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(1)AGH - University of Science and Technology Faculty of Mechanical Engineering and Robotics Department of Process Control. Doctor of Philosophy Dissertation. Ultrasonic nondestructive methods in inspection of steel.. by. mgr in». Tomasz ukomski. Supervisor: prof. dr hab. in». Janusz Kowal Co-supervisor: dr hab. in». Tadeusz Stepinski, prof. at Uppsala University. Kraków, 2012.

(2) To my family..

(3) Abstract. This thesis presents new ultrasound nondestructive methods of inspection of steel. The main aim of this work is to show that there still exist problems in evaluation of steel and steel objects, that can be solved by new ultrasonic methods. Three dierent solutions of implementation were presented for various types of material evaluation. The rst is the ultrasound imaging based on usage of virtual transducer for purity inspection of high quality stainless steel. Another application presents resonant ultrasound spectroscopy for hardness evaluation of steel rings. The last described method introduces a new way of hardness evaluation in steel plates by measuring ultrasound elastic waves velocities and taking into account chemical analysis of the material. All presented experiments results are an eort of solving real life industry problems. Streszczenie. Niniejsza praca przedstawia nowe metody nieniszcz¡cych bada« ultrad¹wi¦kowych do inspekcji stali. Celem jest pokazanie i» nadal istniej¡ problemy przy ocenie stali oraz obiektów stalowych, które mo»na rozwi¡za¢ za pomoc¡ nowych metod ultrad¹wi¦kowych. Przedstawiono trzy ró»ne zastosowania ultrad¹wi¦ków do ró»nych typów oceny materiaªu. Jako pierwszy przedstawiono sposób obrazowania ultrad¹wi¦kowego z zastosowaniem wirtualnego przetwornika do oceny jako±ci stali nierdzewnej. Kolejna aplikacja przedstawia wykorzystanie rezonansowej spektroskopii ultrad¹wi¦kowej do oceny twardo±ci pier±cieni stalowych. Ostatnia przedstawiona metoda opisuje sposób okre±lania twardo±ci stalowych pªyt za pomoc¡ pomiarów pr¦dko±ci ultrad¹wi¦kowych fal elastycznych przy uwzgl¦dnieniu skªadu chemicznego próbek. Wszystkie przedstawione eksperymenty s¡ prób¡ rozwi¡zania rzeczywistych problemów wyst¦puj¡cych w przemy±le. 3.

(4) Acknowledgements. I would like to express my gratitude to all people who encouraged and supported me during my work on this thesis. Especially, I would like to thank my supervisor prof. dr hab. in». Janusz Kowal for all his help, encouragement and support. I want also to thank my co-supervisor dr hab. in». Tadeusz Stepinski professor at Uppsala University for his guidance, knowledge and for giving me the opportunity to work with his very inspiring group. Support received from the JERNKONTORET's (The Swedish Steel Producers' Association) Committee TO44 within the project 44030 nanced by Vinnova (The Swedish Governmental Agency for Innovation Systems) as part of its Strategic Steel Research Programme is gratefully acknowledged. I would also like to thank dr Tomas Olofsson also from Uppsala University and M.Sc Martin Hansen Skjelvareid from Tromsø University for valuable and stimulating discussions and for patience while explaining sometimes very basic aspects. I also acknowledge all the people who work in AGH - Univ. of Science and Technology and Uppsala University who made my work easier and sometimes funnier. I am also very grateful to my friends at the Signals and System group and at the Department of Process Control for all those fun and happy moments which helped me to "re-charge my batteries". Finally, I would like to express my deepest gratitude to my wife Gosia, my parents, and my sister for their endless patience and support. Thank you!. 4.

(5) Contents. Contents. 5. 1. Introduction. 1.1 Non-destructive testing . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Ultrasound imaging method . . . . . . . . . . . . . . . . . . . 1.1.2 Virtual transducer method . . . . . . . . . . . . . . . . . . . . 1.1.3 Resonant Ultrasound Spectroscopy method . . . . . . . . . . . 1.1.4 Ultrasound hardness evaluation method . . . . . . . . . . . . . 1.2 Goals of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Thesis contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7. 7 8 9 9 10 11 12 13. 2. Ultrasound imaging. 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Current state of art . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Wave propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Types of waves in NDT . . . . . . . . . . . . . . . . . . . . . 2.3.2 Characteristic acoustic impedance, reection and transmission 2.3.3 Refraction and diraction . . . . . . . . . . . . . . . . . . . . 2.3.4 Near eld, far eld and beam spread . . . . . . . . . . . . . . 2.4 Methods of wave generation . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Piezoelectric transducers . . . . . . . . . . . . . . . . . . . . . 2.4.2 Electromagnetic acoustic transducer . . . . . . . . . . . . . . . 2.4.3 Laser transducers . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Imaging with ultrasonic arrays . . . . . . . . . . . . . . . . . . . . . . 2.6 Presentation methods of ultrasound images. . . . . . . . . . . . . . .. 14. 3. Synthetic Aperture Focusing Techniques. 29. 14 14 15 15 16 17 19 20 21 22 23 23 27. 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Current state of art . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.

(6) 3.3 SAFT in time domain . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4 SAFT in frequency domain . . . . . . . . . . . . . . . . . . . . . . . . 32 4. Virtual transducer element method. 34. 5. Resonant Ultrasound Spectroscopy in diagnostics of steel. 57. 6. Ultrasound steel evaluation based on velocity of elastic waves.. 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Relation between elastic wave velocities and elastic constants . 6.2.2 Relation between hardness and mechanical properties of solids 6.2.3 Velocity measurements . . . . . . . . . . . . . . . . . . . . . . 6.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 67. 7. Concluding remarks and future research. 80. 4.1 4.2 4.3 4.4 4.5 5.1 5.2 5.3 5.4 5.5. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Virtual transducer principles . . . . . . . . . . . . . . . . . . . . . . . Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34 35 37 43 56 57 57 59 61 65 67 67 67 68 69 69 72 78. Bibliography. 82. List of Symbols and Abbreviations. 86. List of Figures. 89. List of Tables. 92. 6.

(7) Chapter 1 Introduction. 1.1. Non-destructive testing. Non-destructive testing (NDT) is a wide group of methods used in science and in industry to determine properties or quality of materials, objects or constructions without causing any damage to them. Due to this fact NDT is very popular because it allows saving time and production costs. The basic NDT methods include visual inspection, ultrasound testing, radiography, eddy current testing and many more. Those methods are mainly used in industry during production process for quality assessment and also for structural health monitoring of constructions, for example, in airplanes or wind turbines. Ultrasounds covers two main areas described as low power and high power depending on their inuence on the material. The low power methods include spectroscopy, defectoscopy, medical diagnostics and ultrasonography. The high power methods contain medical therapy, ultrasound cleaning, soldering (excluding aluminium), and many more [1]. The rst ideas for application of ultrasound testing (UT) appeared in 1912 after the "Titanic" had sunk. However the development of UT applications was possible in the 40s of the 20th century, thanks to discoveries of Floyd Firestone, Donald O. Sproule and Adolf Trost who conducted research on ultrasound generation. Trost invented a system with two transducers placed on opposite sides of a plate. Sproule placed both transducers on the same side, what resulted in double-crystal probes. Firestone modied a radar instrument to send short pulses and receive a reected echo with only one transducer. Therefore he is considered as the inventor of the widely used pulse-echo method. Following the Krautkrämer brothers Josef and Herbert presented the rst UT aw detector. Since that time a large progress in ultrasound techniques has been visible, both in the theory eld and applications [2]. The main advantages of ultrasound, such as low price and simplicity, and also 7.

(8) the development in elds of digital techniques and signal processing made the UT commonly used not only in science and in industry but also in medicine and sonar. Nowadays a large variety of applications are known; new processing algorithms allow enhancing the results of ultrasound tests. Nevertheless, new solutions are still created and there are more and more elds where ultrasounds can be successfully applied. 1.1.1 Ultrasound imaging method. After Firestone's creation of the transducer that allows working in pulse-echo mode, scientist from Japan started tests with imaging in medicine. They ended up presenting 2D grayscale images. They used ultrasounds to detect breast masses, tumours etc. This was the beginning of ultrasound imaging. Nowadays ultrasound imaging is the most popular in medicine. Technology development and increase of the computer processing power, along with phased arrays and advanced signal processing algorithms resulted in the possibility of generating 3D or 4D images, where 4D are 3D images that change in real time. Moreover, ultrasound tomography and holography have been developed to enhance the image quality and to gather more information about the interior of the human body [3]. As stated in chapter 2 there are many ways to present ultrasound images. The most common is an amplitude plot (A-scan). Most of the UT inspections are performed with help of defectoscopes that show results only as A-scans. Unfortunately, it is the least reliable method because A-scans are very dicult to interpret without proper training. The easier way for inspection which doesn't need an extensive training is by generating an image of the object by integration of A-scans. A uniform resolution is obtained in near eld N by using a non-focused transducer. Beyond N the resolution is depth dependent. An alternative is to use a focused transducer but then the image will only be focused in a very narrow space. To perform a full volume scan, it would be necessary to perform few scans with transducers focused on dierent depths, or with help of the phased array. The solution to those problems is synthetic aperture imaging (SAI). It is based on coherent summation of received signals by a transducer placed in dierent locations in order to mimic a physical lens. This technique was rstly developed for radar systems in the 1950s. Since that time SAI was implemented in many other elds where better image resolution was signicant, e.g. seismic exploration of the earth interior, medical diagnostic, sonar and non-destructive testing [4]. 8.

(9) 1.1.2 Virtual transducer method. There are many ways of imaging in ultrasound NDT, one of them is a Virtual Transducer (VT) method. The VT concept was rstly developed in medical application by Passman and Ermert [5] for high frequency skin imaging. This method assumes that focal point of the focused transducer or array is a source of spherical ultrasonic wave. The main advantage of this assumption is ability to perform SAFT in immersion tests or in layered objects by placing VT on the object's surface or at the beginning of the new layer and simply neglecting layers before virtual transducer. There are many scientic papers known which describe the theory and dierent applications concerning virtual transducers. The main implementations pertain to medical applications. Parameters, such as lateral resolution and aspects concerning SNR, can be found in [6]. There are also new algorithms that allow focusing before and after the focal point. They are based on the assumption that the wave shape beyond the focal point is an inverse of the wave before VT [7]. Other presented methods concerning VT take a wave propagation model into consideration during the postprocessing to improve a generated image [8]. However, most of the available papers concentrate on imaging inside the human tissue or detecting objects immersed in water. What is more, those papers are generally about proving a concept and are not applied in real life applications. Doctor [9] and also some other authors mention the application of VT in imaging inside solid objects [8],[10], however, there are no papers proving this concept. et al.. 1.1.3 Resonant Ultrasound Spectroscopy method. It has been known for a long time that dierent shape, size and material of an elastic object result in dierent resonant frequency spectrum; for example, sound of a bell diers in respect to its size, shape or material. Moreover, imperfections, inclusions or cracks can inuence the bell's sound. The resonant spectrum is unique for each elastic object and can be used as its ngerprint. Comparison of frequency spectra of two elastic bodies can reveal deviations in their mechanical parameters. Relation between resonant frequencies and object's features can be revealed either theoretically by solving the so-called inverse problem, or experimentally by correlating measurement results. Resonant Ultrasound Spectroscopy (RUS) is a non-destructive material characterization technique that uses the information contained in the ultrasound frequency band of a mechanical resonant spectrum of an oscillating specimen. In a typical RUS setup a small sample with a simple geometry (sphere, cylinder, or rectangular paral9.

(10) lelepiped) is placed between two ultrasonic transducers. One transducer excites an elastic wave of constant amplitude and varying frequency in the specimen, while the second detects sample's mechanical response in an ultrasonic frequency band. The information about resonance frequencies acquired in a RUS test contains useful data about mechanical properties of the tested sample; the detected resonant frequencies generally correspond to the size, shape and an elastic module of the inspected material. A more detailed description of RUS can be found in Maynar [11], Migliori [12], [13] and Zadler [14]. RUS is mainly used for material characterization mainly to determine its elastic module; however it can also be successfully used for non-destructive evaluation (NDE) of dierent objects, e.g. metal or ceramic products. Heyliger and Ledbetter [15] applied RUS to detect surface cracks in a steel block as well as delaminations in composite laminate. They found that RUS can be used as a NDE technique for detecting aws in materials. Adachi [16] used RUS for the evaluation of micro-cracks in a ceramic ferrules for optical ber connectors. By comparing the dierences between the resonant frequencies, they could distinguish between the acceptable ferrules and the defective ones. The same method was used for the quality assessment of varistor ZnO structures by Hasse [17]. Lukomski in [18] and [19] also presented an application for evaluating parameters and detecting aws in the tested objects. et. al.. et al.. et al.. et al.. 1.1.4 Ultrasound hardness evaluation method. et al.. Common applications of ultrasound to NDT concentrate on detection and characterization of material aws or measurement of material thickness. Ultrasonic measurements can also be used for characterization of material properties; parameters, such as elastic modulus, material microstructure, hardness, etc. can be estimated from the ultrasonic measurements [20], [21]. Elastic modules (Young's modulus, bulk modulus, Poisson's ratio, etc.) can be calculated directly from the shear and longitudinal wave velocities. Strength, toughness or hardness, which are determined by the chemical composition and thermal treatment of steel product, can be inferred indirectly from the ultrasonic measurements using theoretical relationships and empirical correlations [22]. Standard destructive hardness tests require taking samples, which is time consuming as well as expensive during the in-line production. If a high accuracy is needed the instruments used for this kind of tests are generally bulky and heavy. Light hand-held testers are also available but they have generally much lower accuracy or they need to be calibrated for each material separately. Some portable 10.

(11) non-destructive testers have been developed, for instance, the instruments based on the ultrasonic contact impedance method [23]. When correctly calibrated for the specic material under test, an ultrasonic contact impedance instrument is capable of providing correct results expressed in all hardness scales (Rockwell, Vickers, Brinell or Shore). However, its operation requires a physical contact with the surface of tested sample. Also, testers that combine few methods, such as the ultrasonic contact impedance and rebound method, have been developed in order to increase reliability of the results [24]. Another non-destructive solution is to estimate hardness level basing on the correlation between ultrasound wave velocity and attenuation, with the real hardness values measured using traditional methods. Papadakis [20] described an experiment carried out by Yee in 1971, where an ultrasonic method for evaluating an average hardness in structures made of D6ac steel was used. Their method was based on the surface wave velocity measurement and an assumption that it depends on hardness in the same way as the longitudinal velocity, which had been previously established by the authors. Other results, presented in [21] prove that material hardness can be determined only by the measurements of ultrasound wave velocity and attenuation. The measurements showed parabolic relation between hardness and ultrasonic velocity, while attenuation changed linearly along with hardness. Relations between the steel hardness, ultrasound velocity and the attenuation were also presented in [25]. In each of the reports mentioned above the results were obtained only for one specic type of material, and various materials showed dierent relations between hardness and ultrasound velocity 1.2. Goals of the thesis. The overall goal of this thesis is to develop and present three new applications of ultrasound for non-destructive evaluation and inspection of steel and steel products. Additionally, it is an attempt to solve the real life industrial problems concerned with quality control of the steel products during the production process. Since three various methods are considered in this thesis describes each of them has slightly dierent goals and assumptions: Virtual transducer element method.. The VT method is proposed as a solution to a problem of stainless steel purity assessment. The goal is to prove that ultrasound imaging using VT along with SAFT algorithm can be applied in volume imaging of a steel block, which leads to 11.

(12) substantial improvement of lateral resolution and signal-to-noise ratio. Additionally, size of the test setup can also be reduced. Resonant Ultrasound Spectroscopy in diagnostics of steel.. The goal of the RUS application is to show that it can be successfully applied to evaluate not only elastic modulus or presence of aws, but also for the evaluation of technological parameters, such as hardness of objects with regular geometry, e.g. rings. Ultrasound steel evaluation based on velocity of elastic waves.. Velocity measurement of elastic waves propagating in steel is proposed as a method to determine hardness rolled steel plates. It is possible to create a model that allows to evaluating hardness of dierent types of martensitic steel by taking under consideration its chemical analysis. Additionally, the contactless electromagnetic acoustic transducer (EMAT) used in the tests is could be used to perform continuous measurement of steel hardness during the production process. 1.3. Thesis contribution. Ultrasonic non-destructive methods has been developed for at least 50 years. Throughout this time many methods and techniques have been created. Here, I present my contribution aimed at improving the existing methods and developing new ones. Virtual transducer:. development of the method that provides better lateral resolution and signalto-noise ratio than the techniques currently used in the inspection of stainless steel purity during production process; • successful implementation of the virtual transducer in imaging of solid objects immersed in water; • determination of transducer's parameters that inuence quality of the postprocessed image; • simulations, design of the experimental setup, software implementation, measurements •. Resonant ultrasound spectroscopy:. •. proving RUS feasibility for evaluating material technical parameters that cannot be directly derived from the elasticity constants, such as, hardness; 12.

(13) development of a simple and fast method of a hardness inspection of steel rings; • simulations, measurements, data analysis. •. Hardness evaluation based on ultrasound wave velocity:. development of the statistical model based on multiple regression analysis accounting for the information about chemical analysis and practical verication of this model for martensitic steel; • concept of the continuous inspection of steel hardness during the production process; • measurements, software implementation, data analysis. •. 1.4. Thesis outline. This thesis is divided into 7 chapters introducing three dierent methods of the ultrasonic non-destructive testing. Chapter 2, 3 and 4 concern the ultrasonic imaging method. Chapter 2 is an introduction to the ultrasonic wave propagation and methods of generating, recording and presenting a wave. In Chapter 3 a review and theory of synthetic aperture algorithms are presented. Chapter 4 regards the virtual transducer (source) method, along with its principles. Results of a performed experiment are presented with conclusions. In Chapter 5 Resonant Ultrasound Spectroscopy method is introduced in the application of hardness evaluation of steel rings, supported with experiments and conclusions. Chapter 6 concerns the method of steel evaluation based on shear and longitudinal wave propagation, concerning dierent steel types using basic statistics. Concluding remarks and future research concerning introduced methods are presented in chapter 7.. 13.

(14) Chapter 2 Ultrasound imaging. 2.1. Introduction. After World War II the industry needed new solutions in quality control. At the beginning the focus was set only on detecting aws in tested objects. First of all, the technology development concentrated on detecting smaller aws. Additionally, development in new elds of science, such as fracture mechanics or fatigue limits allowed determining if the specic aw can sustain a certain load, and testing or predicting its growth under cyclic loading. This opened a new eld for the NDT community. Detecting aws was not enough anymore; additional information was needed, such as the position of aw and its size. Especially the defense and nuclear industry were interested in new solutions. It occurred that a perfect solution to this problem was ultrasound imaging [3]. Imaging is used, for example, for purity inspection of high quality steel or welds inspection and many more. Imaging is usually used where information about size and position of the aw is crucial. Permanent research is conducted to develop new techniques, solutions and algorithms to improve generated images. 2.2. Current state of art. The NDT progress in automation and robotization allowed improving the accuracy of performed measurements. What is more, mechanical solutions allow easier measurements, for example, water tanks used for immersion test can be replaced by squirting systems. It is a system of water nozzles where sound travels in the water column. New algorithms such as SAFT (see Chapter 3) allowed generating images with high resolution. Also, new software to simulate wave propagation is widely used to optimize the performance of the real tests and to design experiments [3]. 14.

(15) 2.3. Wave propagation. To perform any post-processing of the recorded signals, it is necessary to know the principles of the ultrasonic wave propagation in materials. To correctly perform a measurement one must know the type of wave, acoustic impedance of the tested object, and refraction-diraction eects that might occur during the test. 2.3.1 Types of waves in NDT. There are many types of waves that can propagate in materials. They can be divided depending on the direction of vibration in relation to their direction of travel [26]. •. Longitudinal waves. •. Shear waves. •. Rayleigh waves. •. Lamb waves. Longitudinal waves are the most commonly occurring. They can propagate in solids, liquids and gases. In this type of waves particles have the same direction of vibration as the wave travel direction (Fig. 2.1 (a)). There occur local compressions and decompressions of the material. Shear waves are as important as longitudinal waves. They can propagate only in solid objects. Shear waves are polarized, because particles vibrate only in one direction in plane perpendicular to travel direction (Fig. 2.1 (b)). While changing the position of a shear wave source, the plane of particle vibration is also changing. The velocity of a shear wave is always lower than the velocity of a longitudinal wave; therefore, with the same frequency they have dierent wave lengths. Rayleigh waves are also known as surface wave because they propagate only at the surface of the material (Fig. 2.1 (c)). They penetrate the object only at the depth approximately equal to the wavelength. The particle vibration direction consists of two vectors. A vector that is perpendicular to the wave travel direction has a greater value than a vector that is parallel to that direction. Hence, the particles move in ellipses in planes perpendicular to the surface and parallel to the direction of propagation - the major axis of the ellipse is vertical. Lamb waves occur in objects such as plates, where the size in one dimension is approximately the same as the wavelength. There are two types of Lamb 15.

(16) waves, symmetric (Fig. 2.1 (d)) and asymmetric (Fig. 2.1 (e)). Symmetric and asymmetric waves can propagate with dierent velocities depending on their frequency and plate thickness.. (a) Longitudinal wave. (b) Shear wave. (c) Rayleigh wave. (d) Lamb wave - symmetric (e) Lamb wave - asymmetric Figure 2.1: Particle movement during wave propagation for dierent types of waves. 2.3.2 Characteristic acoustic impedance, reection and transmission. Acoustic impedance is a measure of the resistance that is oered by the material in which a wave propagates. The impedance is a material property described by the relation:. (2.1) where ρ is material density and c is a longitudinal wave velocity in the material. The ultrasonic wave is reected at boundaries between materials where there is a dierence in the acoustic impedance. The greater the dierence, the greater amount of energy will be reected. When the acoustic impedance is known at both sides, it is possible to calculate the intensity of a reected wave. The value is known as the reection coecient and is presented by the formula: Z = ρcL. L. (2.2) Since the amount of reected energy plus the transmitted energy must be equal to the total amount of incident energy, the transmission coecient is calculated by simply subtracting the reection coecient from one: T =1−R (2.3) . R=. Z2 − Z1 Z2 + Z1. 16. 2.

(17) Following reection and transmission eects at the interfaces of the component, it can be seen that only a small percentage of the original energy makes it back to the transducer, even when the attenuation is neglected. In Figure 2.2 an example of the immersion test of a steel block is presented. It can be seen that only 1.3% of the energy returns to the transducer after being reected from the bottom of the sample. 9.3% Transducer. 1.3%. 10.6%. 100%. 12% 88%. Water. 1.4%. Steel. Figure 2.2: Reection and transmission of sound wave at the water/steel boundary. 2.3.3 Refraction and diraction. When an ultrasonic wave passes from one medium to another at any angle other than 0 or 90 it is reected, refracted and in some cases a mode conversion occurs. Refraction is a change of wave travel direction at the boundary between two materials due to the change in its propagation velocity. It is described by Snell's law which states that the ratio of the sines of the angles of incidence Θ and refraction Θ is equivalent to the ratio of phase velocities in the two media, or equivalent to the opposite ratio of the indices of refraction (see Fig. 2.3 (a) and Eq. 2.4). ◦. ◦. 1. 2. (2.4) where c is the wave velocity in the respective medium and n is the refractive index (which is unitless) of the respective medium. When a longitudinal wave reaches the interface between two solid materials at an angle, some of the energy can cause particle movement in the transverse direction to start a shear wave [26]. This phenomenon is called mode conversion (see Fig. 2.3 (b)). Snell's Law holds true for shear waves as well as longitudinal waves and can be written down as follows: sinΘ1 c1 n2 = = sinΘ2 c2 n1. (2.5) where c and c stands for longitudinal and shear velocity respectively in the materials. 17 sinΘL2 sinΘS1 sinΘS2 sinΘL1 = = = cL1 cL2 cS1 cS2. L. S.

(18) 0S1. L. 01. 0L1. S1. L1. 0L1 1 2. 1 2 0L2. 02. 0S2. L2. S2. (a) Snell's law (b) Mode conversion Figure 2.3: Wave refraction and mode conversion on the interface between two solid objects.. Another important aspect of wave propagation is a diraction eect. This can be illustrated by Huygens principle which says that every point to which a luminous disturbance arrives, becomes a source of a spherical wave, and the sum of these secondary waves determines the form of the wave. When the propagating plane wave passes through an opening, the spherical elementary waves again form the plane wave in the centre zone of the opening. The edge eect adds to this. In the case of straight edge the elementary waves of the edge form a cylindrical wave whose axis is the edge. Superimposing the plane wave and edge wave produces a eld of maxima and minima of the sound pressure [27]. This eect is presented in Figure 2.4 where dots represent pressure maxima. Diraction is most pronounced when the object's size is comparable with the wavelength. The ratio of the radiator diameter d and the wavelength λ determines the eld spread and the number of minima and maxima. Diraction occurs with all types of waves, such as, acoustic waves, water waves and electromagnetic waves (light, radio, x-rays).. Plane wave. Screen. Figure 2.4: Diraction of the plane wave according to Huygens principle.. 18.

(19) 2.3.4 Near eld, far eld and beam spread. As mentioned earlier, diraction eect determines a position of the pressure maxima and minima. The eld between the transducer and the last pressure maximum is called the near-eld N ; the eld beyond it is the far-eld. The near-eld length is determined by the radiator's diameter d and the wavelength λ and is an important characteristic of the sound eld. The sound pressure on the axis of the transducer is given by the formula: π p p = p 2 sin (d/2) + z − z (2.6) λ where z is the distance on the axis from the center point of the disk and d is its diameter. 2. 0. 2. Figure 2.5: Pressure in water on the axis of the at transducer: d=12mm, f=10MHz.. The position of the pressure maxima can be calculated from the sinus function in Eq. 2.6. When solved, it is then possible to determine the position of the last pressure maximum which is equal to the near-eld length N . The relation for N is given by the formula: d −λ d N= ≈ (2.7) 4λ 4λ In large distances from the radiator it can be considered as a point source of the spherical wave. The further away from N , the approximation is more accurate. Therefore, in far-eld the beam spread angle is an important measure and it make sense to describe the sound eld by the angular characteristic. The relation between the pressure at the distance z and the angle γ is given by: J (X) (2.8) p = 2p X 2. 2. 1. z. 19. 2.

(20) where X = π(d/λ)sinγ. J (X) is the Bessel function of the rst kind, the values of which one can nd in mathematical tables, p is the pressure value at z where we have J (X)/(X) = 1 (2.9) With above formula o it is possible to determine the divergence angle, and also angles of sidelobes. 1. z. 1. Figure 2.6: Ultrasound beam pattern of polar transducer in water.. However, it is possible to reduce the calculations to the relation: sin(γ0 ) = 1.22(λ/d). where γ is the angle of divergence. Typically a -6dB angle (γ physical properties of the beam and it is described as::. −6dB. 0. sin(γ−6dB ) = 0.7(λ/d). (2.11). B = 2z tan(γ) ≈ 2zsin(γ). (2.12). The beamwidth B at the distance z can be calculated: 2.4. (2.10) ) is used due to. Methods of wave generation. There are many ways to generate an ultrasound wave. Every method can generate a dierent type of waves, and each method is used in dierent applications. The most common are piezoelectric transducers (PZT), but there also exist electro-magnetic acoustic transducers and laser transducers. 20.

(21) The acoustic wave is generated by the transducer, which transforms an electrical signal into acoustical form and vice versa. It can be compared to a loudspeaker and a microphone combined in one device. An input can be a sinusoidal signal resulting in narrowband continuous wave or wideband impulse signal. Ultrasound imaging with continuous wave is very dicult to perform due to the problems with distinguishing the wave that was sent from the reected one. The solution is using impulses that are sent with proper delays, so they do not overlap with the wave reected from scatterers. It is also possible to observe the transmitted wave on the opposite side of the sample. 2.4.1 Piezoelectric transducers. As mentioned earlier, piezoelectric transducers are the most common. A typical transducers scheme based on a piezoelectric element is shown in Figure 2.7 A piezoelectric crystal is placed between two electrodes. An electrical signal applied to the electrodes causes expending and contracting of the crystal. This phenomenon is used to generate an ultrasound wave. The piezoelectric crystal is protected by a ceramic wear plate from one side and is attached to a highly attenuating backing medium to reduce resonant oscillations from the other side. Connector. Case Backing. Piezoelectic material. Electrodes. Wear plate. Figure 2.7: Schematic view of the piezoelectric transducer for contact scanning.. Piezoelectric transducers can be divided into two categories: contact (Fig.2.7) and immersion transducer (Fig.2.8). Contact transducers are placed directly on the surface of the tested object. Gel, oil or water are used as a coupling layer for ecient energy transfer into the object. Immersion transducers are very similar to contact transducers. However, they are placed at a distance from the tested object and there is a water column between them as a couplant. The main dierence is that the ceramic wear plate is replaced by the quarter-wavelength matching layer on its surface (Fig.2.8(a)). The quarter-wavelength layer is specially designed to allow an ecient transfer of the acoustic energy into the water. Immersion transducers can also have an acoustic 21.

(22) lens (Fig.2.8(b)) to focus the acoustic eld in one point. The piezoelectric element can also be concave to eliminate the lens.. Quarter-wave plate. Acoustic lens. (a) Flat transducer (b) Focused transducer Figure 2.8: Immersion transducers.. Figure 2.9: Photography of the immersion piezoelectric transducers; source: http://ndtsystems.com/ 2.4.2 Electromagnetic acoustic transducer. Electromagnetic acoustic transducer (EMAT) uses a Lorenz force phenomenon to generate ultrasound wave in the material. Contrary to piezoelectric transducers, EMAT does not need a couplant or even any contact with the material. However, they can only be used with conductive materials [ ]. ?. Figure 2.10: Photography of the EMAT; source: http://www.sonemat.com/. 22.

(23) Dierent positions of magnets and coils in EMAT result in dierent types of waves. EMAT can generate radial polarized shear waves, plane polarized shear waves, surface waves, lamb waves and longitudinal waves. Systems based on EMAT can be used for weld inspection, railroad and wheel inspection or material characterization. However, the large size of the transducer itself excludes it from high resolution ultrasound imaging. 2.4.3 Laser transducers. Another means of generating ultrasound waves in materials is a laser. A short laser impulse is shot in the direction of the sample; the material is locally heated, a change in pressure due to temperature change causes the wave propagation in the material. Another method is to use the ablation phenomenon, that is removing part of the material from its surface by direct vaporization with skipping the liquid state. This method is not 100% non-destructive, since it causes local damage to the tested object, however, the changes on the surface are extremely small so they can be neglected. The main advantage of the laser ultrasound method is that it is a non-contact method and it also can be applied in high temperature processes. For example, a specially designed piezoelectric transducer can work at maximum 250 C, EMAT with a special cooling system can work up to 550-600 C, while the laser method allows working in temperatures even higher than 1000 C. The main disadvantage of that kind of wave generation is a very complex form of the signal. When laser hits the material, it generates longitudinal and transversal waves. Moreover, to record a received signal, very complicated and expensive interferometers are needed. The received signal ,due to its complexity, needs additional signal processing before it can be used in further analysis. ◦. ◦. ◦. 2.5. Imaging with ultrasonic arrays. For high resolution images focused transducers are usually used. Unfortunately, in this type of transducers the focal depth is xed, what reduces its usability to thin objects only, or it is necessary to perform a number of scans with the focal point placed on dierent depths. That is the reason why phased arrays have become very popular in the ultrasound imaging. Due to their properties they are much more exible in use than a single transducer. 23.

(24) Nowadays the structure of a phased array is based on composites. The piezoelectric composite is a combination of piezoelectric ceramic and non-piezoelectric polymer. Combined together, they create a new piezoelectric material. A wide number of composite structures have been studied for ultrasonic applications. In transducer the most common structure is where long thin PZT rods are held parallel to each other by a passive polymer (Fig. 2.11). There are dierent methods of producing piezocomposites. They allow enhancing the quantiable material properties, and give signicant advantages during the design of an ultrasound transducer. Composites can be exible, therefore, it is easy to form complex shapes for focusing the acoustic beam [28]. PZT rods. Polymer. Figure 2.11: Piezoelectric composite, consisting of thin PZT rods held by polymer. There are mainly two types of arrays: linear (1D) or two-dimensional (2D) as shown in Figure 2.12(a) and (b). However, there are also dierent congurations; for example, circular arrays, where transducers are of ring shape with dierent diameters which are placed concentrically, or ring arrays where transducers are placed on the perimeter of the circle.. (a) 1D (linear) array (b) 2D array Figure 2.12: Ultrasound phased arrays.. All of the methods of ultrasound imaging with phased arrays can be classied in two main groups: synthetic aperture imaging and physical array imaging. In synthetic aperture imaging takes place by successive data recording from dierent transducers in the array. Small transducers used in the array generate the wide beam what reduces resolution of the obtained image. However, while imaging with the physical array, it is possible to steer the ultrasound beam and also focus it 24.

(25) in dierent depths. The focal depth in phased arrays can be dynamically changed allowing fast full volume scanning of the object with focused beam. The most popular application of phased arrays is found in the medical ultrasonography. Arrays can also be classied by the working method. Firstly, there is a monostatic conguration (Fig.2.13(a)) popular in synthetic aperture, where one element transmits the ultrasound wave and then records the reected echo. Secondly, the bistatic conguration (Fig. 2.13(b)), where one element transmits the wave and the other one records it. This conguration is used in Time of Flight Diraction method ,where a wave is diracted at the crack tips , and time dierences between wave arrivals are measured to determine the aw size. Phased arrays can be classied as an example of a multistatic conguration (Fig.2.13(c)), where many elements are used to send the wave and also many are used to record the reections. Transmitter and receiver. (a) Monostatic. Receiver. Transmitter. Transmitters. (b) Bistatic Figure 2.13: Array imaging methods.. Receivers. (c) Multistatic. To generate a focused beam with the array, it is necessary to solve the beamforming problem of the ultrasound beam. The basic rule is to apply adequate time delays of the signal for every element in the array. Beamforming can be gained by analogue or digital circuits. An example of focusing with a phased array is shown in Figure 2.14 (b), where it is compared to an acoustic lens (Fig. 2.14 (a)). Focusing in phased array is achieved by generation of the wave in its element in dierent time instants. The beam generated by the phased array can also be steered to dierent angles Figs 2.14(c), (d). Therefore, it is possible to scan a relatively large object without a need to move the transducer; it can work similarly to a radar. The wave reception is similar to transmission; to every receiving element a specic delay is added, and then all signals are summed to emulate a single piezoelectric crystal. Additionally, a signal apodization is used to reduce side lobes and grating lobes, which could inuence the nal signal. 25.

(26) ............ Time. (a) Focused acoustic lens ............. ............. ............. ............. ............. ............. ............. .............. Time delay. (b) Focused array ............. ............. ............. ............. ............. ............. ............. .............. Time delay. (c) Steered array ............. ............. ............. ............. ............. ............. ............. .............. Time delay. (d) Steered and focused array Figure 2.14: Comparison of generating an ultrasound wave by an acoustic lens (a), a focused phased array (b), steered phased array (c), and steered and focused phased array(d). The disadvantage of the phased array is its discretization, both in time (delays) and space (element size and spacing between them). It can result in some unwanted eects in a received signal, for example, grating lobes mentioned above that occur when the spacing between elements is greater than a half wavelength. Despite this fact, this method is commonly used and highly rated. Minor disadvantages are compensated by its exibility and versatility. 26.

(27) 2.6. Presentation methods of ultrasound images.. The standard imaging method is a pulse-echo method, in which the same transducer acts as a transmitter and receiver. The transducer generates a wave into the material and then records the reected echo. Knowledge of the wave velocity in the material helps to localize the aw. Typical scheme of the 2D ultrasound imaging in immersion is presented in Figure 2.15. Ultrasound transducer. Water. Movement. Sent wave. Reflected wave Scatterer. Figure 2.15: Scheme for ultrasound imaging in immersion. Amplitude signals are called A-scans (Fig.2.16(a)). It is a basic visualization of the ultrasound wave, used in defectoscopy for aw detection and measurements of the velocity and/or attenuation of the wave. It can also be used for thickness measurements. This method is limited only to the depth detection at which the aw is present. To obtain information about aw's width one can perform a Bscan, which is a number of recorded A-scans placed side-by-side. This produces characteristic (hyperbolic) shape of the aw (Fig.2.16(b)). This shape is a result of the geometrical properties of the ultrasound wave; a more detailed description is presented in Chapter 3. To evaluate the aw position in all dimensions, it is necessary to perform so called C-scan (Fig.2.16(c)). To generate a C-scan, a specic range in each A-scan must be determined from which the maximum value is gathered and placed in proper x-y coordinates. A-, B- and C-scans are the most basic and common methods of ultrasound imaging, where no signal processing is needed. They help to visualize aws in the material; however, there are some limitations. For example, the user should be properly trained to interpret the results, which might be complicated, for example, by presence of many aws in the material. Additionally the resolution of the image is depth dependent, that means if the aw is deeper it, appears wider than it is in reality. This causes observation error. 27.

(28) A - Scan. B-Scan 76.8. 1. 77 77.2 77.4. Time [ s]. Normalized amplitude. 0.5. 0. -0.5. 77.6 77.8 78 78.2. -1. 78.4 76.8. 77. 77.2. 77.4. 77.6 77.8 Time [ s]. 78. 78.2. 78.4. 0. 2. 4. 6. (a) A-Scan. 8 10 12 X position [mm]. 14. 16. 18. 20. (b) B-Scan C-Scan. 0 1. Y position [mm]. 2 3 4 5 6 7 8 0. 2. 4. 6. 8 10 12 X position [mm]. 14. 16. 18. 20. (c) C-Scan Figure 2.16: Methods of ultrasound signal presentation: amplitude plot - A-Scan(a), slice image B-Scan (b), and maximum values along one dimension ("bird view") - C-Scan(c).. 28.

(29) Chapter 3 Synthetic Aperture Focusing Techniques. 3.1. Introduction. Development of synthetic aperture imaging in nondestructive testing began in early 1970s [9] and those research showed a possibility to improve NDT applications. The simplest version of synthetic aperture imaging in NDT is known as SAFT - Synthetic Aperture Focusing Technique. Since 1980s it has been widely used. Since that time many dierent approaches to this problem has been presented. SAFT is based on a post-process signal processing, it means that the raw data is recorded and then processed by a computer . First application were performed in time domain, but they were quickly followed by frequency domain implementation. 3.2. Current state of art. Nowadays implementation of SAFT in NDT is usually in frequency domain due to ecient computation. SAFT solutions in NDT are usually conversions of imaging methods used in radars, seismography or medical ultrasounds, those elds were very intensively developed and NDT stayed a little behind. Moreover, some assumptions needed in NDT are omitted in other eld, therefore it is sometimes hard to implement solutions directly from other elds to NDT. The most modern techniques used in NDT concentrate on array systems, and implementation of seismography algorithms. Array systems allow to perform numerous scans without moving a transducer. Additionally, its beamforming property is a high rated feature. Modern image reconstruction algorithms used with array allow to perform only two scans to achieve focused image after postprocessing [29]. 29.

(30) New algorithms in NDT, based on migration techniques rstly implemented in seismology for the imaging of the earth's interior, are developed. They can be implemented in both monostatic and multistatic case. More information can be found in section 3.4. 3.3. SAFT in time domain. The basic implementation of SAFT is performed in time domain. Using delay-andsum operation on recorded signal it is possible to focus ultrasound beam in every point in the material during post processing. To perform SAFT it is necessary to remember assumptions: • inspected object is isotropic and homogeneous • source of the ultrasound wave is treated as a point, therefore SAFT is only applicable in far eld. During generating of a B-scan, due to the beam spread and the main lobe width, a transducer records echoes of the point scatterer even when it is not placed directly above it. The wave has to travel dierent distance between the source and the reector in subsequent positions. It results in generating a hyperbola shape of the scatterer in the nal image. A scheme of this eect is presented in Figure 3.1. This eect is also responsible for the wider shape of the hyperbola if the scatterer is deeper. Beam width is strictly connected to the transducer parameters such as diameter and its center frequency. Information about beam spread of the at transducer was presented in section 2.3.4. Ultrasound transducer x. Point scatterer z,t. Figure 3.1: Image obtained during B-scan. 30.

(31) During post-process calculation and image reconstruction the SAFT algorithm takes those hyperbolas into account. In simple words it scans a recorded image and calculates hyperbola pattern in every pixel of the image as if there was a point scatterer. Then the SAFT compares the calculated pattern to the actual pixel surroundings to determine if there really is a scatterer. The geometry of the SAFT is presented in Fig. 3.2. Scanning x0 direction x n. x L-1. .... x. 2. 2. R = (xp- x n) + zp. z,t. (xp, zp). Figure 3.2: Scheme of the geometry of the synthetic aperture. To perform SAFT calculation rstly it is necessary to take under assumption the fact that the size of the transducer is innitesimal, and the medium is homogenous. In region of interests (ROI) there is only one point scatterer at position ~x = (x , z ). The transducer is placed in the position ~x = (x , 0) and the reected echo of the transmitted wave will arrive to the transducer at time: p. n. p. p. n. (3.1) where c is the speed of sound in the material. If the transmitted signal is g(t) then, in ideal case, the reected wave is the same original signal only delayed in time and scaled. Therefore the recorded echo is: 2 2q 2 tp (~xn ) = |~xn − ~xp | = | zp + (xn − xp )2 c c. (3.2) where σ is the backscattering coecient. Considering that there is a number of point scatterers in ROI the received signal in transducer position ~x becomes: X 2q s(t, x ) = σ g t− z + (x − x ) (3.3) c 2q 2 2 s(t, xn ) = σp g t − tp (~xn ) = σp g t − zp + (xp − xn ) c . p. n. n. 2 p. p. p. n. 2. p. The originally recorded scattered signal can be ltered with matched lter [30] before SAFT algorithm to compensate the phase shift introduced to the signal by the transducer, both at transition and reception. 31.

(32) The reconstructed image is then calculated as a sum over all n positions in the synthetic aperture: (3.4) To reduce sidelobes the apodization can be applied to the recorded signal. Then the nal reconstructed image will be dened as: q X 2 r(z , x ) = w s z + (x − x ) , x (3.5) c X 2q X 2 2 r(zp , xp ) = s tp (xn ), xn = s zp + (xp − xn ) , xn c n n. p. p. n. 2 p. p. n. 2. n. n. where w is the apodization weight. As mentioned before this method is limited only to one medium with constant sound velocity. It is also worth noting that time domain SAFT is best suited for transducers with very wide main lobe and the amplitude of the spherical wave varies very little with the aperture angle. n. 3.4. SAFT in frequency domain. Due to properties of the Fast Fourier Transform (FFT) the frequency domain synthetic aperture is less troublesome than its equivalent in time domain. It is more ecient and needs less calculations. What is more, is possible to implement physical properties of the transducer and also physics of the propagating wave including Snell's law in frequency domain SAFT (FD-SAFT). This fact enables use of SAFT in immersion tests and inspection of layered objects. What is impossible in time domain. The basic implementation of FD-SAFT employs property of the Fourier transform that says that time delay in time domain is equal to the phase shift in frequency domain. Due to that fact, all recorded data are transformed with use of two-dimensional Fourier transform to frequency domain, and all delays are calculated as phase shifts. Then the reconstructed image is obtained by performing inverse FFT. More advanced implementations are based on the wavenumber and the frequency (k, ω) [31]. This solution were rstly used in synthetic aperture radar (SAR) and synthetic aperture sonar (SAS) and then implemented into ultrasound tests. This algorithm takes under consideration nite size of the transducer, its physical aperture and wave propagation in the medium. In presented thesis another algorithm has been used. It is called Phase Shift Migration (PSM), and was developed at the Uppsala University. It is based on 32.

(33) migration techniques used in imaging of Earth's interior. The algorithm can be implemented in 2D (for line scans) or 3D version (for full volume scans). Both versions have been used in this thesis, however only 2D case will be shortly described. The 3D case is a straight forward implementation. This implementation allows to conduct inspection of layered objects and/or tests in immersion. However, this feature was not needed in experiments presented in Section 4.3. The main assumption of PSM is that scatterer is treated as a source of the ultrasound wave, that "explodes" at time t = 0. Then it needs to be adapted to the monostatic scenario when the wave is sent by a single transducer and then reected. Recorded signal at depth z = 0 is described as s(t, x, z = 0) for 2D case. This yields the Fourier domain data as S(ω, k , z = 0). Data in frequency domain is extrapolated to other depths with step ∆z, using repeated multiplication by the phase shift factor: α(ω, k , ∆z, c) = e (3.6) where ω is the angular frequency, k is a wave number in x direction and c is sound velocity at the current depth. An image line is extracted at each depth level with imaging condition t = 0. This can be calculated as: ZZ Im(x, z) = S(ω, k , z)e dk dω (3.7) which can be also presented as summation over ω, followed by inverse Fourier transform. More details about the algorithm can be found at [10]. x. −j∆z. x. q. 4ω 2 −kx2 c2. x. x. 33. jkx x. x.

(34) Chapter 4 Virtual transducer element method. 4.1. Introduction. The method of synthetic aperture, described in previous chapter, is well known in ultrasound nondestructive testing. Its advantages such as improving lateral resolution of the image and increasing signal-to-noise ratio resulted in its popularity. However its quality strongly depends on a acoustical eld generated by the transducer. First aspect is the lateral resolution. The fundamental relation for lateral resolution of synthetic aperture comes from radar d ∼ δ (4.1) = 2 where d is the transducer's diameter (antenna's length)[32] Another issue is a refraction eect on the boundary between water and solid objects during immersion tests. In section 3.4 a Phase Shift Migration algorithm has been introduced which can handle with this problem. The solution to both those problems can be a virtual transducer (VT) assumption sometimes also called virtual source (VS). Due to very small diameter of the virtual source and along with SAFT relation for resolution (Eq. 4.1) it can signicantly improve lateral resolution of the generated image. Another positive aspect of the VT assumption is a smaller size of the testing stand. Due to a fact that focal point is always closer to the transducer than far eld N . Therefore it is possible to place the transducer closer to the surface of the tested object. As distance between sample and the transducer increases, the SNR decreases. This is a reason why putting the transducer closer to the objects results with higher SNR. The reason behind using VT-SAFT was real life problem of high quality stainless steel purity evaluation. In case studied in this thesis, during the process of quality control of the nal product, typically a at transducer with a central frequency 34 3dB.

(35) is used. The tested object is placed inside the water tank and then the scan is performed in the near eld of the transducer. What is worth noting, no signal processing is used. Therefore the gathered results may suer from nonuniform resolution and the grain noise may inuences the SNR. It is possible with this method to detect aws with size approximately 0.3 mm. However, lateral resolution strongly depends on transducer diameter and. SAFT algorithm increases signal-to-noise ratio and unies the resolution. Additionally, applying VT allows to signicantly improve the lateral resolution. First solution was to use standard SAFT algorithm along with at transducer. However, due to transducer parameters (very long near eld N ) it did not brought satisfactory results. That is why a virtual transducer has been proposed along with SAFT-PSM algorithm to improve lateral resolution and increase signal-to-noise ratio. f = 10 M Hz. 4.2. Virtual transducer principles. VT technique is based on the assumption that focal point of a focused transducer (Fig. 4.1(a)) can be treated as a point-like source of a spherical ultrasonic wave with spread angle Θ. VT can also be created using phased array provided with an adequate beamforming [7] (cf Fig. 4.1(b)). Beam spread created by a spherically focused transducer, after the focal point is approximately an inverse of the beam narrowing before focal point and is dened by a simple geometrical relation d Θ = 2tan , (4.2) 2z where d is the diameter of the focused transducer or array, and z is the focal distance or curvature radius. Since perfect synthetic aperture imaging is possible only for a spherical wave emitted by a point source, the VT should be well suited for further post-processing with SAFT algorithm. As mentioned before, lateral resolution of the post-processed image with SAFT is depth independent (cf eq. 4.1) and it depends only on the transducer's diameter. Since virtual transducer has much smaller diameter than the real focused transducer used to create it, the reconstructed image should have better resolution than the image created with unfocused transducer with the same diameter as the focused one. Thus the main reason for using the VT technique combined with SAFT is its ability of creating small and strong source of ultrasound wave. Moreover, since focal 35 −1. f. f.

(36) D. zf. D. VT. O. O. (a) Focused trans- (b) Focused phased ducer with an array with a proper acoustic lens beamforming Figure 4.1: Methods of generating virtual transducer with focused transducer (a), and focused array(b).. point of a focused transducer or an array is always closer to the transducer than the respective near eld distance N , it can be placed closer to the sample surface, which facilitates test conditions. When using a focused transducer one must realize that not only geometrical properties of the transducer take part in forming an ultrasound beam. A large role in focusing plays also a diraction eect. A spherically curved circular transducer with geometry and theoretical beam pattern dened as shown in gure 4.2 generates the axial pressure given by the Equation 4.3 [27]. Geometrical beam spread. d. r. Divergence angle. h. r. z Geometrical focus. Figure 4.2: Theoretical beam pattern of the focused transducer.. (4.3) where and is curvature radius. The rst hyperbolic factor represents the inuence of the oscillators geometry and the other stands for the diraction. Figure 4.3 shows pressure eld calculated with help of Eq. 4.3 for transducer T1 from Table 4.1 in water. The eld is calculated for harmonic signal and one specic frequency. 36

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(49) Figure 4.3: Pressure on the axis of the focused transducer with parameters as for T1.. It is clearly visible that maximum pressure value is not at the distance r, as expected. Considering only geometrical conditions the pressure would have an innite value in that point. Diraction phenomenon causes slightly shift in maximum pressure therefore it has a nite value. For strongly focused transducers with relatively small r the geometrical focusing eect is the main one the opposite eect is when the oscillator is weakly focused. Due to that fact the focal distance can never be larger than the near-eld length. 4.3. Experiment. In reported experiments two stainless steel blocks with articial defects were tested to verify the VT assumption. Moreover, two blocks with natural inclusions were scanned to show usability of the method in real life application. All tests were performed in a water tank in the setup shown in Fig. 4.4.. VT. zf. Movement in X direction. Water. Figure 4.4: Virtual transducer testing setup.. First tested block had side drilled holes (SDH) as shown in Figure 4.5(a). SDH had dierent diameters and were placed at two depths. Those closer to the surface had diameters from d = 0.5 mm to d = 0.1 mm, all holes placed below them had the same diameters d = 3 mm. 37.

(50) Second tested block (Fig. 4.5(b)) had at bottom holes (FBH). All FBH had the same diameter d = 3 mm. They were drilled with dierent depth starting from l = 5 mm and ending at l = 35 mm with 10 mm step. 16.5. 16.5. 16.5. 16.5. 50. 17.5. 15. 16.5. 100. 5. 10. 10. 45. 10. (a) Block with side drilled holes. 20. 20. 20. 20. (b) Block with at bottom holes Figure 4.5: Stainless steel test blocks used for the immersion test.. Firstly two focused transducer were used in four immersion tests of presented blocks. One test fore each transducer and each test block. Secondly two immersion tests were performed with use of the focused phased array for test block with at bottomed holes. Last experiment was performed on two stainless steel blocks with natural inclusions using only the focused transducer. A computerized test system equipped with the ultrasonic board USPC3100LA from Socomate International, France, was used for data acquisition in the single transducer test. The USPC board was controlled by Labview graphic user interface. Its sampling frequency was set to 50 MHz and the spatial sampling step for B-scan acquisition was ∆x = 0.5 mm. For the SAFT post-processing the PSM algorithm was used with the spatial sampling step in z dimension ∆z = 0.1 mm. The value of sound velocity, needed for VT-SAFT processing was measured in the stainless steel test block and set to c = 5750m/s. For the phased array experiment FAAST system was used provided also by Socomate International. The FAAST system was controlled by Matlab graphic user 38.

(51) interface and toolbox. Sampling frequency, spatial sampling length and parameters of the SAFT algorithm were the same as those used for the single transducer test. Parameters of the focused transducers (referred later as transducer T1 and T2) and the phased array (referred later as array A1 and A2) used in the experiment are presented in Table 4.1 and 4.2. Beam patterns and sound pressure on the axis for transducers and for arrays, for wave propagating in water, are presented in gures 4.6-4.9. The X axes in pressure plots were normalized in respect to focal length of the corresponding transducer. Theoretical pressure was calculated with Eq. 4.3 for harmonic signal and one specic frequency. The realistic beam pattern and sound pressure were obtained by calculating a spatial impulse response (SIR). The SIR is found from Rayleigh integral [33]: Z δ(t − |r − r |/c) h(r, t) = α(Θ)dS (4.4) 2π|r − r | where S is an aperture mounted in an innite, rigid bae. The r donates the position of the eld point and r donates the position at the aperture. To obtain a beam pattern for a real transducer it is necessary to convolve SIR with a real signal emitted by the transducer (a wide band pulse). The analytical spatial impulse responses are available only for a few simple transducer geometries. Therefore a numerical method must be used for arbitrary transducer shape [34]. A method based on discretization of the Rayleigh integral formula was implemented in DREAM (Discrete REpresentation Array Modeling) toolbox for Matlab [35]. This toolbox was used for calculating presented sound elds. DREAM uses numerical methods for computing discrete spatial impulse response. 0. 0. S. 0. (a) Acoustic eld generated by the focused transducer Figure 4.6. 39.

(52) (b) Normalized acoustic pressure on axis of the focused transducer Figure 4.6: Patterns of the acoustic elds generated by the transducer T1 (a), and its normalized pressure along the axis (b).. (a) Acoustic eld generated by the focused transducer. (b) Normalized acoustic pressure on axis of the focused transducer Figure 4.7: Patterns of the acoustic elds generated by the transducer T2 (a), and its normalized pressure along the axis (b).. 40.

(53) (a) Acoustic eld generated by the focused phased array. (b) Normalized acoustic pressure on axis of the array Figure 4.8: Patterns of the acoustic elds generated by the array A1 (a), and its normalized pressure along the axis (b).. (a) Acoustic eld generated by the focused phased array Figure 4.9. 41.

(54) (b) Normalized acoustic pressure on axis of the array Figure 4.9: Patterns of the acoustic elds generated by the array A2 (a), and its normalized pressure along the axis (b).. In the gures 4.8(b) and 4.9(b), presenting normalized sound pressure on the axis of the radiator. There are visible two pressure peaks. One of them is a result of the geometrical curvature of the array, and the other one is a result of the beamforming. Table 4.1: Parameters of the focused transducers. [MHz] d [mm] z [mm] Θ [ ] T1 5 6.35 25.4 14.25 T2 5 25.4 190 7.65 f. [mm] K 1.75 0.75 3.10 0.35. ◦. f. b−6dB. Table 4.2: Parameters of the focused phased array. [MHz] n A1 3.5 32 A2 3.5 32 f. zf. [mm] r [mm] Θ [ ] 50 50 45.56 200 50 11.99 ◦. [mm] K 0.75 0.05 2.82 0.2. b−6dB. In Table 4.2 n denotes number of array elements and r is a radius of the geometrical curvature of the phased array in the -direction (array width). K denotes ratio of the focal distance to the near-eld length of an unfocused aperture, referred to as the z K= ; 0 < K ≤ 1. (4.5) N Focus factor K describes the degree of focusing; if its value is greater than 0.6 the transducer can be considered as weakly focused and when it is less then 0.3 it can be said that it is strongly focused [27]. Parameter b is a -6dB beam width at the focal point calculated from b = K· b , (4.6) y. focus factor. f. −6dB. −6dB. N. 42.

(55) where b is a -6dB beam width of the at transducer with the same diameter as the focused one at the end of its near eld N [27]. Beamwidth can be calculated as stated in section 2.3.4 Another step in testing usability of the VT was to use it for measurements of the blocks with natural inclusions and compare results to the original data gathered in the steel mill during the production process. N. 4.4. Results. Results of the rst test series performed using the single are presented in Fig 4.10 and 4.11. They were gathered for transducer T1 and T2 with parameters specied as in the Table 4.1 for the block with side drilled holes as shown in Fig. 4.5(a). B-scans before and after VT-SAFT processing are marked in gures as (a) and (b), respectively, while prole plots, calculated as the maximum magnitude value in each A-scan, are shown in gures marked as (c) and (d). Signal magnitude in Figure 4.10 and 4.11 is displayed in the range from 0 to -40dB in the logarithmic scale.. (a) Raw data. (b) Focused image Figure 4.10. 43.

(56) (c) Prole plot for small SDH. (d) Prole plot for large SDH Figure 4.10: Results for test block with side drilled holes and transducer T1. (a) Raw data Figure 4.11. 44.

(57) (b) Focused image. (c) Prole plot for small SDH. (d) Prole plot for large SDH Figure 4.11: Results for test block with side drilled holes and transducer T2. 45.

(58) Results for the transducer T1 shows improvement in lateral resolution, especially for larger side drilled holes which were placed deeper in the material. As for transducer T2 the improvement in lateral resolution was very small, both for small and for large SDH. A thing worth noticing for transducer T2 is an unusual shape of response from defects (Fig. 4.11(a)). It does not have the assumed hyperbola shape, but is more irregular. Due to that, SAFT does not process the data as expected, what results with no improvement in resolution after postprocessing. Numerical values concerning resolution for this test are placed in table 4.3. Table 4.3: -3dB resolution for test block 1 and transducer T1 (a), and transducer T2 (b). (a) Transducer T1 (b) Transducer T2. small SDH Hole Raw Foc 1 1.88 1.37 2 2.16 1.36 3 1.73 1.47 4 1.77 1.35 5 2.01 1.40. large SDH Raw Foc 3.76 1.61 3.40 1.46 3.79 1.54 3.38 1.52 . small SDH Hole Raw Foc 1 2.24 2.20 2 2.52 2.10 3 2.42 2.09 4 2.27 2.25 5 2.40 2.06. large SDH Raw Foc 3.12 2.79 3.45 2.79 3.32 2.66 3.06 2.42 . Second test series was performed on the block with at bottom holes (Fig. 4.5(b)). Results, obtained for transducer T1 and T2, presenting raw data, postprocessed image and prole plots are shown in Fig. 4.12 and 4.13.. (a) Raw data for focused transducer, z Figure 4.12. 46. f. = 25.4mm.

(59) (b) Focused image for focused transducer, z. f. = 25.4. (c) Prole plot comparison for focused transducer, z = 25.4 Figure 4.12: Imaging FBHs using transducer T1: raw data (a), post-processed image (b), comparison of prole plots (c). f. In tests using transducer T1, lateral resolution of the postprocessed image have been slightly improved. Unfortunately, for transducer T2 there was almost no improvement visible. In this case also, the representation of aws in the raw data has dierent shape than expected. Therefore, SAFT algorithm cannot improve the lateral resolution of the postprocessed image. What is more, it was shown. (a) Raw data for focused transducer, z Figure 4.13. f. 47. = 190mm.

(60) (b) Focused image for focused transducer, z. f. = 190. (c) Prole plot comparison for focused transducer, z = 190 Figure 4.13: Imaging FBHs using transducer T2: raw data (a), post-processed image (b), comparison of prole plots (c). f. in Figs 4.13(b) that after postprocessing some artifacts appeared near to the two holes closest to the surface and to the virtual source. Numerical values concerning resolution for this test are listed in Table 4.4(a). Another test series was performed with use of the phased array. Firstly it was focused by beamforming at depth z = 50 mm (array A1 in Table 4.2) (Fig. 4.14). f. (a) Raw data Figure 4.14. 48.

(61) (b) Focused image. (c) Prole plot comparison Figure 4.14: Imaging FBHs using phased array A1 focused at the depth zf = 50mm: raw data(a), postprocessed image (b), comparison of prole plots (c).. Signal magnitude in Figs 4.14(a) and (b) presenting B-scans before and after postprocessing is displayed in the range from 0 to -30dB in the logarithmic scale. From the comparison of raw and focused image in Figs 4.14(a) and (b) it is clearly visible that the resolution of the image have been improved after processing. Looking at the prole plot it can be seen that in raw data, response from the holes closest to the bottom are very weak and it is dicult to estimate their -3dB width. On the other hand focused image is clear and easy to evaluate. Values concerning resolution are presented in table 4.4(b). The last test in this experiment was performed with the same array but this time focused at the depth z = 200 mm (array A2 in Table 4.2). The respective results are presented in Figs 4.15(a), (b) and (c). Signal magnitude in Figs 4.15(a) and (b) is displayed in the range from 0 to -25dB in the logarithmic scale. In this case it can also be observed improvement in the resolution. However, due to the large distance between the transducer and the inspected block surface the recorded signal is weaker than in the previous experiments. Moreover some additional artifacts are present in the processed B-scan, probably due to the mismatch f. 49.

(62) between the geometrical and electronic focusing of the array A2. The region of interest is located far beyond the geometrical focus of the A2, which can result in some undesired artifacts. Values for this experiment resolution are listed in Table 4.4(c).. (a) Raw data. (b) Focused image. (c) Prole plot comparison Figure 4.15: Imaging FBHs using phased array A2 focused at the depth zf = 200mm: raw data(a), postprocessed image (b), comparison of prole plots (c).. It is worth noting, that in all presented cases a signal-to-noise ratio was improved. In this work SNR was expressed in terms of ratio of the maximum amplitudes in the B-scans. Comparing results from Table 4.3 and 4.4 it can bee seen, that for transducer T1 and arrays A1 and A2 the improvement in -3dB resolution is well pronounced. Images generated by VT-SAFT and transducer T2 did not show better resolution in comparison to raw data. A number of factors can contribute to that, for instance, 50.