Resonance-based acoustic technique applied to the determination of Young’s modulus in granites

The natural stone industry plays an important role in construction sector activity, and due to this fact the accurate knowledge of the physico-mechanical properties of this kind of materials is indispensable for the configuration of their quality standards. In this work we have optimized an acoustic technique, based on the measurement of the fundamental mode resonance frequency of the longitudinal wave, to determine Young's modulus in different granite variety specimens. The equipment employed was an Erudite MK3 test system (CNS Farnell) working in the range 1 to 100 kHz. The resonance frequencies obtained ranged from 4 to 10 kHz, depending on the granite variety. Based on these resonance frequencies, we obtained values of the longitudinal wave velocities ranging from 2500 to 6000 m/s and of the dynamic Young's modulus from 20 to 100 GPa. We also compared the dynamic modulus results with the static Young's modulus obtained by destructive techniques, and analysed its relationship with other significant mechanical properties. INTRODUCTION The worldwide market of ornamental stone is characterized by its high degree of concentration, since only 10 countries account for more than 80% of production. Spain ranks first in slate production, second in marble, and is the top European producer of granite. Within the national panorama of the ornamental stone sector, more than 40 varieties are produced in the region of Extremadura which is second ranked nationally in the extraction of this type of stone [1]. There is ever more widespread use of granites as construction materials. It is therefore indispensable to have the maximum of rigorous information about their physico-mechanical characteristics so that one can foresee their potential deterioration under the effects of external and internal agents. In this context, our teams of researchers from the University of Extremadura, from the Technological Institute of Ornamental Stone and Construction Materials (INTROMAC), and from the Institute of Acoustics (CSIC) have been studying a broad range of specimens corresponding to 39 varieties of granite from industrial quarries of different locations in Extremadura [2], [3]. Of these, 35 have been subjected to some type of acoustic analysis. The fundamental goal has been to analyze these granites using both destructive and non-destructive techniques for their petrological and physico-mechanical characterization. Acoustic tests were conducted on six 30×10×5 (cm) prismatic cube specimens of each variety determining the resonance frequency of the acoustic waves in this pieces. The longitudinal wave velocity was determined by means of a resonance-based method using an Erudite MK3 test device of working frequency range 1 Hz to 100 kHz, with EMAT vibrator and piezoelectric receiver (Figure 1). The frequency range of the equipment covers sonic and ultrasonic frequencies, but due to the dimensions of the specimens the fundamental resonances obtained were in the sonic range. As one sees in the figure, the specimens are placed in a special device for their correct measurement, there being three support points on its base (at the ends and in the centre) to facilitate the formation of the fundamental resonance mode in the sample. The equipment automatically varies the emission frequency of the pulse until an amplitude maximum is detected indicative of resonance of the wave in the specimen. At least 6 readings of the resonance frequency were made in each sample, all in the direction of greatest length of the specimen (30 cm). From this value of the frequency and knowing that the longitudinal wavelength in the fundamental resonance mode is twice the length of the specimen, we get the value of the longitudinal ultrasound wave velocity. Figure 1.Acoustic resonance-based experimental device. We used the value of the resonance frequency of 35 of the varieties to obtain their dynamic Young's modulus according to the expression [4]: T F l GPa E L D × × × × = ρ 2 2 4 ) ( ( Eq. 1) where l is the length of the specimen in m, FL the resonance frequency in Hz, ρ the density in kg/m, and T a factor that depends on the relative dimensions of the specimen. Additionally, we performed a complete physico-mechanical analysis of the granite varieties studied, determining their compressive, flexural, and impact strength, Knoop hardness, breaking load, porosity, absorption, and density. Likewise, we made destructive tests of 12 of the varieties to determine their static Young's modulus. This test was carried out on at least 4 cylindrical specimens of 6 cm diameter and 120 cm height. The specimen is subjected to a continuously increasing load at the rate of 0.49 to 0.98 MPa/s until breakage, using a 150 ton press. All the tests were done according to the procedures stipulated in the norms established by Spanish legislation. MEASUREMENT RESULTS The first columns of Table I summarize the measured resonance frequencies and the magnitudes (longitudinal wave velocity and Young's modulus) derived from those measurements. The longitudinal wave velocity values are comparable to those reported by 19th INTERNATIONAL CONGRESS ON ACOUSTICS – ICA2007MADRID 2 other workers for stone materials, and for granites in particular: e.g., for granite, the value reported by Sheriff et al. is some 4500 m/s [6], and by the ASTM is 3470 m/s [7]. The dynamic Young's modulus values (ED) given in Table I were also comparable to the literature values for rocks. Thus, for cylindrical specimens of argillite, Liao et al. [8] find values of around 50 GPa, Yale et al. [9] values of 15–55 GPa for sandstone, and Song et al. [10] values of 50–70 GPa for granites. In addition, other physico-mechanical variables were measured by means of appropriate techniques. For these magnitudes, the results were comparable to those reported by other workers and to the systematic studies done by the INTROMAC for this type of stone [5]. Table I. Statistical summary of the physico-mechanical variables measured in the tests carried out on the set of granite varieties studied. Reson. Freq. FL (Hz) Reson.-Based Velocity VR-B (m/s) Dynamic Young’s Modulus ED (GPa) Static Young’s Modulus ES (GPa) Water Abs. Capillarity C (g/m s) Water Abs. Atm. Press. Ab (%) Mean 7162 4297 50.3 33.8 0.48 0.21 Median 7124 4274 49.6 33.6 0.45 0.20 SD 991 594 14.6 13.2 0.24 0.10 Range 4265-9865 2559-5919 20.3-100.4 16.1-53.1 0.11-1.19 0.1-0.5