Available online at www.sciencedirect.com Procedia Engineering 48 (2012 ) 562 567 MMaMS 2012 Monitoring of Mechanical Properties Evolution of the Cast Gypsum Tomáš Plachý a *, Pavel Tesárek a, Richard oupek a, Michal Polák a a Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, Prague 6, 166 29, Czech Republic Abstract The gypsum is one of the building materials, which is ignored as the load bearing material at present time. Its most useful properties are simple production technology and quick increase of mechanical properties in time. The paper will present the evolution determination of the gypsum mechanical properties using nondestructive impulse excitation method. The advantage of this method is that the same specimen can be tested in different time instants repeatedly. The first 14 days are the most important for material properties evolution. After that time, the mechanical properties are not changing significantly. 2012 The Authors. Published by Elsevier Ltd. 2012 Published by Elsevier Ltd.Selection and/or peer-review under responsibility of the Branch Office of Slovak Metallurgical Society at Faculty Selection of Metallurgy and/or peer-review and Faculty under of Mechanical responsibility Engineering, of the Branch Technical Office University of Slovak of Košice Metallurgical Open access Society under at CC Faculty BY-NC-ND of Metallurgy license. and Faculty of Mechanical Engineering, Technical University of Košice. Keywords: gypsum; impulse excitation method; Young s modulus; shear modulus; Nomenclature l length of a specimen (m) b width of a specimen (m) t thickness of a specimen (m) m mass of a specimen (kg) f l fundamental longitudinal resonant frequency (Hz) f f fundamental flexural resonant frequency (Hz) f t fundamental torsional resonant frequency (Hz) E dl dynamic Young s modulus determined from fundamental longitudinal resonant frequency (Pa) E df dynamic Young s modulus determined from fundamental flexural resonant frequency (Pa) G d dynamic shear modulus (Pa) T 1 correction factor for fundamental flexural mode to account for finite thickness of bar and Poisson s ratio [6] A empirical correction factor dependent on the width-to-thickness ratio of the specimen Greek symbols μ dl Poisson s ratio determined from E dl μ df Poisson s ratio determined from E df * Corresponding author. Tel.: +420224354401; fax: +420224310775. E-mail address: plachy@fsv.cvut.cz. 1877-7058 2012 Published by Elsevier Ltd.Selection and/or peer-review under responsibility of the Branch Office of Slovak Metallurgical Society at Faculty of Metallurgy and Faculty of Mechanical Engineering, Technical University of Košice Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2012.09.554
Tomáš Plachý et al. / Procedia Engineering 48 ( 2012 ) 562 567 563 1. Introduction The gypsum has been used as a building material for several thousands of years. As an old-new material, it got an interest in building industry in the second half of the 20 th century and the renaissance of this material was in nineties, when its usage spread to interiors, especially as a plasterboard systems. At present time, the plasterboards are used in new constructions and also during reconstructions, they are modified for these purposes. From the view of experts and also general public, the gypsum is a material, which is used in the building industry for its excellent usage properties (fast hardening, good mechanical and thermal properties, good workability) but only in interiors. The little knowledge of this material does not allow extending its use in exteriors. From the chemical view, it is calcium sulfate dihydrate in most cases (60-98%). The gypsum binder can contain also other modifications of the system calcium sulfate water [1]. Therefore, it is interesting to investigate this material also on microlevel and to determine the content of the gypsum phases in the investigated gypsum using the nanoindentation technics [2]. The problem with gypsum usage starts to be complicated when the additives are added to the gypsum mixture to improve the chosen properties [3], [4]. The time dependent changes of the silicate based materials has been tested for several years at the workplace of authors. From the view of the mechanical properties evolution, the behavior of the gypsum is specific and different from the other porous building materials based on cement or lime binders. Especially, it is very fast creation of a solid structure (removing of the gypsum from the mold 30 minutes after mixing gypsum binder with water) and also nontraditional decrease of the mechanical properties in the first week after making the gypsum [5]. Three gypsum specimens were made for the purpose to monitor and identify the gypsum mechanical properties evolution in more detail. 2. Specimens For the purpose of this test, three gypsum specimens of dimensions 0.04 0.04 0.160 m were made with the standard water/gypsum ratio 0.71 in a stainless mold with three sections. Tested specimens were made according to Czech standard CSN 722301 from the commercial gypsum grey which is produced by company Gypstrend. This binder is made from two different dihydrates, namely naturally gypsum and gypsum from chemistry industry, ratio is half to half. These specimens were put off the mold after twenty minutes and the experimental determination of the dynamic modulus of elasticity, dynamic shear modulus and Poisson s number started immediately. 3. Impulse excitation method The impulse excitation method was used for determination of dynamic Young s modulus, shear modulus and Poisson s ratio because of its nondestructive character, very quick measurement of these characteristics and availability of the measurement line. The method is based on calculation of these characteristics based on measured resonant frequencies of longitudinal, flexural or torsional vibration of the specimens. 3.1. Longitudinal vibration The specimen was supported in the fundamental longitudinal nodal position in the middle of its span. The acceleration transducer Brüel&Kjær of Type 4519-003 was placed at the center of one end surface of the specimen. The opposite end surface of the specimen was struck perpendicular to the surface by the impact hammer Brüel&Kjær of Type 8206. The waveforms of the excitation force and the acceleration were recorded and transformed using Fast Fourier Transform (FFT) to the frequency domain. The Frequency Response Function (FRF) was evaluated from these signals using the vibration analyzer Brüel&Kjær Front-end 3560-B-120 and program PULSE 13.5. The test was repeated four more times for each specimen and the average was saved. From an averaged FRF, the fundamental longitudinal resonant frequency was determined for each specimen. Based on the equation for longitudinal vibration of the beam with continuously distributed mass with free-free boundary condition, the dynamic Young s modulus E dl was determined [6-7] using the relation E dl 2 4lmfl = (1) bt 3.2. Flexural vibration The specimen was simply supported in the distance 0.224 of the span on both ends, the fundamental flexural nodal positions. The acceleration transducer was placed at the end of the specimen on the upper face. The upper surface of the
564 Tomáš Plachý et al. / Procedia Engineering 48 ( 2012 ) 562 567 opposite end of the specimen was struck by the impact hammer. The fundamental flexural resonant frequency was evaluated using the same procedure as the above described longitudinal one. The dynamic Young s modulus E df based on flexural resonant frequency was determined [6-7] using the relation 3.3. Torsional vibration E 0.9465l mf T bt 3 2 f 1 df = (2) 3 The specimen was supported in the torsional nodal position of the first torsional mode of vibration, in the middle of its span. The acceleration transducer was placed at the end of the specimen in the right upper corner of the side surface. The left lower corner of the same side surface of the specimen was struck by the impact hammer. The first torsional resonant frequency was evaluated using the same procedure as the above described longitudinal one. The dynamic shear modulus G d was determined [6-7] based on the equation where B is defined as G 2 4lmft = [ B /(1 A)] (3) bt d + B b / t + t / b 2 4( t / b) 2.52( t / b) + 0.21( t / b) = 6 (4) 3.4. Poisson s ratio The Poisson s ratio can be determined from E dl or from E df based on the equation μ ( E / 2G ) 1 (5) d = d d Because the correction factor T 1 in the equation (2) depends on the µ d, an iterative process has to be used for µ df and E df determination. As the first approximation can be used µ dl calculated from E dl. The iterative process of equations (2) and (5) can stop when the values of µ df for the previous and the next steps will not differ more than 1%. 4. Time dependent changes of mechanical properties Nondestructive impulse excitation method was used for determination of time dependent changes of the gypsum mechanical properties. Using this method, the fundamental longitudinal, flexural and torsional frequencies were measured every one hour during the first 60 hours after casting the gypsum. The dynamic Young s modulus, dynamic shear modulus and Poisson s ratio were calculated for each measured frequency in each time of measurement. The graphs of time dependent changes of these properties are presented in Fig. 1-4. 5. Conclusions The evolution of the investigated mechanical properties of the chosen gypsum binder is interesting. Several changes occurred during their evolution in the first three days. It is interesting that values of dynamic Young s modulus and dynamic shear modulus decreased after three hours from making the specimens while they were increasing until this time. It was the phase when the solid structure created. Hydration process, during which the big amount of hydration heat is produced, was also finished after three hours. After three hours from the beginning, the values of mechanical properties started to decrease about 10%. Approximately after two days, the values started to increase very rapidly and they increased to the time of seven days. After this time, the values increased very slowly and after 14 days they were stable. Only Poisson s ratio seems to be constant from the beginning of the measurement to the end, the average value was 0.33. The effect, which influences mechanical properties evolution, is the water content in a specimen. It is necessary to add more water to a specimen during
Tomáš Plachý et al. / Procedia Engineering 48 ( 2012 ) 562 567 565 its making because of workability then it would be necessary for theoretic hydration. Next processes are probably connected with creation of the solid structure during the first day. The trend of mechanical properties evolution was monitored earlier but in comparison with literature there were not done such amount of measurements in such short intervals. The most of previous measurements were done using classic destructive methods, the results of which are dependent on technological discipline during preparing specimens, during testing but they are also dependent on the conditions where they are placed (especially on temperature). The trend of mechanical properties evolution was verified nondestructively on the same specimens for the whole time. Thus the above mentioned effects and problems during destructive testing were eliminated. Fig. 1. The time dependent changes of the dynamic Young s modulus of gypsum determined based on the fundamental longitudinal resonant frequency.
566 Tomáš Plachý et al. / Procedia Engineering 48 (2012) 562 567 Fig. 2. The time dependent changes of the dynamic Young s modulus of gypsum determined based on the fundamental flexural resonant frequency. Fig. 3. The time dependent changes of the dynamic shear modulus of gypsum determined based on the fundamental torsional resonant frequency.
Tomáš Plachý et al. / Procedia Engineering 48 (2012) 562 567 567 Fig. 4. The time dependent changes of the Poisson s ratio of gypsum determined based on Edl. Acknowledgements This outcome has been achieved with the financial support of the Czech Technical University in Prague SGS12/117/OHK1/2T/11. References [1] Deal, B., Grove, A., 1965. General Relationship for the Thermal Oxidation of Silicon. Journal of Applied Physics 36, p. 3770. [2] Fachinger, J., 2006. Behavior of HTR Fuel Elements in Aquatic Phases of Repository Host Rock Formations. Nuclear Engineering & Design 236, p. 54. [3] Quintiere, J. G., 2006. Fundamentals of Fire Phenomena. John Wiley & Sons. Ltd, Chichester, U. K. [4] Clark, T., Woodley, R., De Halas, D., 1962. Gas-Graphite Systems, in Nuclear Graphite R. Nightingale, Editor. Academic Press, New York, p. 387. [5] Samochine, D., Boyce, K., Shields, J., 2005. Investigation into staff behaviour in unannounced evacuations of retail stores - Implications for training and fire safety engineering. Fire Safety Science - Proceedings of the 8th International Symposium, International Association for Fire Safety Science, pp. 519-530. [6] ASTM E1876-01, 2006, Standard Test Method for Dynamic Young s Modulus, Shear Modulus, and Poisson s Ratio by Impulse Excitation of Vibration, Annual Book of ASTM Standards, American Society for Testing and Materials. [7] ASTM C215, 1991, Standard Test Method for Fundamental Transverse, Longitudinal, and Torsional Resonant Frequencies of Concrete Specimens, Annual Book of ASTM Standards, American Society for Testing and Materials. [8] Fachinger, J., den Exter, M., Grambow, B., Holgerson, S., Landesmann, C., Titov, M., Podruhzina, T., 2004. Behavior of spent HTR fuel elements in aquatic phases of repository host rock formations. 2nd International Topical Meeting on High Temperature Reactor Technology. Beijing, China, paper #B08. [9] Deep-Burn Project: Annual Report for 2009, Idaho National Laboratory, Sept. 2009. [10] Melzerová, L., Kuklík, P., 2010. Variability of Strength for Beams from the Glued Laminated Timber. Proceeding of Experimental Stress Analysis 2010, Olomouc: Palacky University, p. 257-260. [11] PadevČt, P., Zobal, O., 2010. Change of Material Properties of the Cement Paste CEM I. Proceeding of Experimental Stress Analysis 2010. Olomouc: Palacky University, p. 307-310.