Inversion algorithm for Lamb-wave-based depth characterization of acoustic emission sources in plate-like structures.

An inversion algorithm (termed AEDep) is proposed for estimating the depth of acoustic emission (AE) sources in plate-like structural components. The work is motivated by the need for characterizing early-stage fatigue crack growth in such components. The algorithm achieves depth estimation by automatically extracting the depth-dependent amplitude ratio between the fundamental Lamb modes which comprise the AE signals. A finite element model is designed to study the frequency-dependent forward problem of Lamb wave motion due to a given source, from which the relation between source depth and amplitude ratio is established. Elastodynamic theory is used to validate the model in the frequency domain, as well as to derive a sensor tuning factor which may be incorporated into the solution. The proposed algorithm was tested on two plate-like specimens: a 6061-T6 aluminum plate and a 2025-T6 aluminum aircraft fuselage panel. Validation of the algorithm was achieved by generating controlled AE sources at various depths along the edges of the specimens, in the form of Hsu-Nielsen pencil lead breaks. Good agreement was found in the aluminum plate between the true and estimated source depths. A slight decrease in accuracy was found in the fuselage panel between the true values and their estimations. However, both experimental cases demonstrated the ability to distinguish between sources originating near the mid-plane of a plate-like structure from those near the surface. Lastly, the fast computation of the inversion algorithm shows strong potential for real-time monitoring applications.

Computation of propagating and non-propagating guided modes in nonuniformly stressed plates using spectral methods.

This paper presents a numerical approach based on spectral methods for the computation of guided ultrasonic wave modes (i.e., Lamb and shear horizontal) in nonuniformly stressed plates. In particular, anisotropic elastic plates subjected to a normal stress profile, which varies nonuniformly over their thickness, are considered. The proposed approach computes the modeshapes and the full three-dimensional dispersion spectrum (i.e., real frequency, complex wavenumber). It therefore includes both propagating (real wavenumber) and non-propagating (complex wavenumber) modes. Furthermore, an approach for robustly post-processing the dispersion spectra in order to compute the group velocity of propagating modes is presented, which is based on a spectral quadrature method. Numerical results are presented for two case studies: (1) a bending profile in a fiber-reinforced graphite/epoxy plate, and (2) an exponential profile in a silver plate. The results show the computational efficiency (i.e., spectral convergence) of the proposed method compared to other existing approaches such as the sublayering and finite element methods.

Higher order longitudinal guided wave modes in axially stressed seven-wire strands.

This paper investigates the effect of axial stress on higher order longitudinal guided modes propagating in individual wires of seven-wire strands. Specifically, an acoustoelastic theory for a rod is used to predict the effect of stress on the phase velocity of guided modes in a strand. To this end, the exact acoustoelastic theory for an axially stressed rod is adapted for small deformations. Aside from the exact theory, approximate phase velocity changes (derived from both theory and experiment) are proposed, without the need to solve for dispersion curves. To validate the use of rod theories for strands, a custom-built prestressing bed was designed to apply axial load (up to 50% of yield) to a strand while conducting guided wave measurements. Higher order modes were excited in individual wires, and their phase velocity change under stress is compared to the exact acoustoelastic theory. Furthermore, it is shown that the proposed approximate phase velocity changes derived from theory and experiment only differ by roughly 2% from their exact counterparts. Higher order modes are shown to have stable stress dependence near their peak group velocity, which is beneficial for stress measurement. Additionally, linear stress dependence is observed, which is predicted by rod theories. Due to the unavailability of third order elastic constants for the steel strand, constants for a steel with similar Carbon content (0.6% C Hecla 17) were used as representative values in the theory. Using the Hecla 17 constants, roughly 15% mismatch in the slope of the linear stress dependence was observed when compared to the measurements on a steel strand.

The effect of applied stress on the phase and group velocity of guided waves in anisotropic plates.

This paper presents an analytical formulation for the phase and group velocity of acoustoelastic guided waves in anisotropic plates. Uniform in-plane applied stress is considered, with both arbitrary propagation and stress directions. An expression for the energy velocity in a stressed anisotropic plate is derived, from which the group velocity is computed. Since the wavefront and group velocity directions generally differ, the deviation angle between the two is also studied. A method is proposed for verifying the consistency of the formulation, based on the correspondence between a direct and an indirect formulation. Analytical results are presented for a unidirectional fiber-reinforced graphite/epoxy composite plate. The plate is considered homogeneous for large wavelength to fiber diameter ratios. Results for the phase velocity, group velocity, and deviation angle are presented for two uniaxial applied loading cases. These are used to study the effect of stress for various propagation and stress directions. The linearity of the deviation angle with respect to stress is also demonstrated. Exact correspondence between the direct and indirect formulations is observed, which verifies consistency. The importance of accounting for shear strain in the indirect formulation is also demonstrated, which has not been noted in previous guided wave studies.

Effect of pressurization on helical guided wave energy velocity in fluid-filled pipes.

The effect of pressurization stresses on helical guided waves in a thin-walled fluid-filled pipe is studied by modeling leaky Lamb waves in a stressed plate bordered by fluid. Fluid pressurization produces hoop and longitudinal stresses in a thin-walled pipe, which corresponds to biaxial in-plane stress in a plate waveguide model. The effect of stress on guided wave propagation is accounted for through nonlinear elasticity and finite deformation theory. Emphasis is placed on the stress dependence of the energy velocity of the guided wave modes. For this purpose, an expression for the energy velocity of leaky Lamb waves in a stressed plate is derived. Theoretical results are presented for the mode, frequency, and directional dependent variations in energy velocity with respect to stress. An experimental setup is designed for measuring variations in helical wave energy velocity in a thin-walled water-filled steel pipe at different levels of pressure. Good agreement is achieved between the experimental variations in energy velocity for the helical guided waves and the theoretical leaky Lamb wave solutions.