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今回で特集「非線形超音波法による非破壊検査・評価」も6 回目となります。前回までの「非線形超音波法による非破壊検査・評価」に関する特集号でも紹介されましたが，2006 年度から2 年間ごとに「非線形現象を利用した非破壊検査・材料評価研究会」（主査：京都大学 琵琶志朗教授），「非線形超音波研究会」（主査：湘南工科大学 大谷俊博教授），「非線形超音波の基礎と応用に関する研究会」（主査：富山大学（現 東北大学） 三原 毅教授），「非線形超音波による非破壊評価の高度化研究会」（主査：慶應義塾大学 杉浦壽彦教授），「材料の非線形現象を利用した非破壊評価研究会」（主査：京都大学 林高弘准教授）と続き，現在「非線形現象を利用した非破壊計測技術に関する研究会」（主査：小原良和）として，年間2 ～ 3 回の研究会を開催しております。
さて，そもそも，この非線形超音波法の「非線形」とは何が線形ではない（線形からずれる）のでしょうか？その答えは，固体材料の場合，応力ひずみ関係です。例えば，金属材料の場合，弾性域では応力ひずみ関係を「線形」と近似（フックの法則）しても実用上問題ない場合が多いですが，無傷の材料でも，厳密には，応力ひずみ関係はわずかに「非線形」の性質を示します。これは熱膨張とも密接に関係することなどから，この非線形性に起因して発生する高調波の計測の研究が1960 年代から行われております。現在では，このような非線形性は「古典的非線形性（Classical nonlinearity）」と呼ばれています。一方，1970 年代後半に，疲労き裂の閉口現象を研究していたグループにより，接触界面や疲労き裂において明瞭な高調波の発生が観察され，これにより界面が局所的に強い応力ひずみ関係を示すことが発見されました。これは，超音波による界面（き裂面など）の開閉振動，すべり，跳ね上げなどの非線形接触振動によると考えられており，「古典的非線形性」の理論では説明できません。それゆえ，最近では「非古典的非線形性（Non-classical nonlinearity）」として明確に区別されています。
これまで，国内外で非線形超音波法に関する様々な計測法が提案され，多くの有益な実験結果が蓄積されてきました。一方，測定の精度・確度向上に伴い，新たな非線形現象が発見されることも多く，依然として理論的に未解明の点も多いのが実情ですが，その過程で開発された種々の測定法は，現時点でも非破壊検査の発展に貢献できるものが少なくないように感じられます。
本特集号では，昨今，非線形超音波法の研究が，海外でも非常に盛んであることを鑑み，国際的に第一線で活躍されている国内外の先生方にご執筆をお願いしました。そのため，測定法や適用対象（コンクリート，金属，砂岩，ガラス）も多岐にわたり，いずれも今後の非線形超音波法の発展に大きく貢献する重要な内容の解説記事となっております。これらが読者の皆様の貴重な情報源として少しでもお役に立てば幸甚です。
最後に，本特集号の企画にあたってご協力いただいた執筆者の方々，研究会開催時にご協力いただいた講演者およびご参加いただいた方々，関係各位に深く感謝申し上げます。
Generation of Very High Intensity Aerial Ultrasonic Waves and Application for
Non-contact and Non-Destructive Inspection
College of Science and Technology, Nihon University Youichi ITO and Ayumu OSUMI
キーワード:非接触法，強力空中超音波，集束音波，非線形超音波，固体内欠陥，超音波振動
はじめに
強力空中超音波を利用した各種の応用技術１）−３）の研究開発を行っている。空中超音波の最大の魅力は，音波を非接触で作用できることであり，実動においては操作性と利便性が極めて向上することが期待される。しかし，強力音波を利用する応用技術は，これまであまり多くなかった。その理由は，強力空中超音波の発生そのものが難しかったことにある。気体媒質の音響インピーダンスは液体や固体媒質に比べて数千～数万分の一の大きさであるため，音波エネルギーを効率よく発生させることは極めて困難である。例えば，スピーカの電気音響変換効率（電気エネルギーを音のエネルギーに変換する効率）は，わずか数パーセントと極めて低い。もう一つは，音波エネルギーを集中させて強力音波を作り出す効果的な技術がなかったことである。しかし，その後両技術を実現する方法が開発され，強力空中超音波を利用した応用研究が精力的に進められてきた。ここで使用する音波は音圧150 dB 以上の強力なものであり，これらの音波が生み出す特徴的な作用とその効果は極めて魅力的である。このような効果は，音波が強力なほど顕著に現れるため，更なる強力音波の発生が要望されていた。
このような状況の下，最近新たな集束方式の強力空中超音波音源４），５）が開発された。この音源は，従来のもの６）−９）と比較して数段強力な音波を発生させることができる。しかも，これまで以上に強い非線形性を有した特徴ある音波になっていることから，それを生かした新たな応用も期待されている。その一つが，非破壊検査分野への応用である。音波が極めて強力であるため，音響インピーダンスが大きく異なる空気−固体間においても，わずかではあるが音波を固体中に入射させることができる。しかも，この音波には基本波とその整数次の高調波音波が含まれているため，同時に複数周波数の振動を固体表面に発生させることが可能となる。
本稿では，まず空中に高強度の非線形超音波を発生させるための音源の原理とその基本特性について述べ，次いでこの音波を利用した固体内欠陥の非接触高調波イメージングの一例を紹介する。
Nonlinear Ultrasonic Characterization of Damage Evolution
in Consolidated Granular Media
Dept. of Applied Science and Technology, Politecnico di Torino (Italy)
Marco SCALERANDI and Antonio S. GLIOZZI
Dept. of Structural, Geotechnical and Building Engineering, Politecnico di Torino (Italy)
Paola ANTONACI and Giovanni ANGLANI
Abstract
This paper is a summary of the main results achieved in the past ten years about the practical application of a nonlinear ultrasonic technique denoted as Scaling Subtraction Method (SSM), developed at Politecnico di Torino. Several case studies are reported, involving various types of consolidated granular media and different damage mechanisms. The effectiveness of the SSM in describing damage evolution is compared with other techniques and discussed with reference to both diffuse damage, as induced by mechanical loads, thermal actions or corrosion, and localized damage, as due to degradation of the interfaces between different portions of a masonry system under chemical attack. The reverse process of crack repair due to a healing agent is also analyzed.
Key Words: Nonlinear ultrasounds, Scaling subtraction method, Cracks, Diffuse damage, Localized damage, Concrete,Consolidated granular media
Introduction
The strong interconnection between the propagation characteristics of elastic waves in consolidated granular media and the mechanical and structural properties of the latter, at different spatial scales, makes ultrasound-based techniques some of the most effective and widely used non-destructive tools for damage assessment of a large variety of construction materials. Above all, such features as ultrasonic pulse velocity or ultrasonic wave attenuation are at the basis of commonly used diagnostic techniques, as shown in 1 ), 2 ). Although sufficiently accurate for a wide range of practical applications, these non-destructive techniques do not usually account for the contribution deriving from the possible nonlinear dependence of the elastic response on the excitation amplitude. On the other hand, it has been revealed that the excitation of cracks,grain boundaries and interfaces, at the micro- or meso-scale,by large mechanical deformations can generate nonlinear elastic waves able to propagate through the material３），４）.
The formation of such nonlinear elastic waves is strictly related to the presence of damage and is associated with several physical manifestations, that can be easily detected by varying the excitation amplitude. More specifically, a complex phenomenology including the shift of the resonance frequency ５）, the generation of higher-order harmonics６） or sidebands７）,the break of proportionality８）, the occurrence of conditioning and relaxation phenomena９）, etc. can be observed in nonlinear ultrasonic experiments. Such measurable nonlinear effects are more strongly related to damage at different scales than linear elastic parameters. For this reason, nonlinear ultrasounds are more sensitive to the degradation of the material properties than linear techniques, even at early stages of damage.
Starting from the considerations reported above, a novel nondestructive technique based on nonlinear ultrasounds has been developed in recent years８），10）. It is called Scaling Subtraction Method (SSM) and is based on the detection of nonlinear effects in the elastic response of solids to a sequence of ultrasonic excitations with increasing amplitudes. Unlike most frequencydomain filtering-based techniques 11）, the SSM offers the advantage that no parameter-tuning is needed for the analysis,hence a higher reliability and an easier implementation can be obtained. Furthermore, it takes into account also the nonlinear phase delay and attenuation effects occurring at the same frequencies as the excitation: this allows to use narrow-band sensors, that are usually cheaper and more readily available than broad-band transducers; in addition, these nonlinear elastic effects usually have higher amplitudes than those observed for sub- or super-harmonics and therefore a higher robustness can be achieved, especially in noisy environments.
For these reasons, the SSM turns out to be very promising inview of potential applications for damage assessment of existing structures. We report here the main results obtained from its application to several case studies, involving different types of consolidated granular media and several types of damagemechanisms. The effectiveness of the SSM is discussed with reference to both diffuse damage (as caused by mechanicalstress, thermal actions or corrosion attack) and localized damage (as caused by chemical expansion in a discontinuousregion). Finally, the capability of the SSM to provide information on the reverse process of damage repair is also evaluated and the monitoring of a time-dependent repair process induced by asodium silicate is presented here as a case study.
What Can We Learn about the Elastic Properties of a Material by
Monitoring the Propagation of a Finite-Amplitude Elastic Pulse?
Los Alamos National Laboratory Marcel REMILLIEUX
Abstract
As an elastic wave propagates in a solid, it interacts with its constituents, including its defects. It is not surprising then that elastic waves have been used for decades to characterize materials and evaluate structural integrity in various fields. One interesting fact about damaged materials is their ability to distort elastic waves under certain conditions due to an accumulation of nonlinear effects along the propagation paths of the waves. These effects may be observed even when the wavelength is much larger (by orders of magnitude) than the defects. In this paper, we will study these effects in a long thin bar of Berea sandstone by carefully monitoring the propagation of a finite-amplitude elastic pulse. The simplicity of the experimental arrangement, i.e. longitudinal wave propagating in the axial direction of a sample with a 1D-like geometry, gives us the opportunity to focus on the mechanisms at stake, namely: classical nonlinearity, hysteretic nonlinearity, and non-equilibrium dynamics.
Key Words: Elastic pulse, Classical nonlinear elasticity, Non-equilibrium dynamics, Nonlinear mesoscopic elastic materials
Introduction Dependence of the wave speed and damping parameters on strain amplitude, slow dynamics, harmonic generation, and hysteresis with end-point memory are some of the interesting properties related to nonlinear and nonequilibrium dynamics and exhibited by natural and man-made materials such as many rocks, thermally damaged concrete, and metallic components filled with micro-cracks. Such systems belong to a wider class of materials referred to as Nonlinear Mesoscopic Elastic Materials (NMEMs)１）. From a mechanical point of view, NMEMs can be thought of as a network of mesoscopic-sized “hard” elements (e.g., grains with characteristic lengths ranging from tens of microns to a few centimeters) cemented together by a“ soft” bond system. The effects of this particular structural arrangement on the propagation of elastic waves is relevant to various natural and industrial processes, ranging in scales and applications, e.g., the onset of earthquakes and avalanches in geophysics２），３）, the aging of infrastructures in civil engineering４），５）, the failure of mechanical parts in industrial settings６）−８）, bone fragility in the medical field９），10）, or the design of novel materials, including nonlinear metamaterials,for shock absorption, acoustic focusing, and energy-harvestingsystems11）.
A Review of Nonlinear Ultrasonic Array Imaging
Department of Mechanical Engineering, University of Bristol, UK. Jack POTTER
Abstract
This paper presents a review of techniques for the imaging of elastic nonlinearity using ultrasonic phased arrays. Such methods are applied within the field of nondestructive testing of materials, most notably in application to the imaging of tightly closed cracks. The methods of nonlinear imaging are grouped into three distinct classes. The underlying principles of each class are detailed and key experimental imaging results reported.
Key Words:Ultrasonics, Nonlinear elasticity, Phased arrays, Subharmonics, Fatigue cracks
Introduction
Elastic nonlinearity is a modality of significant importance within the field of nondestructive testing. Both micro-structural changes that are a precursor to macroscopic damage formation and, later-stage, discrete defects such as closed cracks exhibit contrast in elastic nonlinearity. The fundamental effect of elastic nonlinearity on a propagating ultrasonic field is some form of spectral distortion, that is a movement of energy from the transmitted frequencies to some other component. The principle of nonlinear ultrasonic nondestructive testing is to infer elastic nonlinearity through measurements of these distortions. In recent years an area of focus has been the development of techniques which use ultrasonic phased arrays to image elastic nonlinearity. Such methods have demonstrated particular success in the imaging of closed fatigue cracks, which exhibit weak contrast in conventional linear imaging modalities.
This review groups nonlinear array imaging techniques into three distinct types. Those which measure a scattered subharmonic wave, those which infer nonlinearity through amplitude dependence of a wave scattered at the fundamental frequency and those which measure local nonlinearity through analysis of the subsequent diffuse energy. This should be not considered a comprehensive review of the field since many permutations of these techniques have been proposed. Rather,the main approaches and underlying principles of nonlinear array imaging are detailed and key results reported.
Review of a Nonlinear Frequency-Mixing Photo-Acoustic Method for Imaging a Crack
Le Mans University Sylvain MEZIL, Nikolay CHIGAREV, Vincent TOURNAT and Vitalyi GUSEV
Abstract A two-dimensional imaging of a crack achieved by a nonlinear frequency-mixing photo-acoustic method is reported. Nonlinear acoustic waves are initiated by the absorption of radiation from two laser beams that are intensity-modulated at two different frequencies. The first one modulates the local crack rigidity by initiating crack breathing that can be seen as repeated closing and opening of the crack. The second laser beam generates an acoustic wave in the same location, interacting with the breathing crack. The detection of acoustic waves at combination frequencies, absent in the initial frequency spectrum of the modulations of these beams, provides the opportunity of detecting the crack. Two-dimensional imaging with an amplitude dynamics up to 40dB and a spatial resolution better than 100μm is obtained by scanning of the sample and mapping the nonlinear sidelobe amplitudes.
Key Words: Laser ultrasonics, Nonlinear acoustics, Nondestructive testing, Crack imaging, Frequency-mixing
Introduction
Nonlinear acoustics is known to be extremely sensitive to the presence of imperfect contacts in a material, and thus of cracks１）−17）. Various methods have been developed to detect cracks using phenomena such as harmonic４）− ８），18）and subharmonic５），19） generation, nonlinear resonances, nonlinear modulation, for example. The use of laser ultrasonics has the advantage over in-contact methods, to avoid nonlinear phenomena that could take place at the interfaces of acoustic actuators with the sample. The detection of nonlinear components is then a signature of phenomena occurring in the sample.
However, due to the low efficiency of the photo-acoustic conversion process, achievable acoustic wave amplitudes in optical generation are usually much lower than those generated by piezo-transducers. As a consequence, exciting crack nonlinearity by laser generated acoustic waves is not straightforward. Several nonlinear ultrasonic methods using piezo-transducers or laser ultrasonics have been used to realize one-dimensional scans to detect a crack in an advantageous position11）− 14），20）− 25） (i.e., to detect a part of a crack with high nonlinearity, typically the tip), but are rarely implemented for two-dimensional scans where the diminishing of the local crack nonlinearities and/or the evolution of the distance between the crack faces prevent its detection along its whole length.Therefore, on two-dimensional scans, the crack is detected only in favourable areas13），14）.
The method used in this paper induces periodic opening and closing of the crack that is a source of non-analytic non-classical nonlinearity. It has already been used to realize one- and twodimensional scans24）−26） over samples with surface breaking cracks. Such non-classical nonlinearity is much stronger than the classic ones (quadratic, cubic), and we review here how it can be used to produce two-dimensional imaging of a crack along its whole length.
Higher-harmonic Imaging of Artificial Closed Flaws with Variable Gaps
Hitoshi ISHIDA and Koichiro KAWASHIMA
Abstract
Artificial closed cracks were made by the diffusion bonding of one stainless steel block with another block, to make the crack gap of sub-micro meter. The crack surfaces were visualized by an immersion higher harmonic ultrasonic method. As excitation voltage was increased, the crack area visualized by the higher harmonic increased. This could be explained by the closed crack surfaces being opened by a large amplitude incident wave. Furthermore, we confirmed that the closed cracks where the gap was decreased to 0 from the maximum gap of about 6 μm were made, by cutting the specimens after higher harmonic measurement.
Key Words:Ultrasonic testing, Nonlinear ultrasonic w Key Words ave, Higher harmonic method, Closed flaw, Crack gap, Diffusion bonding
緒言
各種プラントの定期点検においては，疲労き裂，応力腐食割れ（SCC：Stress Corrosion Cracking）などのき裂状欠陥の非破壊検査による検出，サイジングが求められる。特に原子力発電所の設備に対しては，欠陥が検出された場合には，その設備の健全性を評価するために，欠陥寸法の正確な測定が必要とされている。
き裂面が部分的に接触するNi 基合金のSCC １）では，超音波が接触部を一部透過するため反射波振幅が低下することにより，従来の超音波法では検出・画像化が困難なものがある。原子力発電所の原子炉容器の管台異材継手部のNi 基合金溶接部で検出されたSCC ２）はこのような閉口き裂であったと著者らは推定する。
このような問題に対処するため，非線形超音波法による閉口き裂の可視化が試みられてきた。高調波法により，Ni 基合金溶接部の粒界SCC ３），４），鋳造ステンレス鋼内の疲労き裂４）が可視化された。従来のパルス反射法では困難な，閉口き裂面を可視化できるという点が，高調波法の優位な点である。また分調波法５）によりステンレス鋼試験片の閉口疲労き裂の画像化が進められてきた。
非線形超音波法によるこのような閉口き裂の検出およびき裂寸法評価手法を確立するために最も重要な検討項目の一つは，部分的に接触するき裂を持つ試験体を製作し，非線形超音波法の探傷条件を体系的に変化させた実験的検討を行い，受信高調波振幅と閉口き裂寸法，間隙幅などとの関係を明らかにすることである。
しかし，き裂状欠陥に対する標準試験片はまだ存在しない。フィンランドのTrue Flaw 社は熱疲労により開口幅数μm の狭いき裂を含む試験体を製作しているが６），き裂先端部近傍の間隙を制御することは困難なようである。また従来からの欠陥の検出技術や寸法測定技術の開発，改良を目的とする試験片では，付与する欠陥の深さ，長さ以外の閉口き裂の間隙寸法，残留圧縮応力などは制御できず未知であり，各試験で得られた結果の評価および相対的位置付けが困難である。
このような状況において，閉口き裂部の間隙幅を一定範囲内で制御できる人工き裂を含む試験体を製作できれば，部分接触を伴うごく狭い間隙を持つき裂状欠陥に対する標準試験片として利用できる可能性がある。
本稿では，接合する面に深さが10 μm から0 μm まで直線状に減少して傾斜した凹みを加工した後，拡散接合７）により模擬閉口き裂を含む試験片を製作し，水浸高調波法により模擬き裂部を可視化した。励起電圧の増大に伴い模擬き裂部からの反射（散乱）波の面積（以下，反射面積）が増大するという結果から，模擬き裂面の部分的開閉口により高調波が発生していることを実証し，さらに試験片の切断・SEM 観察により模擬閉口き裂間隙を実測し，励起電圧の増大によるき裂部からの高調波反射面積の拡大とき裂間隙幅との関連を明らかにした。
