Ultrasound wave propagation in glass-bead packing under isotropic compression and uniaxial shear

Abstract

The axial-stress dependence of sound wave velocity in granular packing is experimentally investigated with tri-axial and uni-axial devices. Preparing samples by repetitive loadings and unloadings in a range of 20 kPa-1000 kPa, we find that the axial-stress dependence of sound wave velocity approaches the Hertz scaling with an exponent of 1/6 for large axial stresses (> 400 kPa). Weak deviation from the Hertz scaling is seen at low stresses. Repetitive axial loadings slightly reduce this deviation, and sound velocities increase nonlinearly approaching some saturated values. Velocities for uni-axial case are found slightly to be bigger than those for tri-axial isotropic compression case. These effects are discussed in the frameworks of granular solid hydrodynamics (GSH) and effective medium theory (EMT), which indicate that they cannot be explained with density nor Janssen ratio only. Dissipation occurring during wave propagation may be a non-negligible factor.

Influence of particle packing structure on sound velocity

“…For example, the relationship between the normal stress p and sound velocity of the disordered packing granular system obtained by the time of flight method v tof meets v tof ∝ p 1/6 while this dependence is at higher pressures, but the behavior at lower confining pressures is more like v tof ∝ p 1/4 . [7,15,20] However, the sound velocity calculated from the stiffness tensor v c meets the relation v c ∝ p 1/6 . [2,8,21,22] The compression waves are more sensitive to the stress-induced anisotropy, whereas the shear waves are more sensitive to the fabric anisotropy.…”

“…[13] In the acoustic experiment, the determination of the sound velocity is usually done by the time of flight method. [14,15] This method obtains the time and the corresponding velocity of the sound wave in the granular system through the real path because sound waves favor speed and amplitude along force chains. [16,17] The waveform and velocity obtained by the time of flight method reflect information such as stress, strain, stiffness tensor, and attenuation along the wave propagation path.…”

“…If the granular system is regarded as a continuous medium, the elastic potential energy of the system can be calculated according to the contact relation based on the effective medium theory (EMT) [8] or granular solid hydrodynamics (GSH) theory. [15] Then, the stress can be obtained by taking partial derivative of the potential energy with respect to strain, and the sound velocity can be obtained from the fourth-order stiffness tensor. [18,19] EMT and GSH theories usually deal with homogeneous cases without considering the inhomogeneity of geometry and stress distribution, and the given stiffness tensor and sound velocity are the average effect of the whole system.…”

“…[18,19] EMT and GSH theories usually deal with homogeneous cases without considering the inhomogeneity of geometry and stress distribution, and the given stiffness tensor and sound velocity are the average effect of the whole system. [15] Whether from the time of flight method or the stiffness tensor, the sound velocity is the response of the system stress structure. For example, the relationship between the normal stress p and sound velocity of the disordered packing granular system obtained by the time of flight method v tof meets v tof ∝ p 1/6 while this dependence is at higher pressures, but the behavior at lower confining pressures is more like v tof ∝ p 1/4 .…”

Energy Transfer Efficiency Based Nonlinear Ultrasonic Testing Technique for Debonding Defects of Aluminum Alloy Foam Sandwich Panels

“…Because the second harmonic in the traditional nonlinear ultrasonic detection is weak, it needs to be artificially amplified, so it is rare to associate the fundamental wave with the second harmonic by energy transfer, and also the attenuation caused by sound waves propagating through isotropic solids is often ignored [ 19 ]. However, the testing object in this research is thin plate, the propagation distance is very close and the energy attenuation is very small, so the magnitude of the second harmonic is very significant.…”