L (1)
Where,E is Young’s modulus and β is 2nd order nonlinear elastic
coefficient which will be called the nonlinear parameter in this paper.
In order to explain the generation of higher order harmonic waves,
let’s now consider the ca where a single frequency ultrasonic wave (longitudinal) incident upon one end of a thin circular rod propagates
through the rod with degradation and is detected on the other end.
If it is now assumed that the attenuation can be neglected, then
the equation of motion for longitudinal and planar waves in the thin
circular rods can be reprented as follows:
2
2
u
t x
σ
ρ
∂∂
=
∂∂
(2)
Fig. 2 Distortion in the waveform during propagation by the
nonlinear elasticity and higher harmonic generation; β is a nonlinear
厦门黄厝海滩parameter defined by the ratio of cond harmonic amplitude and
power of fundamental
Fig. 3 2nd harmonic generation in the quadratic nonlinear system
Where, ρ is the density of the medium, x is the propagation distance,
σ is the stress and u is the displacement. Using Eqs. 1 and 2 and the elationship between strain and displacement, we can obtain the nonlinear wave equation for displacement u(x,t) as follows:
Fig. 4 Nonlinear relationship between stress and strain
2222222u u u u E E t x x x
ρβ∂∂∂∂=+∂∂∂∂ (3) Where, we considered Eq. 1 up to the 2nd order term. In order to obtain a solution, a perturbation theory is applied. For this purpo, the displacement u is assumed as in Eq. 4,
0'u u u =+ (4)
Where, u o reprents the initially excited wave and u’ reprents the first order perturbation solution. If we t u o to a sinusoidal single frequency wave form, or
01cos()u A kx t ω=− (5)
then, we can obtain the perturbation solution up to the 2nd order as
follows:5,6
012'cos()sin 2()u u u A kx t A kx t ωω=+=−−− (6) with
22218
A A k x β= (7)
The 2nd term in Eq. 6 reprents the 2nd
harmonic frequency component and its magnitude depends on β. This means that the parameter β can be evaluated from the magnitude of the 2nd
harmonic frequency component, as shown in Eq. 8. 22218A k x A β= (8) The magnitude of harmonic waves depends on medium material
properties. Thus, it would be possible to evaluate the degradation of
elastic property by monitoring how much magnitude of higher harmonic wave is generated in the transmitted wave.12-17
求职简历免费模板2.1.2 Evaluation of Fatigue Damage
Fatigue is one of the most common material degradation mechanisms in industry. The classical approaches of prediction of the residual life of cyclically loaded materials and structures are bad on the u of the fatigue life curves of the material measured on small laboratory specimens. But this can only predict the number of cycles necessary for the appearance of the cracks who dimensions are comparable with the laboratory specimen and in a number of cas this approximation results in appreciable errors in life estimation. Hence the importance of evaluation of fatigue damage in a nondestructive way is growing.
A promising technique to overcome this limitation is nonlinear ultrasonics. When a purely sinusoidal ultrasonic wave propagates through a solid medium, it distorts and generates higher harmonics of the fundamental waveform as a result of the non-linearity of the propagation medium. It is known that the microstructural feature which is predominantly altered during fatigue damage progression is the distribution of dislocations which caus significant change in the material’s non-linear elastic wave behavior. This behavior manifests itlf in harmonic generation.
Recent experimental studies and new physical models are also demonstrating the potential of nonlinear ultrasonics (or the cond-harmonic generation technique) to quantitatively detect and characterize fatigue damage in metals. This fatigue damage first appears in the form of dislocation substructures, such as veins and persistent slip bands (PSBs), and the PSBs accumulate at grain
boundaries to produce strain localization and, then finally, microcrack initiation with increasing fatigue cycles.18
Fig. 5 Overall dependency of ultrasonic nonlinearity on the damage; β0 is the initial value at undamaged (no fatigue) state
The dislocations (and resulting microplastic deformation) do not cau a large change in the linear macroscopic properties (such as elastic moduli, sound speed, and attenuation) of a material; the
changes in the linear ultrasonic values are not large enough to be
幼儿行为accurately measured with conventional linear ultrasonic techniques. However, the accumulation of dislocations throughout the continuum (with increasing fatigue) will cau a nonlinear distortion in an
ultrasonic wave propagating in the material, and thus generate higher harmonic components in an ini
tially monochromatic ultrasonic wave signal.
For this reason, nonlinear ultrasonic (acoustic) waves can be ud to quantify the prence and the density of dislocations in a metallic
material, and thus measure fatigue damage in a quantitative fashion. In addition, nonlinear ultrasonics has the potential to promote an
understanding of the evolution and accumulation of the dislocation
substructures in the very early stages of fatigue. To date, a number of investigators 18-25 have applied nonlinear
ultrasonic techniques to asss fatigue damage in different materials. A direct correlation between dislocation density levels within the fatigued material and an increa in harmonic ultrasonic signals has been reported.19 The effect of dislocation density on the nonlinear
ultrasonic parameter in quenched steels with different carbon contents has been also reported.20,21 The nonlinear parameter was found to increa monotonically with carbon content and hardness over a range of 0.1-0.4 mass %.
Frouin24 performed in situ nonlinear ultrasonic measurements during fatigue testing, and related the measured increa in the acoustic nonlinearity parameter-in the vicinity of the fracture surface-to an increa in the dislocation density. Sagar prented the correlation between a nonlinear ultrasonic parameter and progression of fatigue damage manifested by the changes in dislocation structures from the virgin state to almost the end of life, where the total fatigue life was covered.26
Many other rearches have carried out for various materials also, aluminum 2024-T4, stainless steel 410Cb, titanium Ti-6Al-4V alloys, etc.12,27-29 A substantial increa in the cond harmonic amplitude (180% increa in nonlinear factor) was obrved in Ti alloy at different stages of fatigue life.29 Overall tendency of results was summarized in Fig. 5.
唯美英文The measurements have shown dramatic changes in the nonlinear parameter due to fatigue while in the ca of conventional ultrasonic measurements; the variation is negligible. The results clearly show the potential for making quantitative NDE measurements of fatigue state using nonlinear ultrasonics.
2.1.3 Applications to Other Failure Mechanisms
Besides of fatigue damage, other failure mechanisms such as hardening,30 thermal aging,31-33 and
corrosion have been studied for the nonlinear ultrasonics to be applied.
Hurley30 investigated the correlation of nonlinear ultrasonic characteristics with precipitate-hardening in ASTM A710 steel containing copper-rich precipitates. They showed the variation of parameter β with final aging treatment and the increa in β with increasing strain. Choi31 and Park32 investigated the applicability of nonlinear ultrasonic method to the evaluation of thermal ageing in 2.25Cr-1Mo steel. Fig. 6 shows a result, where the relative changes in the magnitude of nonlinear parameter β when increasing of aging time was demonstrated with the fundamental amplitude A1 for the comparison. We can e much bigger nsitivity in the parameter β. In recent, more systematic approach has been made to study the precipitation kinetics of maraging steel using higher harmonic analysis.33
Also reported in literature are creep assisted microstructure variations in CrMoV rotor steels.3 CrMoV steel samples were heat-treated and fracture appearance transition temperature (FA TT) was determined as a function of aging time for calculating fracture toughness. The cond harmonic measurements correlated with FA TT data.
Fig. 6 Differences in relative change rate of A1 and for aging time (Ref. 31) 2.1.4 Nonlinearity of Surface Wave
Most of work to date has been concerned with the u on longitudinal waves propagated through the bulk of a material. The difficulty of using longitudinal waves propagating through the bulk of a materia
l is the requirement of access to both sides of the material for transmission and reception of the ultrasonic waves. On the other hand, the u of surface only requires access to one side, and may provide additional nsitivity becau the acoustic energy is bounded in a region just below the surface of the material where the exposure to fatigue and thermal damage is most vere. Also surface wave does not exhibit dispersion in a homogeneous material, so that different harmonics can efficiently interact during the wave propagation and it attracts special attention in view of practical applications for monitoring the surface damage.
The nonlinearity of surface wave was firstly discusd in a review article by Viktorov.34 Experiments on SAW (surface acoustic wave) harmonic generation were first reported in aluminum and steel by Rischbieter.35 V ella discusd the nonlinear interaction of two collinear SAWs, where the rigorous theory of thermoelasticity was ud to derive exact expressions for the nonlinear force and stress fields.36 The theoretical studies were also extended to anisotropic materials and generalizations for this ca were also derived.37,38 Bad on tho basic investigations, many studies for applications have been carried out; recent examples include the u of surface waves to evaluate the nonlinear respon of materials, Ti-6Al-4V and Inconel 718,39 and the asssment of material damage in a nickel-bad superalloy,40 aluminum alloy 2024 and 6061.41 Fig. 7 shows a measurement result of nonlinearity in surface wave by using contact wedged transducers.
Recently, lar techniques for generation of nonlinear SAW puls were developed resulting in the obrvation of strong nonlinear effects, such as the formation of shock fronts and drastic changes of the pul shape and duration.42 It was demonstrated that a nonlinear compression as well as an extension of a SAW pul may take place depending on the nonlinear acoustic parameters.43
心理绘画
Fig. 7 Experimental system to measure ultrasonic nonlinearity in surface wave and the measured result showing the relationship between A12 and A2
2.1.5 Solitary Wave
Solitary waves are pul-like entities of nonlinear excitations that propagate through a system without change of their shape.44 From the theoretical point of view, tho solitary waves are spatially localized solutions of nonlinear dispersive evolution equations describing wave propagation in the system. In the ca of surface waves on shallow water, this is the Korteweg–de Vries (KdV) eq
uation, which is integrable via the inver scattering transform.
The phenomenon of solitary waves is a ubiquitous one that has been obrved and thoroughly studied in many branches of science, such as fluid dynamics, optics, plasma physics, etc.45 In the field of acoustic wave propagation in solids, comparatively few experimental studies have been reported with the aim of obrving solitary waves. This is partly due to the difficulties encountered in exciting acoustic waves with sufficiently high intensity in a controlled way. Another important obstacle is the fact that the elastic nonlinearity in a solid is very small. In spite of that, rearch in this field would continue becau of their unique feature.
Thin film layer coated on the substrate is an attractive target of SAW nonlinearity application.46-48 Lomonosov47 obrved the solitary surface elastic puls for the first time in a lar-bad pump-probe experiment by allowing the two major sources of distortion to compensate each other. Eckl48 showed that solitary acoustic puls can propagate along the surface of a coated homogeneous and inhomogeneous medium and showed how the nonlinear surface acoustic waves evolve out of initial pullike conditions generated by puld lar excitation.
2.1.6 Nonlinearity of Lamb Wave
个人艺术写真
Lamb waves, or plate waves, are both types of guided waves, which travel along a material propagating in a direction parallel to its surface. The waves are able to propagate through plates, rods, hollow cylinders, and as well as samples with irregular shapes, bends, or corners (commonly referred to as a waveguide). Due to the Lamb waves and guided waves ability to propagate along the sample, in some cas for veral meters, the waves have been found to be a uful for material characterization and nondestructive evaluation (NDE).49,50
Although non-linear elastic wave propagation is a subject of considerable interest, most of the rearch has focud on bulk51 and surface waves.52 Bulk and surface waves are nondispersive, and therefore all frequency components propagate at the same speed. In contrast, waveguide modes are highly dispersive, and they can propagate in a wide variety of modes. There are very few studies of guided non-linear elastic waves despite the focus in NDE on plates, rods and shells. Thin non-linear waveguides have been studied using approximate 1-D theories to describe the displacement vector. The approximate theories are valid only when the wavelength is large compared with the thickness of the waveguide. In this long wavelength (low frequency) regime the effect of dispersion is weak. Non-linearity and weak dispersion can result in the existence of stationary solutions (solitons) for this kind of problem.53
An investigation of cond-harmonic generation in isotropic plates has been reported recently by Deng,54 where the primary and condary fields are reprented by pairs of plane waves that satisfy stress-free boundary conditions on the surfaces. Only the ca of resonant cond-harmonic generation is considered, requiring the existence of a cond-harmonic wave who pha speed matches that of the primary wave. All non-resonant cond-harmonic waves that are generated are ignored. On the other hand, Lima55 formulated this problem for isotropic elastic waveguides, where all modes of the condary wave field are taken into account, not just tho in resonance with the primary wave.
The rearches described that the amplitude of the condary lamb wave grows linearly in the direction of propagation when two conditions which are pha matching and transfer of power from the primary to the condary wave are satisfied. Pha matching means that pha velocity of cond-harmonic wave matches that of the primary wave. Non-zero power flux reprent that a symmetric (antisymmetric) primary Lamb wave mode does not excite antisymmetric (symmetric) condary Lamb wave modes.
However, Lamb wave propagates at group velocity in the shape of packet in practical application. Lee56 suggested additional conditions for generating cumulative nonlinear Lamb wave in such ca.
It was the group velocity matching that the cond harmonic component, generated by fundamental Lamb wave during propagating, can be arrived at the same time on a received point, and therefore be cumulative.
2.2 Contact Acoustic Nonlinearity (CAN)57
When ultrasonic wave with large amplitude is incident to imperfect interfaces, higher harmonic waves are generated also. This effect is so-called as contact acoustic nonlinearity (CAN), and it is recently attracting increasing attention regarding the characterization of clod defects or imperfect bond interfaces.58-62
This phenomenon originates in repetition of collisions between the two surfaces caud by incident ultrasonic waves. When ultrasonic waves reach an imperfect contact interface, the compressional part of the waves can penetrate it, but their tensile part cannot penetrate it, as shown in Fig. 8. Thus, after penetrating the interface, the waves become nearly half-wave rectification, which means they have obvious nonlinearity. This nonlinearity can be detected by higher harmonics.
Since the pioneering experimental obrvation63 and theoretical analysis64 on the generation of anomalously high cond order acoustic nonlinearity from interfaces and cracks, there have been nu
merous investigations due to its potential application to the ultrasonic inspection of imperfect interfaces and cracks.61,62,65-74 Especially when a crack is clod, it may remain undetected by the linear ultrasonic techniques75 even though it can be excited ultrasonically to generate measurable cond and higher order harmonic signals.63
When the characteristic length of the imperfectness is much smaller than the wavelength, the interaction of acoustic waves with an interface can be described by the interfacial stiffness in the quasistatic approximation.76 This continuum interface model is ud widely in different problems where the interface plays a role.77,78 Although the
Fig. 8 Schematic diagram showing the concept of CAN at micro crack; only compressional part of ultrasonic wave can penetrate the interface of crack
