73 Muazu, Muhamad Azizi & Norhayati / Jurnal Teknologi (Sciences & Engineering) 78:9 (2016) Abstrak

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1 73 Muzu, Muhmd Azizi & Norhyti / Jurnl Teknologi (Sciences & Engineering) 78:9 (2016) Jurnl Teknologi COMPARISON OF WEIBULL AND NORMAL PROBABILITY DISTRIBUTION OF FLEXURAL STRENGTH OF DENSE AND POROUS FIRED CLAY Muzu Aukr, Muhmd Azizi Mt Yjid, Norhyti Ahmd * Deprtment of Mechnicl Engineering, Byero University no, Nigeri Fculty of Mechnicl Engineering, Universiti Teknologi Mlysi, UTM Johor Bhru, Johor, Mlysi Full Pper Article history Received 26 Novemer 2015 Received in revised form 10 April 2016 Accepted 15 August 2016 *Corresponding uthor nhyti@mil.fkm.utm.my Grphicl strct Astrct Crcks In this reserch, dense nd porous fired cly were produced t firing temperture of 1300 C. The flexurl strength dt of the dense nd the porous fired cly were determined using three point ending test. Two-prmeter Weiull nd norml proility distriutions were used to estimte the reliility of the flexurl strength dt of the dense nd the porous fired cly. From the result, the Weiull proility distriution scle prmeter for the dense (36.31MP) nd Porous (18.85MP) fired cly re higher thn the men strength vlue for the dense (33.84MP) nd the porous (17.87MP) of the norml distriution. Distriutions of flws in the dense nd the porous fired cly hve significnt effect on the Weiull nd norml distriution prmeters. The frctured surfce of the dense fired cly shows rndom distriution of crcks while tht of the porous fired cly shows distriution of pores in the morphology. The norml distriution considers filure t 50% of the flexurl strength dt while Weiull proility distriution is filure t 62.3% of the strength dt. Therefore, two-prmeter Weiull is the suitle tool to model filure strength dt of the dense nd porous fired cly. eywords: Weiull distriution, norml distriution, fired cly, flexurl strength Astrk Tnh lit yng pdt dn erling dihsilkn dlm penyelidikn ini pd suhu pemkrn 1300 C. ekutn lenturn untuk tnh lit kr yng pdt dn erlling ditentukn menggunkn pengujin lenturn tig titik. Du prmeter turn kerngklin Weiull dn norml digunkn untuk mengnggrkn keolehpercyn dt kekutn lenturn gi tnh lit kr yng pdt dn erling. Dripd keputusn eksperimen, skl prmeter untuk turn kerngklin Weiull gi tnh lit kr yng pdt (36.31 MP) dn yng erling (18.85 MP) dlh tinggi dripd nili kekutn purt untuk turn kerngklin norml gi tnh lit kr yng pdt (33.84 MP) dn yng erling (17.87 MP). Turn kecctn gi tnh lit kr mempunyi kesn yng penting kepd prmeter turn Weiull dn norml. Morfologi permukn pth tnh lit kr yng pdt menunjukkn turn retk secr rwk, sementr tnh lit yng erling menunjukn turn ling-ling. Turn kerngklin norml mempertimngkn keggln 50% dripd dt kekutn lenturn mnkl turn kerngklin Weilull mempertimngkn keggln pd 62.3% dripd dt kekutn. Oleh itu, du prmeter Weiull leih sesui untuk model dt kekutn keggln gi tnh lit kr yng

2 74 Muzu, Muhmd Azizi & Norhyti / Jurnl Teknologi (Sciences & Engineering) 78:9 (2016) pdt dn erling. t kunci: Turn Weiull, turn norml, tnh lit kr, kekutn lenturn 2016 Penerit UTM Press. All rights reserved 1.0 INTRODUCTION Cermic mterils hve gined generl cceptnce from more trditionl pplictions to dvnced technologies such s nozzles, memrnes, iomedicl implnts, solid fuel cells, molten metl filters nd ctlyst supports. In ddition, high cost of engineering cermics hs mke reserchers to use cly s strting mteril to fricte dense nd porous cermic mterils for specific pplictions. Cly minerl cn e chep source of cermic mterils such s mullite, which hs good mechnicl, therml nd chemicl resistnt properties. In engineering mterils requiring lod ering for structurl pplictions, strength reliility is highly required [1]. Though cermic mterils hve high hrdness compred to metllic mterils, the strength reliility of cermic mterils is very low. The poor in reliility strength normlly rise due to distriution of flws, crcks nd porosity which re intrinsic properties of cermic mterils. As result, cermic mterils under the sme friction conditions tend to hve different mechnicl properties. The strength of cermic mterils is determined y the most criticl flw; therefore, the strength hs to e presented y distriution function, which exhiit the size distriution of flws (in the form of crcks nd porosity) in the specimen. A wide flw distriution cuses lrge sctter of strength[2]. While uniformly distriution of flws cuses smll sctter of the strength. The vriility in strength of rittle mterils is est modeled using Weiull nd norml distriutions [3]. The Weiull proility distriution is sed on the wekest link theory concept. In other words, the lrgest flw provides the crck initition site. It is elieved tht the Weiull proility distriution is the model of distriution of the minimum filure stress chrcterized y flws if numer of rndom flws re present in stressed volume[4]. There is no reserch on which of these two proility distriutions will est fit to model the strength dt of dense nd porous fired cly. In this work, we nlyze the flexurl strength dt of dense nd porous fired cly using two-prmeter Weiull nd norml proility distriutions. Comprison of two-prmeter Weiull nd norml distriution is lso considered. Also, the distriution of flws in the dense nd the porous fired cly will e discussed. 2.0 METHODOLOGY The rw cly used in this reserch ws otined from locl miners in Nigeri. The chemicl composition of the cly nd phses present in the cly nd fired cermic ws determined using XRF nd XRD respectively. The dense nd the porous fired cly (33 smples ech) were compcted t pressure of 60MP nd fired t temperture of 1300 C for twohours. The flexurl strength of the smples of dimension mm nd spn 40mm ws determined using three-point ending test t loding rte of 0.5mm/min using Instron 100-N electro-mechnicl testing mchine ccording eqution 1: The flexurl strength vlues of the dense nd porous fired cly lie in the rnge 24-46MP nd MP respectively, 3PL 2 2d (1) where P is the lod, L is the spn which is 40mm, is the width nd d is the thickness. 2.1 Two-Prmeter Weiull The two-prmeter Weiull cumultive distriution is given y m P 1 exp (2) o Where P is the proility of filure t stress, m is the Weiull modulus nd is the scle prmeter. Linerizing Eqution 2, y tking doule logrithm to otin: ln(ln( 1/(1 (3) P)) mln mln The plot of ln(ln( 1/(1 P)) o o vs ln gives stright line grph with slope (Weiull modulus) m nd intercept mln the scle prmeter ws o

3 75 Muzu, Muhmd Azizi & Norhyti / Jurnl Teknologi (Sciences & Engineering) 78:9 (2016) estimted using the intercept nd the Weiull modulus Modified pln Meier (Hzn) estimtor ws used to determine the proility of filure since it gives the less is of the Weiull modulus ( m ) for numer of smples greter thn 20 for estimting the Weiull prmeters of cermics nd rittle mterils [5], [6], [7]. P r 0.5 N (4) where N is the smple size nd P is the proility of filure for the r th rnked position. 2.2 Descriptive Sttistics Norml distriution nd oxplot re presented y minimum, first qurtile, medin, upper qurtile mximum, men nd stndrd devition (SD) of the flexurl strength of the dense nd the porous fired. 3.0 RESULTS AND DISCUSSION The chemicl composition from the XRF nlysis ws found to e wt% SiO2, wt% Al2O3, 1.15 wt% 2O, 0.27 wt% Fe2O3, 0.05wt% CO, 0.04 wt% TiO2, 0.04 wt% MgO, 0.01 wt% MnO, 0.01 wt% P2O5 nd wt% LOI [8]. The XRD result of the rw cly (Figure 1) shows kolinite is the predominnt phse in the rw cly with trces of illite nd qurtz [9]. In ddition, the XRD of the fired cly shows predominnt mullite phse t firing temperture of 1300 C [7]. The two-prmeter Weiull proility plot Modified pln Meier estimte of dense nd porous fired cly using liner regression is shown in Figure 2. From the figure, it cn e shown tht the proility dt points lie close to the line of est fit, with the points t the lower til of the plot lying closer to the line of est fit. This is one chrcteristics of liner regression nlysis, which chses the lower strength dt points of Weiull proility plot [6]. From the plot, the line of est fit of the porous fired cly lies to the left of the plot while tht of the dense fired cly lies to the right, this ehvior cn e ttriuted to the fct the strength rnge of the dense fired cly is higher thn tht of the porous fired cly. From the estimtes of the Weiull prmeters, the Weiull modulus of the dense cermic shows vlue of 6.52 while tht of the porous fired cly shows vlue of 9.22, this shows tht the Weiull modulus of the porous fired cly is higher thn tht of the dense fired cly. Also, this supports tht the vriility in the flexurl strength of the porous fired cly is higher thn tht of the dense fired cly. Intensity (r. units) kolinite, I illite, Q qurtz, M Mullite M M M Fired Cly C M M M M Rw Cly Figure 1 XRD nlysis of rw nd fired cly t 1300 C The scle prmeter of the dense fired cly hve vlue of MP while the porous fired cly hs vlue of MP; this shows tht the strength t which 63.2% of the dense fired cly mteril will fil is higher thn tht of the porous fired cly. This reson is due to the fct tht the porous fired cly hs pore former ddition, which urns out during sintering this cretes voids in the fired smples. These voids ct s defects in the porous smples, therey, decresing the strength. ln(ln(1/(1-p))) I I Q Figure 2 Weiull proility plot of dense nd porous fired cly Hzen method Tle 1 gives the summry of stndrd devition (SD), minimum, medin, men nd mximum of the flexurl strength computed from the oxplot. From the results, the men strength of the dense nd porous fired cly is found to e 33.84MP nd MP respectively. The vlues of the men strength re lower thn the scle prmeter vlues of the dense nd the porous fired cly using two-prmeter Weiull proility distriution. The reson for this ehvior is tht the chrcteristic strength is the strength vlue t proility of filure equl 63.2% D e n s e P o r o u s ln F l e x u r l S t r e n g t h ( M P )

4 76 Muzu, Muhmd Azizi & Norhyti / Jurnl Teknologi (Sciences & Engineering) 78:9 (2016) while the men strength vlue is t proility of filure equls to 50%. Similr oservtion ws reported y [6]. The lower qurtile nd upper qurtile of the dense nd porous fired cly re computed to e 29.06MP; MP nd 16.51MP; MP respectively. The interqurtile rnge of the porous fired cly (2.36 MP) is lower thn tht of the dense fired cly (8.54); this shows tht the vriility of the flexurl strength of the dense fired cly is higher thn tht of the porous fired cly. This grees with the vlues of the two-prmeter Weiull modulus. The stndrd devition, further confirmed less vriility in the flexurl strength of the porous fired cly with vlue of 2.36 MP s compred with the dense fired cly with vlue of 6.28 MP. Flexurl Strength (MP) Tle 1 Men, medin SD, interqurtile rnges, mximum nd minimum of flexurl strength of dense nd porous fired cly t 1300 C 10 Dense Porous Prmeter Dense Porous Men (MP) SD (MP) Minimum (MP) Q1 (MP) Medin (MP) Q3 (MP) Mximum (MP) IQ Rnge (MP) Boxplot of the flexurl strength of oth the dense nd the porous fired cly t 1300 C sintering temperture is depicted in Figure 3. The dense fired cly gives wider interqurtile rnge while the porous fired cly shows nrrower interqurtile rnge, the wider interqurtile rnge of dense fired cly is due to the high vriility of the flexurl strength nd the nrrow rnge of the interqurtile rnge of the porous fired cly cn e ttriuted to the low vriility in the flexurl strength. This grees with the two-prmeter Weiull proility distriution, which shows wide nd nrrow proility distriution for the dense nd the porous fired cly respectively. In ddition, the whisker of the dense fired cly to the right is longer thn tht to the left, these show there re extreme vlues (devition from the medin) towrds the positive end nd the distriution is positively skewed. However, the whisker of the porous fired cly to the left is longer thn to the right, this mens there re some extreme vlues from the medin towrds the negtive end nd the distriution is negtively skewed. Furthermore, the porous fired cly presents three outlier points (outer fence points) to the right end of the distriution; this mens tht the three outlier points re much higher thn the other vlues of the flexurl strength. Figure 3 Boxplot of dense nd porous fired cly t 1300 C Figure 4 shows the Weiull nd norml distriution proility density plot of the dense fired cly. The density plot of the Weiull distriution shows skewness to the right of the proility density grph. The skewness in the distriutions hs popultion concentrted t vlue close to the scle prmeter. While in the norml distriution, there is no skewness in the proility density plot. The grph is distriuted uniformly round the men. Also, Figure 5 gives the Weiull nd norml distriution proility density plot of the porous fired cly. Like the dense fired cly, the density plot shows skewness to the right, which is concentrted t the scle prmeter vlue while the norml distriution density plot shows no skewness with the plot uniformly distriuted round the men. The skewness of Weiull distriution cn e ttriuted to the fct tht the scle prmeter is strength t 63.2% while tht of the norml distriution is strength t 50% [6]. This shows tht norml distriution gives conservtive estimte of proility of filure compred with Weiull proility distriution.

5 77 Muzu, Muhmd Azizi & Norhyti / Jurnl Teknologi (Sciences & Engineering) 78:9 (2016) Norml Weiull 0.20 Norml Weiull Density Density Flexurl Strength (MP) Flexurl Strength (MP) Figure 4 Density plot of dense fired cly Weiull nd norml distriutions Figure 5 Density plot of porous fired cly Weiull nd norml distriution From Figures 4 nd 5, nrrow flexurl strength distriution of the porous fired cly is due to its high vlue of the Weiull modulus nd smller stndrd devition vlue for Weiull nd norml distriution respectively while the dense mteril hs more spred distriution due to the low vlue of the Weiull modulus nd high stndrd devition of Weiull nd norml distriution respectively. The wider spred of the proility density is due to rndom distriution of crcks which resulted in the scttering of the flexurl strength. The nrrow spred of the proility density is due reltive distriution of porosity in the morphology of the porous fired cly which gives nrrow distriution of the flexurl strength. This mkes the Weiull modulus of the porous fired cly higher nd with higher density (Figure 3) s reflected y the nrrow distriution of the proility density plot. This oservtion hs good greement with previous studies [10],[11]. The nrrower distriution curve suggests less vriility in the flexurl strength of the porous fired cly. In ddition, predicting proility of filure using Weiull distriution is higher thn norml distriution (Figures 4 nd 5) for oth the dense nd the porous fired cly, s result, more suitle to model the flexurl strength dt of the dense nd the porous fired cly. The microgrphs of frctured surfce of the dense nd porous cermic with 10wt% strch ddition re shown in Figures 6 nd 6. From the microgrphs, it cn e depicted tht the dense cermic mteril contins rndom distriution of crcks while the porous cermic contins reltive distriution of porosity. Brittle mterils under the sme friction conditions tend to hve vriility in their mechnicl properties due to porosity nd crcks which re inherent in their microstructure [6]. This vriility in mechnicl properties needs to e model with Weiull proility distriution. The frctogrphy nlyses of dense nd porous fired cly t 1300 C ech show single distinct flw distriution (crcks nd reltive porosity). Crcks Figure 6 Frctured surfce morphology of () dense nd () porous fired cly t 1300 C

6 78 Muzu, Muhmd Azizi & Norhyti / Jurnl Teknologi (Sciences & Engineering) 78:9 (2016) CONCLUSION In this pper, two different proility distriutions were tested in determining the reliility nlysis of dense nd porous fired cly. The scle prmeter in Weiull distriution is higher thn the men strength in norml distriution, ecuse norml distriution provides filure t 50% of the mterils while Weiull modulus provides filure t 63.2%. The porous fired cly hs higher reliility nd filure cn esily e predicted thn the dense fired cly. The porous fired cly hs reltive distriution of porosity while the dense fired cly hs rndom distriution of crcks. Weiull distriution will e suitle tool to model the filure strength of dense nd porous fired cly since it provides due to its high proility density. Acknowledgement This reserch is sponsored y Universiti Teknologi Mlysi through reserch grnt (RUG-00M51) nd contrct reserch grnt (4C044). Specil thnks go to Ministry of Higher Eduction Mlysi (MOHE FRGS 4F552) nd TET fund through Byero University no Nigeri for sponsoring one of the uthors. References [1] Bsu, B., Tiwri, D., undu, D. And Prsd, R Is Weiull Distriution The Most Approprite Sttisticl Strength Distriution For Brittle Mterils? Cermics Interntionl. 35(1): ,. [2] Bermejo, R., Supncic, P., And Dnzer, R Influence Of Mesurement Uncertinties On The Determintion Of The Weiull Distriution. Journl Of The Europen Cermic Society. 32(2): [3] Lu, C., Dnzer, R., And Fischer, F. D Influence Of Threshold Stress On The Estimtion Of Weiull Sttistics. Journl Of Americn Cermic Society. 85(6): [4] Todinov, M. T Is Weiull Distriution The Correct Model For Predicting Proility Of Filure Initited By Non-Intercting Flws? Interntionl Journl Of Solids And Structures. 46(3-4): [5] Pprgyris, A. D Estimtor Type And Popultion Size For Estimting The Weiull Modulus In Cermics. Journl Of The Europen Cermic Society. 18(5): [6] Quinn, J. B. And Quinn, G. D A Prcticl And Systemtic Review Of Weiull Sttistics For Reporting Strengths Of Dentl Mterils. Dentl Mterils : Officil Puliction Of The Acdemy Of Dentl Mterils. 26(2): [7] Aukr, M., Aliyu, A. B., And Ahmd, N Flexurl Strength Anlysis Of Dense And Porous Fired Cly Using Weiull Proility Distriution. 761: [8] Aukr, M., Tmin, M. N., Sleh, M. A., Udy, M. B., & Ahmd, N Preprtion And Chrcteriztion Of A Nigerin Mesoporous Cly-Bsed Memrne For Urnium Removl From Underground Wter. Cermics Interntionl. 42: [9] Aukr, M., Aliyu, A. B., And Ahmd, N Chrcteriztion Of Nigerin Cly As Porous Cermic Mteri. 845: [10] Roos, M. And Stwrczyk, B Evlution Of Bond Strength Of Resin Cements Using Different Generl- Purpose Sttisticl Softwre Pckges For Two-Prmeter Weiull Sttistics. Dentl Mterils : Officil Puliction Of The Acdemy Of Dentl Mterils. 28(7): [11] Stwrczyk, B., Ozcn, M., Trottmnn, A., Hämmerle, C. H. F., And Roos, M Evlution Of Flexurl Strength Of Hipped And Prefired Zirconi Using Different Estimtion Methods Of Weiull Sttistics. Journl Of The Mechnicl Behvior Of Biomedicl Mterils. 10: