Christopher M. Kube

Mode-converted diffuse ultrasonic backscatter

Diffuse ultrasonic backscatter describes the scattering of elastic waves from interfaces within heterogeneous materials. Previously, theoretical models have been developed for the diffuse backscatter of longitudinal-to-longitudinal (L-L) wave scattering within polycrystalline materials. Following a similar formalism, a mode-conversion scattering model is presented here to quantify the component of an incident longitudinal wave that scatters and is converted to a transverse (shear) wave within a polycrystalline sample. The model is then used to fit experimental measurements associated with a pitch-catch transducer configuration performed using a sample of 1040 steel. From these measurements, an average material correlation length is determined. This value is found to be in agreement with results from L-L scattering measurements and is on the order of the grain size as determined from optical micrographs. Mode-converted ultrasonic backscatter is influenced much less by the front-wall reflection than an L-L measurement and it provides additional microstructural information that is not accessible in any other manner.

Stress-dependent changes in the diffuse ultrasonic backscatter coefficient in steel: Experimental results

In this article, the effects of uniaxial compressive loading on the ultrasonic scattering from polycrystalline grains are shown for 10 MHz ultrasound in annealed, 1018 steel. The results show a decreasing value of the stress-dependent backscatter coefficient for normal incident ultrasound when the compression loading is perpendicular to the scattering direction. The change due to scattering is about 2 orders of magnitude greater than changes observed by others using ultrasonic wavespeed measurements. It is anticipated that this research can serve as the basis for many methods associated with nondestructive determination of stress in structural materials.

Acoustic attenuation coefficients for polycrystalline materials containing crystallites of any symmetry class

This letter provides a theoretical extension to the elastic properties of polycrystals in order to describe elastic wave scattering from grain boundaries. The extension allows the longitudinal and shear attenuation coefficients for scattering to be derived and is valid for polycrystals containing crystallites of any symmetry class. Attenuation curves are given for polycrystalline SiO2, ZrO2, and SnF2, which contain monoclinic crystallites. This work will allow ultrasonic techniques to be applied to new classes of materials containing nontrivial microstructures.

Acoustic nonlinearity parameters for transversely isotropic polycrystalline materials

This article considers polycrystalline materials with macroscopic elastic anisotropy and the effect of the anisotropy on the quadratic nonlinearity parameter used to describe second harmonic generation in solids. The polycrystal is assumed to have transversely isotropic elastic symmetry, which leads to a directional dependence of the nonlinearity parameters. Additionally, the anisotropy leads to second harmonic generation from an input shear wave. Estimates of the longitudinal and shear wave nonlinearity parameters are given as a function of single-crystal elastic constants, macroscopic anisotropy constants, and propagation direction. An inverse model is presented that relates measured nonlinearity parameters to the macroscopic anisotropy constants. The estimates of the nonlinearity parameters can be used to approximate the damage-free or baseline nonlinearity parameter of structural components, which helps the effort toward absolute measures of material damage.

A self-reciprocity calibration method for broadband focused transducers

A procedure is developed for self-calibration of broadband, spherically focused ultrasonic transducers based on reciprocity. The input and received signals are measured in a pulse-echo configuration. These signals are used in conjunction with a multi-Gaussian beam model to obtain the electromechanical transfer function of the transducer. This calibration procedure is advantageous because it reduces the experimental configuration to a single transducer and a reflector. Experimental results indicate that the transfer function is insensitive to on-axis reflector placement. This result supports the feasibility of integrating the calibration procedure into actual testing in some situations.

Stress-dependent second-order grain statistics of polycrystals.

In this article, the second-order statistics of the elastic moduli of randomly oriented grains in a polycrystal are derived for the case when an initial stress is present. The initial stress can be either residual stress or stresses generated from external loading. The initial stress is shown to increase or decrease the variability of the grains elastic moduli from the average elastic moduli of the polycrystal. This variation in the elastic properties of the individual grains causes acoustic scattering phenomenon in polycrystalline materials to become stress-dependent. The influence of the initial stress on scattering is shown to be greater than the influence on acoustic phase velocities, which defines the acoustoelastic effect. This work helps the development of scattering based tools for the nondestructive analysis of material stresses in polycrystals.

Voigt, Reuss, Hill, and self-consistent techniques for modeling ultrasonic scattering

An elastic wave propagating in a metal loses a portion of its energy from scattering caused by acoustic impedance differences existing at the boundaries of anisotropic grains. Theoretical scattering models capture this phenomena by assuming the incoming wave is described by an average elastic moduli tensor Cijkl0(x) that is perturbed by a grain with elasticity Cijkl(x′) where the scattering event occurs when x = x′. Previous models have assumed that Cijkl0(x) is the Voigt average of the single-crystal elastic moduli tensor. However, this assumption may be incorrect because the Voigt average overestimates the waves phase velocity. Thus, the use of alternate definitions of Cijkl0(x) to describe the incoming wave is posed. Voigt, Reuss, Hill, and self-consistent definitions of Cijkl0(x) are derived in the context of ultrasonic scattering models. The scattering-based models describing ultrasonic backscatter, attenuation, and diffusion are shown to be highly dependent on the definition of Cijkl0(x).

Measurement of thermally induced stresses in continuously welded rail through diffuse ultrasonic backscatter

The relationship between grain scattering and uniaxial stress has recently been theoretically developed [1]. The scattering results because of reflections at grain boundaries and discontinuities in the microstructure. The acoustoelastic response of individual grains due to temperature and stress gradients has a direct influence on the strength of the scattering. Measurements of mechanically-induced uniaxial compressive stress on a rail section and thermal stresses within continuously welded rail (CWR) were performed. It was found that this technique can produce measurement resolution of at least 10−4/MPa.

Statistics associated with the scattering of ultrasound from microstructure

HIGHLIGHTSThe statistical behavior of ultrasonic scattering in polycrystals is investigated.Maximum scattering amplitudes can be theoretically predicted.Bounds and confidence levels on scattering amplitudes are derived.The extreme value statistics theory is applied to ultrasound scattering.The statistics are relevant for any finite number of waveforms N. ABSTRACT The spatial statistics of an ensemble of waveforms containing ultrasonic scattering from microstructure are investigated. The standard deviation of the waveforms is of primary interest, because it is related to the maximum scattering amplitudes in the extreme value statistics theory. Further statistical measures are employed to define theoretical confidence bounds, which bound the experimentally calculated maximum amplitude when a finite number of waveforms are included in the ensemble. These statistical measures are applied in conjunction with a previously developed ultrasonic backscatter model. It is validated through ultrasonic scattering measurements performed on a stainless‐steel pipe sample. These considerations are important for forward models related to the probability of detection (POD) of defects and inverse models used for characterization of polycrystalline microstructures.

Scattering of harmonic waves from a nonlinear elastic inclusion

This article considers the scattering of harmonics stemming from the interaction of a primary wave with a heterogeneous and elastically nonlinear inclusion present in an otherwise linearly elastic host medium. The elastodynamic equations of motion are derived for general elastic anisotropy up to a third-order in displacement nonlinearity (cubic nonlinearity). The method of successive approximations is applied in order to decouple the equations of motion into a linear system of equations. The linear equations permit the use of Greens functions to obtain the scattering amplitudes from an arbitrarily shaped inclusion. General forms of the scattering amplitudes are given as functions of scattering-based quadratic and cubic acoustic nonlinearity parameters. Shape factors are offered for some simple geometries in order to arrive at closed-form solutions. An explicit example is given in the case of a spherically shaped inclusion with isotropic elastic moduli. The influence of the second-, third-, and fourth-order elastic stiffnesses, primary and scattered wave mode types, and scattering angles are highlighted. Potential experimental techniques, based on the present scattering model, offer an alternative method of probing the nonlinear elastic properties of materials.