Monitoring of Mechanical Properties of Gypsum Using the Impulse Excitation Method

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1 Monitoring of Mechanical Properties of Gypsum Using the Impulse Excitation Metho RICHARD ŤOUPEK, TOMÁŠ PLACHÝ, MICHAL POLÁK, PAVEL TESÁREK Department of Mechanics, Faculty of Civil Engineering Czech Technical University in Prague Thákurova 7, Praha 6, CZECH REPUBLIC plachy@fsv.cvut.cz Abstract: - The paper presents results of gypsum mechanical properties monitoring using non-estructive impulse excitation metho. The avantage of the metho is that the same specimen can be teste in ifferent time instants repeately without any amage. The first 14 ays are the most important for material properties evolution. After that time, the mechanical properties are not changing significantly. The article escribes the evelopment of mechanical properties (Dynamic Young s Moulus, Dynamic Shear Moulus, Poisson s ratio) of grey gypsum uring its harening. Key-Wors: - gypsum; impulse excitation metho; Young s moulus; shear moulus 1 Introuction The gypsum has been use as a builing material for several thousans of years. At present time, it is use in plasterboars. They are use in new constructions an also uring reconstructions. From the view of experts an also general public, the gypsum is a material, which is use in the builing inustry for its excellent usage properties (fast harening, goo mechanical an thermal properties an goo workability) but only in interiors. The little knowlege of this material oes not allow extening its use in exteriors. From the chemical view, it is calcium sulfate ihyrate. The gypsum biner can contain also other moifications of the system calcium sulfate water [1]. Therefore, it is interesting to investigate this material also on microlevel an to etermine the content of the gypsum phases in the investigate gypsum using the nanoinentation technics []. The problem with gypsum usage starts to be complicate when the aitives are ae to the gypsum mixture to improve the chosen properties [3], [4]. The time epenent changes of the silicate base materials has been teste for several years at the workplace of authors. From the view of the mechanical properties evolution, the behaviour of the gypsum is specific an ifferent from the other porous builing materials base on cement or lime biners. Especially, it is very fast creation of a soli structure (removing of the gypsum from the moul 30 minutes after mixing gypsum biner with water) an also non-traitional ecrease of the mechanical properties in the first week after making the gypsum [5]. Three gypsum specimens were mae for the purpose to monitor an ientify the gypsum mechanical properties evolution in more etail. Material an Specimens The grey gypsum prouce by Gypstren co. Lt. was use for making the specimens. It is compose of two ifferent ehyrates. These two components are natural gypsum an gypsum from chemical inustry mixe in one-to-one ratio. Water/gypsum ratio equal to 0.71 was use for making the specimens an it correspons to the gypsum paste with normal consistence. For the purpose of this test, three ientical gypsum specimens of imensions mm were mae in a stainless moul with three sections. These specimens were put off the moul after twenty minutes an the experimental measurement of the Dynamic Young s Moulus, Dynamic Shear Moulus an Poisson s ratio starte immeiately. 3 Impulse Excitation Metho The Impulse Excitation Metho (IEM) was chosen for etermination of ynamic Young s moulus, shear moulus an Poisson s ratio because of its non-estructive character. This metho is quick, the measurement line is small enough an mobile. The mechanical characteristics were etermine base on the equation for vibration of the isotropic beam with continuously istribute mass, base on ISBN:

2 measure resonant frequencies of longituinal, flexural an torsional vibration of the specimens, imensions of the beam an its mass. The measurement line (Fig. 1) consiste of the acceleration transucer Brüel&Kjær of Type , the impact hammer Brüel&Kjær of Type 806, the vibration analyzer Brüel&Kjær Front-en B-10 an program PULSE The vibration was inuce by the strike of the impact hammer. The waveforms of the excitation force an the acceleration were recore an transforme using Fast Fourier Transform (FFT) to the frequency omain. The Frequency Response Function (FRF) as the ratio of acceleration to the excitation force was evaluate from these signals using the vibration analyzer an program PULSE The test was repeate four more times for each specimen an the average function FRF was save. From an average FRF, the funamental longituinal resonant frequency was etermine for each specimen. where: E l is the Dynamic Young s Moulus [Pa], f l is the funamental longituinal frequency [Hz], b is the with of the specimen [m], t is the height of the is the mass of the specimen [kg]. Fig. Test arrangement for the longituinal vibration 3. Dynamic Young s Moulus Flexural Vibration Another way how to etermine Dynamic Young s Moulus is flexural vibration. The specimen was simply supporte in the istance 0.4 of the span on both ens, the funamental flexural noal positions (Fig. 3). The acceleration transucer was place at the en of the specimen on the upper surface (Fig.3 right sie). The opposite en of the surface was struck by the impact hammer (Fig.3 left sie). Fig.1 The measurement line Brüel&Kjær 3.1 Dynamic Young s Moulus Longituinal Vibration The specimen was supporte in the funamental longituinal noal position in the mile of its span (Fig. ). The acceleration transucer was place at the centre of one en surface of the specimen (Fig. right sie). The opposite en surface of the specimen was struck perpenicular to the surface by the impact hammer (Fig. left sie). The mass an imensions of the specimen were measure, the FRF was evaluate an the ynamic Young s moulus E l was etermine [6-7] using the relation Fig. 3 Test arrangement for the flexural vibration The mass an imensions of the specimen were measure, the FRF was evaluate an the Dynamic Young s Moulus E f was etermine [6-7] using the relation E l 4lmf l (1) l mf f T1 Ef () 3 ISBN:

3 where: E f is the Dynamic Young s Moulus [Pa], f f is the funamental longituinal frequency [Hz], b is the with of the specimen [m], h is the height of the is the mass of the specimen [kg] an T 1 is the correction factor for funamental flexural moe to account for finite thickness of bar an Poisson s ratio [6]. 3.3 Dynamic Shear Moulus Torsional Vibration The ynamic shear moulus was etermine base on the torsional vibration. The specimen was supporte in the mile of the span, the funamental torsional noal positions (Fig. 4). The acceleration transucer was place at the en of the specimen in the right upper corner of the sie surface (Fig.4 right sie). The opposite left lower corner of the same sie was struck by the impact hammer. Fig. 4 Test arrangement for the flexural vibration The mass an imensions of the specimen were measure, the FRF was evaluate an the ynamic shear moulus E f was etermine [6-7] using the relation G 4lmf t [ B /(1 A)] (3) where: G is the ynamic shear moulus [Pa], f t is the funamental torsional frequency [Hz], b is the with of the specimen [m], t is the height of the is the mass of the specimen [kg], A is the empirical correction factor epenent on the with-tothickness ratio of the specimen an B is efine as 3.4 Poisson s Ratio The Poisson s ratio can be etermine from E l or from E f base on the equation ( E / G ) 1 (5) Because the correction factor T 1 in the equation () epens on the µ, an iterative process has to be use for µ f an E f etermination. As the first approximation can be use µ l calculate from E l. The iterative process of equations () an (5) can stop when the values of µ f for the previous an the next steps will not iffer more than 1%. 4 Results The first establishe value was the Dynamic Young s Moulus etermine from the longituinal vibration (Fig. 5). As it can be seen in Fig. 5, value of Dynamic Young s Moulus E l increase from the average value 3.8 GPa to 3.95 GPa in the first 3 hours after prouction of the specimens. Then the values a little bit ecrease an uring the next two ays the value of E l remaine relatively stable between 3.7 GPa an 3.9 GPa. After two ays, the values starte to increase very rapily an they increase to the time of seven ays then they became stable or increase very slowly. During the last ten hours of laboratory tests, the maximal release of free humiity occurre. Initial weight of the specimens was about 395 g an it ecrease to the values about 70 g. The secon variant of Dynamic Young s Moulus etermination was the flexural vibration (Fig. 6). As it can be seen from the comparison of the Fig. 5 an the Fig. 6, both results correspon very well. Only the values etermine from the flexural vibration are a little bit less accurate than the results from longituinal vibration. b / t t / b B 6 (4) 4( t / b).5( t / b) 0.1( t / b) Fig. 5 Dynamic Young s moulus E l ISBN:

4 Fig. 6 Dynamic Young s moulus E f Fig. 7 Dynamic shear moulus E l The changes of ynamic shear moulus are presente in the Fig. 7. The changes at the beginning of the gypsum harening are not bigger than the inaccuracy of the use metho. In the final stage of measurements, increase of G values occurs similar to the case of E measurements. G values increase by 17 % to 1.75 GPa uring weight loss of the last 10 g of free humiity from the gypsum samples. Base on the calculate values of E an G, the Poisson s ratio was calculate for each measurement of the specimen (Fig. 8). 5 Conclusion The article presents the results of an experiment uring which the evelopment of Dynamic Young s Moulus, ynamic shear moulus an Poisson s ratio of three gypsum specimens were monitore. Several changes occurre uring evolution of these characteristics after prouction of the specimens an starting their harening. There is visible increase of values at the beginning (Fig. 5-7 right sie). Then the values of mechanical properties starte to ecrease a little bit. At the en of monitoring, when the specimens lost about 100 grams of their weight, the values starte to increase very rapily. The effect, which influences mechanical properties evolution, is the water content in a specimen. It is necessary to a more water to a specimen uring its making because of workability then it woul be necessary for theoretic hyration. Next processes are probably relate to the formation of the soli structure uring the first ay. Resulting values of Poisson s ratio varies because they are very sensitive to inaccuracies uring measurement of E an G. Even small uncertainty of etermination E an G influences Poisson s ratio significantly. The average value seems to be constant from the beginning of the measurement to the en. The average value is The tren of mechanical properties evolution was monitore earlier but in comparison with literature there was not one such amount of measurements in such short intervals. The most of previous measurements were one using classic static methos, the results of which are epenent on technological iscipline uring specimen preparation an uring testing but they are also epenent on conitions where they are place (especially on temperature). The tren of mechanical properties evolution was verifie nonestructively on the same specimens for the whole time. Thus the above mentione effects an problems uring static testing were eliminate. This outcome has been achieve with the financial support of the Ministry of Eucation of the Czech Republic uner the No.: MSM Fig. 8 Poisson s ratio References: [1] Deal, B., Grove, A., General Relationship for the Thermal Oxiation of Silicon, Journal of Applie Physics, Vol. 36, 1965, p [] Fachinger, J., Behavior of HTR Fuel Elements in Aquatic Phases of Repository Host Rock Formations. Nuclear Engineering & Design Vol. 36, 006, p. 54. ISBN:

5 [3] Quintiere, James G., Funamentals of Fire Phenomena, John Wiley & Sons. Lt, Chichester, U. K., 006. [4] Clark, T., Wooley, R., De Halas, D., Gas- Graphite Systems, in Nuclear Graphite R. Nightingale, Eitor. Acaemic Press, New York, 196, p [5] Samochine, D., Boyce, K., Shiels, J.,. Investigation into staff behaviour in unannounce evacuations of retail stores - Implications for training an fire safety engineering, Fire Safety Science - Proceeings of the 8th International Symposium, International Association for Fire Safety Science, 005, pp [6] ASTM E , Stanar Test Metho for Dynamic Young s Moulus, Shear Moulus, an Poisson s Ratio by Impulse Excitation of Vibration, Annual Book of ASTM Stanars, American Society for Testing an Materials, 006. [7] ASTM C15, Stanar Test Metho for Funamental Transverse, Longituinal, an Torsional Resonant Frequencies of Concrete Specimens, Annual Book of ASTM Stanars, American Society for Testing an Materials, [8] Paevět P., Zobal O., Change of Material Properties of the Cement Paste CEM I, Proceeing of Experimental Stress Analysis 010. Olomouc: Palacky University, 010, pp ISBN: