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epoxy composites
Ultrasonics International 87 abstracts with dimensions of the order of the wavelengths employed, have been the subject of both experimental and numerical investigations. The experimental results are normally in the form of time dependent surface displacements which are obtained using lasers for both ultrasound generation and for detection. Interpretation of the results obtained using such systems has been the subject of debate as no analytical results are available for the mid-frequency scattering encountered at features such as the surface slot. A wide range of otherwise analytically intractable elastic wave scattering problems have been investigated using numerical models based on finite difference methods. This study has brought together both experimental and numerical model data generated for identical configurations. The laser probe records sets of the vertical components of displacement and the models also provide the vertical components of displacement on the surface and also numerical visualisations which show snapshots of the complete wave field. Both sets data are in good agreement, showing the same primary pulses. Comparison and analysis of this data has provided improved understanding of the various scattered and mode-converted waves generated at the 90 ° and 270 ° corners, and for a range of different series of slots with variations in both their width and their depth.
Full field mapping of transient surface acoustic waves using heterodyne holographic interferometry
J.W. Wagner, The Johns Hopkins University, Baltimore, USA Heterodyne techniques applied to holographic interferometry provide an increase in sensitivity of nearly three orders of magnitude over classical holographic interferometry. Consequently, surface displacements on the order of Angstroms may be mapped with great precision using these techniques. When combined with pulsed holographic recording, it is possible to measure and map surface displacements associated with high speed transient phenomena such as acoustic waves. There are several attractive features of holographic techniques for studying acoustic interactions with materials and structures. Unlike piezoelectric transducers, holographic techniques are noncontacting and require no couplant. Data is obtained simultaneously for all points on a specimen surface and may be archived on the hologram for detailed study long after the acoustic event. Obviously one sacrifices the continuoustime data record provided by single point transducers in order to obtain full field data acquisition and display. Also there are some practical limitations on heterodyne holographic techniques making them somewhat less sensitive than piezoelectrics. However several options are being pursued which promise to improve system performance and thus expand the role of holographic techniques in the study of acoustic phenomena.
Laser doppler heterodyne interferometry for photoacoustic applications
H.L Ringermacher, United Technologies Research Center, E. Hartford, USA A great variety of laser optical detection methods are being used to sense photoacoustic or thermal wave responses in materials. These include Michelson interferometry and heterodyne techniques for both ultrasonics and photoacoustics, as well as Mirage or Optical Beam Deflection and surface reflectance techniques for thermal waves. In this paper we discuss an FM detected Doppler Heterodyne technique for
photoacoustics and ultrasonic sensing. This method offers the advantage of large dynamic range for input light intensity by virtue of its sensitivity to the Doppler shift of the return light rather than the signal amplitude. Initial results incorporating this detection scheme will be presented with applications to photoacoustic imaging of subsurface defects in metals and ceramics.
N o n - l i n e a r acoustics Ultrasonic characterization of the non-linear elastic properties of graphite/epoxy composites
W.H. Prosser and R.E. Green, Jr, The Johns Hopkins University, Baltimore, USA Nonlinear elastic properties are of great importance in materials characterization and nondestructive evaluation of materials. They provide information about the interatomic bonding in crystals and are related to anharmonic properties such as thermal expansion. Nonlinear properties are also used in the nondestructive determination of applied and residual stress and attempts have been made to use them to nondestructively determine the ultimate strength of materials. Ultrasonics provides a practical way to measure these properties. Harmonic generation, elastic wave interactions to produce other waves, and changes in wave velocity as a function of applied stress or temperature are all manifestations of nonlinear elastic wave propagation phenomena. Measurement of these effects can be used to calculate the nonlinear elastic moduli. In the present research, measurements were made of the stress and temperature dependence of the ultrasonic 'natural" wave velocity in a unidirectional graphite/epoxy composite (T300/5208). These measurements were made using a pulsed phase locked loop interferometer operating at 2.25 MHz. The stress dependence measurements were made under conditions of both hydrostatic and uniaxial stress. Twenty-seven different combinations of stress, wave mode, and propagation direction were evaluated. The temperature dependence of velocity was measured for nine different combinations of wave mode and propagation direction. Theory predicts that the relationship between the normalized change in 'natural" velocity and stress is linear if terms up to third order are considered. However, the stress dependence of normalized "natural" velocity was nonlinear (quadratic) for several wave modes which indicated higher than third order nonlinear effects. Although unidirectional fiber composites are usually modeled as being tranversely isotropic, the present experiments demonstrated measurable deviations from tranversely isotropic behaviour. These results indicate that the material more correctly possessed orthotropic symmetry although the deviations from transverse isotropy were small. Using the slopes of the stress-velocity curves and the previously measured second order elastic moduli, some of the values for third order elastic moduli were determined. These were calculated for both the transversely isotropic and orthotropic models using a least-squares fit to reduce the data. Graphite/epoxy composites offer great potential for applications in the aerospace industry because of their high strength and light weight. However, there is a need to nondestructively evaluate important engineering properties such as ultimate strength and residual strength after impact and fatigue loading. The present research provides preliminary measurements for a study of the relationships between nonlinear elastic properties and these important engineering properties permitting development of new nondestructive evaluation methods for these materials. The present measurements also provide the basis for ultrasonic techniques to determine residual stress (strain) which may develop upon
Ultrasonics 1987 Vol 25 November
345
Ultrasonics International 87 abstracts curing of composite materials due to the different coefficients of thermal expansion between fiber and matrix.
Taking diffraction into account in non-linear parameter acoustic tomography
A. CaL Y. Nakagawa, W. Hou, N. Arnold and G. Wade, University of California, Santa Barbara, USA When two collinear acoustic beams with different frequencies are launched into a nonlinear medium waves at the difference frequency will be generated. This phenomenon has recently been put in use for tomographically imaging the acoustic non-linear parameter in biological specimens. However, in presently employed reconstruction methods, the acoustic energy is assumed to travel in straight-line paths. In this paper, we describe an approach to take diffraction into account. Instead of narrow beams, we use planner waves. Two of them with different frequencies are projected in the same direction. The forward scattered wavefields at these two frequencies as well as at the difference frequency are measured. The algorithmic formulation relies on the use of two simultaneous governing wave equations for the incident and difference-frequency waves. In this paper, we demonstrate the validity of the equations for tomographic application. Approximations are introduced to make the reconstruction problem solvable. The relationship between the measured data and the acoustic properties of the medium is derived. Algorithms to obtain tomograms of the non-linear parameter and the refractive index are presented.
Non-linear propagation in focused fields: experiment and theory
A.C. Baker, K. Anastasiadis and V.F. Humphrey, University of Bath, UK This paper presents the results of an extensive experimental study of finite-amplitude effects in focused acoustic fields. The results are compared with theoretical predictions obtained from a numerical solution of Kuznetsov's equation. Comparisons are also made with similar results for a plane transducer. The experimental results were obtained with a circular 2.25 MHz planar transducer to which perspex (polymethylmethacrylate) piano-concave lenses were added to give focused fields with gains of 3.7, 7.6 and 11.5. The pressure wavefields were measured with a 1 mm diameter PVdF membrane hydrophone mounted on a computer controlled translation stage that enabled the fields to be sampled with a high spatial frequency. The hydrophone output was digitized and Fourier analysed to provide details of the harmonic build up. The experimental results obtained at low drive levels confirmed that the transducer on its own and in combination with the focusing lenses performed as expected. Results for the magnitude of the fundamental and first four harmonics at high drive levels are presented for each configuration used, together with data for the relative phase of the second and the third harmonic. The axial variations show a number of similarities; in particular, the oscillations of the harmonics in the nearfield and the rapid build up beyond the last axial minimum before the focus. The experimental results are compared with theoretical predictions of a perturbation model (for the second harmonic) and a numerical solution of Kuznetsov's equation which incorporates the effects of non-linear distortion and diffraction (Aanonsen, S.I. et aL, J Acoust Soc Am (1984) 75(3) 749-768).
346
Ultrasonics 1987 Vol 25 November
Application of an enhanced parametric source
A.W.D. Jongens, University of Cape Town, South Africa The paper describes an enhanced parametric source and its application to the investigation of the properties of materials immersed in water. In the case of conventional methods of measuring the insertion loss and echo reduction of plates of material, which are typically half a metre in extent, the effect of the diffracted wave around the sample results in a lower limit in measuring frequency of approximately 50 kHz. The size of the plate is equivalent to 17 wavelengths at that frequency. Humphrey 1 employed a parametric source to produce an improved amplitude shading across the plate and was able to extend the lower frequency limit to approximately 10 kHz for the same size of plate. This paper describes how the lower frequency limit is extended still further by almost a decade by employing a principle first described by Ryder et al. 2. Two finite amplitude waves with a mean primary frequency of 1 MHz are radiated by a small transducer mounted in one end of a 650/~m thick PVC tube filled with a liquid with a sound speed half that of water. The length of the tube is short compared to the interaction length of the parametric array being equivalent to the collimated nearfield length at the mean primary frequency. An acoustic low-pass filter is attached to the other end of the tube. This attenuates the primary frequencies by more than 40 dB thereby permitting only the low difference frequency wave to insonify the plate and also to prevent nonlinear distortion to occur in the measuring hydrophone due to the primary waves. Use of the low sound speed liquid produces a 15 dB gain in difference frequency thereby significantly increasing the signal-to-noise ratio of the signal and an attendant decrease in signal processing time by an order of magnitude compared to Humphrey's experiments. The increased pressure amplitude is accompanied by an increased directivity and smaller 3 dB spot size resulting in the reduction in amplitude of the edge diffracted wave. These two factors permit the lower frequency limit to be reduced to approximately 2 kHz for the size of the tube and the liquid used. The size of the plate at this frequency is of the order of one wavelength across. References 1. Humphrey, V.F. The measurement of acoustic properties of limited size panels by use of a parametric source J Sound Vibr (1985) 98(1 ) 67-81 2. Ryder, J.D., Rogers, P.H. and Jarzynski, J. Radiation of difference frequency sound generated by nonlinear interaction in a silicone rubber cylinder. JASA (May 1976) 59(5) 1077-1086 Numerical simulation of ultrasonic flowmeters
A. Lygre, M. Vestrheim, P. Lunde and V. Berge, Chr. Michelsen Institute, Dept. of Science and Technology, N-5036 Fantoft-Bergen, Norway Transit-time ultrasonic gas flowmeters offer several advantages compared to other current flowmeter technology, and they have the potential of being developed into cost-effective and reliable flowmeters. One important step towards implementing more fully the advantages of ultrasonic flowmeter technology is to apply flowmeter simulation models in the design process. A simulation model which describes the signal transmission for a single acoustic beam in an ultrasonic transit-time flowmeter, is described here. Some of the capabilities of the model in predicting several important effects in the functioning of a flowmeter signal transmission channel are demonstrated for a given simplified set of design parameters.
Full field mapping of transient surface acoustic waves using heterodyne holographic interferometry
J.W. Wagner, The Johns Hopkins University, Baltimore, USA Heterodyne techniques applied to holographic interferometry provide an increase in sensitivity of nearly three orders of magnitude over classical holographic interferometry. Consequently, surface displacements on the order of Angstroms may be mapped with great precision using these techniques. When combined with pulsed holographic recording, it is possible to measure and map surface displacements associated with high speed transient phenomena such as acoustic waves. There are several attractive features of holographic techniques for studying acoustic interactions with materials and structures. Unlike piezoelectric transducers, holographic techniques are noncontacting and require no couplant. Data is obtained simultaneously for all points on a specimen surface and may be archived on the hologram for detailed study long after the acoustic event. Obviously one sacrifices the continuoustime data record provided by single point transducers in order to obtain full field data acquisition and display. Also there are some practical limitations on heterodyne holographic techniques making them somewhat less sensitive than piezoelectrics. However several options are being pursued which promise to improve system performance and thus expand the role of holographic techniques in the study of acoustic phenomena.
Laser doppler heterodyne interferometry for photoacoustic applications
H.L Ringermacher, United Technologies Research Center, E. Hartford, USA A great variety of laser optical detection methods are being used to sense photoacoustic or thermal wave responses in materials. These include Michelson interferometry and heterodyne techniques for both ultrasonics and photoacoustics, as well as Mirage or Optical Beam Deflection and surface reflectance techniques for thermal waves. In this paper we discuss an FM detected Doppler Heterodyne technique for
photoacoustics and ultrasonic sensing. This method offers the advantage of large dynamic range for input light intensity by virtue of its sensitivity to the Doppler shift of the return light rather than the signal amplitude. Initial results incorporating this detection scheme will be presented with applications to photoacoustic imaging of subsurface defects in metals and ceramics.
N o n - l i n e a r acoustics Ultrasonic characterization of the non-linear elastic properties of graphite/epoxy composites
W.H. Prosser and R.E. Green, Jr, The Johns Hopkins University, Baltimore, USA Nonlinear elastic properties are of great importance in materials characterization and nondestructive evaluation of materials. They provide information about the interatomic bonding in crystals and are related to anharmonic properties such as thermal expansion. Nonlinear properties are also used in the nondestructive determination of applied and residual stress and attempts have been made to use them to nondestructively determine the ultimate strength of materials. Ultrasonics provides a practical way to measure these properties. Harmonic generation, elastic wave interactions to produce other waves, and changes in wave velocity as a function of applied stress or temperature are all manifestations of nonlinear elastic wave propagation phenomena. Measurement of these effects can be used to calculate the nonlinear elastic moduli. In the present research, measurements were made of the stress and temperature dependence of the ultrasonic 'natural" wave velocity in a unidirectional graphite/epoxy composite (T300/5208). These measurements were made using a pulsed phase locked loop interferometer operating at 2.25 MHz. The stress dependence measurements were made under conditions of both hydrostatic and uniaxial stress. Twenty-seven different combinations of stress, wave mode, and propagation direction were evaluated. The temperature dependence of velocity was measured for nine different combinations of wave mode and propagation direction. Theory predicts that the relationship between the normalized change in 'natural" velocity and stress is linear if terms up to third order are considered. However, the stress dependence of normalized "natural" velocity was nonlinear (quadratic) for several wave modes which indicated higher than third order nonlinear effects. Although unidirectional fiber composites are usually modeled as being tranversely isotropic, the present experiments demonstrated measurable deviations from tranversely isotropic behaviour. These results indicate that the material more correctly possessed orthotropic symmetry although the deviations from transverse isotropy were small. Using the slopes of the stress-velocity curves and the previously measured second order elastic moduli, some of the values for third order elastic moduli were determined. These were calculated for both the transversely isotropic and orthotropic models using a least-squares fit to reduce the data. Graphite/epoxy composites offer great potential for applications in the aerospace industry because of their high strength and light weight. However, there is a need to nondestructively evaluate important engineering properties such as ultimate strength and residual strength after impact and fatigue loading. The present research provides preliminary measurements for a study of the relationships between nonlinear elastic properties and these important engineering properties permitting development of new nondestructive evaluation methods for these materials. The present measurements also provide the basis for ultrasonic techniques to determine residual stress (strain) which may develop upon
Ultrasonics 1987 Vol 25 November
345
Ultrasonics International 87 abstracts curing of composite materials due to the different coefficients of thermal expansion between fiber and matrix.
Taking diffraction into account in non-linear parameter acoustic tomography
A. CaL Y. Nakagawa, W. Hou, N. Arnold and G. Wade, University of California, Santa Barbara, USA When two collinear acoustic beams with different frequencies are launched into a nonlinear medium waves at the difference frequency will be generated. This phenomenon has recently been put in use for tomographically imaging the acoustic non-linear parameter in biological specimens. However, in presently employed reconstruction methods, the acoustic energy is assumed to travel in straight-line paths. In this paper, we describe an approach to take diffraction into account. Instead of narrow beams, we use planner waves. Two of them with different frequencies are projected in the same direction. The forward scattered wavefields at these two frequencies as well as at the difference frequency are measured. The algorithmic formulation relies on the use of two simultaneous governing wave equations for the incident and difference-frequency waves. In this paper, we demonstrate the validity of the equations for tomographic application. Approximations are introduced to make the reconstruction problem solvable. The relationship between the measured data and the acoustic properties of the medium is derived. Algorithms to obtain tomograms of the non-linear parameter and the refractive index are presented.
Non-linear propagation in focused fields: experiment and theory
A.C. Baker, K. Anastasiadis and V.F. Humphrey, University of Bath, UK This paper presents the results of an extensive experimental study of finite-amplitude effects in focused acoustic fields. The results are compared with theoretical predictions obtained from a numerical solution of Kuznetsov's equation. Comparisons are also made with similar results for a plane transducer. The experimental results were obtained with a circular 2.25 MHz planar transducer to which perspex (polymethylmethacrylate) piano-concave lenses were added to give focused fields with gains of 3.7, 7.6 and 11.5. The pressure wavefields were measured with a 1 mm diameter PVdF membrane hydrophone mounted on a computer controlled translation stage that enabled the fields to be sampled with a high spatial frequency. The hydrophone output was digitized and Fourier analysed to provide details of the harmonic build up. The experimental results obtained at low drive levels confirmed that the transducer on its own and in combination with the focusing lenses performed as expected. Results for the magnitude of the fundamental and first four harmonics at high drive levels are presented for each configuration used, together with data for the relative phase of the second and the third harmonic. The axial variations show a number of similarities; in particular, the oscillations of the harmonics in the nearfield and the rapid build up beyond the last axial minimum before the focus. The experimental results are compared with theoretical predictions of a perturbation model (for the second harmonic) and a numerical solution of Kuznetsov's equation which incorporates the effects of non-linear distortion and diffraction (Aanonsen, S.I. et aL, J Acoust Soc Am (1984) 75(3) 749-768).
346
Ultrasonics 1987 Vol 25 November
Application of an enhanced parametric source
A.W.D. Jongens, University of Cape Town, South Africa The paper describes an enhanced parametric source and its application to the investigation of the properties of materials immersed in water. In the case of conventional methods of measuring the insertion loss and echo reduction of plates of material, which are typically half a metre in extent, the effect of the diffracted wave around the sample results in a lower limit in measuring frequency of approximately 50 kHz. The size of the plate is equivalent to 17 wavelengths at that frequency. Humphrey 1 employed a parametric source to produce an improved amplitude shading across the plate and was able to extend the lower frequency limit to approximately 10 kHz for the same size of plate. This paper describes how the lower frequency limit is extended still further by almost a decade by employing a principle first described by Ryder et al. 2. Two finite amplitude waves with a mean primary frequency of 1 MHz are radiated by a small transducer mounted in one end of a 650/~m thick PVC tube filled with a liquid with a sound speed half that of water. The length of the tube is short compared to the interaction length of the parametric array being equivalent to the collimated nearfield length at the mean primary frequency. An acoustic low-pass filter is attached to the other end of the tube. This attenuates the primary frequencies by more than 40 dB thereby permitting only the low difference frequency wave to insonify the plate and also to prevent nonlinear distortion to occur in the measuring hydrophone due to the primary waves. Use of the low sound speed liquid produces a 15 dB gain in difference frequency thereby significantly increasing the signal-to-noise ratio of the signal and an attendant decrease in signal processing time by an order of magnitude compared to Humphrey's experiments. The increased pressure amplitude is accompanied by an increased directivity and smaller 3 dB spot size resulting in the reduction in amplitude of the edge diffracted wave. These two factors permit the lower frequency limit to be reduced to approximately 2 kHz for the size of the tube and the liquid used. The size of the plate at this frequency is of the order of one wavelength across. References 1. Humphrey, V.F. The measurement of acoustic properties of limited size panels by use of a parametric source J Sound Vibr (1985) 98(1 ) 67-81 2. Ryder, J.D., Rogers, P.H. and Jarzynski, J. Radiation of difference frequency sound generated by nonlinear interaction in a silicone rubber cylinder. JASA (May 1976) 59(5) 1077-1086 Numerical simulation of ultrasonic flowmeters
A. Lygre, M. Vestrheim, P. Lunde and V. Berge, Chr. Michelsen Institute, Dept. of Science and Technology, N-5036 Fantoft-Bergen, Norway Transit-time ultrasonic gas flowmeters offer several advantages compared to other current flowmeter technology, and they have the potential of being developed into cost-effective and reliable flowmeters. One important step towards implementing more fully the advantages of ultrasonic flowmeter technology is to apply flowmeter simulation models in the design process. A simulation model which describes the signal transmission for a single acoustic beam in an ultrasonic transit-time flowmeter, is described here. Some of the capabilities of the model in predicting several important effects in the functioning of a flowmeter signal transmission channel are demonstrated for a given simplified set of design parameters.