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921-3535-1-PB | Young's Modulus | Strength Of Materials


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  Gazi University Journal of Science GU J Sci 25(3):761-768 (2012) ORIGINAL ARTICLE ♠ Corresponding author, e-mail: skurama@anadolu.edu.tr Characterization of Mechanical Properties of Porcelain Tile Using Ultrasonics Elif EREN, Semra KURAMA ♠    Anadolu University, Department of Materials Science and Engineering, 26555, Eskisehir, TURKEY  Received: 01.03.2012 Accepted:07.03.2012 ABSTRACT Ultrasound affords a very useful and versatile non-destructive method, using a large application area, for evaluating the microstructure and mechanical properties of materials. In this study, porcelain tiles were sintered at different temperatures to change their porosity. Following this, the time of flight of both longitudinal and shear waves was measured through the tile. The time of flight of ultrasonic waves was measured using a contact ultrasonic transducer operating on a pulse-echo mode. Using the time of flight of the ultrasonic wave and thickness of tiles, the velocity of the waves and dynamic Young’s modules were determined. To calculate the firing strength and the static Young’s modulus of the tiles a three point bending test analysis was used. The results were considered by comparing the change in velocity with the firing strength. Utilizing the dynamic Young’s modulus of porcelain tiles, their firing strength estimated nondestructively. Additionally, measurement of ultrasonic velocity utilized to predict strength and dynamic Young’s modulus of porcelain tiles. In addition, the two methods, used in measuring Young’s modules, were compared. It was determined that the dynamic Young’s modulus of porcelain tiles was greater than the static Young’s modulus of porcelain tiles.  Key Words : Ultrasonic, porcelain tile, mechanical properties, Young’s modulus.  762  GU J Sci, 25(3):761-768 (2012)/ Elif EREN, Semra KURAMA   t d V   ×= 2 1. INTRODUCTION A general definition of nondestructive testing (NDT) is the examination, testing, or evaluation performed on any type of test object without changing or altering the object in any way, in order to determine the absence or presence of conditions or discontinuities that may have effects on the usefulness or serviceability of that object. Nondestructive tests may also be conducted to measure other test object characteristics, such as size, dimension, configuration, or structure, including alloy content, hardness, grain size, and so on. The simplest of all definitions is basically an examination that is performed on an object of any type, size, shape or material to determine the presence or absence of discontinuities, or to evaluate other material characteristics [1]. Ultrasound is one of the mostly employed non-destructive method for evaluating the microstructure and mechanical  properties of materials. Ultrasonic echoes can be displayed as seen on an ordinary oscilloscope; X representing the time of flight of the pulses converted into distance travelled by the pulses (depth of penetration), with the deflection parallel to the Y-axis representing the amplitude of the echoes. This type of presentation is called an ‘  A- scan ’. It shows the situation with the probe stationary in one position. An A-scan presentation is still the most common mode of display in ultrasonic testing. Since the information that is available in an A-scan is basically one dimensional, interpretation with accompanying sketches and calculation is required to characterize the flaw [2]. Ultrasound parameters, such as transducer frequency, have  been analyzed to determine the necessary system conditions for obtaining areal image maps based on differences in either the intensity of the collected ultrasound signals (reflected signal amplitudes) or the transit time of ultrasound energy through materials, otherwise known as time-of-flight (TOF). While TOF scans have been used to show changes in thickness, acoustic wave velocity, density and acoustic impedance, reflected signal amplitude scanning has recently been employed to analyze attenuation or loss, through a test specimen [3]. Also, the determination of ultrasonic velocities can be used to measure the modulus of elasticity or Young’s modulus of materials [4]. In this study, dynamic Young’s modulus of porcelain tiles, sintered at different temperatures,   was determined by transmission and reflection of ultrasonic waves.   To calculate the firing strength and static Young’s modulus of the tiles a three point bending test analysis was employed.   The results were discussed by comparing changes in velocity with the firing strength. Additionally the two methods, used in the measurement of Young’s modulus, were compared. 2. MATERIAL AND EXPERIMENTAL 2.1. Material and Sample Preparation Standard porcelain tile granules were used in the  preparation of samples in this study. Samples were  prepared using the uniaxial pressing technique in a 50 mm x 100 mm rectangular die at 450 kg/cm 2 , and dried at 110ºC. The firing step was carried out in a fast-firing laboratory roller kiln (Nannetti ER-30) at temperatures of  between 1150-1230ºC with an industrial fast-firing cycle (total 45 min. including cooling). 3 samples were sintered for each temperature. 2.2. Measurement of Ultrasonic Velocity After the sintering of the samples, the time of flight of the longitudinal and the shear waves was measured through the tile (Fig.1) with an Olympus Panametrics-NDT Model 5800 Computer Controlled Pulser/Receiver. This analysis was repeated for three samples, and sintered at the same temperatures, for all the sintering temperatures. The time of flight of the ultrasonic waves (longitudinal and shear waves) was measured with contact ultrasonic transducers operating on a pulse-echo mode. The centre frequencies of the transducer were 5 MHz for longitudinal waves and 2.25 MHz for shear waves. The time of flight measurements for the ultrasonic signals was performed using a digital oscilloscope (Tektronix TDS 1012 Two Channel Digital Storage Oscilloscope). For each of the samples the time of flight of ultrasonic wave measurements were 10 times repeated. The transit time was determined to within an accuracy of ± 40 nsec. The thickness of the samples was measured with a micrometer (0.01 mm resolution Mitutoyo M110-25 DS micrometer). 2.3. Mechanical Characterization The mechanical behavior of a ceramic part is clearly important when the tile is used for the primary purpose of carrying a load. There are basically two ways to measure the elastic properties of ceramic tiles. The first is to measure strain in response to some quasi statically applied stress, commonly in conjunction with strength testing. The elastic modulus which is calculated by this method is known as  static Young’s Modulus . The second,  and generally preferred method of measuring elastic  properties, is one of two sets of wave motion measurements. This elastic modulus is known as dynamic Young’s Modulus.   One basic method for this measurement is the transmission of ultrasonic waves, or the transmission and reflection of pulses (i.e., pulse echo). Another method of measuring elastic properties is the wave method calculated by the resonance vibration of specimens [5].  Dynamic Young’s Modulus By using the time of flight of the ultrasonic waves (Fig. 1) and the thickness of the tiles, the velocity of the waves and the dynamic Young’s modulus were determined. The velocity of the waves was determined by Eq. 1 [6]: as it travelled through the material. (1) V  : Velocity of the wave (m/s) d  : Sample thickness (m) t  : Arrival time between the front and back reflection (s).   GU J Sci, 25(3):761-768 (2012)/ Elif EREN, Semra KURAMA   763  )1()21)(1( 2 σ σ σ  ρ  −−+= l  v E  )22( )21( 22 bb −−= σ   Figure 1. A-scan displays showing the time of flight of a sintered standard tile. Assuming that the samples used in this analysis are isotropic, standard velocity-elasticity relationships can be used to calculate the Young’s modulus. These relationships are: (2) (3) where ν l is the longitudinal wave velocity (m/s), ν s  the shear wave velocity (m/s),  ρ  is the density, E the Young’s modulus (pascals), σ the Poisson’s ratio and b = ν s / ν l [7].   Ultrasonic velocities and densities were used to calculate the dynamic Young’s modulus of the tiles.  Static Young’s Modulus The Young modulus of elasticity (  E  ) is the slope of a plot of stress as a function of strain: (4) where σ  i  is the stress, and ε i  the strain in the same direction i , without restraint in the orthogonal directions. When σ   is increased beyond a critical value, typically 0.01  E   to 0.001  E  , fracture occurs, that is, the strain to failure is small, ~0.01 to ~0.001 [8]. The term strength (the stress required to cause fracture) is normally taken (if not specified) to mean bend strength. Bend strength, in three or four-point loading, is easy to measure, once test bars have been machined to the requisite size and surface finish. The three-point bend strength ( σ  max ) for a rectangular cross-section bar is obtained from the load (  F  ) required to cause failure using the standard expression: (5) where l   is the distance between the two outer knife-edges, b  is the breadth, and d   the thickness of the bar. The value of σ  max  is the maximum stress experienced by the bar, along a line on the bar face, opposite the central knife-edge, which is where failure should occur [8]. The bend strength and static Young’s modulus of tiles were measured three times for each temperature using the three-point bending test (model 5581, Instron) at a loading rate of 1 mm/min (ISO-EN 10545-4). 2.4. Porosity measurement The total porosity (open and closed pores) of a material was measured by using pycnometry using Eq. 6: 100)(%  ×−= bbt  d d d  P   (6) where d  t  =true density and d  b =bulk density. The bulk density can be determined using the techniques, e.g., liquid or powder immersion of the bulk sample [9]. In this work, it was determined by water immersion. The measure of pycnometry used the Quantachrome Model  No:MVP-1 Multipycnometer. 3. RESULTS AND DISCUSSION Sound waves are mechanical vibrations involving movement within the medium in which they are travelling. The particles in the medium vibrate, causing it to distort, thus transferring energy from particle to particle, along the wave path [10]. Whereas particles oscillate parallel to the direction of propagation for longitudinal waves, they oscillate transverse to the direction of propagation for shear waves [11]. This is why the time of flight of shear waves is greater than the time of flight of longitudinal waves and longitudinal ultrasonic velocity is greater than shear ultrasonic velocity. The times of flight and the ultrasonic velocities can be seen in Table 1. When the firing temperature is increased, densification is increased and volume fraction porosity is decreased until over firing. 1150°C is the lowest firing temperature in this study (Table 2). Therefore, the total  porosities (%) of samples sintered at 1150°C, are the greatest. Pores obstruct the path of the ultrasonic signal and retard the ultrasonic wave’s speed. This is why the time of flight of the samples sintered at 1150°C is the greatest and why the ultrasonic velocity is the lowest. During porcelain tile densification, liquid phase begins to form which surrounds the particles and produces a  process-driving capillary pressure at the contact points. The capillary pressure brings the particles closer together, increasing shrinkage and lowering porosity, while concurrently altering pore size and shape. Raising temperature increases the quantity of liquid phase and lowers porosity [12]. This is the reason of obtaining the highest densification and minimum total porosity (%) at 1230°C. Therefore the ultrasonic velocity also reaches to the highest value at this temperature. ii  E  ε σ  = 2max 23 bd  Fl  = σ   764  GU J Sci, 25(3):761-768 (2012)/ Elif EREN, Semra KURAMA   Table 1. Change of mechanical properties with temperature. Temp. (ºC) d (mm) t longitudinal (ns) t shear (ns)  ν longitudinal (m/s)  ν shear (m/s) Strength (N/mm 2 ) Dynamic E (GPa) Static E (GPa) E static /E dynamic 1150 7.81 ± 0.02 4590 ± 10 6753.3 ± 46.2 3403.1 ± 8.2 2313 ± 916.9 26.9 ± 1.5 23.8 ± 0.2 14.2 ± 0.4 0.60 1160 7.74 ± 0.04 4240 ± 26.46 6206.7 ± 11.6 3651.1 ± 35.3 2494.1 ± 7.3 28.7 ± 0.9 28.2 ± 0.4 16.2 ± 0.6 0.58 1170 7.71 ± 0.02 3943.3 ± 40.4 5866.7 ± 57.7 3910.7 ± 39.8 2628.6 ± 23.6 33.2 ± 3.5 32.8 ± 0.7 19.6 ± 1.2 0.60 1180 7.55 ± 0.06 3503.3 ± 50 5266.7 ± 28.9 4308.3 ± 28.1 2865.9 ± 36.7 35.1 ± 2.8 40.7 ± 0.8 24.3 ± 1.6 0.60 1190 7.43 ± 0.02 3250 ± 50 4933.3 ± 76.4 4570.9 ± 58.3 3011.2 ± 38 41.8 ± 4.9 46.2 ± 1.1 28.6 ± 1.1 0.62 1200 7.44 ± 0.04 3110 ± 45.8 4783.3 ± 15.3 4787.1 ± 43.8 3112.2 ± 10.6 44.6 ± 5.07 50.8 ± 0.4 29.7 ± 3.6 0.58 1210 7.39 ± 0.11 3070 ± 60.8 4766.7 ± 104.1 4814.7 ± 33.1 3101 ± 22.4 46.1 ± 1.63 50.8 ± 0.7 30.7 ± 1.7 0.60 1220 7.34 ± 0.11 2953.3 ± 64.3 4540 ± 79.4 4971.2 ± 37.2 3233.6 ± 10.2 53.2 ± 1.5 55.2 ± 0.6 32.3 ± 5.3 0.59 1230 7.35 ± 0.03 2806.7 ± 11.6 4383.3 ± 28.9 5235.2 ± 12.9 3352.1 ± 12.4 54.7 ± 6.2 60.4 ± 0.2 36.0 ± 2.4 0.60 Table 2. Bulk density, true density and total porosity of porcelain tiles. Temperature (ºC) Bulk density (g/cm 3 ) True density (g/cm 3 ) Total porosity (%) 1150 2.07±0.0003 2.58±0.008 24.28±0.37 1160 2.13±0.002 2.57±0.005 20.43±0.26 1170 2.18±0.003 2.56±0.008 17.37±0.54 1180 2.25±0.005 2.54±0.004 13.13±0.38 1190 2.28±0.002 2.53±0.002 10.73±0.11 1200 2.31±0.004 2.52±0.002 8.90±0.11 1210 2.31±0.0002 2.51±0.004 8.92±0.18 1220 2.33±0.004 2.50±0.005 7.63±0.42 1230 2.33±0.005 2.49±0.006 6.85±0.03
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