INFLUENCE OF POROSITY AND MOISTURE ON MECHANICAL PROPERTIES OF CERAMIC BRICK ANALYTICAL HOMOGENISATION APPROACH

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2 53 Proc. Int. Sym. Brittle Matrix Comosites 11 A.M.Brandt, J.Olek, M.A.Glinicki, C.K.Y.Leung, J.Lis, eds. Warsaw, Setember 28-30, 2015 Institute of Fundamental Technological Research INFLUNC OF POROSITY AND MOISTUR ON MCHANICAL PROPRTIS OF CRAMIC BRICK ANALYTICAL HOMOGNISATION APPROACH Andrzej WINNICKI, Teresa STRYSZWSKA, Stanisław KAŃKA, Szymon SRĘGA Cracow University of Technology, Institute of Building Materials and Structures 24 Warszawska St., Cracow, Poland, ABSTRACT For two tyes of ceramic brick, differing in hase comosition and orosity, Young modulus is measured in dry and fully saturated states and chemohysical roerties are investigated. A simle elastic model for comosite is adoted based on homogenization theory assuming that brick can be treated as three-hase continuum (skeleton, air ores and ores filled with water). Based on exerimentally measured arameters Young modulus and Poisson ratio are redicted theoretically for dry and fully saturated states. The redictions are comared with exerimentally obtained values leading to conclusion, that such a simle theory cannot render roerly elastic roerties of brick in fully saturated state. Keywords: Brick, orosity, saturation, mechanical roerties, homogenization theory, shelby s solution, self-consistent and Mori-Tanaka schemes INTRODUCTION The exerimental research is carried out on two ceramic materials with significantly different hase comosition and orosity structure. The research rogram includes tests of Young modulus for ceramic brick dry and wet. The aim of the aer is to comare results of exerimental tests with an adoted mechanical model based on homogenisation theory. The comarison is restricted to exerimentally obtained and theoretically redicted values of Young modulus. For descrition of mechanical roerties of ceramic brick with different level of orosity and moisture a three-hase material model is roosed ceramic skeleton, air ores and ores filled with water. lastic isotroic roerties are assumed for all hases. These assumtions make ossible use of different schemes of analytical homogenisation, esecially those based on the classical shelby's solution. CHARACTRISTICS OF INVSTIGATD MATRIALS Physicochemical roerties Two tyes of bricks (denoted and L) are investigated. They have similar hysical roerties but different chemical comosition and mechanical roerties. Chemical comosition is investigated using sectral method XRF and diffraction method XRD. Volumetric (aarent) and absolute density is found using enveloe density analyzer (GeoPyc 1360) and gasycnometer (Quantachrome Ultrayc 1200e). Obtained results are given in Tables 1-3.

3 54 Andrzej WINNICKI, Teresa STRYSZWSKA, Stanisław KAŃKA, Szymon SRĘGA Table 1. Chemical comosition of the studied materials Brick Parameter L Content of mass [%] SiO Al 2 O Fe 2 O CaO MgO Cr 2 O 3 <0.10 <0.10 MnO K 2 O P 2 O <0.10 SO <0.10 Na 2 O TiO ZrO 2 <0.10 <0.10 BaO - - Ignition losses Table 2. Phase comosition of the studied materials Brick Phase L Content of mass [%] Quarz Albite 7.0 Microcline Calcite Montmorrillonit Anorthite Hematite Metaholloysite Halloysite Table 3. Physical roerties Parameter Brick L Bulk density [g/cm 3 ] Skeleton density [g/cm 3 ] Water absortion by weight [%] ,3 Total orosity [%] Oen orosity [%] Close orosity [%]

4 Influence of orosity and moisture on mechanical roerties of ceramic brick Porosity Porosity is measured using mercury intrusion method (Quantachrome Poremaster Nova 1000e orosimeter). Results are resented in Figs 1 and 2. Fig. 1. Cumulative curves of ores volume distribution Fig. 2. Poulation curves of ores volume distribution Following the obtained results, the analysed ores are divided into four categories deending on their diameters (Table 4). The structure of orosity is different for both materials, desite of similar total orosity. Material denoted has a definitely larger amount of ores with smaller diameters. Cumulative volume of ores with diameters smaller than 1000 nm is 85%. To the contrary, in material denoted L volume of ores with diameters in the range from 100 to nm is 80%.

5 56 Andrzej WINNICKI, Teresa STRYSZWSKA, Stanisław KAŃKA, Szymon SRĘGA Table 4. Pore categorization for ceramic materials Category Brick L [nm] W*[cm 3 /g] [%] W*[cm 3 /g] [%] < > V ores ** *W volume contribution of ores determined based on ore distribution curves of oulation **V ores total ore volume Mechanical roerties Young modulus Young modulus is measured on the cylindrical secimens with diameter 30 mm and height 60 mm drilled from bricks Gerle and Podwórny [1] Malecki and Polesiński [2]. Half of the secimens is tested in dry condition (dried to constant mass), whereas the second half is tested fully saturated (after soaking in distillated water for 2 months). In tests the loading direction coincides with the direction of brick formation. Strain are measured on the gauges equal to ½ height of secimen. Test is erformed using the testing machine Z100 Zwick/Roell (Fig. 3) with maximum and minimum load levels equal to 1/3 and 0.05 of the comressive strength, resectively, and load rate equal to 0,1 MPa/s. The obtained secant Young modulus is measured during the third cycle of loading after two revious cycles of loading/unloading. Fig. 3. Measurements of Young modulus Fig. 4 shows an exemlary stress-elongation curve during measurements of Young modulus for the material in dry state.

6 Influence of orosity and moisture on mechanical roerties of ceramic brick Table 5. Values of Young modulus Brick Parameter L dry wet dry wet Samle size Mean value [GPa] ,8 8,8 6,1 Maximum value [GPa] ,2 11,1 7,7 Minimum value [GPa] ,0 5,4 5,3 Standard deviation [GPa] 4.3 4,1 1,9 0,7 Fig. 4. Stress-elongation curve for material in dry state THORTICAL STIMATION OF TH LASTIC PROPRTIS Assumtions For descrition of mechanical roerties of ceramic brick with different level of orosity and moisture a three-hase material model is roosed ceramic skeleton, air ores and ores filled with water. Only the total volumetric amount of ores is taking into account. The structure of orosity and diameters of ores are neglected. lastic isotroic roerties are assumed for all hases. In addition, a sherical shae of ores is assumed. These assumtions make ossible use of analytical homogenisation based on classical shelby's solution for a sherical inclusion in an elastic matrix Zaoui [3], Zaoui [4]. Knowing elastic roerties of searate hases and their volume fractions it is ossible to derive closed form solutions for global stiffness and comliance oerators for three-hase material Hellmich and Mang [5]. Both Mori-Tanaka and self-consisted homogenisation schemes are used. The latter aroach leads to the solution in an imlicit form requiring an iterative rocedure Hellmich and Mang [5], Pichler and Hellmich [6]. In addition, the simlest Voigt s homogenisation scheme is also adoted.

7 58 Andrzej WINNICKI, Teresa STRYSZWSKA, Stanisław KAŃKA, Szymon SRĘGA Mathematical details The global elastic stiffness oerator D is comuted as an average of the stiffness oerators of searate comonents D taking into account volumetric fractions f and fourth order localization (or concentration) tensors A ( = s,a,w for skeleton, air ores and water, resectively) D f D : A (1.1) In the simlest Voigt s homogenizations scheme assuming arallel connection of all comonents tensors A are equal to the fourth order unit tensor I A I (1.2) In the more refined self-consisted or Mori-Tanaka homogenization schemes tensors A are derived based on shelby s solution for an inclusion erfectly bonded to infinite matrix using shelby s tensors S for each comonent : : : f q q : : q q A I S D D I I S D D I (1.3) The only difference between the self-consisted and Mori-Tanaka schemes lies in the formulation of the aroriate shelby s tensor in the self-consisted scheme it is related to the whole comosite whereas in the Mori-Tanaka scheme to the skeleton. It is assumed that all comonents are elastic and isotroic ones. In such a case a stiffness oerator for comonent can be slit in the volumetric and deviatoric arts D 3 K 2 J, (1.4) where K and J are volumetric and deviatoric arts of the fourth order unit tensor I, resectively K 1 δδ, JIK (1.5) 3 and δ is the second order unit tensor (the Kronecker s delta). In turn, κ and µ are bulk and shear moduli of comonent related to its Young modulus and Poisson s ratio µ k, 3(12 ) 2(1 ) (1.6) In the same way the stiffness oerator of the comosite (as the sum of isotroic comonents) has the form D 3K 2J, (1.7) where κ and µ are bulk and shear moduli of the comosite related to its Young modulus and Poisson s ratio µ.

8 Influence of orosity and moisture on mechanical roerties of ceramic brick k, 3(12 ) 2(1 ) (1.8) Concerning the shelby s tensor it is assumed that both air and water are inclusions of sherical form embedded in skeleton. This leads to the general formulation SJ K (1.9) where for self-consistent scheme α and β coefficients are related to the roerties of the whole comosite 3 6( 2 ), 3 4 5( 4 ) (1.10) and for Mori-Tanaka scheme to the roerties of skeleton 3s 6( s 2 s), 3 4 5( 4 ) s s s s (1.11) Inserting the isotroic forms of stiffness oerators (1.4) and (1.7) together with shelby s tensor in the form (1.9) into the formulae for concentration tensors (1.3) and the general global elastic stiffness oerator (1.1) leads to searate equations for global bulk and shear moduli f a f a, f q b f b (1.12) both for self-consisted and Mori-Tanaka schemes. For self-consisted scheme the coefficients a and b read a 1, b 1 (1.13) Because the coefficients a and b are functions of the global bulk and shear moduli κ and µ the equations (1.12) are imlicit ones and have to be solved in an iterative way. In turn, for the Mori-Tanaka scheme the coefficients a and b are functions of the bulk and shear moduli of skeleton s s a 1, b 1 (1.14) s creating therefore an exlicit equations for the global bulk and shear moduli. Due to the simle form of the concentrations tensors (1.2) for the Voigt s scheme the global bulk and shear moduli in that case are averages of the values of searate comonents s

9 60 Andrzej WINNICKI, Teresa STRYSZWSKA, Stanisław KAŃKA, Szymon SRĘGA (1.15) f, f To summarize, for the known volumetric ratios f and bulk and shear moduli for searate comonents κ and µ the global bulk and shear moduli κ and µ can be comuted either using equations (1.12) (self-consisted or Mori-Tanaka scheme) or equations (1.15) (Voigt s scheme). Results The assumed material arameters for searate comonents of the two analysed tyes of bricks are given in the Tables 6 and 7. Comonent Table 6. Proerties of comonents of brick f [GPa] [GPa] skeleton air ores water Comonent Table 7. Proerties of comonents of brick L f [GPa] [GPa] skeleton air ores water Fig. 5. Young modulus for material

10 Influence of orosity and moisture on mechanical roerties of ceramic brick Fig. 6. Young modulus for material L In the comutations four levels of saturations are assumed starting from dry material (f w =0.000, f a =0.316 for material and f w =0.000, f a =0.340 for material L) and ending with full saturation (f w =0.316, f a =0.000 for material and f w =0.340, f a =0.000 for material L). For each level of saturation the global bulk and shear moduli κ and µ are comuted using selfconsisted, Mori-Tanaka and Voigt s homogenization schemes. Using these values the global Young modulus is obtained. The results are resented in Figs 5 and 6. CONCLUSIONS It is evident, that only the self-consisted scheme leads to the roer theoretical estimation of Young modulus values for dry state. Both Mori-Tanaka and Voigt s schemes overestimate Young modulus considerably for dry state. None of the analysed schemes redict Young modulus value correctly for the fully saturated state. In reality, during saturation rocess, skeleton in brick undergoes chemical reactions, mostly of hydration and hydrolysis tye which lead to deterioration of its mechanical roerties. The adoted homogenization schemes neglect this fact. In order to redict Young modulus values for saturated brick more sohisticated mechanical theories are needed taking into account a chemo-mechanical couling similarly to an aroach resented in Zaoui [3], Zaoui [4]. A scalar arameter describing reaction kinetics develoment which is directly related to saturation level has to be introduced. Accordingly, the elastic roerties of skeleton have to be degraded as a function of this arameter. Finally, such a model has to be calibrated using available exerimental data.

11 62 Andrzej WINNICKI, Teresa STRYSZWSKA, Stanisław KAŃKA, Szymon SRĘGA RFRNCS 1. Gerle, A., Podwórny, J., Comaring of Young Modulus of Chamotte Refractories Determined by Static and Dynamic Methods. Scientific Works of Institute of Ceramics and Building Materials 12, 2013, (in Polish) 2. Malecki, I., Polesiński, Z., Rećko, W.M., Dynamic and Static Young Modulus of Ceramics. Glass and Ceramics 52, 2001, 2-8. (in Polish) 3. Zaoui, A., Continuum Micromechanics: Survey. J. ngng Mech., ASC, Vol. 128, No 8, 2002, Zaoui, A., Structural Morhology and Constitutive Behavior of Microheterogeneous Materials. in: P. Suquet (d.), Continuum Micromechanics, Sringer, Wien - New York, 1997 (CISM Courses and Lectures No 377), Hellmich, Ch., Mang, H., Shotcrete lasticity Revisited in the Framework of Continuum Micromechanics: From Submicron to Meter Level. J. Mat. Civ. ngng, ASC, Vol. 17, No 3, 2005, Pichler, B., Hellmich, Ch., Uscaling quasi-brittle strength of cement aste and mortar: A multi-scale engineering mechanics model. Cem. Concr. Research, 41, 2011,

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