Guided Wave Inspection of Supported Pipe Locations Using Electromagnetic Acoustic Transducers

Transcription

1 Guided Wave Inspection of Supported Pipe Locations Using Electromagnetic Acoustic Transducers by Nicholas Andruschak A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Mechanical and Industrial Engineering University of Toronto Copyright by Nicholas Andruschak 2014

2 Guided Wave Inspection of Supported Pipe Locations Using Electromagnetic Acoustic Transducers Abstract Nicholas Andruschak Master of Applied Science Mechanical and Industrial Engineering University of Toronto 2014 The goal of the work in this thesis is to develop a rapid and reliable NDT system to detect hidden corrosion at pipe-support interfaces using Electromagnetic Acoustic Transducers (EMATs). Since there are often many support interfaces over a piping run, information is needed on the support interface conditions to optimize subsequent detailed inspections. In this work it is important to be able to isolate the effects produced from the support interface and the incident guided wave. To do this an optimum EMAT operating point is first selected, then the support interfaces and wall loss type defects are independently analyzed through experimentally validated finite element models. It is found that operating the SH1 plate wave mode near the knee of its dispersion curve gives a high sensitivity to wall loss type defects while experiencing a minimal effect from the support contact region. ii

3 Acknowledgments I would like to thank my supervisors, Dr. Anthony Sinclair and Dr. Tobin Filleter, for their patience and guidance over the past two years. Their attention to detail and ongoing assistance in moving the project forward was essential in getting me to where I am today. I would also like to thank Gabriel Turcan and Mequaltech Inc., Montreal for their support and encouragement over the past two years. Finally, to my mom and dad in Vancouver for always being there and providing me with their love, advice and support. iii

4 Table of Contents Acknowledgments... iii Table of Contents... iv List of Tables... viii List of Figures... ix Chapter 1 Introduction Introduction Introduction Objectives Thesis Outline... 2 Chapter 2 Background and Literature Review Background and Literature Review Overview of Corrosion in Industrial Piping Corrosion Cell Operational Trouble at Pipeline Supports Electromagnetic Acoustic Transducers Lorentz Force Mechanism Guided Wave Theory Introduction Guided Waves in Plates Dispersion Guided Waves in Pipes Specific NDT Configurations Periodic Permanent Magnet (PPM) EMAT s Spatial Bandwidth iv

5 2.5 Non-Destructive Testing Basics Configurations Measurement Techniques Pipe Support Rough Surface Contact Interfaces Introduction Contact Stiffness Contact Damping Finite Element Modelling Introduction FE Techniques For Modelling Wave Propagation Guided Wave Inspection at Supported Pipe Locations Axial Wave Propagation Circumferential Wave Propagation Chapter 3 EMAT Construction EMAT Design & Construction Introduction Proposed System Configuration Equipment Details Operating Point Details EMAT Construction PPM Array Construction Enclosure Construction Chapter 4 Wave Propagation FE Modelling Wave Propagation FE Modelling Introduction Brief Evaluation on Wave Propagation FE Techniques v

6 4.3 Infinite Domains Generation and Reception of Waveforms Generation Reception Discussion COMSOL 4.3b Implementation Chapter 5 Support Investigation Support Investigation Introduction FE Modelling of Contact Interfaces Experimental Verification Introduction Experimental Set-up Load Application Results Contact Damping Chapter 6 Defect Investigation Defect Investigation The Introduction FE Modelling of Wall Loss Defects Experimental Validation Analysis Verification of Model Sources of Error Conclusions Review of Thesis vi

7 7.2 Summary of Findings Future Work References vii

8 List of Tables Table Measured Defect Dimensions Table 6-2 Relative Amplitude and Delay Data for Experimental Test Specimens Table FE Results of Test Cases viii

9 List of Figures Figure Racetrack Coil (a) and Cross Section [4] (b)... 6 Figure 2-2 Free Plate Problem Geometry [8] Figure Group Velocity vs. Frequency-Thickness Product for Mild Steel Figure 2-4 Phase Velocity vs. Frequency-Thickness Product for Mild Steel Figure 2-5 Reference Coordinates For a Hollow Cylinder [9] Figure 2-6 PPM EMAT with Racetrack Coil Figure 2-7 PPM EMAT Top View [15] Figure 2-8 a) Pulse Echo, and b) Pitch-Catch [17] Figure 3-1 Side View of Inspection System Orientation Figure Innerspec PBH Instrument Figure Signal Conditioning Module (L) and Enclosed Tuning Module (R) Figure Dispersion Curve with Ideal Wavelength Excitation Line Figure 3-5 Dual Racetrack Coil Configuration with Active Coil Area Indication Figure PPM EMAT Bandwidth Figure Magnet Array (left) and Wrapped Flex Coil (right) Figure Schematic of PML Domain Layout Figure FFT of Hanning Windowed Input Figure 4-3 Normalized SH1 Voltage Waveform at Receiver Location Figure Schematic of FE Contact Interface Model Figure FE Model Received Signal Relative Amplitude vs. Interfacial Stiffness Figure FE Model Received Signal Delay Time vs. Interfacial Stiffness Figure Schematic of Setup Figure Picture of the Steel Bar Supported Clamp Region Figure Support Load Region Configuration ix

10 Figure Experimental Received Signal Relative Amplitude vs. Applied Load Figure Experimental Received Signal Time Delay vs. Applied Load Figure FE and Experimental Received Signal Relative Amplitude vs. Stiffness/Area Figure FE and Experimental Received Signal Delay vs. Stiffness/Area Figure FE Model Relative Amplitude vs. Imaginary Stiffness per unit area for 3 Support Figure FE Model Arrival Delay vs. Imaginary Stiffness per unit area for 3 Support Figure Schematic of defect cross section Figure Received Signal Amplitude vs. Defect Feature Length Figure Received Signal Arrival Time vs. Defect Feature Length Figure 6-4 Specimen #1 - FE results Verification Figure Specimen #2 - FE results Verification Figure Specimen #3 - FE results Verification Figure 6-7 Displacement Magnitude for Specimen #1 and #3 at a single receiver node x

11 1 Chapter 1 Introduction 1 Introduction 1.1 Introduction Corrosion is a significant issue in the petrochemical industry. Because piping and pipelines often run long distances to move products, they must be supported at regular intervals. This leads to a large number of pipe-support interfaces over a piping run. These interfaces between the supports and pipe are prime locations for corrosion to occur, as they can trap water and other contaminants and are inherently difficult to inspect as the corrosion is hidden underneath the support interface. Due to the large number of these supports, this gives rise to the need for a rapid and reliable nondestructive testing (NDT) technique to quickly identify severe corrosion at these interfaces. One such NDT technique features ultrasonic guided waves which have been shown to be effective in locating various types of corrosion defects in both plates and tubes. To generate these guided waves, Electromagnetic Acoustic Transducers (EMAT s) are increasingly used as they exhibit several advantages over conventional piezoelectric transducers, most importantly that limited surface preparation is required and specific wave modes of interest can be generated. Since a rapid inspection technique is being developed in this thesis, preparing surfaces at each support interface is not acceptable and extremely time consuming, so only EMAT s are considered. 1.2 Objectives The general objective of this thesis is to develop a medium range guided wave NDT system in order to rapidly and reliably detect hidden corrosion at pipe support interfaces. This objective inherently implies two things. The first is that the guided wave EMAT system should be sensitive to corrosion defects, so that a clear recognizable change in the signal occurs when corrosion is present. Secondly, the effects of the support on the received signal must be minimized so that the response of the received signal to the defect can be isolated, enabling the defect to be identified.

12 2 These objectives can further be broken down into smaller fundamental objectives needed to achieve a working EMAT inspection system. First a guided wave mode must be selected as well as a frequency and wavelength in order to determine the characteristics of the transducers. These parameters need to be selected in order to be sensitive to corrosion wall loss and be reasonably insensitive to support related effects. Once these parameters are determined the EMAT s can be designed and built. In NDT studies, it is important to be able to analytically model the wave propagation and interaction with specific geometrical features. This allows prediction of the effects of these features on wave propagation; it also enables optimization of the NDT system. Constructing models of both the effects of the support as well as a representative corrosion defect should enable an understanding of system performance as well as facilitate future iterations of this design. Furthermore, as with any engineering project, it is important to provide validation for any analytical model proposed. In this work the analytical models of the defect and support produce different effects on the waveform and thus these effects are validated independently. 1.3 Thesis Outline This thesis begins with background discussion in Chapter 2 on corrosion in industrial piping networks, EMAT s, guided wave theory for both plates and pipes, NDT inspection techniques and some existing pipe-support inspection methods. More general background on engineering topics such as Finite Element Modelling (FEM) and rough surface contact is covered as well. In Chapter 3 the considerations in constructing an EMAT such as selecting an operating point and other key parameters such as wavelength, frequency and specimen thickness are discussed. Also covered is how the selected operating point translates to the physical characteristics of a periodic permanent magnet (PPM) EMAT, such as the number of magnets in the PPM array as well as their thickness. In Chapter 4 a fundamental guided wave finite element model is developed for a uniform isotropic plate. Important aspects of this model are discussed such as simulating infinite domains using perfectly matched layers (PML s), techniques for implementation into the FE program COMSOL Multiphysics 4.3b, and techniques to approximate the generation and

13 3 reception of guided waves by a PPM EMAT. This model is developed with the intent that other geometrical features can be added later such as support interfaces and corrosion defects. In Chapter 5, the effects of the support interface are analyzed. First an analytical model is constructed by modifying the fundamental FE model developed in Chapter 4; then this model is verified through experiments approximating conditions at a pipe-support interface. The parameters used in the FE model and experiments are discussed as well. Also, the results and comparison between the analytic FE model and experiments are explored in this chapter. In Chapter 6, the effects of a representative wall thinning defect are considered. An FE model of a gradual wall-thinning type defect is developed as an addition to the model discussed in Chapter 4. The experimental verification procedure is then discussed including the manufacture of test specimens as well as the comparison of model results with measurements. In Chapter 7, a summary is provided on the findings of this thesis. Also additional topics that will be the subject of future work are detailed.

14 4 Chapter 2 Background and Literature Review 2 Background and Literature Review 2.1 Overview of Corrosion in Industrial Piping Corrosion occurs due to the reaction of metals with their surroundings. It causes costly and untimely failures of structures such as piping and pipelines. Support locations are difficult to inspect and often the only solution is a visual inspection. This usually involves lifting the pipe off the support to inspect the interface; this is time consuming and costly [1], particularly if the pipe is wrapped with insulation. It has been found by plant maintenance professionals that 80-85% of all corrosion on pipes takes place at pipe supports, with the remaining 15-20% occurring primarily at elbows [2] Corrosion Cell For corrosion to occur, a corrosion cell is required. A corrosion cell consists of an anode, cathode, electrolyte and a metallic pathway. At the anode, material is lost through oxidation and the valence state increases. The opposite is true at the cathode, which undergoes a reduction reaction and a decrease in valance state. The electrolyte is an electrically conductive solution that must be present to transmit positive ions from cathode to anode, while in the metallic pathway electrons flow from negative to positive, or from anode to cathode [3]. Further details on the types of corrosion cells and the corrosion process may be found in [3] Operational Trouble at Pipeline Supports At pipe supports, corrosion develops because the geometry of the support allows for water to be trapped and held in contact with the surface of the pipe. This causes the initial failure of the paint system, as often coatings are not designed for submersion service. The small amount of steel now exposed due to this initial failure begins to corrode. Once the general corrosion has spread and compromised most of the paint in the support region, crevice corrosion initiates. Crevice corrosion is driven by a differential aeration cell, caused by the different concentrations of oxygen at the cathode and anode or inside and outside the support [1]. For further details on crevice corrosion see [3].

15 5 2.2 Electromagnetic Acoustic Transducers Electromagnetic Acoustic Transducers (EMAT s) are devices that can generate and detect ultrasound in metals. Fundamentally EMAT s consist of a permanent or electro-magnet and a current-carrying coil. The permanent magnet is used to provide a static bias field while the coil is used to introduce dynamic magnetic fields in the skin depth of the inspection piece. Through the coupling of the electromagnetic and elastic fields in the surface skin, ultrasound is generated and received. Inherent in EMAT s and as summarized in [4], there are three primary coupling mechanisms: Lorentz forces, magnetostrictive forces and magnetization forces. Optimally designing an EMAT for a specific task requires an understanding of these coupling mechanisms. Additionally, by changing EMAT geometry such as orientations of the coil and magnets, many different guided wave modes can be excited [4]. Guided wave fundamentals will be discussed in Chapter 2.3. EMAT s have long been investigated for their potential in non-destructive testing as they have many benefits over conventional piezoelectric transducers. Some benefits are: they do not require contact with the test piece; they can direct ultrasonic waves at any direction into the test piece, and they can easily generate horizontally-polarized (SH) waves in plates or torsional waves in pipes. These SH waves are difficult to produce utilizing conventional piezoelectric transducers and are desired in certain non-destructive testing applications due to their unique characteristics [4] [5]. The main drawback of EMAT s is a relatively poor signal-to-noise ratio due to the inefficiency of the transduction mechanism. To compensate, techniques such as electrical impedance matching of system components, high amplification, band-pass filtering of the received signal, and excitation with a narrow tone burst are utilized [6]. In regards to this present work, only the Lorentz force transduction mechanism is considered. The magnetization coupling is not considered as it is much smaller in magnitude than both the Lorentz and magnetostrictive couplings, so it is often neglected in both Lorentz force and magnetostrictive based EMAT`s. Magnetostrictive based EMAT`s are not considered for this application as magnetostriction is highly non-linear and the magnetostriction curve (strain vs. magnetic field) is highly material dependant. Specifically, the curve shows hysteresis, dependence on the current stress state of the material, the exact history of magneto-mechanical

16 6 loading, the excitation frequency and the surface conditions. In comparison, the Lorentz force is linear and its magnitude is dependant primarily on the static bias field and coil excitation current, which are two parameters that can be controlled in practice [5]. The Lorentz force-based EMAT is described further in the next section Lorentz Force Mechanism Lorentz force EMAT s typically use a racetrack coil (Figure 2-1a) in order to provide unidirectional current in a localized area under a bias magnet. This is better visualized in Figure 2-1b where a cross sectional view of the highlighted area in Figure 2-1a is shown. a. b. Figure Racetrack Coil (a) and Cross Section [4] (b) In Figure 2-1b the x-direction is perpendicular to the current-carrying wire and parallel to the surface of the specimen. The z-direction is perpendicular to both the current carrying wire and the surface of the test specimen. A good summary of the previous research into the Lorentz force coupling mechanism in EMAT s is outlined in [4]. The Lorentz force is the cross product between magnetic flux density and eddy current within the skin depth of the specimen: = (1) The details for this derivation can be found in [4]. As the eddy current density decreases exponentially from the surface of the specimen, the skin depth δ is defined as the depth from the

17 7 surface to where the eddy current density has decreased to 1/e of its peak value. It can be approximated as: = 2 μ μ (2) Where ρ is the resistivity of the conductor, µ r is the relative permeability, µ 0 is the permeability of free space and ω is the angular frequency. The Lorentz force shown in (1) can be expressed as a function of the input current to the coil. This is explained in some depth in [4] and again summarized below. First the eddy current density from (1) is expressed as a function of the magnetic field H: = (3) Next, realizing that changes along the z-axis are typically much larger than changes along the x- axis the following approximate relation holds in our EMAT s: (4) Applying the right hand side of (3), the second term of (4) can be seen to be much smaller than the first, and is neglected in most situations. This means (1) can be written as: = (5) =

18 8 The alternating magnetic field generated from the coil H M x, is approximately linearly proportional to the input current I. For the specific arrangement shown in Figure 2-1 containing n wires of unidirectional current, this relation is: = 2 (6) Where δ is the skin depth and z is the position on the z-axis. Therefore if (5) and (6) are combined, the Lorentz force can be seen to be a product of the static magnetic field and the input current. 2.3 Guided Wave Theory Introduction Guided mechanical waves are stress waves that propagate within the boundaries of a structure. They are composed of a variety of different waves that reflect, mode convert and super-impose to produce guided wave packets that travel within structural boundaries [7]. In comparison, a bulk wave travels inside a material away from the boundaries, hence they travel in the bulk of the material. Both guided and bulk waves are governed by the same set of partial differential equations. The difference is that guided waves must satisfy some additional physical boundary conditions. These additional boundary conditions typically make an analytical solution difficult to find [8]. The Navier governing equation of motion for a linear elastic isotropic material is derived in many publications such as [8] [9] or [10] and shown below: +μ, +μ, + =, =1,2,3 (7) Where λ and µ are Lame s constants, ρ is the material density, is the displacement vector and is the force vector. Next using the Helmholtz decomposition as shown in [8] and [11], the vector u can be expressed as the gradient of a scalar potential (ϕ) plus the curl of a vector potential (H):

19 9 = +, =0 (8) Substituting (8) into (7) yields the following: +2 + =0 (9) Looking at the above equation, it is only satisfied when both terms in square brackets disappear. Therefore equating each term in brackets to zero, and re-arranging each expression yields the following: = 1 and = 1 (10) With c L and c T defined as: = +2 and = (11) The above equations shown in (10) are known as the wave equations Guided Waves in Plates The free plate is an approximation and not fully physically realizable, however it provides a good approximation to a number of practical configurations of engineering components, and is often used to illustrate important guided wave principles [10]. The free plate is considered homogenous and elastically isotropic with traction free surfaces. Therefore, it is governed by the equation of motion shown in (7), with traction free boundary conditions at ±d/2 (Figure 2-2).

20 10 y d/2 z -d/2 Figure 2-2 Free Plate Problem Geometry [8] Exact solutions to this problem can be obtained in different ways, but the displacement potential method using the Helmholtz decomposition shown in (8) is popular. Assuming the only rotations are about the x-axis (H y = H z =0) and assuming zero particle displacement in the x- direction (u x = 0), equation (10) reduces to: 1 (12) + = 1 (13) + = The solutions to the above equations (12) and (13) are referred to as Lamb waves. Lamb wave modes contain wave vector components both normal and parallel to the vertical particle motion. For particle motion in the z-direction (u z ), the solutions can be seen to be either symmetric (S) or anti-symmetric (A) about the z-axis (mid-plane of the plate) due to the presence of cosine and sine functions in their solutions respectively. The full derivation for these solutions can be found in [8]. Additionally, as summarized in [11] and adapted from [10], there is another family of guided waves present in the traction free plate medium, they are referred to as horizontally polarized shear (SH) wave modes. SH wave modes are the solutions to (12) and (13) when the scalar potential vanishes, meaning essentially only (13) is considered. Also the only particle motion is

21 11 assumed to occur in the x-direction (u y = u z = 0). Applying these considerations to (12) and (13) yields: 1 (14) = Additionally H x = 0 since u y = u z = 0. The solutions to (14) give the shear horizontal (SH) family of plate wave modes that will be the focus of this study. Further details on the solution procedure can be found in [10] or [12]. In [8] the final SH wave equation is expressed as: + 1 (15) = Dispersion Guided waves are dispersive as their phase velocities vary with frequency, meaning that they spread out over time and space when excited by a finite duration signal. This is observed as an increase in signal duration as a function of propagation distance, which reduces the time resolution of the pulse. There is also an accompanying decrease in signal amplitude since energy must be conserved. This reduces the sensitivity of the inspection system [13] [14]. For the case of shear horizontal waves in a traction free isotropic plate, a dispersion relation can be derived by considering the solutions to (15). The procedure is shown in [8], and the final dispersion relation is given below: = =0,1,2,3 (16) Where c p is the phase velocity defined in (17), c T is the shear speed defined in (11), d is the specimen thickness in Figure 2-2 and ω is the angular frequency. Dispersion relationships are usually visualized on a dispersion curve, where the group velocity or phase velocity relationships shown in (17) are plotted as a function of the frequency-thickness product [10]. This is shown in Figure 2-3 and Figure 2-4.

22 12 = = (17) = In (17), λ is the wavelength, f is the frequency, ω is the angular frequency and k is the wavenumber. One very important point on dispersion curves is that for non-zero n in (16), a cutoff frequency-thickness product exists which must be exceeded for a given wave mode to propagate. The cut-off frequency thickness product is obtained by solving (16) for the phase velocity and then setting the denominator to zero. This is demonstrated in [8], and the final result is shown below: = 2 (18) 4000 Group Velocity Dispersion Curves - SH W aves SH0 Group velocity (m/s) SH1 SH2 SH3 SH4 SH Frequency-Thickness (MHz-mm) Figure Group Velocity vs. Frequency-Thickness Product for Mild Steel

23 Phase Velocity Dispersion Curves - SH W aves SH1 SH2 SH3 SH4 SH5 Phase velocity (m/s) SH Frequency-Thickness (MHz-mm) Figure 2-4 Phase Velocity vs. Frequency-Thickness Product for Mild Steel Similarly for Lamb waves, dispersion relations can be derived using the solutions to (10). Again the details can be found in [8], but the end result is shown below: tan h tan h = 4 (19) With p and q defined as: = = (20) Where k is the wave number, h is half the plate thickness and n = 1 for symmetric modes and -1 for anti-symmetric modes. Similarly to SH waves, Lamb waves are often depicted on a dispersion curve showing the group or phase velocity plotted as a function of the product of frequency and thickness [8].

24 Guided Waves in Pipes Guided wave inspection of cylindrical shells such as piping or steel tubes is also prominent in industry. Techniques similar to the ones used to analyze guided wave propagation in the free plate can be used. To start, consider guided wave propagation in an infinitely long hollow cylinder, such as shown in Figure 2-5. Figure 2-5 Reference Coordinates For a Hollow Cylinder [9] The inner and outer surfaces of the infinitely long cylinder are considered traction free, and the equation of motion for an isotropic elastic medium shown in (7) can be applied. The solutions to this boundary value problem were first solved in [9]. Following the terminology employed in [8], the assumed particle displacements to satisfy the boundary value problem are of the form: = cos cos + (21) = sin cos + = cos sin + In these equations, U r, U θ and U z represent displacement amplitudes corresponding to Bessel or modified Bessel Functions. Selection criteria for the Bessel or modified Bessel functions are shown in [9] and [8] as well as other sources. Additionally n is the circumferential order and u r, u θ and u z represent displacements in the radial, circumferential and axial directions respectively.

25 15 Looking at (21), it can be seen that if n = 0, the resulting wave modes will be axisymmetric, as the θ dependence is removed. These resulting wave modes are referred to as the longitudinal and torsional modes respectively. For nonzero n, displacement is dependent on circumferential position. This gives rise to the flexural wave modes. To denote this, following the notation in [8], the longitudinal modes are numbered L(0,m), the torsional modes are numbered T(0,m), and the flexural modes are numbered F(n,m). In this notation n is still the circumferential order while m is the mode number. The frequency equation for n = 0 takes the form of a 6x6 matrix and is shown in [8]. This result is adapted from Demos Gazis [9], who completed much of the initial work in hollow cylindrical wave propagation. It is shown that if the modes are axisymmetric (n = 0), the frequency equation can be written as a product of sub-determinants: = =0 (22) Where the solutions of D 1 = 0 correspond to the longitudinal modes, and the solutions to D 2 = 0 correspond to the solutions of the torsional modes [9]. In terms of polarization, the longitudinal modes are polarized in the (r,z) plane, with no circumferential component. Conversely, torsional modes are polarized in the circumferential plane [8]. Relating these modes back to the plate wave modes, the longitudinal modes are analogous to the Lamb plate wave modes and the torsional wave modes are analogous to the SH wave modes. This is because for both torsional and SH plate waves, particles move perpendicularly to both the direction of wave propagation and the surface normal. Similarly, both Lamb and longitudinal waves contain particle motion perpendicular to SH and torsional modes. Flexural modes have displacement in both the radial and circumferential directions and are often avoided in applications due to complexity of the wave structure and non-symmetric characteristics as the displacements in all three dimensions are coupled [8] Specific NDT Configurations In comparison to conventional ultrasonic testing where probes must be scanned over the entire structure, guided wave testing allows an entire structure to be inspected from a single location

26 16 [13]. Dispersion curves are very important as they contain a large amount of information necessary to design a guided wave non-destructive test. For example, they show the phase and group velocities of the possible wave modes that exist at each frequency-thickness product. This aids in selecting an operating point to ensure that the possible wave mode group velocities adequately differ so there is separation in time between received pulses over the propagation distance [7]. Another fundamental concern when designing a guided wave non-destructive test is the structure of the selected wave. This includes the in-plane and out of plane particle displacements, as well as the variance of the stress distribution throughout the material thickness. This is important when trying to increase sensitivity to a specific defect or for increasing penetration power when inspecting under coatings [7]. For example, for the detection of a surface defect, a wave mode with maximum power and particle displacement on the outer surfaces would be desired [8]. To optimize for sensitivity or penetration power, often an iterative, experimental tuning process is used [7]. 2.4 Periodic Permanent Magnet (PPM) EMAT s To produce horizontally polarized shear waves utilizing the Lorentz force, a periodic permanent magnet (PPM) arrangement is used. A PPM EMAT consists of two rows of magnets of alternating polarity atop unidirectional current-carrying conductors. This configuration is shown in Figure 2-6, where the pattern using the front four magnets repeats to include all magnets in each row. S N N S z S N y x Coil Symmetry Line Figure 2-6 PPM EMAT with Racetrack Coil

27 17 As can be seen in Figure 2-7, using a racetrack coil causes each row of magnets to be atop unidirectional current flow. The alternating permanent magnet configuration in each row creates a periodic flux density in the surface of the test specimen equal to the acoustic wavelength of the wave. This causes a periodic Lorentz force with the same period as the magnet arrangement [4]. Also, since the current flow is in opposite directions on each side of the coil centerline, the polarity of each magnet across the centerline must also alternate for an additive Lorentz force. This can be seen in Figure 2-6 with an eight magnet per column PPM array and Figure 2-7 with a six magnet per column PPM array. Figure 2-7 PPM EMAT Top View [15] Also the curved section of the racetrack coil will have a minimal effect on the generated wave since there are no magnets located on top of this section of the coil Spatial Bandwidth The finite size of the PPM arrangement gives rise to a spatial bandwidth with the dominant wavelength corresponding to the period of the magnet arrangement. This term is defined as follows: Assume two columns of eight magnets as seen in Figure 2-6. The resulting Lorentz force projected onto a y-z plane (as orientated in Figure 2-6) is approximately sinusoidal over space. This has been shown multiple times in literature [6] [16]. This can also be inferred by looking at the Lorentz force relation and noting the alternating polarity of the magnets and the alternating current flow direction across the coil centerline (Figure 2-7) which cause alternating eddy current

28 18 polarizations. If a spatial Fast Fourier Transform (FFT) of this result is computed, a spatial bandwidth can be defined by looking at the magnitude function of the FFT. The peak of this magnitude function is the dominant wavelength. This process is shown in [16]. The spatial bandwidth can then be defined as the range between some fixed amplitude drop from the peak of the amplitude function, such as -6dB or -3dB. Alternatively, to define the spatial bandwidth, a spatial FFT of the magnetic field from one column of the PPM arrangement can be taken as an approximation in 2D. If a transmitter and receiver are both used then the spatial bandwidth narrows, as it is now the product of both the receiver and transmitter transfer functions [16]. 2.5 Non-Destructive Testing Basics Configurations Pulse-Echo Pulse-echo is an ultrasonic NDT configuration where one sensor is used as both the transmitter and receiver. An ultrasonic pulse is generated, and any reflections from a defect return to the probe. The location of the defects can be determined based on the time a pulse takes to return to the probe [17]. This is shown in Figure 2-8a Pitch-Catch In a pitch-catch configuration, both a transmitter and receiver probe is used. The receiver probe can either be located on the same side of the defect as the transmitter, or on the opposite side. In this thesis, only the orientation where the transmitter and receiver are on opposite sides of the defect is considered so that the through transmission effects can be studied. Therefore a wave is generated and it propagates through the corroded area and then is received on the opposite side. This is shown in Figure 2-8b. The corrosion geometry will cause different features to appear in the received waveform. Measurements of changes in group and phase velocity, mode conversion and transmission coefficients can be used to characterize the corrosion damage [17]. This will be further discussed in Section

29 IEEE Figure 2-8 a) Pulse Echo, and b) Pitch-Catch [17] Measurement Techniques There are three different guided wave characteristics that may typically be used in ultrasonic guided wave testing: wave cut-off mode phenomena, changes in group or phase velocity, and changes in transmission/reflection amplitudes. Each has their own advantages and disadvantages. Additionally, aside from time-of-flight velocity measurements which can only be used in locating a defect, each method offers unique information about a defect s geometry and size [18] Cut-Off Phenomena Many different ultrasonic guided wave modes may be present in a specimen at a single instant. For a specified specimen thickness, there exists a frequency below which each wave mode will not propagate. This is referred to as the mode s cut-off frequency; the one exception is the fundamental mode (which has no cut-off frequency). Therefore, by conducting a wide-band frequency sweep, it is possible to locate corrosion defects by examining received wave modes to determine which modes have propagated to the receiver, and which have not [18].

30 Group or Phase Velocity Changes Since guided wave modes are generally dispersive, a comparison between the group or phase velocities of the pulse in a corroded section of pipe and the group or phase velocity in a noncorroded zone can be made. Any differences may be correlated to the decrease in material thickness through the dispersion relation. This effect can be studied on a dispersion curve [18] Amplitude Changes The amplitudes of the reflected and transmitted wave modes can be used to determine corrosion depths assuming either calibration or reference data is available. The transmitted and reflected pulse amplitudes are dependent on defect geometry, as this determines the angle at which the incident wave contacts the defect. For example, a crack will typically have a steeper incident angle than a gradual thinning-type defect due to the sharpness of the transition between the damaged and undamaged portions of the test piece [18]. 2.6 Pipe Support Rough Surface Contact Interfaces Introduction When two surfaces are brought into contact (usually by some applied load) contact does not occur over the entire surface area of the interface unless the surfaces are perfectly smooth. As practical engineering surfaces are not perfectly smooth, contact is visualized as being between only a few asperities. These asperities that are in contact define the real contact area of the interface, which is often much less than the total apparent contact area. This is an extremely important topic in tribology, as the estimation of real contact area is necessary in predicting wear, contact stiffness, adhesion and electrical and thermal contact resistances [19] Contact Stiffness When two surfaces are pressed together by a normal force, both tangential and normal contact stiffness can be defined. In literature many different models have been proposed to estimate these contact stiffness parameters such as statistical methods or fractal geometries. A good summary of the different techniques is contained in [19], and is out of the scope of this thesis. One prominent model pursued in this study is the Greenwood-Williamson (G-W) model [20]. This model considers the contact between two rough surfaces as the contact between a rigid

31 21 plane surface and a second surface that is the combination of all the deformable features of the two rough surfaces. The asperities of the deformable surface are considered spherical, and a distribution of asperity heights is assumed. The asperity height distribution is usually taken as Gaussian or exponential [21]. Further details on the G-W theory can be found in [20] [22] [23]. A convenient expression [21] based on the G-W theorem for analyzing the contact interfaces of machined steel plate specimens is: 3 (23) Where K n is the normal contact stiffness, P is the pressure and σ s is the standard deviation of asperity summit heights. This is shown in [21] and is derived by assuming an exponential distribution of asperity heights in the G-W theorem to guarantee a closed form solution [24], then fitting a Gaussian distribution to this exponential distribution [25]. The linear expression for the contact stiffness based on the exponential distribution assumption is also shown in [26] and [27]. It should also be noted that these contact stiffness expressions are derived assuming no-slip. What is useful about the above relation is that the only statistical roughness parameter required is the standard deviation of summit heights (σ s ). As indicated in [21], σ s can approximately be taken to equal the average roughness (R a ), for which some tabulated values are given in literature for a variety of surfaces. Then to obtain the tangential contact stiffness the following relation is used [28]: = (24) Contact Damping Contact damping occurs due to micro-slip at the asperity level, which occurs prior to the static friction condition being exceeded. Once the static friction condition is exceeded, relative motion between two surfaces occurs. Fundamentally this micro-slip may be viewed as a fretting loop where the input energy at one surface is not equal to the energy transferred to the second surface

32 22 as some energy is dissipated. Thus an energy lost per cycle value is often calculated and used to quantify this fretting effect. To estimate contact damping, a convenient formulation is proposed in [29] and displayed below: = μ 5 6μ (25) Where η is the loss factor, F is the total normal load, T is the total tangential load and µ is the coefficient of friction between surfaces. This method is derived by considering the contact interface to have a fractal geometry. Fractals have been used in many studies to better understand different parameters of rough surface contact interfaces such as shown in [30] [31] [29] and [32]. Fractals are particularly useful as they are scale invariant, as expressions are formulated in terms of fractal dimension (D), fractal roughness (G) and scaling parameter (γ) and not the statistical parameters used in the G-W theorem that depend on sampling length and resolution. Although (25) is derived using fractals, it is not explicitly dependant on these fractal parameters as they cancel out. The tangential contact stiffness can also be derived using fractals, but due to a lack of sufficient tabulated data to calculate fractal parameters for a range of contact interfaces, this is not pursued in this thesis. 2.7 Finite Element Modelling Introduction Finite element analysis (FEA) is a numerical technique for finding approximate solutions to boundary value problems for differential equations. In this section discussion will be restricted to finite element techniques utilized in the modelling of guided waves. In this thesis the finite element software utilized is COMSOL 4.3b.

33 FE Techniques For Modelling Wave Propagation When configuring a wave propagation finite element (FE) simulation there are a few guidelines that should be followed to obtain an accurate solution. As discussed in [12], for wave propagation problems at least 7 elements are required per wavelength for acceptable accuracy. 7 (26) Where x is the element size and λ min is the minimum wavelength within the signal bandwidth. This quickly leads to large memory requirements and simulation times if the ratio between any structural dimension and wavelength is large. Often this makes 3D simulations impractical especially if the wave is to travel a distance of many wavelengths. In published literature, the two prominent solution methods to model guided wave propagation are time domain simulation and frequency domain simulation Time Domain Solution Procedures When setting up an FEA study in the time domain, it is important to note the difference between explicit and implicit time marching schemes. Implicit schemes are inherently stable, and dynamic equilibrium is satisfied at the end of the time step or at t+ t. Displacements are obtained by solving the equation of motion, meaning that at each time step the stiffness matrix must be inverted. This is what makes implicit schemes unconditionally stable and thus larger time steps may be used. Conversely, explicit schemes are conditionally stable and the time step must be smaller than some calculated critical time step. Dynamic equilibrium is enforced at the beginning of the time step (time t). As a consequence, this means that the stiffness matrix does not need to be inverted for the solution of displacements at t+ t, see [33], [34] and [11]. The advantage of an implicit scheme is that the time step can be chosen without respect to the critical time step requirement as required in an explicit scheme. This can be advantageous as acceptable accuracy may still be achieved in the solution while utilizing less resources. However in wave propagation problems, explicit schemes are preferred as the time step required for acceptable accuracy is often less than the critical time step, thus the explicit scheme is

34 24 advantageous as the stiffness matrix does not need to be inverted at each step. This makes explicit schemes much more efficient for these types of problems and thus implicit time schemes for wave propagation will no longer be discussed in this thesis [11] Frequency Domain Solution Procedures Another finite element method is modelling the wave propagation in the frequency domain. In this technique the waveguide is subjected to a continuous harmonic excitation and the steady state response at a single frequency is calculated. If this is done for all frequencies in the signal bandwidth then the time domain signal can be recovered by calculating the Inverse Fast Fourier Transform (IFFT). In the FE software used in this thesis (COMSOL 4.3b) solutions for the frequency domain equations are computed implicitly. To obtain an equivalent simulation time to an explicit time marching scheme, the frequency step should be calculated as: = 1 (27) Where N is the number of time steps in the time simulation and t is the time step. The frequency step must also satisfy Nyquist criteria. It is also important to note, that prior to performing the IFFT on the resulting complex nodal displacements to obtain the time dependant signal, appropriate zero padding should be performed. This is important because as shown in [35] it is essential to reproduce the correct shape of the time dependant waveform. 2.8 Guided Wave Inspection at Supported Pipe Locations Guided wave testing has made it possible to inspect a large section of a pipe from a single location by propagating waves axially down the pipe. This serves as a rapid inspection technique but suffers from difficulties due to signal attenuation over large propagation distances. Thus the T(0,1) mode is often used to try and mitigate signal losses as this mode exists at low frequencies where attenuation tends to be relatively low, features shearing action, and is easier to interpret as it is non-dispersive.

35 25 Another option is to propagate guided waves circumferentially around a pipe. Theoretically, since the circumferential distance is shorter than the axial propagation distance, higher frequencies and more dispersive wave modes can be used. This allows for smaller defects to be resolved. Additionally, the wave structure can be optimized to be sensitive to specific types of defects. However, the disadvantage is that the sensor configuration must be moved down the pipe axis for multiple measurements as the wave is not guided in the axial direction. This can cause inspections to take longer. The following two sections summarize previous literature in the areas of ultrasonic defect detection and characterization at supported sections of pipe Axial Wave Propagation Pulse-echo configurations have often been investigated for guided wave testing since only one access point is needed on the pipe; this is advantageous as often pipes are buried or otherwise difficult to access [36]. Since the T(0,1) guided wave mode is axisymmetric, it is only able to provide information on the axial position of a defect. An array of active elements such as piezoelectric transducers encircling a pipe may be used to generate the T(0,1) mode. A low frequency (8-25 khz) commercial system based on this principle is used in [37] to investigate the T(0,1) mode interaction with simple pipe supports to develop an inspection procedure. It is observed that when the support contact area becomes a significant fraction of the wavelength, the fundamental torsional mode exhibits a non-zero cutoff frequency [37]. Other investigations into support interactions with the T(0,1) mode include clamped supports [38] and welded supports [39]. In [38] an experimental investigation measured reflection amplitudes as a function of torque applied from the clamped support. It is concluded that higher torques lead to higher reflection amplitudes [38]. In [39] the reflection peak from a welded support is found to be delayed from its actual physical location. At low frequencies, this could lead to confusion, as the echo from the pipe support might overlap with reflections from defects located past the support.

36 Circumferential Wave Propagation Performing an inspection using waves that propagate circumferentially around a pipe is a slower inspection method as it requires some form of axial translation to inspect an entire length of pipe. Often the translation is accomplished either manually or by mounting the transducers on a rig that can travel down the pipe axis autonomously. For example, horizontally polarized waves, such as the SH0 and SH1 plate wave modes are investigated for the detection of just external [40] and both internal and external [41] corrosion of pipes. Both of these studies take advantage of the different properties of the SH0 and SH1 wave modes in order to locate and identify different types of defects. Although these studies are not specifically directed to the detection of corrosion around pipe supports, often the rigs the transducers are mounted on must pass over supported pipe sections. Deviating slightly from horizontally polarized guided wave inspection, propagating higher frequency Lamb waves circumferentially has been used to detect pinhole type defects at supports. As the wave propagation distance is shorter, higher frequencies and more dispersive wave modes may be used. This is important as pinhole defects are small, and the wave pulse must have a wavelength on the order of the dimension of the defect (or less) to get a wellresolved image of the damage. In [42] a piezo-crystal transducer in pulse echo mode is used to detect and size pitting type corrosion at the pipe-support interfaces. Recently, Higher Order Mode Cluster s (HOMC s) have been used to inspect pipe support interfaces. HOMC s are composed of many individual wave modes and occur at high frequencythickness products (15-35 MHz-mm) at which the group velocities of all observed modes are similar [43]. Thus all these modes form a cluster and may be seen to approximately propagate as a single non-dispersive envelope. Due to the relatively high frequencies and thus small wavelengths of the HOMC, this inspection method has been applied to detection of small pitting type defects in pipe support regions using circumferential propagation in [44], and axial wave propagation in [43].

37 27 Chapter 3 EMAT Construction 3 EMAT Design & Construction 3.1 Introduction In the design of an EMAT, the first step is determining an appropriate operating point based on knowledge of the probe configuration and desired operating characteristics. Coils and magnets are then purchased and combined to achieve this operating point using well known EMAT design steps to select parameters such as operating frequency and the number and width of the magnets. In this chapter, an outline of the chosen EMAT inspection arrangement is first discussed, followed by the selection of a suitable operating point. Finally a description of the EMAT design and construction procedure is given. 3.2 Proposed System Configuration As the goal of this thesis is the detection of corrosion at pipe-support interfaces using a medium range guided wave system, an orientation using a pitch-catch EMAT probe configuration orientated axially on a pipe is investigated (Figure 3-1). In this orientation the probes are translated circumferentially. Since waves are generated in both +/- y-directions in Figure 2-6 by an EMAT probe, the axial probe orientation simplifies the signal processing as the second wave generated by the EMAT will not interfere with the results since it propagates away from the inspection area. Additionally there is more flexibility with this arrangement as the two transducers are not restricted to being in-line along the pipe circumference. This allows the separation distance to be adjusted, as well as support geometries such as clamps or hangers to be evaluated without changing the system geometry.

38 28 Pipe Transmitter Receiver Wave Propagation Probe Translation Support Figure 3-1 Side View of Inspection System Orientation To simplify this situation with reasonable accuracy it is assumed that the effect of a guided wave propagating in a pipe axially over a short distance approximates that of a guided wave in a plate [45]. This approximation can be made if the ratio between wall thickness and the radius is small. This implies that the pipe curvature is neglected. The SH family of modes were pursued as they only contain particle motion in the surface plane of the specimen, normal to the direction of wave propagation. This means the particle motion will be normal to the direction of load application from the support, likely minimizing the effect on the received wave. All of our transducer development work is conducted for the inspection of a 3mm mild carbon steel plate, but the basic steps are also applicable to other specimen thicknesses. 3.3 Equipment Details The Temate PowerBox H (PBH) 1, handheld pulser and receiver is used due to its small footprint and ease of use in the field (Figure 3-2). 1 Innerspec Technologies, Lynchburg Virginia

39 29 Figure Innerspec PBH Instrument A convenient aspect of this instrument is that it is accompanied by a catalogue of stock coils that easily interface to the instrument through a signal conditioning module (Figure 3-3) that is mounted on the top. Figure Signal Conditioning Module (L) and Enclosed Tuning Module (R) The PBH generates high voltage tone-bursts with an adjustable frequency, repetition rate and cycles per tone-burst to power a transmitter EMAT. The pulser is capable of generating 1200V or 8kW peak power at a pulse repetition rate of up to 300 pulses per second. It also contains a low noise amplifier with a high gain that connects to a receiver EMAT. A pulse-echo configuration is also possible for cases where the same EMAT transmits and receives the ultrasonic signal (Chapter ).

40 30 The EMAT coils connect to the PBH through a signal conditioning module shown in Figure 3-3. This signal conditioning module interfaces with a tuning module designed to interface with a specific coil (Figure 3-3-right). It also contains the appropriate impedance matching network for the coil. Therefore all that is required when changing coils/transducers is swapping this detachable tuning module to the one that accompanies the new coil/transducer. 3.4 Operating Point Details The SH1 mode is selected for use in this inspection system since it is dispersive. As discussed in Chapter 2.3.3, dispersion causes changes in signal duration and amplitude due to geometrical changes in a waveguide. Thus in comparison to the non-dispersive SH0 mode, additional information through arrival time and phase changes can be obtained. From this logic, it follows then that operating in a more dispersive region of the dispersion curve (steeper slope) will yield larger group delay and phase delay changes due to any asymmetry (defect, contact interface, etc.) in the plate. For the gradual thinning type defect considered in this thesis, these dispersive characteristics are desired as they will indicate a change in specimen thickness. There is also a concern that any reflected energy due to the gradual nature of this thickness change may be small if using a non-dispersive mode such as SH0 [46], making SH0 mode ineffective in detecting the corrosion. For this study an operating point is selected at the knee of the SH1 dispersion curve (730 khz) for a 3 mm mild steel plate. This point is chosen to yield sufficient group delay changes for any geometrical change in the plate, as well as to be sufficiently far from the cut-off frequency. This will allow the SH1 mode to continue to propagate for a reasonable range of wall losses, allowing a range of measurements to be made prior to the frequency-thickness product decreasing to below the cut-off (Figure 2-3). Once an operating point is selected, a line is then drawn through this point intersecting the plot origin on a phase velocity dispersion curve. The slope of this line is equal to the dominant or peak wavelength referred to in Chapter This is shown in Figure 3-4 where the slope of the line is 6.6 mm. Also it is important to note that the dominant wavelength line intersects the SH0 wave mode line as well. This means it can also be generated with this wavelength at an excitation frequency equal to the frequency of the intersection point. This implies the need for a narrowband excitation so that only the desired mode is excited.

41 Phase Velocity Curves with Possible Wavelengths Phase velocity (m/s) SH0 Dominant Wavelength Line SH Frequency (khz) Figure Dispersion Curve with Ideal Wavelength Excitation Line 3.5 EMAT Construction PPM Array Construction To construct the PPM EMAT s for the selected wavelength of 6.6mm and frequency of 730 khz, the first step is to select a magnet thickness. Referring to Chapter 2.4, for a PPM EMAT, the wavelength is equal to double the magnet thickness. Standard magnet sizes are less expensive, so magnets mm (1/8 in) thick were selected as this is close to half the desired wavelength of 6.6 mm. Additionally the Innerspec LP-R kHz tuning module is selected as its recommended frequency range is khz which contains the optimum SH1 excitation frequency of 730 khz (Figure 3-4). The accompanying coil is the Innerspec PC-LA-R , which is dual wound in order to increase the amount of current under the static magnetic field. As mentioned in Chapter 3.3, it is also matched in terms of impedance to the selected tuning module. It also has approximately a one inch active area [47].

42 PPM Array Width 32 1in Active Area Coil #1 Upper Layer Current Out to Coil #2 Current In From Pulser Current Out to Pulser Coil #2 Lower Layer Current In From Coil #1 Figure 3-5 Dual Racetrack Coil Configuration with Active Coil Area Indication Eight magnets per column were used for the PPM array, based on the active area of the coil. Thus the magnet array is epoxied together as two columns of eight magnets (Figure 2-6), with a spacing between magnet rows of approximately mm to give an effective wavelength of 6.6 mm. It is noted that the final epoxied magnet array exceeds the active area of the coil slightly and encroaches onto the curved area of the racetrack shape coil (Figure 3-5). This encroachment is small, and any additional waves generated from the direction change of the induced eddy current and the encroached bias field will be orders of magnitude less than what is generated from the active portion, so the effect is ignored. The eight magnets used in one of the PPM array columns are used in defining the spatial bandwidth of this EMAT. As discussed in Chapter 2.4.1, the spatial bandwidth can roughly be calculated by taking the magnitude of the spatial FFT of the magnetic field distribution from a column of the PPM array. The field roughly takes the form of a windowed sinusoid, where the number of periods is equal to half the number of magnets in one column of the array and a period is equal to twice the magnet thickness. As discussed in Chapter 2.4.1, the -6dB amplitude drop

43 33 of the FFT magnitude profile is then used to define the spatial bandwidth. The -6dB spatial bandwidth is shown plotted on the dispersion curve in Figure 3-6 as red dashed lines. The spatial bandwidth shows all the wavelengths that can be generated at sufficient amplitude due to a specific PPM configuration. Therefore in Figure 3-6 all the lines that can be drawn that intersect the origin and any point on the SH1 dispersion curve between the red dashed lines falls within the spatial bandwidth of the transmitter-receiver pair. The frequencies encapsulated by the -6dB dashed red lines and the desired wave mode (in this case SH1) should be well separated in frequency from the intersection of the -6dB red dashed lines and other wave modes (in this case SH0). This is because if a sufficiently narrowband excitation is used (long time duration), it is possible to excite only the desired wave mode. Alternatively, if a sufficiently narrowband excitation is not possible, having sufficient frequency separation between the intersection of the -6dB lines and each mode allows for the undesirable wave modes (in this case SH0) to be filtered out after being generated since they will be contained in much different frequency bands. In Figure 3-6, the -6dB spatial bandwidth of the transmitter-receiver pair intersects the SH0 mode at approximately 410 khz to 560 KHz and the SH1 mode at 680 khz to 780 khz, with the majority of the energy occurring at the dominant wavelength (twice the magnet thickness). Therefore the intersection of the -6dB lines and each mode are well separated in frequency, meaning any SH0 component that is generated can be filtered out using a simple digital filtering algorithm in the received signal. It is important to note that often iteration is required between selecting a desired operating point and wavelength (Chapter 3.4) and the number of magnets (which controls the width of the spatial bandwidth) to achieve a final design.

44 Phase Velocity Curves with Spacial Bandwidth SH1 Phase velocity (m/s) Dominant Wavelength -6dB Spacial Bandwidth SH Frequency (khz) Enclosure Construction Figure PPM EMAT Bandwidth Aluminum enclosures are designed to hold the magnet array and coil in place. These enclosures are solid aluminum blocks with a section milled out of the bottom to allow the magnet array to be inserted (Figure 3-7 Left). The magnet array is then epoxied in place. The flexible coil is then wrapped around the base of the enclosure and bolted in place (Figure 3-7 Right). Figure Magnet Array (left) and Wrapped Flex Coil (right)

45 35 Chapter 4 Wave Propagation FE Modelling 4 Wave Propagation FE Modelling 4.1 Introduction Analytical wave models are effective in modelling guided wave propagation in uniform structures. However with the introduction of structural features such as defects or contact interfaces, discrete methods are needed. Finite element modelling (FEM) is an effective tool for modelling the interaction of guided waves with asymmetrical structural features [34]. The purpose of this section is to develop a fundamental model for guided wave propagation in a uniform plate. This is so that structural features such as a supported section or a thinned section can subsequently be added to determine their effect on the SH1 wave. It is also important that the FE model be efficient so parameter iteration studies can be carried out quickly and efficiently. Additionally the guided wave propagation modelling is done in two dimensions, meaning that the geometry is unchanging over the plate width. This is done to reduce the computational intensity of the model and for simplicity as the effects of the wave spreading around any geometrical features will be neglected. 4.2 Brief Evaluation on Wave Propagation FE Techniques As seen in Chapter 2.8, guided wave finite element modelling can be done either in the frequency domain or the time domain (explicit). In this thesis, frequency domain simulations are pursued as they are more efficient and align more closely with the stated objectives of the model. This is because time marching through the large number of time steps (thus solving for the large number of nodal displacements at each time step) is computationally intensive, and can be avoided with a frequency domain model. In the frequency domain model all that is required is a frequency sweep over the signal band of interest. Since EMAT s are narrowband, this amounts to a much shorter simulation time.

46 Infinite Domains One other significant advantage of frequency domain simulations is that there are a variety of well-understood ways to simulate an infinite domain. Simulating an infinite domain removes unwanted reflections that occur from the boundaries of a finite domain. Often in time domain simulations, the simulation domain must be enlarged so that any reflections are well separated from the signal of interest (Alternating Layers with Increasing Damping (ALID) may also be used, see [37] or [34] but will not be discussed further in this thesis). Lengthening the simulation domain is undesirable as it increases the number of elements and the time of simulation. One computationally efficient technique to simulate an infinite domain that is readily implementable in the frequency domain is using Perfectly Matched Layers or PML s. PML s are absorbing domains that may be added to the extremities of the simulation domain (Figure 4-1). PML Domain Simulation Domain (Plate) PML Domain Generate Wave Receive Wave Figure Schematic of PML Domain Layout At the boundary between the PML layer and the simulation domain, the impedance is perfectly matched, thus there should be no reflection of the incident wave. The damping in the PML domain then increases exponentially until the wave reaches the end of the PML domain where it reflects. By the time the wave re-enters the simulation domain it should be almost totally attenuated [34]. One of the challenges in implementing a PML is proper selection of the layer parameters. Parameters such as the absorption rate and length of the PML domain should be optimized to successfully damp out the wave, while minimally contributing to the computational intensity of the model. This is addressed by Mikael Drozdz in [34], where analytical relations for the various

47 37 layer parameters were devised. These relations are used in defining the PML parameters in this thesis. In keeping with the notation and technique in [34] but adapting for the form of the SH wave equation shown in (14), the change of axis variable z would be: 1+ (28) Where the z-direction is as shown in Figure 2-2 and α z is a variable that controls the level of dissipation in the PML. Alternatively (and also much simpler), this can be viewed as replacing all the partial derivatives with respect to the direction of propagation (z-direction) with the following expression (29) Where α z is defined as: = (30) Here p is the attenuation parameter and is taken to be at least 2 for continuity (details in [34]). The parameter A z used in defining α z is defined as: +1 = (31) Where k max is the maximum wavenumber, L or is the shortest wavelength and RC db is the acceptance criterion for the reflected wave. In [34] the acceptance criterion is taken to be a 99.99% reduction of the incident wave or -60dB. The length of the PML region is then defined as:

48 38 = (32) With k min being the minimum wavenumber. One word of caution on PML s is that evanescent waves are not correctly dealt with, so it is necessary that the PML be located a sufficient distance away from any feature that can produce evanescent waves, such as defects or excitation sources. This is because since evanescent waves decay on their own as a function of distance from the feature that produced them, so locating the PML sufficiently far away allows these waves to decay naturally prior to entering the PML. This distance is given as: = (33) Where k min is the smallest evanescent wavenumber in the signal bandwidth. 4.4 Generation and Reception of Waveforms In order to simulate the generation and reception of waves by the transmitter and receiver PPM EMAT s in a 2D wave propagation model, the following procedure is implemented Generation To simulate the generation of the SH wave, first the FFT of a Hanning windowed 5-cycle 730 khz excitation pulse is computed (Figure 4-2). This is analogous to the excitation current. The resulting frequency transform is then multiplied with a spatially dependent windowed sinusoidal function. This function is analogous to the PPM magnetic field. For the eight-magnets-percolumn PPM EMAT s described in Chapter 3.5.1, the magnetic field profile must have four complete cycles. As can be seen in Figure 4-2, the majority of the signal energy is between approximately 500 khz and 900 khz, so the frequency sweep in the FE model will be conducted in this frequency range.

49 39 1 FFT of 5-cycle Sinusoid Normalized Amplitude Frequency (Hz) x Reception Figure FFT of Hanning Windowed Input The reception process essentially works in the reverse of transmission. In the frequency domain the FE simulation yields a series of frequency-dependant nodal displacements. To convert this to a time dependant amplitude, the IFFT of the frequency dependant results must be computed to obtain time dependant nodal displacements. Then as shown in [48], the induced electric field can be calculated as: = (34) Where u is the particle velocity and B is the magnetic field density. Thus to simulate the reception process for an EMAT in this 2D model, the time dependent nodal displacements at a specified receiver location are now differentiated with respect to time. The resulting particle velocities are then multiplied with the same spatially dependent windowed sinusoidal waveform representing the magnetic field as used for the transmitter. The resulting signal is then integrated over the length of the receiving EMAT s active area. This is because all nodes that compose the representative spatially dependent windowed sinusoid contribute to the induced electric field. If

50 40 the voltage signal is required, multiplication by the appropriate constants will yield the time dependant voltage signal Discussion It is noted that as seen in [6], the PPM field is largest at the ends of the two columns of magnets and therefore not exactly in the shape of a rectangular windowed sinusoid. However since the results will always be taken relative to a simulation on a homogenous, unsupported and undamaged plate, this effect will be negligible. Specifically results will be computed as a relative amplitude and time delay relative to a homogenous plate simulation with the same reception and generation procedures. This should cancel any amplitude effects and any effects on the computation of the spatial bandwidth (Chapter 2.4.1) will be small. 4.5 COMSOL 4.3b Implementation Since the structural mechanics module in COMSOL 4.3b does not allow for boundary conditions on out-of-plane displacements, the Wave-equation Physics of the Mathematics PDE module is used and is governed by the following equation: + = (35) Where e a is labelled as the mass coefficient, c labelled as the diffusion coefficient and f is the source term. The techniques mentioned in Chapter 4.3 to implement the PML domains were adapted for implementation into the COMSOL PDE interface. The implementation is described below. First to formulate (35) as the standard SH wave equation shown in (15) but in the frequency domain, the e a coefficient is set to zero, f is set to ρω 2 u and c is set to isotropic and equal to ρcs 2, where ρ is the plate density and c s is the shear speed in steel. Next, to aid in the following discussions a parameter S z is defined as the coefficient on the right side of (29) and shown below [34]:

51 41 1 = 1+ (36) To implement the PML s using the allowable inputs (e a, c and f) to (35), the c parameter is now changed to anisotropic to implement the change of variable in the direction of wave propagation shown in (29), and the original value of the f parameter (ρω 2 u) is divided by S z. The final result is shown below: = (37) 0 = 0 Thus as shown in Figure 4-1 the FE model consists of a propagation domain with a PML domain attached on each end. It is important that S z be equal to 1 in the propagation domain, so the governing equation in (37) will simplify to (35), as the PML should have no effect in this domain. Then in the PML domains S z varies according to the relationships given in Chapter 4.3. This is implemented through a piece-wise function. A simulation result is shown in Figure 4-3 for the case of a 30 cm distance between the generation and reception locations for a 3mm thick steel sheet. Since this result is computed on an isotropic homogeneous plate, the maximum amplitude of this result is used to normalize future simulations and the arrival time is used to compute the pulse arrival delay of future simulations. The result is displayed in Figure 4-3 normalized by its peak amplitude. In this simulation, the input excitation is shown in Figure 4-2 and the windowed sinusoidal spatial distribution of the magnetic field has a period of 6.6 mm. The generation and reception processes of the SH1 waveform were as discussed in Chapter and Chapter respectively. Parameters used for carbon steel were a shear speed of 3230 m/s and density of 7800 kg/m 3. The required wavelength and wavenumber values for determining the PML domain

52 42 parameters were calculated using the input frequency band of 500kHz to 900kHz and the dispersion curves of Figure 2-3 and Figure 2-4. Normalized SH1 Waveform 30cm from Excitation Normalized Amplitude Time (s) x 10-4 Figure 4-3 Normalized SH1 Voltage Waveform at Receiver Location To verify the presence of the SH1 mode, the group velocity of this received waveform is calculated by computing the arrival time of the waveform in Figure 4-3 (30 cm transducer separation), then computing the arrival time of a similar simulation but with a transducer separation of 25cm. The group velocity is then computed as the difference in separation distance divided by the difference in arrival time. The resulting group velocity is approximately 2172 m/s which compares well to the group velocity shown on the dispersion curve in Figure 2-3 for a 730 khz excitation (2180 m/s). The small discrepancy is likely due to the approximations made in the generation and reception mechanisms in the FE model. Overall, in this chapter the generation, propagation and reception of the SH1 wave mode on a homogeneous isotropic plate is discussed. This is done to compute a baseline result for comparison in subsequent chapters where geometrical effects such as support interfaces and corrosion type defects are introduced to the FE model.

53 43 5 Support Investigation 5.1 Introduction Chapter 5 Support Investigation The purpose of this chapter is to determine the effect of a contact interface on the SH1 mode of propagation. To do this a finite element model is developed. The finite element model is implemented as a modification to the foundational model developed in Chapter 4. The FE model is then experimentally validated within a practical load range by comparing the experimental results to the theoretical FE results. 5.2 FE Modelling of Contact Interfaces To construct the FE model, a similar approach is adopted to that used in [49] for Lamb waves, but adapted for SH wave propagation. As mentioned in Chapter 2.6, the contact interface can be represented by an interfacial stiffness parameter connecting two surfaces. The modelling of the interfacial stiffness is implemented as shown in [49] as a displacement discontinuity between two domains, with the boundary force per unit area on the plate and support surface equal to: = (38) = Where σ s and σ p are the force per unit area on the support and plate domains respectively, K T is the stiffness parameter (N/m 3 ) and u s and u p are the displacements of the support and plate domain nodes respectively. Thus an additional domain is introduced into the FE model developed in Chapter 4 to represent the steel support, and is shown in Figure 5-1. The boundary interface between the plate and support is then configured using (38) with the interfacial stiffness parameter assumed to be real-valued (no damping/losses). This interfacial stiffness parameter is treated as the dependant variable in the study, and a range of values is assessed using a frequency sweep over the signal bandwidth at a given support length. The support length is defined as the length of the contact boundary in 2D between the support and plate domains (shown in red in Figure 5-1). All other parameters were the same as indicated in Chapter 4.

54 44 PML Domain Support Domain PML Domain Simulation Domain (Plate) Elastic Boundary Figure Schematic of FE Contact Interface Model The amplitude of the received signal is calculated as the peak of the Hilbert transform magnitude function, while the arrival time is calculated as the time at which this peak value occurs. Then as mentioned in Chapter 4, all results in this thesis are reported relative to the homogeneous plate base case computed in Chapter 4.5. Thus the delay time is the arrival time difference between a given support simulation case and the homogeneous plate case, and the relative amplitude is the amplitude of the support simulation case divided by the peak amplitude of the homogeneous case. The results of varying the contact stiffness at a given support length on the amplitude and arrival time of the received SH1 signal are shown in Figure 5-2 and Figure 5-3 respectively. In these figures, the data points are connected with dashed lines to better emphasize the trend between support lengths. Considering the formulations (23) and (24), the effect of varying the stiffness for a given support length is equivalent to varying the applied load at this support length. Also, the effect of changing the support length between runs is equivalent to changing the nominal area of contact. The reason we approached the simulations with this methodology is that it allows for the effect of increasing the stiffness and the effect of applying a given stiffness over a larger portion of the wave propagation path to be independently analyzed.

55 Relative Amplitude vs. Stiffness per Unit Area 1 Relative Amplitude " Support 4" Support 6" Support Stiffness per unit area (N/m 3 ) Figure FE Model Received Signal Relative Amplitude vs. Interfacial Stiffness 6 x 10-6 Delay vs. Stiffness per Unit Area 5 4 Delay (s) " Support 4" Support 6" Support Stiffness per unit area (N/m 3 ) Figure FE Model Received Signal Delay Time vs. Interfacial Stiffness

56 46 As can be seen from the results, increasing the stiffness per unit area has a minimal effect on the amplitude and delay of the received wave until a critical value is reached, which we will refer to as the knee. After this knee is exceeded, there are large relative amplitude decreases and delay time increases. Another observation is that the support length has a minimal effect on the knee location, as changes in amplitude and arrival time start occurring at approximately the same stiffness per unit area regardless of the support length. However once the stiffness per unit area exceeds this knee value, increasing the support length will increase both the slope of the amplitude drop and the slope of delay increase. Based on these observations, it can be seen that the main factor affecting the SH1 propagation is the stiffness per unit area parameter and not the length of the support. An analogous conclusion is reached in [37] regarding the change of the transition point of the reflection coefficient with support length. 5.3 Experimental Verification Introduction The purpose of this section is to experimentally verify the results of the FE simulation in Chapter 5.2. To do this an experimental arrangement is constructed to represent a contact interface between a plate and a steel bar. As indicated in Chapter 1, since this situation is supposed to be a simplified representation of a pipe in contact with a support, the experimental load range considered is kept within a range that would be expected on a pipe support. As a starting point for this range we used the ASME guidelines for support spacing and then calculated what the load would be due to a section of this length. Using the guidelines for a ¼ thick empty pipe it is found the expected load would be of the order of 1000N. For experimental purposes a range of 0 to approximately 6000N is used in order to account for extreme cases as well as obtain a better understanding of the situation Experimental Set-up The experiments were conducted on a 3mm thick, m wide and 1.22 m long mild carbon steel plate. To minimize reflections from the plate edges as well as properly support the plate, the plate is supported at the edges by pieces of foam. The central region or load region as seen in Figure 5-4 consists of the plate resting on a steel bar running the width of the plate (into the page). A photograph of this arrangement can be seen in Figure 5-5. This steel bar is then raised

57 47 and rests on steel blocks to allow for the clamps to fit underneath the arrangement. The location of the clamps can be seen in the cross section of the load region in Figure 5-6. Since the plate is relatively thin (3mm), this support structure must be rigid to mitigate any effects due to plate bending when clamped on the received waveform. The support is then centered between the transmitter and receiver which are separated by 30cm. Transmitter Wood Receiver Plate Steel block Steel Bar Load Region Foam Figure Schematic of Setup Figure Picture of the Steel Bar Supported Clamp Region