Quantitative imaging of Young’s modulus of solids: A contact-mechanics study

Abstract

We developed equipment and methods for measuring quantitatively the local Young's modulus of solids. It consists of an electrodeless langasite oscillator and line antennas, and oscillator vibrations are generated and detected contactlessly. A constant biasing force results from oscillator mass and is independent of surface roughness. The effect of material anisotropy on the measured stiffness is theoretically discussed for studying the limitation of the quantitative measurement. The microscopy has been applied to polycrystalline copper, and the measured modulus is compared to calculations based on electron-backscatter-diffraction measurements. Also, we applied it to a duplex stainless steel and an embedded silicon-carbide fiber. The results reveal textured regions, defects with high sensitivity, and even stiffness distribution in a single grain.

Calibration-free portable Young’s-modulus tester with isolated langasite oscillator

“…Therefore, measured Young's modulus is affected by orientation of grains involved in the detectable region in such a locally anisotropic material. Using the Willis approach for Hertzian contact with an anisotropic specimen [11,14], we calculated the distribution of strain energy in the transverse-isotropically oriented (111) Cu specimen. The result is shown in Fig.…”

“…The change in the resonance frequency then depends on the elastic stiffness of the solid in contact. It is then possible to determine the elastic constants of the solid through the change in the resonance frequency of the oscillator [11].…”

“…The contact interface between the tip and specimen can be considered as an elastic spring, which connects the oscillator and rigid surface as shown in Fig. 1, and the spring constant K depends on elastic constants of the tip and specimen, the tip radius R, and the biasing force F [11,12] as…”

“…3 (a) to minimize the influence of contacts for support on the frequency response. We used antennas near the oscillator for exciting and detecting the resonance frequency of the electrodeless oscillator contactlessly [11]. The acoustical isolation of the langasite probe was achieved in these ways.…”

“…Only one quantity, the resonance frequency of the oscillator, yields Young's modulus without any other parameters. This method is based on resonant ultrasound microscopy (RUM) [9,10,11], which we developed for measuring local Young's modulus of solids. RUM allows one to measure Young's modulus images on a solid quantitatively, but it requires one unknown parameter, the radius of the diamond tip [11], and a large and expensive instrument for high-power excitation of the small electrodeless piezoelectric oscillator.…”