Feasibility of using nonlinear ultrasonics for detection of debonding in bone cement-metal structures

Transcription

1 DRAFT Draft. 005; 00: 6 Feasibility of using nonlinear ultrasonics for detection of debonding in bone cement-metal structures G. Rus, N. Saffari and R. Gallego Dept. Structural Mechanics, University of Granada, Politécnico de Fuentenueva, 807 Granada, Spain Dept. Mechanical Engineering, University College London, Torrington Place, London WCE 7JE, UK SUMMARY The results presented here demonstrate the feasibility of using the signature of harmonics contained in transmitted ultrasonic signals versus excitation energy to evaluate damage at an interface, by means of standard laboratory equipment. Positive identification of a fatigue defect has been achieved at the interface between PMMA (polymethylmetacrylate) and steel, commonly used in orthopaedic implants. The use of ultrasonic excitation energy and frequency spectrum analysis is proposed as an alternative to the two common methods for the use of material nonlinearity for the investigation of defects as reported in the literature: the direct appearance of second harmonics, and the excitation of side bands around the main excitation frequency due to the interaction with a second lower frequency excitation. Here, the amplitude of harmonics due to the increasing constitutive nonlinearity of the interface with the excitation energy is studied in a transmission setup, both in immersion and in gel-coupled contact. A high intensity ultrasonic beam is transmitted generating a nonlinear wave. This beam is transmitted through different areas of the sample, and analysed in order to compare the relative amplitudes of the various harmonics. A numerical FEM plastic and viscoelastic model of the specimen has been Correspondence to: Guillermo Rus Carlborg Department of Structural Mechanics, University of Granada Politécnico de Fuentenueva, 807 Granada, Spain grus@ugr.es Grant sponsor: ; Grant number: Revised 8 August 005 Received 8 August 005

2 G. RUS, N. SAFFARI AND R. GALLEGO implemented which successfully replicates the experimental results at a qualitative level. key words: ultrasonics; inverse problem; nonlinear ultrasonics; quantitative nondestructuve testing (QNDE); orthopaedic implant; debonding. INTRODUCTION Two main uses of the material nonlinearity for the investigation of defects with ultrasonics appear in the literature. One is the direct appearance of second harmonics due to the nonlinear nature of the material, and the second is the excitation of side bands around the main excited frequency due to the interaction of the nonlinear defect with a second lower frequency excitation. Among the first approach, Jhang et al.[0] explains theoretically the appearance of the second harmonic due to the nonlinearity of the material, and correlates that harmonic with the material degradation. Calle et al.[6] proposes the use of ultrasound-stimulated vibroacoustography (nonlinear phenomena induced by ultrasonics) to extend sonoelasticity imaging to medical science. Vanlandouit et al.[8] test the odd order nonlinear harmonics to determine the fatigue crack evolution in a beam. Delsanto et al.[8, 7] develop a finite difference one-dimensional model of a sample with a nonclassical nonlinear adherent joint and successfully compare the transmission of ultrasonic waves to the experiment. Kawashima et al.[] prepares an FEM model of the nonlinear crack behavior to show that the appearance of a second harmonic in Rayleigh waves is a good method for determination of minute cracks. The second approach is used by Abeele et al.[], who compare two methods recently

3 NONLINEAR ULTRASONICS FOR DETECTION OF BONE-METAL DEBONDING 3 developed for automotive industry, SIMONRAS and NWMS, which compare nonlinear characteristics of the recorded acoustic signal. Donskoy et al.[9] simultaneously describes those methods providing the theoretical explanation of the modulation of the ultrasonic signal by the nonlinearity in the bond and a source of low frequency excitation. Rokhlin et al.[4] effectively use the modulation by frequency shift for the evaluation of imperfect adhesive bonds in an experiment. Solodov et al.[5, 6] thoroughly analyzes the low and high frequency effect of nonclassical nonlinearity in the crack contact, which is concerned with the lack of stiffness symmetry across the interface. Ballad et al.[3] observe that very high harmonics are modulated and are extremely useful for their registration as acoustic emission with air-coupled transducers. To study the theoretical analysis of the crack nonlinearity, Baltazar et al.[4] show that the interfacial stiffness constants in a crack sufficiently characterize them, and the ratio of normal and tangential stiffness can be assumed to be constant. These constants are recovered by ultrasonic spectroscopy. Pecorari[3] develops a nonlinear spring model to obtain the quasistatic reflection and transmission coefficients of an ultrasonic wave through a crack. L. Bjørnø [5] gives an overview of the state of the art in nonlinear ultrasound mechanics in fluids. M. Averkiou [] solves numerically the KZK equation of fluids with diffraction, thermoviscous dissipation and quadratic nonlinearity to show the better directivity of second harmonic beams in application to tissue harmonic ultrasonic imaging (THI). Lewin [] reviews in a very recent paper the emerging importance of harmonic imaging as well as sonoelasticity imaging in medical ultrasound.

4 4 G. RUS, N. SAFFARI AND R. GALLEGO. METHODOLOGY The studied sample simulates a portion of a orthopedic implant composed by a layer of PMMA cement and a substrate of steel. The motivation of the study is to investigate and monitor the fatigue of the cement that is causing a growing number of failures in hip implants and subsequent medical interventions. This sample has been fatigued by cyclic loading and unloading while monitored by acoustic emission, as shown in Fig.... Experiment The harmonic attenuation or appearance due to the nonlinear characteristics of the faulty bonding are studied in a transmission setup, both in gel-coupled contact as well as in immersion, as outlined in Fig. 3. An ultrasonic beam of high energy is transmitted through the media generating thus a nonlinear wave. This beam is transmitted through different areas of the sample and then analyzed in order to compare the relative amplitudes of the various harmonics. This motivates the choice of some scanning areas on the sample as depicted in Fig. 4. In order to excite higher energies and enter the nonlinear regime of some materials, a lower frequency (500 MHz) transducer has been used as a transmitter. The transversal resolution, dependent on the wavelength, has been compromised by the energy since at this stage we are interested in detecting the presence of nonlinear sources appearing from this excitation rather than their spatial location, which is assumed to be at the interface. The information of the electronic setup is detailed in Table I. In order to clearly isolate the arising harmonics, a narrow spectrum signal is transmitted using a sine burst. This implies that the transversal resolution has been compromised even

5 NONLINEAR ULTRASONICS FOR DETECTION OF BONE-METAL DEBONDING 5 more by reading the first 0 cycles of a sine burst (0 µs, during which the longitudinal waves travel several centimeters), which will include many reverberations inside the different layers of the sample (magnitudes of the order of millimeters). The spatial resolution due to the large size of the low frequency transmitter has been increased in the immersion setup by introducing an acoustically isolating apodistion made of polystyrene with a perforated hole of 5 mm to allow a beam of that diameter to pass through to the sample... Signal processing All the data were captured from the oscilloscope to a PC and processed under a Matlab environment following these steps. The signal was shifted to have zero mean and normalized to have unity maximum peak value. A Hanning window was used over the time domain in order to reduce the border mismatch effects in the Fourier transform, which is then made using 3 zero padding. The modulus of the former is used as the power spectrum, and its maxima over frequency window of nf ± 0%f where n is the harmonic order around the fundamental frequency f, are taken as the harmonic amplitudes..3. Normalization Two normalization strategies are used. First, the harmonic amplitudes in every signal are normalized to the incoming excitation, both in terms of voltage. Since the characterization of the nonlinearity should be made with some independency of the arbitrary surface and geometry that will caracterize future in-vivo measurement conditions, the second normalization consists on eliminating the information about the absolute magnitudes by inserting an arbitrary intensity factor that will depend linearly on that surface and geometry

6 6 G. RUS, N. SAFFARI AND R. GALLEGO conditions, thus being independent on the ratio of harmonics and excitation power. This normalization is simply done by representing the amplitudes relative to that of the initial excitation power for each harmonic. To further simplify the visual interpretation, each plot is divided by the typical one, simply computed as the arithmetic average among each harmonic. 3. EXPERIMENTAL RESULTS The analysed signal received at the oscilloscope is windowed to a stable monocromatic burst of the first wavefront, elliminating the first couple of transient cycles, and during 0 µs, which corresponds to 0 cycles of 500 khz. Some examples of that signal are shown in Fig. 5 together with their power spectra, computed as described in section., which clearly shows their harmonics. The bottom figures correspond to a high energy ultrasonic wave transmission, which contrast with the top ones as they show nonlinearities: deviation from the ideal sinusoidal shape and appearance of various harmonics in the power spectrum. Fig. 6 synthesizes the results for the attenuation or appearance of harmonics for different levels of ultrasonic energy and along different positions on the sample. The intensity of the harmonics is represented versus the excitation power for each harmonic from 0 (fundamental frequency) to 6. The intensity is represented in terms of received voltage from the transducer normalized to the transmitted voltage, giving the attenuation due to the electromechanical system together with the sample and defects. Fig. 7 presents the same plots after normalization for the more significative even harmonics only.

7 NONLINEAR ULTRASONICS FOR DETECTION OF BONE-METAL DEBONDING 7 4. TOWARDS A THEORETICAL EXPLANATION To give a theoretical explanation of the experimental results, a mechanical model is solved by FEM that includes an interface layer representing the faulty bonding with two sources of nonlinearity, plasticity and viscoelasticity, with the goal of finding a parallelism with the experimental results. 4.. Mechanical model The material plastic model is a classical bilinear perfect isotropic plasticity model with a Von Mises yield stress criteria and plastic hardening, which is first reached at the interface, later at the PMMA and last at the steel part. Starting from the linear elasticity ε = Cσ () that relates the strain ε with the stress tensors σ through the isotropic elastic compliance tensor C, an additive split of the strain is assumed as ε = ε el + ε pl () An associative flow rule is assumed so that the plastic strain rate may be computed from a yield function F, and the accumulated plastic strain is obtained by ε pl = γ F σ ε pl = t 0 γdτ (3) Isotropic and kinematic hardening are also added to the model. The kinematic hardening is limited to a linear form where it is assumed that α = H kin ε pl where α is the back stress and H kin is the kinematic hardening modulus. The isotropic viscoelastic model represents the relaxation function µ(t) affecting the

8 8 G. RUS, N. SAFFARI AND R. GALLEGO deviatoric stress component only, σ = σ vol + σ dev ε = 3 ε vol + ε dev (4) ε dev = G t µ(t τ) dε dev dτ dτ (5) This model is applied to the interface, and coexists with the plastic model in the PMMA and the steel. The material constants that describe both models are given in Table II. The numerical model consists of a D cross section of the specimen as depicted in Fig. 8, which contains three layers, the PMMA of thickness 3 mm, the interface of thickness mm and the steel base of thickness 5 mm. The contact between the layers is a perfect bonding where the perfect compatibility of displacements is forced as well as the equilibrium of tractions between faces. 4.. Numerical results The preceding mechanical model is solved by FEM using the research code FEAP by Taylor[7]. The measured signal at point x is processed and normalized in the same fashion as the experimental one to obtain Fig. 9. The input ultrasonic beam is simulated by an input force p(t), constant over an area of v =5 mm at the center of the PMMA face, varying over the time according to the signal captured directly through water at the excitation of 000 mv, and scaled with an arbitrary amplitude factor that covers a range to 000. The rest of the boundary conditions is a constrained vertical movement along the upper and lower edges. The output signal is the horizontal displacement measured at point x, at the center of the metal face. The same model is solved with and without interface to simulate the experimental good bonding. In that case, the PMMA is extended over the volume that the interface occupied. The

9 NONLINEAR ULTRASONICS FOR DETECTION OF BONE-METAL DEBONDING 9 model is solved by a HHT (Hilbert-Hughes-Taylor) explicit time integration scheme (conserving alpha method, with parameters β =, γ =, α = ). The time step is 50 ns and the spatial discretization consists of 36 4-noded linear elements of a maximum dimension of 50 µm each. 5. DISCUSSION It is possible to notice the following features from the results in Fig. 6: In even harmonics (fundamental, second and fourth), the damaged signal intensity is clearly lower than for the undamaged case. This is not clearly observed for odd harmonics. An explanation for this may be that their intensity (of the order of 0 7 ) may be below the noise intensity. The amplitude of the fundamental frequency (harmonic 0) decreases with the defect. The amplitude of the fundamental frequency is damped as the excitation power grows, whereas all the higher harmonics increase regularly. In the case of immersion setup, the amplitude of the fundamental frequency decays with the excitation power, while the harmonics first increase and later decay at high power levels. An explanation of this may be the damping effect of water at high pressure waves. From direct observation of the spectrum analysis of the signal, in the case of contact setup, new frequencies are generated (750 KHz, 50 KHz, etc.) that do not correspond to the native contents of the electronic signal. This may be explained by contact phenomena, probably between the transmitter and the sample rather than in a delamination or cracktype defect.

10 0 G. RUS, N. SAFFARI AND R. GALLEGO The following features can be noticed from the normalized data in Fig. 7: In even harmonics after the fundamental one, after normalization, the intensity for damaged case evolves clearly below that of the undamaged case. This is particularly clear for the second harmonic. The former trend does not seem to be always monotonic, as observed for the immersion test case. An explanation of this may be the damping effect of water at high pressure waves. From the comparison between the experimental results in Fig. 7 and the numerical results in Fig. 9: A good qualitative correlation has been attained between experiments and results, which allow to continue working on the idea that the plastic material nonlinearities are responsible for the shown defect charasteristics that allow it to be detected in this simple experimental setup. As a conclusion, despite the simplicity and roughness of the experimental setup, which has a measurement exposure much larger than the size of the defect (lower resolution than the defect), a clear indication of the presence of the defect is observed, which is explained by the nonlinear constitutive laws that characterize damaged material. The study of how higher harmonics signature versus increasing excitation energy allows some independency of the absolute value of the signal (classical attenuation), and hence suggests the possibility of independency of surface and geometry of the sample at the measurement area, which is the case of in-vivo monitorization. REFERENCES

11 NONLINEAR ULTRASONICS FOR DETECTION OF BONE-METAL DEBONDING. Abeelea KEAVD, Sutinb A, Carmelietc J, and Johnson PA. Micro-damage diagnostics using nonlinear elastic wave spectroscopy (news). NDT&E International, 34:39 48, 00.. Averkiou MA. Tissue harmonic ultrasonic imaging. C. R. Acad. Sci. Paris, Applied physics, Biophysics, IV:39 5, Ballad EM, Vezirov SY, Pfleiderer K, Solodov IY, and Busse G. Nonlinear modulation technique for nde with air-coupled ultrasound. Ultrasonics, 4:03 036, Baltazar A, Rokhlin SI, and Pecorari C. On the relationship between ultrasonic and micromechanical properties of contacting rough surfaces. Journal of the Mechanics and Physics of Solids, 50:397 46, Bjørnø L. Forty years of nonlinear ultrasound. Ultrasonics, 40: 7, Calle S, Remenieras JP, Matar OB, Defontaine M, and Patat FE. Application of nonlinear phenomena induced by focused ultrasound to bone imaging. Ultrasound in Med. & Biol., 9(3):465 47, Delsanto PP and Hirsekorn S. A unified treatment of nonclassical nonlinear effects in the propagation of ultrasound in heterogeneous media. Ultrasonics, 4:005 00, Delsanto PP, Hirsekorn S, Agostini V, Loparco R, and Koka A. Modeling the propagation of ultrasonic waves in the interface region between two bonded elements. Ultrasonics, 40:605 60, Donskoy D, Sutin A, and Ekimov A. Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing. NDT&E International, 34:3 38, Jhang KY and Kim KC. Evaluation of material degradation using nonlinear acoustic effect. Ultrasonics, 37:39 44, Kawashima K, Omote R, Ito T, Fujita H, and Shima T. Nonlinear acoustic response through minute surface cracks: Fem simulation and experimentation. Ultrasonics, 40:6 65, 00.. Lewin PA. Quo vadis medical ultrasound? Ultrasonics, 4: 7, Pecorari C. An extension of the spring model to nonlinear interfaces. Review of Quantitative Nondestructive Evaluation, :49 55, Rokhlin S, Wang L, Xie B, Yakovlev V, and Adler L. Modulated angle beam ultrasonic spectroscopy for evaluation of imperfect interfaces and adhesive bonds. Ultrasonics, 4: , Solodov IY. Ultrasonics of non-linear contacts: propagation, reflection and nde-applications. Ultrasonics, 36: , Solodov IY, Krohn N, and Busse G. Can: an example of nonclassical acoustic nonlinearity in solids. Ultrasonics, 40:6 65, 00.

12 G. RUS, N. SAFFARI AND R. GALLEGO 7. Taylor RL. Feap - a finite element analysis program. version 7.5, 003. Rlt@cs.berkeley.edu. 8. Vanlanduit S, Parloo E, and Guillaume P. An on-line combined linearűnonlinear fatigue crack detection technique. NDT&E International, 37:4 45, 004.

13 NONLINEAR ULTRASONICS FOR DETECTION OF BONE-METAL DEBONDING 3 List of Figures Experimental setup. Left: Hip implant prosthesis, with core of cobalt-vanadium and hydroxyapatite cement. Right: test sample of steel with PMMA cement under fatigue testing (with four acoustic emission sensor installed) Scheme of the contact experimental setup Scheme of the immersion experimental setup Geometry of the sample and position labels for the measurements in the respective contact and immersion setups (top view) Example of signals and their spectrum for excitations at maximum power at faulty bonding for the contact and immersion setup respectively Compound representation of the experimental results for the contact setup (above) and immersion setup (below). Blue lines: undamaged measurements (A); Red and green lines: damaged measurements (B and C) Normalized representation of the experimental results for the contact setup (above) and immersion setup (below). Blue lines: undamaged measurements (A); Red and green lines: damaged measurements (B and C) Left: description of the numerical model. Right: example of a finite element mesh, deformed shape and loads at t= µs Numerical simulations. Amplitude of the first six harmonics for different values of the amplitude factor A. Top: Plasticity only model. Bottom: Viscoelasticity model in interface and plasticity model in PMMA and steel. Blue lines: undamaged measurements; Red lines: damaged measurements

14 4 FIGURES Figure. Experimental setup. Left: Hip implant prosthesis, with core of cobalt-vanadium and hydroxyapatite cement. Right: test sample of steel with PMMA cement under fatigue testing (with four acoustic emission sensor installed).

15 FIGURES 5 Oscilloscope Receiver Signal conditioner Specimen Transmitter Waveform generator Power amplifier Figure. Scheme of the contact experimental setup.

16 6 FIGURES Oscilloscope Receiver Signal conditioner Specimen Aposidation Waveform generator Transmitter Tank Power amplifier Figure 3. Scheme of the immersion experimental setup.

17 FIGURES 7 y (mm) y (mm) B 5 0 Specimen x (mm) 0 5 C C B B 0 A A C C Specimen x (mm) Figure 4. Geometry of the sample and position labels for the measurements in the respective contact and immersion setups (top view). A

18 8 FIGURES x 0 3 x Time, t (µs) Time, t (µs) Frequency, f (MHz) Frequency, f (MHz) Figure 5. Example of signals and their spectrum for excitations at maximum power at faulty bonding for the contact and immersion setup respectively.

19 FIGURES 9 Intensity V/V Intensity V/V 0 0 Intensity V/V Intensity V/V x Harmonic x 0 6 Harmonic x 0 4 Harmonic x 0 6 Harmonic x 0 6 Harmonic x 0 7 Harmonic x 0 5 Harmonic x 0 7 Harmonic x 0 6 Harmonic x 0 7 Harmonic x 0 6 Harmonic x 0 7 Harmonic Figure 6. Compound representation of the experimental results for the contact setup (above) and immersion setup (below). Blue lines: undamaged measurements (A); Red and green lines: damaged measurements (B and C).

20 0 FIGURES Normalized intensity Normalized intensity.5 Harmonic Harmonic Harmonic Harmonic Harmonic Harmonic Figure 7. Normalized representation of the experimental results for the contact setup (above) and immersion setup (below). Blue lines: undamaged measurements (A); Red and green lines: damaged measurements (B and C).

21 FIGURES a b c v p(t) x 0 mm PMMA Interface Steel Figure 8. Left: description of the numerical model. Right: example of a finite element mesh, deformed shape and loads at t= µs.

22 FIGURES Harmonic 0 Harmonic Harmonic 4 Normalized intensity Harmonic Harmonic Harmonic 5 Normalized intensity Normalized intensity Normalized intensity Harmonic Harmonic Harmonic Harmonic Harmonic Harmonic Figure 9. Numerical simulations. Amplitude of the first six harmonics for different values of the amplitude factor A. Top: Plasticity only model. Bottom: Viscoelasticity model in interface and plasticity model in PMMA and steel. Blue lines: undamaged measurements; Red lines: damaged measurements.

23 FIGURES 3 List of Tables I Configuration of the experimental setup II Material constants

24 4 TABLES Transmission Table I. Configuration of the experimental setup Reception Waveform Generator model Agilent 330A Oscilloscope Model LeCroy 930 Repetition rate 0 ms Amplitude division variable Burst cycle 4 Time division µs/div Pulse height mv Capture points 000 Frequency 500 khz Capture method Single shot Burst shape sine Averaging 000 RF Power Amplifier model Krohn Hite 760M Signal conditioner model Amplification +4 db Gain +40 db Mode Grounded Damping 0 db Transmitting transducer (contact) Receiving transducer (contact) Central frequency 500 khz Central frequency.5 MHz Bandwidth broadband Bandwidth broadband Diameter.7 mm Diameter 6.3 mm Transmitting transducer (immersion) Receiving transducer (immersion) Central frequency 500 khz Central frequency.5 MHz Bandwidth broadband Bandwidth broadband Diameter 45 mm Diameter.7 mm

25 TABLES 5 Table II. Material constants Material PMMA Interface Steel AISI 4340 Elastic constants Young modulus (Pa) Poisson ratio Plasticity model Yield criteria Von Mises Von Mises Von Mises Yield stress (Pa) Kinematic hardening (Pa) Saturation hardening (Pa) Viscoelasticity model Constant parameter 0.9 Time parameter (s) 0 8