Vamshi Krishna Chillara

Review of nonlinear ultrasonic guided wave nondestructive evaluation: theory, numerics, and experiments

Abstract. Interest in using the higher harmonic generation of ultrasonic guided wave modes for nondestructive evaluation continues to grow tremendously as the understanding of nonlinear guided wave propagation has enabled further analysis. The combination of the attractive properties of guided waves with the attractive properties of higher harmonic generation provides a very unique potential for characterization of incipient damage, particularly in plate and shell structures. Guided waves can propagate relatively long distances, provide access to hidden structural components, have various displacement polarizations, and provide many opportunities for mode conversions due to their multimode character. Moreover, higher harmonic generation is sensitive to changing aspects of the microstructures such as to the dislocation density, precipitates, inclusions, and voids. We review the recent advances in the theory of nonlinear guided waves, as well as the numerical simulations and experiments that demonstrate their utility.

Interaction of guided wave modes in isotropic weakly nonlinear elastic plates: Higher harmonic generation

A generalized approach is presented to analyze the nature of guided wave mode interactions in isotropic weakly nonlinear elastic plates. The problem formulation is carried out in terms of the displacement gradient, which facilitates systematic analysis of mode interactions in general and that of higher harmonic generation in particular. Only cumulative harmonics are analyzed; these (1) have nonzero power flow and (2) are phase matched. Results indicate that the interaction of Rayleigh-Lamb modes of the same nature (symmetric or antisymmetric) can generate only cumulative harmonics that are symmetric modes, while the interaction between modes of opposite nature can generate only cumulative harmonics that are antisymmetric modes. A methodology for assessing cumulative higher harmonic generation (e.g., the third harmonic) is also proposed.

Nonlinear guided waves in plates: a numerical perspective.

Harmonic generation from non-cumulative fundamental symmetric (S0) and antisymmetric (A0) modes in plate is studied from a numerical standpoint. The contribution to harmonic generation from material nonlinearity is shown to be larger than that from geometric nonlinearity. Also, increasing the magnitude of the higher order elastic constants increases the amplitude of second harmonics. Second harmonic generation from non-phase-matched modes illustrates that group velocity matching is not a necessary condition for harmonic generation. Additionally, harmonic generation from primary mode is continuous and once generated, higher harmonics propagate independently. Lastly, the phenomenon of mode-interaction to generate sum and difference frequencies is demonstrated.

Third harmonic shear horizontal and Rayleigh Lamb waves in weakly nonlinear plates

The third order harmonic generation (third harmonics as well as cubic sum and difference harmonics) due to the cubic interaction of two collimated elastic waves in a homogeneous, isotropic, weakly nonlinear plate is investigated by using a fourth order expansion of strain energy density to formulate the nonlinear boundary problems. Waves with both shear horizontal (SH) and Rayleigh Lamb (RL) nature are considered as primary or tertiary wave fields. The non-zero power flux condition is evaluated using characteristic parity matrices of the cubic nonlinear forcing terms and third order harmonic mode shapes. Results indicate that waves with either SH or RL nature receive power flux from a specific pattern of primary mode interaction. Further analytical evaluation of the synchronism condition enables identification of primary SH and RL modes that are able to generate cumulative third harmonics. The primary SH modes are shown to be holo-internal-resonant with third harmonic SH fields. This simply means that all points on the primary dispersion curves are internally resonant with third harmonics, which is not the case for second harmonics. Such flexibility will be advantageous for laboratory and field measurements.

Second harmonic generation in composites: Theoretical and numerical analyses

Second harmonic generation in a transversely isotropic plate and a symmetric compositelaminate is analyzed from a theoretical perspective. The strain energy function for a nonlinear elastic transversely isotropic material is expressed in terms of the five invariants of the Green-Lagrange strain tensor. Internal resonance conditions for the generation of cumulative second harmonics indicate that a cumulative second harmonic exists when the primary-secondary mode pair satisfies the phase matching and non-zero power flux criteria. In particular, for transversely isotropic plates, when the primary mode propagates along the material principal direction, only symmetric second harmonic Lamb-like wave modes can be cumulative. Also, when the primary wave propagates along other directions, only symmetric second harmonic modes can be generated. Additionally, for the case of symmetric compositelaminates, only symmetric modes can be generated as cumulative second harmonics regardless of the propagation direction of the primary mode. To validate the above theoretical predictions, finite element simulations were conducted for mode pairs that are: (i) phase matched but have zero power flux, (ii) not phase matched but have non-zero power flux, and (iii) internally resonant i.e., satisfying both phase matching and non-zero power flux criterion. The results obtained from the simulations corroborate the theoretical findings for both transversely isotropic plates and symmetric compositelaminates.

Guided wave mode selection for inhomogeneous elastic waveguides using frequency domain finite element approach.

This article describes the use of the frequency domain finite element (FDFE) technique for guided wave mode selection in inhomogeneous waveguides. Problems with Rayleigh-Lamb and Shear-Horizontal mode excitation in isotropic homogeneous plates are first studied to demonstrate the application of the approach. Then, two specific cases of inhomogeneous waveguides are studied using FDFE. Finally, an example of guided wave mode selection for inspecting disbonds in composites is presented. Identification of sensitive and insensitive modes for defect inspection is demonstrated. As the discretization parameters affect the accuracy of the results obtained from FDFE, effect of spatial discretization and the length of the domain used for the spatial fast Fourier transform are studied. Some recommendations with regard to the choice of the above parameters are provided.

Nonlinear guided waves in plates undergoing localized microstructural changes

Nonlinear guided wave propagation in plates with localized micro-scale damage is investigated from a numerical standpoint. The role and interplay of three important aspects, namely damage distribution, damage intensity and its spatial extent along the direction of wave propagation on second harmonic generation of guided waves from the S0 mode at 0.5 MHz is studied. Second harmonic generation from the S0 mode (0.5 MHz) and the S1−S2 mode pair (longitudinal wave speed) is also investigated for varying degrees of micro-scale damage through the thickness. While second harmonic generation from the S0 mode was found to depend only on the volume fraction of damage through the thickness, the same for S1 mode revealed a non-monotonic response to through- thickness damage and was more due to the contribution from the surface damage in comparison to volumetric damage. Hence, it appears that second harmonic generation from the S1−S2 mode pair can be used to efficiently characterize and detect surface damage.

Low-frequency ultrasonic Bessel-like collimated beam generation from radial modes of piezoelectric transducers

We present a very simple approach to generate a collimated ultrasonic beam that exploits the natural Bessel-like vibration pattern of the radial modes of a piezoelectric disc with lateral clamping. This eliminates the need for the conventional annular Bessel pattern of the electrodes with individual electrode excitation on the piezo-disc, thus simplifying the transducer design. Numerical and experimental studies are carried out to investigate the Bessel-like vibration patterns of these radial modes showing an excellent agreement between these two studies. Measured ultrasonic beam-profiles in water from the radial modes confirm the profile to be a Bessel beam. Collimated beam generation from radial modes is investigated using a coupled electromechanical finite-element model. It is found that clamping the lateral edges of piezoelectric transducers results in a high-degree of collimation with practically no side-lobes similar to a parametric array beam. Ultrasonic beam-profile measurements in water with both...

Towards a micro-mechanics based understanding of ultrasonic higher harmonic generation

The need for micro-mechanics based understanding leading to meso-scale models for understanding relation between microstructure and ultrasonic higher harmonic generation is emphasized. Three important aspects of material behavior, namely tension-compression asymmetry, shear-normal coupling and deformation induced anisotropy that are relevant to ultrasonic higher harmonic generation are identified. Of these, the role of tension-compression asymmetry in micro-scale material behavior on ultrasonic higher harmonic generation is investigated in detail. It is found that the tension-compression asymmetry is directly related to ultrasonic even harmonic generation and an energy based measure is defined to quantify the asymmetry. Using this energy based measure, a homogenization based approach is employed to quantify the acoustic nonlinearity in material with micro-voids and the findings are discussed.

Higher harmonic guided waves in isotropic weakly non-linear elastic plates

Use of nonlinear guided waves appears to be a promising option for material characterization, but appropriate guided wave mode selection is a critical issue. To that end, an outline of a comprehensive analysis as to which guided wave modes have the capability to generate cumulative second harmonic guided waves is presented. The problem of higher harmonic guided wave generation in plates is studied and an approach to predict the nature of higher harmonics is presented.