TO NONDESTRUCTIVE TESTING NONDESTRUCTIVE TO APPLIED ACOUSTICS NONLINEAR ABSTRACT Sensitive nonlinear acoustic methods are suitable But it is in general difficult to limit the geometrical for material characterization. This thesis describes extent of low-frequency acoustic waves. A techni- NONLINEAR ACOUSTICS APPLIED three nonlinear acoustic methods that are proven que is presented that constrains the wave field to useful for detection of defects like cracks and de- a localized trapped mode so that damage can be TO NONDESTRUCTIVE TESTING laminations in solids. They offer the possibility to located. use relatively low frequencies which is advanta- geous because attenuation and diffraction effects Keywords: nonlinear acoustics, nondestructive tes- are smaller for low frequencies. Therefore large ting, activation density, slow dynamics, resonance and multi-layered complete objects can be investi- frequency, nonlinear wave modulation spectros- gated in about one second. copy, harmonic generation, trapped modes, open Sometimes the position of the damage is required. resonator, sweep rate. Kristian Haller Kristian Haller Blekinge Institute of Technology Licentiate Dissertation Series No. 2007:07 2007:07 ISSN 1650-2140 School of Engineering 2007:07 ISBN 978-91-7295-119-8 Nonlinear Acoustics Applied to NonDestructive Testing Kristian Haller Blekinge Institute of Technology Licentiate Dissertation Series No 2007:07 ISSN 1650-2140 ISBN 978-91-7295-119-8 Nonlinear Acoustics Applied to NonDestructive Testing Kristian Haller Department of Mechanical Engineering School of Engineering Blekinge Institute of Technology SWEDEN © 2007 Kristian Haller Department of Mechanical Engineering School of Engineering Publisher: Blekinge Institute of Technology Printed by Printfabriken, Karlskrona, Sweden 2007 ISBN 978-91-7295-119-8 Acknowledgements This work was carried out at the Department of Mechanical Engineering, Blekinge Institute of Technology, Karlskrona, Sweden. Firstly, I would like to thank my supervisor, Associate Professor Claes Hedberg, and my assistant supervisor, Professor Oleg Rudenko, for their support and guidance through- out this work. I would also like to thank my colleagues and friends at the department and especially Etienne Mfoumou for assistance in experimental setup and interest- ing discussions. I gratefully acknowledge the financial support from the Swedish Research Council, Vinnova and the Faculty Board of Blekinge Institute of Technol- ogy. Also the European Science Foundation programme NATEMIS (Nonlinear Acoustic Techniques for Micro Scale Damage Diagnostics) is acknowledged. Finally, I would like to express my deepest and dearest gratitude to my beloved family, my wife Malin and our wonderful children Anton, Gustav and Rebecca, for always being there. Karlskrona, August 2007 Kristian Haller iii iv Abstract Sensitive nonlinear acoustic methods are suitable for material characterization. This thesis describes three nonlinear acoustic methods that are proven useful for detection of defects like cracks and delaminations in solids. They offer the possibility to use relatively low frequencies which is advantageous because attenuation and diffraction effects are smaller for low frequencies. Therefore large and multi-layered complete objects can be investigated in about one second. Sometimes the position of the damage is required. But it is in general difficult to limit the geometrical extent of low-frequency acoustic waves. A technique is presented that constrains the wave field to a localized trapped mode so that damage can be located. Keywords: nonlinear acoustics, nondestructive testing, activation density, slow dynamics, resonance frequency, nonlinear wave modulation spectroscopy, harmonic generation, trapped modes, open resonator, sweep rate. v Thesis Disposition This thesis comprises an introduction and the following four appended papers: Paper A Haller, K.C.E, and Hedberg, C.M., Three Nonlinear NDT Techniques On Three Diverse Objects, Proc. 17th International Symposium on Nonlinear Acoustics, Penn State, USA (2006). Paper B Haller, K.C.E, and Hedberg, C.M., Frequency Sweep Ratio and Amplitude Influence on Nonlinear Acoustic Measurements. Proc. 9th Western Pacific Acoustic Conference, Seoul, Korea (2006). Paper C Hedberg, C.M., Haller, K.C.E., and Arnoldsson, S., Noncontact Nonlinear Acoustic Damage Localization in Plates, Part 1: Resonance Between Plates. Acta Acustica Acustica 93(1), 13-21 (2007). Paper D Hedberg, C.M., and Haller, K.C.E., Noncontact Nonlinear Acoustic Dam- age Localization in Plates, Part 2: Localized Resonance through Dynamically Trapped Modes. Manuscript is in review for publication in Acta-Acustica Acus- tica, (2007). vi The Author’s Contribution to the Papers The appended papers were prepared in collaboration with the co-authors. The present author’s contributions are as follows: Paper A Responsible for planning and writing the paper. Carried out the experimental investigations. Paper B Responsible for planning and writing the paper. Carried out the experimental investigations. Paper C Took part in writing and planning the paper. Responsible for the experimental investigations. Paper D Took part in writing and planning the paper. Carried out the experimental investigations. vii viii Contents 1 Introduction 1 1.1Background............................. 1 1.2Problemdescription........................ 2 1.3Aimandscope........................... 3 2 Nondestructive testing 5 2.1Nondestructivetestingmethods.................. 5 2.2Nonlinearacousticsfornondestructivetesting.......... 7 3 Acoustics 9 3.1Acoustics.............................. 9 3.2Theoryofnonlinearacoustic.................... 9 3.3Experimentaltechniquesinnonlinearacoustics......... 15 4 Results and discussion 21 5 Summary of papers 29 5.1PaperA............................... 29 5.2PaperB............................... 29 5.3PaperC............................... 30 5.4PaperD............................... 30 6 Conclusions 31 Bibliography 32 Paper A 36 Paper B 43 Paper C 54 Paper D 78 ix Chapter 1 Introduction 1.1 Background In the manufacturing companies of today the amount of material in the prod- ucts is being minimized due to cost reduction demands. This leads to higher stresses which in turn tends to shorten the products’ lifetime. Also, new ma- terials are being introduced, whose long time changes are not well known. Still, rupture and breakdown from erroneous production, overload and fatigue must be prevented. The demand to assemble defect free parts is very high and can, if not met, be dangerous for the user and detrimental to the company. Therefore the interest to detect damage early is steadily increasing. Dam- age can be monitored in many ways. Mostly it is done through use of some NonDestructive Testing (NDT) method [1, 2]. NonDestructive Testing means that the tested object is in the same condition after being examined as it was before - no damage has been added in the testing procedure. This is oppo- site to destructive testing where parts or assembled structures are tested until damage occurs, or are being damaged for subsequent internal examination. For example, the seat belt arrangement in road construction vehicles must be tested until permanent deformation has occurred [3]. Damage is in this thesis referring to a single crack, a collection of cracks, or delaminations. This damage can be caused for example by different types of fatigue loading, overload tension, bending, twisting or mechanical impacts. Alternatively, cracks can be naturally present, for example in materials like rocks, concrete, cast iron or in badly quenched metals. Two main areas are identified for nondestructive testing: manufacturing and maintenance. In a production line damage tests are often performed to ensure quality. It is commonly done through a visual inspection and based upon statistics where a certain number of parts are inspected to represent the population. In sta- 1 K. Haller: Nonlinear Acoustics Applied to NonDestructive Testing tistically based tests a fraction of the total number of parts are tested. In production line testing, the speed of testing and evaluation is of great impor- tance since the production rate usually is high. Maintenance testing is the other field. For example, airplane wings and ship hulls are tested at intervals - predefined by the number of hours of use. These tests make sense only when being nondestructive. Accessibility, the ability to reach the relevant parts, is an important factor which is often limited for complete products. Testing of complicated geome- tries or when only a single side of an object is accessible raise demands on the testing method. The use of advanced testing equipment sometimes require rig- orous safety regulations or complicated analyses, which means that a skilled operator is required. Acoustic nondestructive testing methods have been used for a long time, for example by tapping a crystal glass and intuitively assessing differences in res- onance frequency, harmonic generation and attenuation. Today the acoustic methods in general have been further developed using elec- tronic equipment. The nonlinear acoustic methods in particular are extremely useful in detecting damage, as nonlinearity in solids is directly coupled to im- perfections and discontinuities like cracks and delaminations. One detects the nonlinearity by measuring either the distortion of the acoustic signal, or the resonance frequency shift of a mode. Damage can be detected because it is the damage itself that distorts the wave. The