An effective inverse analysis computer program that integrates nonlinear optimization algorithm and forward dynamic analysis of multilayered medium is developed for inferring structural and material properties (e.g., modulus, thickness, and the number of layers) of the medium. Using dynamic deflection information obtained from forward dynamic analysis of the multilayered medium as a hypothetical deflection measured from the field during pavement nondestructive evaluation (NDE) using falling weight deflectometer, the estimated parameters of the medium are compared with the known true parameters of the medium used to perform the static and forward dynamic analyses. Based on two different multilayered media, a number of important observations and conclusions are made regarding the accuracy and efficiency of the proposed numerical algorithms and developed computer program. The inversion methods presented in this paper show improved NDE results over many of the existing algorithms.

A rigorous theoretical foundation for solving elastodynamic inverse problem of multilayered media under an impulse load is established in this paper. The inversion is built upon the forward dynamic analysis of multilayered elastic media using transfer matrix approach, with which displacement continuity is assumed at the interfaces of upper and lower adjacent layers. Formulations for inverse analysis are derived in both the time domain and the complex frequency domain. Least square estimates and nonlinear optimization algorithms are used to implement parameter identification. The proposed theory and formulae can be utilized to develop a computer software for nondestructive evaluation of laminated civil and aerospace structure (highway and airport pavements, bridge decks, soil foundations, aircraft wing, etc.), exploration and dynamic source detection and identification, and petroleum exploration in geophysics.

The vibratory punch problem for a viscoelastic half-space indented by a padded annular disk is investigated. By virtue of transform methods, the problem is formulated as a set of triple integral equations which are reducible to a Fredholm integral equation of the second kind. In the formulation, the response of a thin buffer which regularizes the load transfer to the semi-infinite solid is approximated via a plane stress-type solution. A set of numerical results is included to demonstrate the effect of padding characteristics on the dynamic system response. Apart from providing an interpretation tool for the nondestructive testing methods involving buffered annular loading systems, the present solution can be used as an effective approximation to the corresponding rigid-punch problem which has so far eluded a rigorous mathematical treatment.

A method of analysis is proposed for nondestructive evaluation of multiple cracks by means of the d.c. (direct current) potential drop technique. Two and three-dimensional multiple cracks are treated. A methodology for considering interaction of cracks based on the equation for an isolated crack is given to calculate the potential drop between both sides of a crack in multiple cracking in a plate. The inverse problem to evaluate the crack depth is analyzed by comparing the potential drop calculated in this way with the measurement. It is shown that the evaluated crack depth is in good agreement with the actual one.

Transient response of a composite plate with a near-surface delamination has been studied in this paper. A new technique developed by the authors to evaluate the Cauchy Principal Value integrals and the weakly singular integrals involved in the boundary integral equations has been employed and modifided to treat the corner points on the boundary. The time harmonic Green’s functions appearing in the boundary integral equation are evaluated by combining a stiffness method and the modal summation technique. To circumvent the difficulties associated with the evaluation of hypersingular integrals for cracks, the multidomain technique is employed. The accuracy and efficiency of the method are checked by comparing the displacements in a uniaxial graphite-epoxy plate containing a delamination with results obtained by a hybrid method. It is shown that the presence of the delamination significantly alters the surface response spectra of the plate. Results are presented in both time and frequency domains. The results show that the technique would be useful for ultrasonic nondestructive evaluation of defects in composite and anisotropic plates, and for studying dynamic response of such plates to impact.

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 general problem of arbitrarily applied harmonic surface tractions is first solved using the normal mode expansion technique in conjunction with the complex reciprocity relation of elastodynamics. This general solution is then specialized to loading situations modelling those commonly used to excite guided waves in layers for use in nondestructive evaluation. 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. Expressions are obtained for the −9 dB wave number and phase velocity bandwidths (σ β and σ ν respectively) which determine the widths of the wavenumber or phase velocity excitation spectra at the −9 dB generation point. Finally, the problem of transient loading is addressed by superimposing time harmonic solutions via an integration over the dispersion curves of the layer.

The scattering of elastic waves by elastic inclusions surrounded by interface layers is a problem of interest for nondestructive evaluation of interfaces in composites. In the present paper the scattering by a single elastic inclusion is studied. The scattering problem is solved by means of the null field approach and the properties of the interface layer enters through the boundary conditions on the inclusion. Various ways of doing this have been tried, from the simpler approach of just keeping the inertia of the layer, to using a membrane type of approximation or a more sophisticated method that includes all effects to first order in the layer thickness. The results obtained by using these different methods are compared numerically and with the exact solution for a layered sphere and with some recent results for a spheroid obtained using a hybrid finite element and wave function expansion technique. The numerical results show significant dependence on parameters containing the thickness and stiffness of the interface layer.

A technique for the complete nondestructive evaluation of plane states of residual stress is presented. This technique is based on the acoustoelastic effect in which the presence of the residual stress causes a shift in the speed at which a wave propagates through the material. The particular acoustoelastic technique considered here employs longitudinal waves propagating normal to the plane of the stress. Such waves experience a shift in propagation speed which, for an isotropic material, is proportional to the sum of the principal stresses. A Poisson’s equation for the in-plane shear stress is obtained from the two-dimensional equilibrium equations in which the forcing function is obtained directly from the measured velocity variations. Once this equation is integrated for the shear stress, the normal stresses may be evaluated directly from the equilibrium equations. In this paper, the basic equations are derived for the case of an anisotropic material. The experimental and numerical procedures are reviewed, and results of residual stresses in an aluminum ring are presented.

A system of boundary integral equations is presented which governs the crack-opening displacements for two-crack configurations. The integral equations are highly singular and they cannot be solved directly by numerical methods. By the approach of this paper the higher order singularities are, however, reduced to integrable singularities, and the integral equations are subsequently discretized and solved numerically. For several configurations numerical results have been obtained for scattered fields and for elastodynamic stress intensity factors. The scattered-field results are interpreted to apply for a partially closed crack as well as for two separate but neighboring cracks. The stress-intensity factors are intended to apply only to the case of separate cracks. The scattered-field results have relevance to the problem of detection and characterization of cracks in the field of quantitative nondestructive evaluation.

Quantitative ultrasonic techniques for determining the serviceability of structural components are reviewed. Particular emphasis is placed on the use of forward and inverse elastic wave scattering theory as a fundamental foundation for predicting such engineering parameters as the probability of flaw detection and for developing improved techniques for flaw sizing. Ultrasonic measurement techniques for the determination of distributed failure-related properties such as residual stresses are discussed, and the status of the prediction of failure by the detection of acoustic emission precursors is reviewed.

A technique previously presented [1] for the nondestructive evaluation of the J integral in cracked samples from ultrasonic measurements of stress, and successfully tested on specimens under mode I loading, is extended here to mixed-mode loading. Experimental results are presented for both the J and L integrals in a specimen with a slanted central crack loaded in tension, which agree well with theoretical values.

The boundary element method is used to calculate the induced electric current flow around cracks in thin conducting plates. A low frequency approximation leads to a Poisson equation for the current density potential or stream function. A kernel is used which produces the correct singularity at the crack tip. The boundary condition on the crack, derived from Faraday’s law, requires the line integral of the current density around the crack to be zero. Numerical results for induced currents due to a circular induction coil ore given. These results show that hot spots, due to Joule heating, can occur at the tips of the crack. Comparison of numerical results with infrared scanning experiments of eddy currents in a cracked plate are given. It is hoped that the numerical method presented here will provide a tool to simulate both new and conventional nondestructive eddy current testing techniques.

Acoustoelasticity has recently been used for the nondestructive evaluation of residual stresses. In making such measurements the assumption has been made that the plastic flow leading to the residual stress state did not change the acoustic response of the material. This paper examines the extent to which that assumption holds for three aluminum alloys. The acoustoelastic theory is summarized and results are presented for tests of specimens under uniaxial tension which are subjected to plastic deformation followed by complete unloading. It is shown that the assumption made does not hold for all materials and that further theoretical development is required for general quantitative residual stress determination.

The usefulness of two conservation integrals, the so-called J and M integrals, in fracture mechanics is reviewed. A method for experimental evaluation of these quantities by direct determination of the values of their integrands at various points along a contour is presented, and contrasted with “compliance” methods which have been used to evaluate J. This technique has been applied to three different specimen configurations, and the experimental results compare favorably with theoretical predictions.

Diffraction of an antiplane shear (SH-) wave by an edge crack in a semi-infinite elastic medium is studied here. Asymptotic expansions for the scattered field both near and far from the crack are obtained for the case when the wavelength is large compared to the length of the crack. Near-field expansion is used to compute the dynamic stress-intensity factor at the tip of the crack. Also, the far-field expansion gives the scattered displacement amplitude, which is useful in ultrasonic nondestructive evaluation.