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

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Hirotsugu Ogi ⇑, Yuto Sakamoto, Masahiko Hirao

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Graduate School of Engineering Science, Osaka University, Japan

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a r t i c l e

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i n f o

Article history: Received 8 April 2014 Received in revised form 30 April 2014 Accepted 2 May 2014 Available online xxxx

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Keywords: Young’s modulus Ultrasonic resonator Electrodeless oscillator

a b s t r a c t A ballpoint-pen-type portable ultrasonic oscillator is developed for quantitative measurement of Young’s modulus on a solid. It consists of an electrodeless rod-shaped langasite oscillator with a tungsten-carbide spherical-shaped tip at the end, permanent magnets for making a constant force at the contact interface, and antennas for exciting and detecting the longitudinal vibration contactlessly. The resonance frequency of the oscillator is changed by contact with the specimen, reflecting Young’s modulus of the specimen at the contact area. The langasite oscillator is supported at the nodal points so that its acoustical contact occurs only at the specimen, making a calibration-free measurement realistic. Young’s moduli of various specimens were evaluated within 15% error just by touching the specimens with the probe. The error becomes smaller than 10% for lower Young-modulus materials (3000 ppm). We excited the langasite oscillator by applying tone bursts with amplitude of 20 Vpp and duration of 10 ms to the generating antenna. After the excitation, the reverberating signals were detected by the receiving antenna. After amplified by 32 dB, the waveform was digitally acquired with a portable digitizer, and Fourier transformation was performed to obtained the amplitude at

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Fig. 3. (a) Laboratory-built measurement system and (b) a closeup near the tungsten-carbide tip.

Fig. 5. Resonance spectra measured in contacts with various specimens.

Fig. 4. Appearance of the ballpoint-pen probe before (upper) and after (lower) contacting a specimen.

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the exciting frequency. By sweeping the frequency of the tone bursts and measuring the amplitude, we obtain the resonance spectrum. The Lorentzian-function fitting procedure determined the resonance frequency.

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4. Results and discussion

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Fig. 5 shows resonance spectra measured in contact with various materials, clearly displaying that the resonance frequency increases as the specimen stiffens. At the noncontacting state, the resonance frequency is near 106 kHz, while the theoretical value is estimated to be 118 kHz using the reported elastic constants and mass density [13]. The peak amplitude decreases with the increase in Young’s modulus of specimen. This is attributed to leakage of vibrational energy of the oscillator into the specimen because the acoustic impedance of the specimen approaches that of the tungsten-carbide tip. We used literature values for the elastic properties of langasite [13] and tungsten carbide (Etip ¼ 630 GPa and mtip ¼ 0:21). For the

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specimen’s Poisson’s ratio, we used a fixed value of mspe ¼ 0:25, which, however, affects insignificantly the resultant Young’s modulus. (For example, the effective modulus E in Eq. (2) varies only by 2% when mspe is changed from 0.25 to 0.3.) We can, therefore, determine the specimen’s Young’s modulus Espe just by measuring the resonance frequency at the contact condition without using any other parameters. Fig. 6 compares Young’s moduli thus measured with reported values for various materials. Despite the calibration-free measurement, they agree with each other within 10% for materials with Young’s modulus lower than 150 GPa. The difference, however, increased up to 15% for larger-Young-modulus materials, because the probe sensitivity deteriorates with the

Fig. 6. Young’s moduli measured by the present method (Emeas ) and those reported (E).

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Fig. 7. Distribution of the strain energy caused by a contact with a (111) face of Cu. a(=17.7 lm) denotes the contact radius. Parameters used are Etip ¼ 630 GPa, mtip ¼ 0:21; Eosc ¼ 118 GPa, mspe ¼ 0:25 and F = 0.455 N.

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specimen’s Young’s modulus, as shown in Fig. 2. Other methods, such as the pulse-echo method, will provide more accurate stiffness, but they require well-shaped specimens, large and expensive instruments, and a long period of time for surface preparation. On the other hand, the present method allows a quick and pointwise measurement even for specimens with arbitrary configurations. Error bars in Fig. 6 indicate standard deviation for five independent measurements on different points. The larger error bars for polycrystalline materials (Cu, carbon steel, and Ni) are caused by different effective Young’s modulus depending on the crystallographic orientation. For example, Young’s moduli of Cu along [1 0 0], [1 1 0] and [1 1 1] are 65, 129, and 189 GPa, respectively. (The aggregated value is 126 GPa.) Although the present method does not represent the normal Young’s modulus directly, the anisotropic effect could alter the effective stiffness by 10% [11]. 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 (1 1 1) Cu specimen. (When the specimen surface is parallel to a (1 1 1) plane of cubic material, it apparently shows the trigonal symmetry, to which the Willis theory is inapplicable. We, therefore, averaged the elastic constants around the axis normal to (1 1 1) plane to yield the transversely isotropic elastic constants [15].) The result is shown in Fig. 7. The contact radius a is 17.7 lm in this case, and the strain-energy penetration depth is close to the contact radius. Our probe is then sensitive to a volume of  ðpa2  aÞ at the surface region, and the measurement is affected by any stiffness variation with this volume order. It is possible to enlarge the mea-

suring volume either by increasing the biasing force or by using a larger radius tip.

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5. Conclusions

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We have successfully developed a portable Young’s modulus tester using a langasite oscillator and a spherical-shaped tungsten-carbide tip. It easily and quickly measures Young’s moduli of solids just by pressing the probe against the surface. Machining and preparation of specimen is basically unnecessary; only a 10mm-diameter flat surface is needed. The measurement accuracy is 10% for materials with Young’s modulus lower than 150 GPa without using any calibration procedures, although the error increased up to 15% for higher-modulus materials. Because of the portability, this system could be adopted for health monitoring and nondestructive evaluation of structures because local defects significantly lower the apparent elastic stiffness.

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References

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Q1 Please cite this article in press as: H. Ogi et al., Calibration-free portable Young’s-modulus tester with isolated langasite oscillator, Ultrasonics (2014), http://dx.doi.org/10.1016/j.ultras.2014.05.002

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

A ballpoint-pen-type portable ultrasonic oscillator is developed for quantitative measurement of Young's modulus on a solid. It consists of an electro...
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