Georgia Tech Sponsored Research

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1 Georgia Tech Sponsored Research Project E-25-L21 Project director Qu Jianmin Research unit Title Mech Engr Ultrasonic Nondestructive Characterization of Adhesive Bonds Project date 5/20/1999

2 Title of the Grant: Ultrasonic Nondestructive Characterization Of Adhesive Bonds Type of Report: Annual Performance Report Name of Principle Investigator: Jianmin Qu Period Covered: 2/22/96-12/22/96 Grantee's Institution: Georgia Institute of Technology, Atlanta, GA Grant Number: NAG Introduction In April of 1996, a student was hired to work on this project. Since then, the research has focused on three tasks: literature search, material selection and acoustoelastic guided wave analysis. The report below briefly outlines results from each of these research tasks. Although the project started somewhat late due to the delay of funding, we are still on target in terms of the research milestones as proposed in the original proposal. In addition to the annotated bibliography, some details of the acoustoelastic guided wave analysis are included in this report as an appendix. Literature Search We have carried out an extensive literature search on the subject of ultrasonic non-destructive characterization of adhesive joints. Some recent papers on this subject are listed in the Annotated Bibliography. The techniques reported in the literature can be classified into two categories based on the type of ultrasonic waves used, namely, bulk waves (reflection and transmission) and guided waves (surface and plate waves). Recent representative publications on bulk wave techniques includes [Aglan, et al., 1994; Pialucha, and Cawley, 1994; Gilath, et al., 1995]. For guided wave techniques, recent representative papers may include [Singher, et al., 1994; Lowe, and Cawley, 1994; Rose, 1995]. After the literature review, it becomes clear to us that almost all the available ultrasonic techniques are based on wave propagation in continuum media. None of the current methodologies considers the microstructure-property relationships of the 1

3 adhesive/adherend and their interfaces. Consequently, these methods, in general, cannot be used to characterize bonding strength, especially fatigue strength. Material Selection We decided to start with FM-73 adhesive. Both Al and Boron/Epoxy composites will be considered as the adherends. This selection is based on the costs, availability of material data, range of applications and the representation of common microstructural features among various adhesive joints. Through extensive literature search, we have found most of the mechanical properties needed except the third order elastic constants (TOE) for the FM-73 adhesive and Boron/Epoxy composites. Since it is imperative to know the TOE in order to use non-linear wave theories, we decided to modify our laser interferometer system for measuring the TOE of polymer adhesives. The key is to increase the operating frequency to receive the higher harmonic waves. Several options are being considered. Although the FM-73/A1 joints will be considered first, the methodologies developed here should be applicable to other types of adhesives and adherends. We are also open to suggestions from NASA and try to accommodate NASA's application in terms of the type of adhesives and adhesive joints. Acoustoel astic Guided waves A systematic approach has been formulated to analyze acoustoelastic guided waves in layered media. The methodology provides a simple and compact formulation that is convenient for numerical evaluation. Preliminary results are obtained for several examples including a pre-stressed aluminum plate, a thin aluminum film on a silicon substrate, and an adhesive layer of FM-73 sandwiched between two aluminum bonding layers. These preliminary results show that the dispersion curves are very insensitive to the residual stresses in a single layer, or a coating layer. However, dispersion curves in a tri-layer medium are very sensitive to residual stresses. Therefore, the magnitude of residual stresses, which usually increases during curing and decreases duo to creep relaxation in the polymer adhesive, can be measured and used as a descriptor of the 2

4 curing and physical aging process. The results also shown that the dispersion curves are fairly sensitive to the change of the third order elastic constants of the adhesive. Since the third order elastic constants are related to the microstructure and non-linear behavior of the materials, it is therefore perceivable that damage and degradation of adhesives may be better characterized by using non-linear parameters, such as the higher order harmonics, that are related to the third order elastic constants. Objectives and Major Tasks for Next Year The objective for next year is to understand the correlation between adhesion, interfacial microstructure and guided wave propagation in the adhesive. To this end, a microscopic description of polymer-metal interface will be developed. Using this model, the amplitudes of the higher harmonics that are generated by the non-linear interfacial bonding forces will be measured, and correlated to the propagation characteristics of acoustoelastic guided waves. Major tasks to be accomplished are 1. Measuring the TOE of FM-73; 2. Parametric studies of the propagation characteristics of acoustoelastic guided waves; 3. Microscopic modeling of polymer-metal interfacial bonding forces; 4. Understanding the dependence of the non-linear parameters of guided waves on interfacial adhesion. 3

5 Annotated Bibliography ( ) Aglan, H., Schhroff, S. and Abdo, Z., 1994, "Influence of Adhesive Type and Substrate Thickness on the Capability of NDE Techniques to Detect Fatigue Disbonds", Review of Progress in Quantitative Nondestructive Evaluation, Vol. 13, The effects of adhesive type and substrate thickness on various NDE (thermal wave imaging, ultrasonic, and electronic speckle pattern interferometry, etc.) capabilities to detect fatigue debonds were studied thoroughly. The measurements have been shown to be consistent with each other as well as microscopic observations taken from the sides of the specimens during testing. Ultrasonic has demonstrated its potential capability in detecting fatigue disbonds in adhesively bonded thick substrate specimens. However, specimen orientation has almost no effect on the ultrasonic measurements of fatigue induced disbonds in specimens bonded using thin substrates. Cawley, P. and Alleyne, D., 1996, "The Use of Lamb Waves for the Long Range Inspection of Large Structures," Ultrasonics, Vol. 34, The use of lamb waves for the long range inspection was investigated. The chief drawback of Lamb wave inspection is that at least two modes exist at allfrequenciesand the modes are generally dispersive, which means that the received signals can be very complicated. The key to the successful application of Lamb waves is the excitation of a single mode in a non-dispersive region. The method of selection, excitation and reception of an appropriate mode was discussed in detail. Examples of the use of Lamb waves for the detection of delaminations in composite materials and corrosion in pipes were given. Ditri, J. J. and Rose, J. L., 1994, "Excitation of Guided Waves in Generally Anisotropic Layers Using Finite Sources," Journal of Applied Mechanics, Vol. 61, The excitation of guided wave modes in generally anisotropic layers by finite sized strip sources placed on the surfaces of the layer is examined. The normal mode expansion technique was used in conjunction with the complex reciprocity relation of elastodynamics. The amplitudes of the generated modes are written as the product of an "excitation function" which depends only on the distribution of the applied tractions and an "excitability function" which depends only on the properties of the specific mode(s) being excited and which determines how receptive the modes are to the applied tractions. The effects of these two functions to the selection of the specific modes have been discussed in detail. The problem of transient loading is addressed by superimposing time harmonic solutions via an integration over the dispersion curves of the layer. Hanneman, S. E. and Kinra, V. K., 1992, "A New Technique for Ultrasonic Nondestructive Evaluation of Adhesive Joints: Part I. Theory and Part II. Experiment," Experimental Mechanics, Vol. 32, No.4, and A new technique for ultrasonic nondestructive evaluation of adhesively bonded joints was reported. An exact solution to the problem of reflection and transmission of a normal incident plane, time-harmonic, longitudinal wave through an N-layered medium was obtained. The solution is valid for perfectly elastic as well as linear-viscoelastic materials, and for isotropic as well as anisotropic materials. The sensitivities of the transfer functions derived for a joint consisting of two adherends joined by an adhesive 4

6 layer to the adhesive and adherend properties have been discussed. The comparison between the measurements in the experiment and the theory was found to be extremely good for all five joints tested. Gilath, I., Englman, R., Jaeger, Z., Buchman, A. and Dodiuk, H., 1995, "Impact Resistance of Adhesive Joints Using Laser-induced Shock Waves," Journal of Laser Applications, Vol. 7, No. 3, The impact resistance of metal-adhesive-metal sandwiches joints was studied using normal incident laser-induced shock waves. The short pulsed waves provide a very suitable method for studying material response at hypervelocity impact conditions. It was observed that the adhesive joints failed in a delamination of ductile mode, showing shock absorbtion ability through plastic deformation. The shock wave is modeled by an expanding stress front, which creates a void population in the laser-impacted layer and extrudes a bulge at the far surface. The calculated extent of the bulge geometry compares very well with that observed in the metal-adhesive-metal sandwiches. Georgiou, G. A., Lank, A. M. and Munns, I. J., 1994, "Mathematical Modeling of Ultrasonic Wave Propagation in Adhesively Bonded Joints," Review of Progress in Quantitative Nondestructive Evaluation, Vol. 13, The mathematical modeling and experimental studies of propagation of ultrasonic Rayleigh, Lamb and Stoneley waves in adhesively bonded joints were carried out in this paper. The explicit finite difference schemes are used to model pulsed wave problem in the context of adhesive joints. The methods of generation of'pure' Rayleigh, Lamb and Stoneley waves were studied in the experiments. It was pointed out that these kinds of waves could provide more information about the joint condition than conventional i techniques. Jansen, D. P., Hutchins, D. A. and Mottram, J. T., 1994, "Lamb Wave Tomography of Advanced Composite Laminates Containing Damage," Ultrasonics, Vol. 32, No. 2, A novel Lamb wave immersion tomography of advanced composite laminates containing damage in the form of fiber failure, matrix cracking and delamination was studied. Images created with this method were correlated with images obtained from C- scan techniques. It was found that both C-scan and Lamb wave tomography were able to identify clearly regions of damage in the two samples. The tomographic imaging technique appears to be able to detect and locate regions of delamination in carbon fibre composites, even in the presence of moderate anisotropy. Lowe, M. J. S. and Cawley, P., 1994, "The Application of Plate Wave Techniques for the Inspection of Adhesive and Diffusion Bonded Joints," J. of Nondestructive Evaluation, Vol.13, No. 4, The application of plate wave techniques for the inspection of adhesive joints was reviewed in this paper and the studies on the detection and characterization of an unwanted layer of brittle alpha case in diffusion bonded titanium were carried out. It was concluded that Lamb wave techniques are limited in both applications by their strong sensitivity to the material properties and the thicknesses of the adherends and their relative insensitivity to those of the bondline layer. It was found, however, that embedded modes were largely insensitive to the adherends and the dispersion curves show a major 5

7 improvement in sensitivity in both applications. Leaky modes may exist in both applications but their exploitation may be limited in practice because it can be difficult to excite and detect them. Matthias, K. T. H., Krishna, M. R. and Rose, J. L., 1994, "Characterization of Aircraft Joints Using Ultrasonic Guided Waves and Physically Based feature Extraction," Proceedings of the IEEE Ultrasonics Symposium, An approach to characterize or classify the inspection region is done by feature selection in order to acquire physically based information. The Double Spring Hopping Probe (DSHP) was designed to implement the guided waves concepts to inspect the delamination of the bonded regions on service damaged aircraft. Results are presented from lab specimens and from measurements on a Boeing specimen manufactured in The classification task is performed with a state-of-the-art neural network classifier. It was reported that the process of pre-classification improved the recognition rate for bond classification by 15% for the lab data and around 20% for the aircraft data. Pilarski, A. and Rose, J. L., 1992, "Lamb Wave Mode Selection concepts for Interfacial Weakness Analysis," Journal of Nondestructive Evaluation, Vol. 11, Nos. 3/ 4, Utilization of specific Lamb wave modes with special cross-sectional wave structure is proposed for the detection of interfacial weakness between an adhesive and adherend. It is based on plate wave behavior in a three-layered medium with imperfections on the individual interfaces. Selection of appropriate modes and frequencies for adhesion weakness detection is obtained by numerical analysis of the dispersion relations and comparisons of the dispersive curves for perfect, welded and imperfect, smooth boundary conditions. The inspection parameters were evaluated by an analysis of displacement, stress, and power distributions across the three-layered asymmetric adhesive structure. Pialucha, T. and Cawley, P., 1994, "The Detection of Thin Embedded Layers Using Normal Incidence Ultrasound," Ultrasonics, Vol. 32, No. 6, A theoretical investigation of the use of normal incidence ultrasonic reflection measurements for the detection and characterization of thin layers embedded between two much thicker media has been carried out. It has been shown that the form of the relationship between the normal incidence longitudinal reflection coefficient and frequency is defined by the reflection coefficient at zero frequency and at half the resonance frequency of the layer. In general, the sensitivity of the reflection coefficient to the presence of the layer increases as the product of frequency and layer thickness increases, the maximum sensitivity being at half the resonance frequency of the layer. The sensitivity is also critically dependent on the relative impedances of the three media and is generally greatest when the half spaces on either side of the layer have the same impedance. Rose, J. L., 1995, "Recent Advances in Guided Wave NDE," Proceedings of the IEEE Ultrasonics Symposium, A review of recent advances in Guided Wave NDE was presented in this paper with emphasis on practical application. The highlights from work done at Penn State University on guided wave analysis over the past five years were summarized as six parts which includes: (1) Dispersion curve and wave structure, (2) Source influence 6

8 considerations, (3) Steam generator tubing inspection, (4) Aging aircraft inspection, (5) Manufacturing possibilities, and (6) Flaw classification potential. Rose, J. L., Rajana, K. M. and Barshinger J. N., 1996, "Guided Waves for Composite Patch Repair of Aging Aircraft," Review of Progress in Quantitative Nondestructive Evaluation, Vol. 15, The global, guided wave inspection technique, which had been developed by the authors for inspecting the integrity of structures with metal to metal adhesive bonds, was used to inspect the bond quality of a composite patch in the repair of both military and civilian aircrafts. It is concluded that through transmission and pulse echo techniques can be successfully designed for a specific composite doubler situation and some special considerations must be taken. Singher, L., Segal, Y. and Segal, E., 1994, "Considerations in Bond Strength Evaluation by Ultrasonic Guided Waves," J. Acoust. Soc. Am., Vol. 96, No. 4, An extensive investigation of the effects of the bonding quality on the propagation of guided acoustic modes towards the possibility of evaluating the degree of adhesion in layered joints was carried out. The interface between the adhesive and the adherend was modeled as a spring-mass structure. This model modifies the boundary conditions to treat the effect of the finite interfacial stiffness. The analysis indicated that measurement of the propagation velocity may provide information about the strength of the bond. Computer simulations led to the derivation of optimal measurement conditions.

9 Title of the Grant: Ultrasonic Nondestructive Characterization Of Adhesive Bonds Type of Report: Annual Performance Report Name of Principle Investigator: Jianmin Qu Period Covered: 12/23/96-12/22/97 Grantee's Institution: Georgia Institute of Technology, Atlanta, GA Grant Number: NAG Introduction Qualitative measurements of adhesion or binding forces can be accomplished, for example, by using the reflection coefficient of an ultrasound or by using thermal waves (Light and Kwun, 1989, Achenbach and Parikh, 1991, and Bostrom and wickham, 1991). However, a quantitative determination of binding forces is rather difficult. It has been observed that higher harmonics of the fundamental frequency are generated when an ultrasound passes through a nonlinear material. It seems that such non-linearity can be effectively used to characterize the bond strength. Several theories have been developed to model this nonlinear effect (Adler and Nagy, 1991; Achenbach and Parikh, 1991; Parikh and Achenbach, 1992; and Hirose and Kitahara, 1992; Anastasi and Roberts, 1992). Based on a microscopic description of the nonlinear interface binding force, a quantitative method was presented by Pangraz and Arnold (1994). Recently, Tang, Cheng and Achenbach (1997) made a comparison between the experimental and simulated results based on this theoretical model. A water immersion mode-converted shear wave through-transmission setup was used by Berndt and Green (1997) to analyze the nonlinear acoustic behavior of the adhesive bond. In this project, the nonlinear responses of an adhesive joint was investigated through transmission tests of ultrasonic wave and analyzed by the finite element simulations. The higher order harmonics were obtained in the tests. It is found that the amplitude of higher harmonics increases as the aging increases, especially the 3 rd order harmonics. Results from the numerical simulation show that the material nonlinearity does indeed generate higher order harmonics. In particular, the elastic-perfect plastic behavior generates significant 3 rd and 5 th order harmonics. Through Transmission Test Through transmission tests were conducted on the bond samples provided by NASA. The objective is to correlate the aging time of the bond joint with the generation of higher harmonics in the through transmission tests. Details of the test and some major results are described below. Experimental Setup A block diagram of the experimental set up is shown in Fig 1. A 40 cycle timeharmonic signal of 2MHz was generated by a Waveteck function generator (the limit frequency is 50MHz). The signal was amplified by a high voltage amplifier (ENT, DC ~ l

10 10MHz, 50dB) to obtain a high amplitude driving voltage of the generating transducer. Typical output signals of the function generator and the amplifier are shown in Fig.2. The highest output voltage of the amplifier used in the experiments was 350 volts. A narrow-band contact PZT transducer was used as the generating transducer. Its center frequency is 2MHz. The incident ultrasonic wave from the generating transducer was transmitted perpendicularly through the adhesive layer. The receiver is a broad-band contact PZT transducer with 2MHz center frequency. The output signalx0 of the receiver was recorded by an oscilloscope (Techtronix, 150MHz) and analyzed on a personal computer. High Voltage Amplifier T Function Generator Transducer Oscilloscope Sample Computer Fig.l Experimental setup. Outputofthe FtrebonGenerator (=lnputoftheamplifier) OutputoftheArpffier (=tnpuoftheexciting Probe) AnpiJefv) Fig.2 Typical output signals of the function generator and the amplifier. The sample and the two contact PZT transducers were fixed by two aluminum plates with a cavity on each side, respectively, to hold the transducers at the same position (see Fig. 3). For efficient signal generation, the two transducers can be held tightly by adjusting the four bolts. Another setup (Fig.4) was tried with a single crystal quartz transducer as the sending probe. A laser interferometer was used as the receiver. It is a broad-band green laser system and the frequency response is from 0 to 10MHz. Due to the inefficiency of the single crystal quartz transducer, we did not obtain high enough ultrasound signal to drive the interface into the nonlinear range. More work is need on this technique for year 3. 2

11 Fig. 3 Adhesive bond sample and the holding of the transducers.

12 Experimental Results A typical sample received from NASA is shown in Fig. 5. Two aluminum plates were bonded together by an adhesive layer. The materials are given below: Adherend Material: AL2024 Adhesive: FM-300 Sheet Form (carrier - nylon material) Bonded Area: 2.0"x 1.0" in overlap, 0.003" in thickness. Fig.5 Adhesive bond sample geometry The ultrasound signal j\t) received by the receiver were recorded along with the increasing driving voltages of the sending transducer. Then, the data were analyzed by the Fast Fourier Transform to obtain the frequency spectra, F(co)= jf(t)exp(io>t)dt (1) The amplitude of the fundamental frequency and the higher harmonic components are defined as A = \Finco, 0) n= 1,2,3... (2) where OJ = 2MHz. U a o. E < Amplifier Output k (Oq = 2MHz 4

13 Receiver Output 5.0»6 1.0»5 1.5»S 2.0* K. A u <S to 0 =2MHz Fig. 6Inputandreceivedsignalsandtheirfrequencyspectra Fig. 6.Theirfrequencyspectraaregiven Examples oftheoutputsignalsfromtheamplifierandthereceiveraregiven inthesame figure. It issenthathigher in bondsample. harmoniccomponentswereindeedgeneratedbythenonlinearresponses oftheadhesive 10 Sample A 8 6 AS RECEIVED V 30 HAT 200 C 60 HAT 200 C 100HAT200 C A,/AO 4-2 i Input (v) Fig. 7aAmplitude Ai forsample A 5

14 0.04 Sample A AS RECEIVED 0.03 AJ/AQ 30 H AT 200 C 60 H AT 200 C 100 H AT 200 C " V V» Input (v) 300 Fig. 7b Amplitude A 2 for sample A 0.03 SAMPLE A 0.02 \ AS RECIEVED 30HAT200 C 60HAT200 C 100HAT200 C 0.01 W 0.00 V N» - " IK V < 1 9 * V V INPUT (V) V 350 Fig. 7c Amplitude A3 for sample A 6

15 Sample D 10 A1/A0 8 6^ AS RECEIVED V 30HAT200T 60 HAT 200T 100HAT200T ml" Input (v) Fig. 8a Amplitude Aj for sample D Sample D A2/A0 AS RECEIVED V 30HAT200 C 60HAT200 C 100HAT200 C. 1 V V 0.02 J Input (V) Fig. 8b Amplitude A2 for sample D 7

16 Sample D AS RECIEVED V 30 HAT 200 C " 60 HAT 200 C ' > 100HAT200 C V A3/A " V V Y V V V 0.00 H M n S 6 '* 1 G Input (v) Fig. 8c Amplitude A3 for sample D Two samples were tested in the condition as received. Then they were placed in a oven for dry aging at 400 F for 30 hours, 60 hours, and 100 hours, respectively. At each aging increment, the samples were taken out of the oven and ultrasonic through transmission tests were performed. The resulted A, as functions of the driving voltage of the sending probe for the two samples A and D are shown in Fig. 7 and Fig. 8, respectively. All results have been normalized by the amplitude of the fundamental component at the lowest driving voltage. From Figs. 7-8, it is observed that (1) the fundamental component is the dominant one. Its amplitude is much higher than other components, (2) aging increases the magnitude of higher order harmonics of the fundamental frequency, and (3) The magnitude of the 3 r harmonics seems to correlate with aging time fairly well. Finite Element Analysis To understand the nonlinear effects of the adhesive layer, transmission through an adhesive layer was analyzed by the finite element method. Elastic-perfect plastic constitutive law was used for the adhesive. The input signals of 0.5MHz and 2MHz are considered. The 1-D numerical model is shown in Fig. 9. A 5 cycle harmonic load of 0.5MHz or 2MHz was applied, respectively, as the input. The thickness of the adhesive layer is 0.003in, which is expressed as kx Fig. 9, where X is the wavelength of the input signal and k is the ratio of the adhesive thickness and the wavelength. Here X = mm for 0.5MHz and X = 3.259mm for 2MHz. The corresponding k is and The adhesive layer is much thinner than the aluminum plate. So, the thickness of aluminum 8

17 parts can be assumed as infinite in the finite element analysis. The stress-strain relations are shown in Fig. 10 for the aluminum and the adhesive, respectively. 0.5MHZOR 2.0MHZ Al FM-73 Al Fig. 9 Finite Element Model Al FM-73 perfect plastic strain strain Fig. 10 Stress-strain relations of Al and FM-73 Numerical results for the ultrasonic signals at three different points in the aluminum and the adhesive layer for the two loading cases are given in Fig. 11 and Fig. 12, respectively. AI/FM-73/AI (ELASTIC) AI/FM-73/AI (ELASTIC-PERFECT PLASTIC) porta - pdrtb ponlc pcinta - point B partc fit) f(t) *6 10*6 15*5 20*6 25*6 3.0*6 3.5*5 TIME(S) 00 &0*«10*5 15*6 20*5 25*5 3.0*5 3.5*5 TIME (S) Fig.l 1 Responses at different points for 0.5MHz load 9

18 10 f(t) AI/FM-73/AI (Elastic) pointa pointb 1.0 AiyFM-73/AI (Elastic-PerfectPlastic) I pointa pointc 0.5 1IL 1 r»>.«'_je 0.0. pointb 0.5 point C 0 50*610*515*520*525*53.0*53.5*5 1.0 mi *61.0*515*520*525*53.0*53.5*5 time(s) Fig. 12 Responses at different points for 2.0MHz load time(s) It is seen from Fig.l 1 and Fig. 12 that the amplitude of the incident wave decreased significantly after passing through the adhesive layer. In the meantime, the yielding of the adhesive material indeed complicated the transmitted ultrasonic waves. In order to see if there is any higher harmonic component caused by the material nonlinearly, the responses and their spectra at point C for the elastic and elastic-perfect plastic cases are compared in Fig. 13 and Fig. 14 for the two loading cases, respectively. The data are normalized by the magnitude of the fundamental component of their spectra. f«) AI/FM-73/AI (pointc) Elastic mn 1.0 Basbc-PerfectPlastic 1 1.0*52.0*5 3.0*5 Time (s) FTof f(t)atpoint C. Elastic - Elastic-Perfaci Plastic j «+62.0e*6 3Oe+6 Frequency (Hz) Fig. 13 Responses at point C and their FFT for 0.5MHz load

19 AI/FM-73/AI (POINT C) - ELASTIC - Elastic-ParfBct Plastic W(a>)\* 0.5 FFT OF f(t) AT POINT ELASTIC C ELAS8CJ>ERFECT PLASTIC 2A-5 2«-5 3A-5 TIME (S) -A... F Q E E+6 8.0E FREQUENCY (HZ) Fig. 14 Responses at point C and their FFT for 2.0MHz load It is seen clearly from Fig. 13 and Fig. 14 that the higher order harmonics are generated by the non-linearity of the adhesive material, which is the plastic deformation of the adhesive material. Especially, significant 3 rd and 5 th order harmonics are generated. The magnitude of the 3 r order harmonics is about 1/25 of the fundamental one. However, the 2 nd harmonic was not predicted by the FEM calculation. These numerical results seem to confirm what was observed experimentally, as described in the previous section. Summary The nonlinear responses of an adhesive joint was analyzed by the through transmission tests of ultrasonic wave and the finite element simulations. Two samples provided by NASA have been tested as received and after the accelerated temperature aging at 400 F for various periods of time. In these tests, a 40-cycles harmonic signal was generated by a 2MHz narrow-band PZT as the input. The output is received by a 2MHz broadband PZT. Due to material non-linearity in the adhesive caused by aging, higher order harmonics of the fundamental frequency is generated as the wave passes through the adhesive layer. The experimental results show that aging increases the magnitude of higher order harmonics of the fundamental frequency and the magnitude of the 3 rd harmonic seems to correlates with aging time fairly well. To model the nonlinear effect of the adhesive layer, transmission through an adhesive joint was analyzed by the finite element method. Elastic-perfect plastic constitutional relation was used for the adhesive material. Results from the numerical simulation show that material nonlinearity does indeed generate higher order harmonics. In particular, the elastic-perfect plastic material behavior generates significant 3 rd and 5 th harmonics. References J. D. Achenbach and O. K. Parikh, "Ultrasonic analysis of nonlinear response and strength of adhesive bonds," J. Adhesion Sci. Technol. Vol. 5, No. 8, pp (1991). L. Adler and P. B. Nagy, Review of Progress in QNDE, Vol. 10B, eds. D. O. Thompson and D. E. Chimenti (Plentium, New York, 1991), pp

20 R. F. Anastasi and M. J. Roberts, "Acoustic Wave propagation in an adhesive bond model with degrading interfacial layers," MTL TR 92-63, U.S. ARMY Materials Technology Laboratory, T. P. Berndt and R. E. Green, "Feasibolity study of a nonlinear ultrasonic technique to evaluate adhesive bonds," Review of Progress in QNDE, 1997(in press). A. Bostrom and G. Wickham, J. of NDE, Vol. 10, pp.139 (1991). S. Hirose and M. Kitahara, Review of Progress in QNDE, Vol. 10B, eds. D. O. Thompson and D. E. Chimenti (Plentium, New York, 1992), p. 33. G. M. Light and H. Kwun, "Nondestructive Evaluation of adhesive bond quality, State-of-the-art review," NTIAC-89-1, June S. Pangraz and W. Arnold, "Quantitative determination of nonlinear binding forces byultrasonic technique," Review of Progress in QNDE, Vol. 13B, eds. D. O. Thompson and D. E. Chimenti (Plentium, New York, 1994), pp O. K. Parikh and J. D. Achenbach," Analysis of nonlinearly viscoelastic behavior of adhesive bonds," J. of NDE, Vol. 11 (3/4), pp (1992). Z. Tang, A. Cheng and J. D. Achenbach, "An ultrasonic technique to detect nonlinear behavior related to degradation of adhesive bonds," Review of Progress in QNDE, 1997(in press). 12

21 Title of the Grant: Ultrasonic Nondestructive Characterization of Adhesive Bonds Type of Report: Final Report Name of Principle Investigator: Jianmin Qu Period Covered: 2/22/96-2/22/99 Grantee's Institution: Georgia Institute of Technology, Atlanta, GA Grant Number: NAG Introduction Adhesives and adhesive joints are widely used in various industrial applications to reduce weight and costs, and to increase reliability. For example, advances in aerospace technology have been made possible, in part, through the use of lightweight materials and weight-saving structural designs. Joints, in particular, have been and continue to be areas in which weight can be trimmed from an airframe through the use of novel attachment techniques. In order to save weight over traditional riveted designs, to avoid the introduction of stress concentrations associated with rivet holes, and to take full advantage of advanced composite materials, engineers and designers have been specifying an ever-increasing number of adhesively bonded joints for use on airframes. Nondestructive characterization for quality control and remaining life prediction has been a key enabling technology for the effective use of adhesive joints. Conventional linear ultrasonic techniques generally can only detect flaws (delamination, cracks, voids, etc) in the joint assembly. However, more important to structural reliability is the bond strength. Although strength, in principle, cannot be measured nondestructively, a slight change in material nonlinearity may indicate the onset of failure. Furthermore, microstructural variations due to aging or under-curing may also cause changes in the l

22 third order elastic constants, which are related to the ultrasonic nonlinear parameter of the polymer adhesive. It is therefore reasonable to anticipate a correlation between changes in the ultrasonic nonlinear acoustic parameter and the remaining bond strength. It has been observed that higher harmonics of the fundamental frequency are generated when an ultrasonic wave passes through a nonlinear material. It seems that such nonlinearity can be effectively used to characterize bond strength. Several theories have been developed to model this nonlinear effect (Nagy and Adler, 1991; Achenbach and Parikh, 1991; Parikh and Achenbach, 1992; Hirose and Kitahara, 1992; and Anastasi and Roberts, 1992). Based on a microscopic description of the nonlinear interface binding force, a quantitative method was presented by Pangraz and Arnold (1994). Recently, Tang, Cheng and Achenbach (1997) presented a comparison between the experimental and simulated results based on a similar theoretical model. A throughtransmission setup for water immersion mode-converted shear waves was used by Berndt and Green (1998) to analyze the ultrasonic nonlinear parameter of an adhesive bond. In addition, ultrasonic guided waves have been used to analyze adhesive or diffusion bonded joints (Lowe and Cawley, 1994, Rose, Rajana and Hansch, 1995, and Rose, Zhu and Zaidi, 1998). In this paper, the ultrasonic nonlinear parameter is used to characterize the curing state of a polymer/aluminum adhesive joint. Ultrasonic through-transmission tests were conducted on samples cured under various conditions. The magnitude of the second order harmonic was measured and the corresponding ultrasonic nonlinear parameter was evaluated. A fairly good correlation between the curing condition and the nonlinear 2

23 parameter is observed. The results show that the nonlinear parameter might be used as a good indicator of the cure state for adhesive joints. The report is arranged as follows. In section 2, a brief introduction is given to show how the higher order harmonics are generated by material nonlinearity. Both analytical and numerical examples are presented based on the asymptotic expansion method and the finite element method, respectively. Section 3 describes the sample and the test method. The results are presented and discussed in Section Generation of Higher Order Harmonics It is well known that non-linearity, either geometrical (Bland, 1969; Richardson, 1979) or material (Kolsky, 1963), in an acoustic medium can generate higher order harmonics. For example, consider a one-dimensional problem of wave propagation through a nonlinear medium. For small strain deformation, the equation of motion can be written as 1 da _ d 2 u pdx'dt 2 ' ( ] where u is the displacement in the JC-direction, p is the mass density and cr(x,t) is the normal stress in the x-direction. For the small strain deformation considered here, the normal strain in the x-direction, e(x,t), is defined as =. (2.2) ox Next, assume that the nonlinear constitutive relationship of the medium is described by a = Ef(e), (2.3) where E can be viewed as the "elastic Young's modulus." Substitution of (2.3) into (2.1) yields 3

24 (2.4) where c = ^E/p can be considered as the "phase velocity." This nonlinear equation can be solved either numerically or asymptotically once /(s) is known. To illustrate the solution characteristics, let us expand /(s) into power series of e and take only the first two terms in the expansion so that f{e) = (l-0.5ye), (2.5) where y is a parameter that indicates the amount of material non-linearity. Obviously, for linear elastic materials, y = 0. Fig. 2.1 shows several stress-strain curves for y = 0, 1.0,10, and 30, respectively. Note that the constitutive equation given by (2.5) dictates that the material behaves differently in tension and compression, although the difference is only to the second order. In the literature, such material behavior is sometimes referred to as pseudo elastic. To describe the complete symmetry in tension and compression, one should retain only the terms with odd exponents of e. Since the primary objective here is to illustrate the possibility of generating second order harmonics, only the term with e 2 is used here for algebraic simplicity. Now, consider a layer of nonlinear material with layer thickness h. The material follows the constitutive law given in (2.5). A plane wave A sin(fcc - cot) is prescribed on the left side of the layer, i.e., «(0, t) = A sin(&>/), (2.6) where k is the wavenumber and co is the circular frequency. The displacement on the right hand side of the layer can then be obtained from (2.4) - (2.6) through a simple asymptotic analysis (Truell, et al., 1969), 4

25 u(h, t) «4 sin(a# - cot) + cos(2m - 2cot), (2.7) where ^k 2 haf =-^To) 2 ha 2. (2.8) 1 8 8c 2 1 It is clear from the above solution that the material nonlinearity distorts the waveform and generates the second order harmonic. In other words, after propagating through a nonlinear medium, a single frequency wave may contain frequency components other than the fundamental frequency. Usually, the amplitudes of the higher order harmonics are much less than the amplitude of the fundamental component. In the reminder of this paper, the amplitude of the fundamental component is simply referred to as the wave amplitude to avoid ambiguity unless otherwise indicated. It is interesting to note the relationship between y and the ultrasonic nonlinear parameter defined by Yost and Cantrell [Cantrell and Yost, 1990; Yost and Cantrell, 1990], P = SA 2 (2.9) k 2 ha 2 By definition, y is an intrinsic material property representing the amount of nonlinearity in the stress-strain relationship. However, because of the asymptotic nature of solution (2.7), the second equal sign in (2.9) only holds for very small values of y. Thus, strictly speaking, /? becomes material constant only when the material nonlinearity is small or when the amplitude of the incident waves is small [Yost and Cantrell, 1990]. For higher values of y, the ultrasonic nonlinear parameter ft becomes dependent not only on the material, but also on the incident wave. Such dependency, in principle, can be found by 5

26 continuing the asymptotic analysis to higher order terms. However, the algebra becomes rather complex. To observe higher order terms more easily, a finite element analysis of the adhesive joint was conducted. The one-dimensional numerical model is shown in Fig A 5-cycle harmonic load of 2MHz was applied as the incident wave. The thickness of the adhesive layer is 0.24mm. At 2 MHz, the wavelength in the adhesive is about 3.3 mm. In the numerical calculations, the stress-strain relationship given by (2.5) was used with y =0,1.0,10, and 30, respectively. The computation was carried out using the finite element program ABAQUS, and stress field was obtained as a function of time. For 7 = 10, Fig. 2.3 shows the Fourier transform of the stresses at three locations, A, B and C, as indicated in Fig Note that, at point A, the wave has not reached the nonlinear region yet and therefore, can be viewed as the incident wave. Point B is at the center of the adhesive, while point C is at a location after the wave has gone through the adhesive. Fig. 2.3 clearly shows that the higher order harmonics are indeed generated by the nonlinearity of the adhesive material. Higher order harmonics can be seen clearly up to the third order (the peak at 6 MHz) for the case considered here. Comparison of the corresponding nonlinear parameter P is given in Fig. 2.4 for different values of y. It is seen clearly from Fig. 2.4 that higher value of y yields higher nonlinear parameter p. However, the relationship between p and y is not linear. This indicates that the asymptotic solution (2.7) has a very limited range of applicability. 3. Through Transmission Measurements Through transmission tests were conducted, in order to measure the higher order harmonics and to correlate the amplitude of the higher order harmonics to the cure state 6

27 of the adhesive joints. This section discusses sample preparation, test setup and the measurement methods used in the through transmission tests. Test Samples The test samples used in this study were provided by the Boeing Co. The samples consist of two aluminum plates bonded together by an adhesive layer. The adhesive is a thermosetting modified epoxy, AF-163-2K, in sheet form (knit supporting carrier) made by the 3M Company. The plates are 2024 aluminum. Relevant material constants are listed in Table 1. As illustrated in Fig. 3.1, the bonded area of the specimen is 12.7 cm x 17.8 cm (5.0 x 7.0 ). The adhesive (bondline) thickness is approximately 0.32 mm (12.6 mils) and the adherend's thickness is 1.6 mm (63 mils). The aluminum plates were anodized and primed prior to application of the adhesive. The joint was then placed in a temperature/pressure oven for curing. All four samples used in this study were prepared with the same procedure except the curing conditions. The different curing schedules for the four samples are listed in Table 2. The resulting bond strengths due to different curing schedules are also listed in Table 2. The normal (optimal) curing schedule is 121 C (250 F) for 90 minutes under 0.34MPa (50 psi). Sample A was cured under this condition. It is seen that samples with different state of curing show drastically different bond strength. It is anticipated that such differences in the curing state can be characterized nondestructively and correlated with the higher order harmonics. Experimental Setup 7

28 A block diagram of the experimental set up is shown in Fig 3.2. A 40 cycle timeharmonic signal of 2MHz was generated by a Wavetek function generator. The signal was amplified by a high voltage amplifier (ENI, DC ~ 10MHz, 50dB) to obtain a high amplitude driving voltage for the generating transducer. A typical output signal of the function generator and the amplifier are shown in Fig The highest output voltage of the amplifier used in the experiment was 350 volts. A narrow-band contact PZT transducer was used as the generating transducer. Its center frequency is 2MHz (Ultran, KC50-2,1.25MHz at -6dB). The incident ultrasonic wave from the generating transducer was transmitted perpendicularly through the adhesive layer. The receiver is a narrowband contact PZT transducer with 4MHz center frequency (Ultran, KC50-4, 3.5MHz at - 6dB). The output signal fit) of the receiver was recorded by an oscilloscope (Tektronix, 150MHz) and analyzed on a personal computer. A typical received signal is shown in Fig The sample and the two contact PZT transducers were fixed by two aluminum plates with a cylindrical cavity on each side, respectively, to hold the transducers at the same position as shown in Fig For efficient signal generation, a coupling liquid was used between the transducer and the sample. In addition, pressure on the transducer/sample interface can be varied by adjusting the four screws on the fixture. Testing and Signal Processing During the through transmission test, a 40-cycle time-harmonic signal of 2MHz was generated by the function generator, then amplified by the high voltage amplifier and sent to the generating transducer. The signal received by the receiving transducer, J[t), 8

29 was recorded by the oscilloscope. Finally, the data was processed using the Fast Fourier Transform (FFT) to obtain the frequency spectra, f m \ = 1 S Y J f(mat)exp(2mmn/n), m = 0, 1,2 AM (3.1) NAt) Ntf where N is the total number of sampling points and At is the time interval between the sampling points. The amplitude of the fundamental frequency and the higher order harmonic components can then be defined as (see Appendix) A. = r nco F 0 ^ In ) n = 1,2,3... (3.2) where co 0 is the fundamental circular frequency of the generating transducer. In this study, f Q = co 0 1 In = 2MHz was used. The amplitude of the fundamental frequency component, A x, in the received signal^') is plotted in Fig. 3.6 as a function of the incident voltage V i. The linear relationship between A { and V i confirms that the generation and receiving systems are operating in their linear regime within the voltage range used. Following (2.9), the nonlinear parameter of the adhesive is thus defined by /? = 4^7 (3-3) This nonlinear parameter will be used to characterize the cure state of the adhesive joints. Since /? depends on the amplitude of the incident wave, care must be given to ensure that the same incident wave is used for all samples, if one needs to compare the /? values between different samples. To this end, the tightness of the transducer/sample 9

30 assembly in each test is adjusted through the adjustable screws in the test apparatus so that the received signals have the same amplitude for all the samples. 4. Results and Observations Values of the nonlinear parameter /3 were measured using the procedures described in the previous sections. The results obtained from the three samples cured under various curing schedules (detailed in Table 2) were obtained and are presented in Fig Note that sample Bl was cured under the optimal conditions, while samples B2 and B3 were under-cured (lower temperature and shorter time). Clearly, the under-cured samples show higher values of the ultrasonic nonlinearity parameter. The more under cured the sample is, the higher the nonlinear parameter (3. As a final remark, it should be mentioned that the analytical and numerical analyses of Section 2 indeed indicate that higher order harmonics are generated by the material nonlinearity, and the experimental tests collaborate this, showing a significant increase in the nonlinear parameter for under-cured adhesives. However, the fundamental relationship between the curing state and the amount of nonlinearity in the adhesive is still an open question; This study only demonstrates that there is indeed a correlation between the nonlinear parameter and the curing state. Further investigation is needed to establish the quantitative relationship between the nonlinear parameter and the degree of curing. References J. D. Achenbach and O. K. Parikh, "Ultrasonic analysis of nonlinear response and strength of adhesive bonds," J. Adhesion Sci. Technol. Vol. 5, No. 8, pp (1991). R. F. Anastasi and M. J. Roberts, "Acoustic Wave propagation in an adhesive bond model with degrading interfacial layers," MTL TR 92-63, U.S. ARMY Materials Technology Laboratory (1992). 10

31 T. P. Berndt and R. E. Green, "Feasibility study of a nonlinear ultrasonic technique to evaluate adhesive bonds," Private communication (1998). D. R. Bland, Nonlinear Dynamic Elasticity, Blaisdell Publishing Company, Waltham, Massachusetts (1969). A. Bostrom and G. Wickham, "On the boundary conditions for ultrasonic transmission by partially closed cracks," J. of NDE, Vol. 10, pp , (1991). J. H. Cantrell and W. T. Yost, "Material Characterization using acoustic nonlinearity parameters and harmonic generation: Effects of crystalline and amorphous structures," Review of Progress in QNDE, Vol. 13B, pp (1990). S. Hirose and M. Kitahara, "Time domian BIE applied to flaw type recognition," Review of Progress in QNDE, Vol. 10A, pp (1992). H. Kolsky, Stress Waves in Solids, Dover Publications, New York (1963). G. M. Light and H. Kwun, "Nondestructive evaluation of adhesive bond quality, State-of-the-art review," NTIAC-89-1, June M. J. S. Lowe and P. Cawley, "The applicability of plate wave techniques for the inspection of adhesive and diffusion bonded joints," J. of NDE, Vol. 13, pp (1994). P. B. Nagy, P. McGowan, and L. Adler, "Acoustic nonlinearities in adhesive joints," Review of Progress in QNDE, Vol. 9, pp (1991). S. Pangraz and W. Arnold, "Quantitative determination of nonlinear binding forces byultrasonic technique," Review of Progress in QNDE, Vol. 13B, pp (1994). 0. K. Parikh and J. D. Achenbach," Analysis of nonlinearly viscoelastic behavior of adhesive bonds," J. of NDE, Vol. 11, pp (1992). J. M. Richardson, "Harmonic generation at an unbounded interface -1. Planar interface between semi-infinite elastic media," Int. J. of Engineering Science, Vol. 17, pp (1979). J. L. Rose, K. M. Rajana and M. K. T. Hansch,"Ultrasonic guided waves for NDE of adhesively bonded structures," J. of Adhesion, Vol. 50, pp (1995). J. L. Rose, W. Zhu and M. Zaidi, "Ultrasonic NDT of titanium diffusion bonding with guided waves," Materials Evaluation, Vol. 56, No. 4, pp (1998). Z. Tang, A. Cheng and J. D. Achenbach, "An ultrasonic technique to detect nonlinear behavior related to degradation of adhesive bonds," Review of Progress in QNDE, 1997 (in press). R. Truell, C. Elbaum and B.B. Chick, "Ultrasonic Methods in Solid State Physics," Academic Press, New York, (1969). W. T. Yost and J. H. Cantrell, "Material Characterization using Acoustic Nonlinearity Parameters and Harmonic Generation: Engineering Materials," Review of Progress in QNDE, Vol. 13B, pp (1990). 11

32 Appendix First, consider a time domain signal /(/) = A n exp(-incot) (A.1) Substitution of (A.l) into (3.2) yields F f m ^ ynatj Next, by making use of the identity _.. nconat. k 2m(m ) 2n N (A.2) J N-l lim V exp 2m(m - n) N = 8. (A.3) in (A.2), one concludes that F f m ^ KNAtj m when NAt m when NAt nco 2n nco In (A.4) or, = A. (A.5) \2n j This proves (3.2). 12