Jiayong Tian

Elastic-stiffness mapping by resonance-ultrasound microscopy with isolated piezoelectric oscillator

A resonance-ultrasound microscopy has been developed for mapping a material’s elastic constant in a localized surface region. It detects the effective elastic modulus through a resonance frequency of free vibrations of a solid probe touching the specimen via a small tungsten-carbide bearing. Langasite (La3Ga5SiO14) crystal is used as a probe because of the low sensitivity of its elastic constants to temperature and its high piezoelectric coefficients. The vibration of the probe is excited and detected with a surrounding solenoid coil. This noncontacting acoustic coupling isolates the probe vibration and measures the resonance frequency with an accuracy better than one part in 105. This microscopic method is applied to a composite material consisting of silicon-carbide (SiC) fibers in titanium-alloy matrix. The stiffness distribution inside a single fiber was determined.

Vibration analysis of an elastic-sphere oscillator contacting semi-infinite viscoelastic solids in resonant ultrasound microscopy

Resonant-ultrasound microscopy evaluates local Young’s modulus of materials by the resonant-frequency shift of a vibrating oscillator. This study presents a dynamic-contact model to analyze free vibrations of an isotropic elastic-sphere oscillator contacting two semi-infinite viscoelastic solids, which sandwich the sphere. Assuming frictionless contacts and smaller vibrational amplitude, dynamic-contact pressure distributions are obtained with the linearized maximum contact pressure and contact radius. Combining the sphere oscillation and the solid motions through contact-displacement boundary conditions, resonant frequencies of the elastic sphere are obtained. Unlike the quasistatic model, this dynamic model agrees well with the measurements.

Vibration analysis on electromagnetic-resonance-ultrasound microscopy (ERUM) for determining localized elastic constants of solids.

In this paper we present a new acoustic-resonance microscopy, Electromagnetic-Resonance-Ultrasound Microscopy (ERUM), to measure the localized elastic stiffness of a solid material. It visualizes the resonance-frequency shift of vibrating piezoelectric crystal (langasite, La3Ga5SiO14) excited by an electric field from a solenoid coil. The acoustic coupling is made only at the tip of the crystal touching the specimen surface. Being based on the calibration for the specimens effective stiffness, the local elasticity is determined from the resonance frequencies of the crystal with the Rayleigh-Ritz method. An approximate model for the specimens effective stiffness predicts the shift of resonance frequencies, for which the conventional Hertz-contact model is improved. As an illustrating example, the mapping of Youngs modulus of a duplex stainless steel is presented, which shows good agreement with the existing study.

Resonant Ultrasound Microscopy with Isolated Langasite Oscillator for Quantitative Evaluation of Local Elastic Constant

A resonant-ultrasound-microscopy method has been developed for measuring the local Youngs modulus of a material. This method detects the effective Youngs modulus through the resonance frequency of a langasite (La3Ga5SiO14) oscillator touching the specimen. Because the vibration of the oscillator is induced and detected with a solenoid coil in noncontacting, wireless, and electrodeless way, it is affected only by its contact with the specimen, achieving an absolute measurement. Elastic-constant mapping was performed on cross sections of a duplex stainless steel and a NbTi/Cu superconducting wire. Analysis with the static contact stiffness predicts the frequency change smaller than that measured, and the necessity of considering the dynamic contact stiffness is discussed.

Effect of elastic anisotropy on contact stiffness in resonance ultrasound microscopy

The classical Hertzian-contact theory for an isotropic material has been adopted to simplify quantitative evaluation of local elastic modulus by resonance-ultrasound microscopy (RUM). However, the validity of this simplified model must be confirmed because most materials show elastic anisotropy in small regions. This study investigates the influence of the elastic anisotropy of the tip and the specimen on the determination of the local elastic modulus in RUM by introducing the Hertzian-contact stiffness for orthorhombic materials. Numerical results reveal that specimen anisotropy significantly affects the contact stiffness and the quantitative evaluation of local elastic modulus even for specimens with weak anisotropy when we consider the anisotropy of the oscillator tip in RUM.

Dynamic-contact stiffness at the interface between a vibrating rigid sphere and a semi-infinite viscoelastic solid

Vibration of a rigid sphere contacting a semi-infinite viscoelastic solid is studied theoretically. The rigid sphere is subjected to an oscillating force while being compressed in the vertical direction by a static force. The contact-pressure distribution and contact radius at the interface vary with the oscillation. Assuming sufficiently small oscillating force, we derive the dynamic-contact-pressure distribution with the constant contact radius, which establishes dynamic contact stiffness between the sphere and the viscoelastic solid. Numerical calculations show the influence of vibration frequency, contact radius, Poissons ratio, and the damping characteristic of the solid.

Local surface elastic constants by resonant-ultrasound microscopy

We report a method—resonant-ultrasound microscopy—for measuring elastic-constant distribution over a solid’s surface. Applying an oscillating electric field to a rectangular-parallelepiped oscillator of langasite (La3Ga5SiO14) crystal by a surrounding solenoid coil, we generated and detected vibrations of the crystal without electrodes and without wires. Acoustic coupling of the specimen to the oscillator is only made at an antinodal vibration point on the crystal’s bottom surface. The crystal’s resonance-frequency shift reflects elastic constants of the specimen in the contacting area. Point-contact measurement permits sensitive, quantitative evaluation of a material’s local elastic constants. As an illustrating example, we measured the elastic-stiffness distribution of a Nb–Ti/Cu resin superconductive wire. We compared our measurements with both static-contact and dynamic-contact models.

Quantitative Evaluation of Local Young’s Modulus of Small‐Scale Solids by Isolated Langasite Oscillator: Resonant‐Ultrasound Microscopy

A resonance‐ultrasound microscopy has been developed to measure material’s local Young’s modulus. It detects the effective Young modulus through a resonance frequency of a langasite (La3Ga5SiO14) oscillator touching the specimen. The vibration of the oscillator is excited and detected with a surrounding solenoid coil in a noncontacting way and it can be affected only by the contact with the specimen, achieving an absolute quantitative measurement.