S. I. Rokhlin

Inverse ultrasonic determination of imperfect interfaces and bulk properties of a layer between two solids

A method for determination of the complete set of physical, geometrical, and interfacial properties of an isotropic layer embedded between two known solids is discussed. These properties are: Lamé elastic moduli, density and thickness of the layer, and complex normal and transverse interfacial stiffnesses between the layer and the substrates. The properties are combined in the form of eight nondimensional parameters, which are determined from experimental reflection spectra at two incident angles: normal and oblique. The conditions for simultaneous determination of bulk layer properties and the interface normal and transverse springs with losses and the stability of the inversion method against data scatter are addressed. The inversion model is validated by experiment on normal and angular ultrasonic reflectivity from a layer between two semispaces in dry mechanical contact and from an environmentally degraded adhesive joint. The layer properties were measured independently, showing good agreement with the reconstructed results.

Ultrasonic waves in layered anisotropic media: characterization of multidirectional composites

Abstract An efficient and stable recursive compliance/stiffness matrix algorithm is presented to model wave propagation in multidirectional composites. The models are applied to clarify angle beam transmission through a multidirectional composite and to process ultrasonic data for determination of the elastic properties of a composite lamina (single ply) from measurements on a multidirectional composite. Ultrasonic characterization of composites using double-through-transmission and time-resolved line focus acoustic microscopy has been addressed. The double-through-transmission measurements and simulations show that the transmission amplitude is highly dependent on ply orientation and angle of incidence. The transmission amplitude decreases rapidly with incident angle deviation from the normal; however, a transmission window is found in the incident angle range 45–60° at frequencies below 2.25 MHz. The time-delay measurements by the double-through-transmission technique have been used to reconstruct lamina properties using the Floquet wave concept. A unidirectional lamina elastic properties measurement using line focus acoustic microscopy of a multidirectional composite sample is also briefly discussed. The effective elastic properties for the composites are determined from the lamina properties by a Floquet wave dynamic homogenization method.

Surface acoustic wave modulation on a partially closed fatigue crack

A quantitative study of the low-frequency parametric modulation of a pulsed surface acoustic wave (SAW) by a partially closed fatigue crack is described. In situ ultrasonic measurements were performed during a fatigue test for different crack lengths and static opening loads. The crack is initiated in the plastic-yielding zone induced by a surface cavity, and clamped due to the constraint of the surrounding elastic medium. Small periodic loading, superimposed on a static crack-opening load, changes the open crack segment length and/or the crack interfacial condition producing nonlinear modulation of the reflected ultrasonic pulses. The modulation spectrum is related quantitatively to the crack length and to the crack opening–closure behavior. It is demonstrated that the application of a small static crack-opening load with the modulation load could considerably enhance crack detectability. The increase of the second modulation harmonic is pronounced when the crack is nearly closed and when it is nearly op...

Determination of embedded layer properties using adaptive time-frequency domain analysis

A general model for determination of the complete set of acoustical and geometrical properties of an isotropic layer embedded between isotropic or anisotropic multilayered solids is developed. These properties include density, longitudinal and shear elastic moduli, layer thickness, and loss factors, simultaneously determined from two measurements, one at normal and one at oblique incidence. The inversion model is an extension of the method proposed by Lavrentyev and Rokhlin [J. Acoust. Soc. Am. 102, 3467 (1997)] which is applicable to thick substrates. In this new method, the inversion model mimics an experiment by using the same time-domain gating of the signal reflected from the embedded layer. This allows application of this method to layered solids when reflections from different layers overlap in the time domain. The sensitivity of the method, its stability against data scatter, and the effect of the oblique incident angle are evaluated. The effect of plane-wave approximation versus beam approximation in the inverse algorithm is discussed. Experimental results are given to demonstrate examples of adhesive layer property reconstruction.

Ultrasonic backscattering in polycrystals with elongated single phase and duplex microstructures

An analytical solution for a three dimensional integral representation of the backscattering (BS) coefficient in polycrystals with elongated (generally ellipsoidal) grains is obtained; it is a natural generalization of the known explicit result for the BS coefficient in polycrystals with spherical grains. New insights into the dependence of the BS signal on frequency and averaged ellipsoidal grain radii are obtained. In particular it has been shown that the dominant factor for the backscattering is the averaged interaction length of the ellipsoidal grain in the direction of wave propagation, instead of the ellipsoidal cross-section. The theory was applied to a simplified model of Ti alloy duplex microstructure and was compared with experiment. For the experimental data analysis directional backscattering ratios are introduced and shown to be advantageous for characterization of duplex elongated microstructures/microtextures. In addition to the geometrical parameters of the elongated microtextures, the BS directional ratios depend on the newly introduced nondimensional material parameter q. The parameter q exhibits the relative contribution of the second phase (crystallites) to the backscattering signal, the effect of which is measurable and important. Comparison of the model with experiment shows there is a significant advantage in using the directional ratios of backscattering coefficients for data analysis.

Shape effect of elongated grains on ultrasonic attenuation in polycrystalline materials

Longitudinal and transverse wave attenuation coefficients are obtained in a simple integral form for ultrasonic waves in cubic polycrystalline materials with elongated grains. Dependences of attenuation on frequency and grain shape are described in detail. The explicit analytical solutions for ellipsoidal grains in the Rayleigh and stochastic frequency limits are given for a wave propagating in an arbitrary direction relative to ellipsoid axes. The attenuation exhibits classic frequency dependence in those frequency limits. However, the dependence on the grain shape in the stochastic limits is unexpected: it is independent of the cross-section of the ellipsoidal grains and depends only on the grain dimension in the propagation direction. In the Rayleigh region attenuation is proportional to effective volume of the ellipsoidal grain and is independent of its shape. A complex behavior of attenuation on the grain shape/size and frequency is exhibited in the transition region. The results obtained reduce to the classic dependences of attenuation on parameters for polycrystals with equiaxed grains.

Effect of texture and grain shape on ultrasonic backscattering in polycrystals.

An ultrasonic backscattering model is developed for textured polycrystalline materials with orthotropic or trigonal grains of ellipsoidal shape. The model allows us to simulate realistic microstructures and orthotropic macroscopic material textures resulting from thermomechanical processing for a broad variety of material symmetries. The 3-D texture is described by a modified Gaussian orientation distribution function (ODF) of the crystallographic orientation of the grains along the macroscopic texture direction. The preferred texture directions are arbitrary relative to the axes of the ellipsoidal grains. The averaged elastic covariance and the directional anisotropy of the backscattering coefficient are obtained for a wave propagation direction arbitrary relative to the texture and grain elongation directions. One particular application of this analysis is the backscattering solution for cubic crystallites with common textures such as Cube, Goss, Brass and Copper. In our analysis, in the texture-defined coordinates the matrix of elastic constants for cubic crystallites takes the form of orthotropic or trigonal symmetry. Numerical results are presented, discussed and compared to the experimental data available in the literature illustrating the dependence of the backscattering coefficient on texture and grain shape.

Explicit model for ultrasonic attenuation in equiaxial hexagonal polycrystalline materials.

Attenuation coefficients for longitudinal and transverse ultrasonic waves are obtained in explicit form for untextured hexagonal polycrystalline materials. The equations obtained are easy to use for interpretation and evaluation of experimental results for ultrasonic characterization of microstructures. The attenuation coefficients are separated into two terms, corresponding to incident wave scattering into longitudinal and transverse waves. It is shown that the general expressions for attenuation coefficients in the long wavelength (Rayleigh) and short wavelength (stochastic) regimes transit to the known classical asymptotics. Simple equations to estimate the frequency range of the transition from the Rayleigh to stochastic regimes are also given. An example of experimental measurements in Ti alloy is provided to illustrate application of the model; the results show reasonable agreement between the experiment and the model with no adjustable parameters.

Far-field scattering model for wave propagation in random media

A simple approximate model is developed for ultrasonic wave propagation in a random elastic medium. The model includes second order multiple scattering and is applicable in all frequency ranges including geometric. It is based on the far field approximation of the reference medium Greens function and simplifications of the mass operator in addition to those of the first smooth approximation. In this approximation, the dispersion equation for the perturbed wave number is obtained; its solution yields the dispersive ultrasonic velocity and attenuation coefficients. The approximate solution is general and is suitable for nonequiaxed grains with arbitrary elastic symmetry. For equiaxed cubic grains, the solution is compared with the existing second order models and with the Born approximation. The comparison shows that the obtained solution has smaller error than the Born approximation and shows reasonably well the onset of multiple scattering and the applicability limit of the Born approximation at high frequency. The perturbed wave number in the developed model does not depend explicitly on the crystallite elastic properties even for arbitrary crystallographic symmetry; it depends on two nondimensional scattering elastic parameters and the macroscopic ultrasonic velocity (those are dependent on the crystallite moduli). This provides an advantage for potential schemes for inversion from attenuation to material microstructure.

Line-focus acoustic microscopy of Ti-6242 α/β single colony: determination of elastic constants

Time-resolved line-focus acoustic microscopy is performed for determining elastic constants of Ti-6242 α/β-single colony and Ti-6 α-phase single crystal. Surface acoustic wave (SAW) velocities are obtained as a function of the propagation angle from measured time-delays of SAW signals. The propagation of surface waves in a semi-infinite half space formed by anisotropic layers inclined arbitrarily to the sample surface is studied to model a quasi-random lamellar structure of the Ti-6242 α/β-single colony. Effective elastic constants of the multilayered structure are derived and verified through the comparison with exact ones, based on which SAW velocities in non-principal planes are calculated. Effective and constituent elastic constants of the α/β-single colony and the α-phase single crystal are inversely determined from the measured and calculated SAW velocities. The α- and β-phase elastic constants from the α/β-single colony so determined are compared with those from the α-single crystal and data in the...