Amid the nondestructive evaluation techniques available for the inspection of composite materials, only a few are suitable for implementation while the component is in service. The investigation examines the application of Lamb waves at low-frequency-thickness products for the detection of delaminations in thick composite laminates. Surface-mounted piezoelectric devices were excited with a tone burst to generate elastic waves in the structure. Experiments were carried out on composite beam specimens where wave propagation distances over 2 m were achieved and artificially induced delaminations as small as 1 cm2 were successfully identified. The feasibility of employing piezoelectric devices for the development of smart structures, where a small and lightweight transducer system design is required, has been demonstrated. The resonance spectrum method, which is based on the study of spectra obtained by forced mechanical resonance of samples using sine-sweep excitation, has been proposed as a technique for measuring the A0 Lamb mode phase velocity. The finite-element method was also used to investigate qualitatively the dynamic response of laminates to wave propagation. Several locations and spatial distribution of the actuators were examined showing the advantages of using transducers arrays for the inspection of large structures.

Real-time nondestructive evaluation of fiber composite laminates using low-frequency Lamb waves

Extraction of dispersion curves for waves propagating in free complex waveguides by standard finite element codes

A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plat theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.

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Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms

Acoustic emission was interpreted as modes of vibration in finite aluminum and graphite/epoxy plates. The `thin plate'' case of classical plate theory was used to predict dispersion curves for the two fundamental modes described by the theory and to calculate the shapes of flexural waveforms produced by a vertical step function loading. There was good agreement between the theoretical and experimental results for the aluminum. Composite materials required the use of a higher order plate theory (Reissner-Mindlin) combined with lamination theory in order to get good agreement with the measured velocities. Plate modes were shown to be useful for determining the direction of motion of a source. Thus, with a knowledge of the material, it may be possible to ascertain the type of the source. For example, particle impact on a plate could be distinguished from a crack growing in the plate. A high fidelity transducer was needed to distinguish the plate modes. After evaluating several types of transducers, a broadband ultrasonic transducer was found which satisfied the fidelity requirement and had adequate sensitivity over the 0.1 to 1 MHz range. The waveforms were digitized with a 5 MHz transient recorder. The dispersion curves were determined from the phase spectra of the time dependent waveforms. The aluminum plates were loaded by breaking a 0.5 mm. pencil lead against the surface of the plate. By machining slots at various angles to the plane of a plate, the direction in which the force acted was varied. Changing the direction of the source motion produced regular variations in the measured waveforms. Four composite plates with different laminate stacking sequences were studied. To demonstrate applicability beyond simple plates, waveforms produced by lead breaks on a thin-walled composite tube were also shown to be interpretable as plate modes. The tube design was based on the type of struts proposed for Space Station Freedom''s trussed structures.

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The propagation characteristics of the plate modes of acoustic emission waves in thin aluminum plates and thin graphite/epoxy composite plates and tubes

Measurements of the velocities of the extensional and flexural plate modes were made along three directions of propagation in four graphite/epoxy composite plates. The acoustic signals were generated by simulated acoustic emission events (pencil lead breaks or Hsu-Neilsen sources) and detected by broad band ultrasonic transducers. The first arrival of the extensional plate mode, which is nond ispersive at low frequencies, was measured at a number of different distances from the source along the propagation direction of interest. The velocity was det ermined by plotting the distance versus arrival time and computing its slope. Because of the large dispersion of the flexural mode, a Fourier phase velocity technique was used to characterize this mode. The velocity was measured up to a frequency of 160 kHz. Theoretical predictions of the velocities of these modes were also made and compared with experimental observations. Classical plate theory yielded good agreement with the measured extensional velocities. For predictions of the dispersion of the flexural mode, Mindlin plate theory, which includes the effects of shear deformation and rotatory inertia was shown to give better agreement with the experimental measurements.

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Plate Mode Velocities in Graphite/Epoxy Plates

Shear deformation and rotary inertia are included in plate theory to determine the dispersion curves for flexural waves propagating in laminated composite plates. The results of a unidirectional laminate are compared with the elasticity solutions for flexural waves traveling in transversely isotropic plates to determine the shear correction factors in the low frequency, long wavelength range. The values of the shear correction factors for the unidirectional composite laminate are in good agreement with the theoretical values calculated from static cylindrical bending. An acousto-ultrasonic technique using narrowband excitation frequencies is used to obtain experimental data for flexural waves. By measuring the phase velocities for different excitation frequencies, dispersion curves are generated. There is excellent agreement between the experimentally determined values and the theoretical results for aluminum and unidirectional composite plates. For symmetric cross-ply and quasi-isotropic laminates, the data definitely have the characteristic of a dispersion curve for flexural waves, although the agreement between analytic and experimental results is not quite as good. The results of the present work indicate that the inclusion of shear deformation and rotary inertia in plate theory improves the prediction of dispersion curves for flexural waves propagating in composite laminates and suggest that the acousto-ultrasonic technique can be used to characterize composite plates with and without damage since each material and stacking sequence gives distinct dispersion curves.

B. Tang

Papers

Low Frequency Flexural Wave Propagation in Laminated Composite Plates