James A. TenCate

Single-channel time reversal in elastic solids

Reverberant volume time reversal in 3D elastic solids (doped glass and Berea sandstone) using a single channel are presented. In spite of large numbers of mode conversions (compressional to shear wave conversions at the walls), time reversal works extremely well, providing very good spatial and time focusing of elastic waves. Ceramics were bonded to the surface as sources (100–700 kHz); a broadband laser vibrometer (dc—1.5 MHz) was used as detector. Temporal and spatial time-reversal focusing are frequency dependent and depend on the dissipation characteristics of the medium. Doped glass (inverse dissipation Q between 2000 to 3000) shows time-reversed spatial focal resolution at about half of the shear wavelength. The Berea sandstone (Q=50) yields a wider focusing width (a bit more than the shear wavelength) due to its lower Q. Focusing in the doped glass is better because the time-reversal (virtual) array created by wave reflections is larger than in the highly attenuating sandstone. These are the first results reported in granular media, and are a first step toward geophysical and field applications.

Nonlinear and nonequilibrium dynamics in geomaterials.

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.

Laboratory study of linear and nonlinear elastic pulse propagation in sandstone

Linear and nonlinear elastic wave pulse propagation experiments were performed in sandstone rods, both at ambient conditions and in vacuum. The purpose of these experiments was to obtain a quantitative measure of the extremely large nonlinear response found in microcracked (i.e., micro‐inhomogeneous) media like rock. Two rods were used, (1) a 2‐m‐long, 5‐cm‐diam rod of Berea sandstone (with embedded detectors) used in previously published experiments and (2) a somewhat smaller 1.8‐m‐long, 3.8‐cm‐diam rod. In the earlier experiments, wave scattering from the embedded detectors was a critical problem. In most of the experiments reported here, this problem was avoided by mounting accelerometers directly to the outside surface of the rod. Linear results show out of vacuum attenuations varied from 1.7 Np/m at 15 kHz (Q=10) for the large rod to 0.4 Np/m at 15 kHz (Q=55) for the small rod; attenuations for the small rod in vacuum were much less, typically about 0.15 Np/m at 15 kHz (Q=150). Wave velocities ranged...

The time reversed elastic nonlinearity diagnostic applied to evaluation of diffusion bonds

With the recent application of time reversed acoustics and nonlinear elasticity to imaging mechanical damage, the development of time reversal based nondestructive evaluation techniques has begun. Here, diffusion bonded metal disks containing intentionally disbonded regions are analyzed using the time reversed elastic nonlinearity diagnostic. The nonlinear results are compared with linear ultrasonic imaging (C scan). Scanning electron microscopy is shown to illustrate the differences between the features seen by the linear and nonlinear methods.

Neutron diffraction study of the contribution of grain contacts to nonlinear stress‐strain behavior

[1] Repeatable, hysteretic loops in quasi-static loading measurements on rocks are well known; the fundamental processes responsible for them are not. The grain contact region is usually treated as the site of these processes, but there is little supporting experimental evidence. We have performed simultaneous neutron diffraction and quasi-static loadingexperimentsonaselectionofrockstoexperimentally isolate the response of these contact regions. Neutron diffraction measures strain in the lattice planes of the bulk of the grain material, so differences between this strain and the macroscopic response yield information about grain contact behavior. We find the lattice responds linearly to stress in all cases, oblivious to the macroscopic unrecoverable strains, curvature, and hysteresis, localizing these effects to the contacts. Neutron diffraction shows that the more granular rocks appear to distribute stresses so that the same strain appears in all the grains, independent of crystallographic orientation. INDEX TERMS: 3909 Mineral Physics: Elasticity and anelasticity; 3902 Mineral Physics: Creep anddeformation;3954MineralPhysics:Xray,neutron,andelectron spectroscopy and diffraction; 3994 Mineral Physics: Instruments and techniques; 3694 Mineralogy and Petrology: Instruments and techniques.Citation: Darling, T. W., J. A. TenCate, D. W. Brown, B. Clausen, and S. C. Vogel (2004), Neutron diffraction study of the contribution of grain contacts to nonlinear stress-strain behavior, Geophys. Res. Lett., 31, L16604, doi:10.1029/2004GL020463.

Atomic pair distribution function analysis of materials containing crystalline and amorphous phases

Abstract The atomic pair distribution function (PDF) approach has been used to study the local structure of liquids, glasses and disordered crystalline materials. In this paper, we demonstrate the use of the PDF method to investigate systems containing a crystalline and an amorphous structural phase. We present two examples: Bulk metallic glass with crystalline reinforcements and Fontainebleau sandstone, where an unexpected glassy phase was discovered. In this paper we also discuss the refinement methods used in detail.

An experimental investigation of the nonlinear pressure field produced by a plane circular piston

An experimental investigation of the nonlinearly generated harmonics in the sound beam of a plane circular piston in water has been carried out. Special attention was paid to the higher harmonic sidelobes called fingers. All experiments were performed using a high precision, computer‐controlled tank facility where movement resolution is better than 50 μm. Harmonic beam patterns generated by a 1‐MHz, 12‐mm radius plane circular piston driven with a face sound pressure level of 223 dB (re: 1 μPa) were measured. Beam patterns of the first ten harmonics (out to the first sidelobe of the fundamental beam pattern) are shown. The first four harmonic beam pattern data are compared with results produced by a numerical solution of the Khokhlov–Zabolotskaya–Kuznetzov (KZK) equation. Agreement between experiment and theory is excellent. Finally, careful measurements of the decay of the fingers were made. The decay of the first finger in the second harmonic beam pattern generated by a 2.2‐MHz, 3‐mm radius circular pis...

Sensitive determination of nonlinear properties of berea sandstone at low strains

Resonant response functions of a sandstone bar, measured at strain magnitudes between 10−8 and 10−6 at several temperatures, are used to extract Youngs modulus and loss tangent as functions of frequency and driving force. Expressing the distorted shape of nonlinear resonances in terms of shifts in the resonant frequency and Q enables correlation analysis of these functions against components of the strain response function. Resonance shifts are found to be strongly correlated with somewhat complicated functions of strain, but only weakly with frequency or phase of the response. Decomposing the data along contours of constant strain magnitude yields the quantitative scaling of resonance shifts with strain, which shows a superposition of both conventional and necessarily hysteretic nonlinear sources. No statistically significant temperature dependence is found in the coefficients of the fits.

Quantifying amorphous and crystalline phase content with the atomic pair distribution function

Pair distribution function (PDF) analysis is a long-established technique for studying the local structure of amorphous and disordered crystalline materials. In todays increasingly complex materials landscape, the coexistence of amorphous and crystalline phases within single samples is not uncommon. Though a couple of reports have been published studying samples with amorphous and crystalline phases utilizing PDF analysis, to date little has been done to determine the sensitivity that the method currently has in resolving such contributions. This article reports a series of experiments that have been conducted on samples with known ratios of crystalline quartz and amorphous glassy silica to examine this question in detail. Systematic methods are proposed to obtain the best possible resolution in samples with unknown phase ratios and some problems that one might encounter during analysis are discussed.

Slow dynamics experiments in solids with nonlinear mesoscopic elasticity

As revealed by longitudinal bar resonance experiments, materials such as rocks and concrete show show a rich diversity of nonlinear elastic behavior. As a function of increasing drive level, resonance frequencies shift downward by several percent, the resonant line shape changes, and harmonics and slow dynamics appear. Slow dynamics [1] refers to the time-dependent recovery of an elastic modulus to its initial value after being softened by large strain. In order to explore the mechanisms of nonlinear response including slow dynamics, we performed experiments on concrete and several different earth materials. The softening (conditioning) and recovery processes appear to be asymmetric. Conditioning takes place quickly; full recovery of the elastic modulus (as measured by drift of the resonance peak) takes minutes to hours, depending on the length of time the conditioning strain was applied. We find that for a wide variety of rocks and concretes, the recovery of the resonant frequency goes as log(time). Loga...