The aim in this work is to develop a log-normal distribution of heterogeneous nucleation substrates for the composite based on AZ91 alloy reinforced by SiC particles. The computational algorithm allowing the restore of the nucleation substrates distribution was used. The experiment was performed for the AZ91 alloy containing 1 % wt. of SiC particles. Obtained from experiment, the grains density of magnesium primary phase and supercooling were used to algorithm as input data

B. Gracz

D. Kalisz

J. Lelito

J. S. Suchy

M. Szucki

P. L. Żak

P. Malinowski

W. K. Krajewski

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204  METALURGIJA 54 (2015) 1, 204-206J. LELITO, P. L. ŻAK, B. GRACZ, M. SZUCKI, D. KALISZ, P. MALINOWSKI, J. S. SUCHY, W. K. KRAJEWSKIDETERMINATION OF SUBSTRATE LOG-NORMAL DISTRIBUTION IN THE AZ91/SICP COMPOSITEReceived – Prispjelo: 2014-02-29Accepted – Prihvaćeno: 2014-07-15Preliminary Note – Prethodno priopćenjeISSN 0543-5846METABK 54(1) 204-206 (2015)UDC – UDK 669.715.5.782.784: 539.12=111J. Lelito, P. L. Żak, B. Gracz, M. Szucki, D. Kalisz, P. Malinowski, J. S. Suchy, W. K. Krajewski. AGH University of Science and Technology, Faculty of Foundry Engineering, Kraków, PolandThe aim in this work is to develop a log-normal distribution of heterogeneous nucleation substrates for the compos-ite based on AZ91 alloy reinforced by SiC particles. The computational algorithm allowing the restore of the nuclea-tion substrates distribution was used. The experiment was performed for the AZ91 alloy containing 1 % wt. of SiC particles. Obtained from experiment, the grains density of magnesium primary phase and supercooling were used to algorithm as input data.Key words: The AZ91/SiCp composite, particle, heterogeneous nucleation, log-normal distribution of substrate.INTRODUCTIONThe AZ91/SiCp composites, with their lower densi-ty and good mechanical properties, are more attractive material for automobile and aerospace industries. The grain size of magnesium primary phase in these com-posites substantially affects their mechanical properties. The effect of the SiC particles in refining the grain size in the matrix phase is not attributed only to enhanced nucleation. There are other effects such as restriction of grain growth arising from the pushing of particles. Par-ticles being pushed could, for example, impede solute redistribution at the solid-liquid interface [1].The literature offers many examples of the applica-tion of the simulation method for the heterogeneous nu-cleation. One of this method is based on the hemispher-ical cap model proposed by Greer et al. [2, 3]. It allows a prediction of the grain size as a function of the particle size log-normal distribution, the volumetric content of ceramic inoculants, the cooling rate and the alloy con-stitution. Because used size of SiC particles (45 μm) and fact that these particles are not good inoculants for AZ91 alloy, the aim in this work is to develop a log-normal distribution of heterogeneous nucleation sub-strates and given by the following formula:  (1)where: N0 – total population of nucleation substrate / m-3; d0 – geometric mean of log-normal distribution / m; σ – geometric standard deviation of log-normal distri-bution; d – mean diameter of nucleation substrate / m.EXPERIMENTAL METHODSThe magnesium alloy AZ91 was selected as the ma-trix for this work, Table 1.Table 1 The chemical composition of AZ91Chemical composition / wt. %Al Zn Mn Si Fe Cu Ni9,0 0,6 0,2 0,03 0,002 0,003 0,001The sample contained 1 wt % sharp SiC particles (from Polmineral) with nominal arithmetic mean diam-eters of 45 μm. The AZ91 alloy was melted in a steel crucible, using an electric resistance furnace filled with SF6 / CO2 shielding gas, and kept at 700 °C for one hour before adding the SiC particles pre-heated to 450 °C. The melt was mechanically stirred for two minutes to ensure a uniform distribution of the SiC particles (simi-lar to the procedure of Luo [4]), and then cast into a resin-hardened sand mould [5, 6]. The mould was de-signed to produce four 100 x 100 mm plates with a thickness of 10, 15, 20 or 30 mm, giving a range of cooling rates.Figure 1  Gating system and model of four plates used for casting four 100 x 100 mm2 composite plates with thicknesses of 10, 15, 20 or 30 mm205METALURGIJA 54 (2015) 1, 204-206J. LELITO et al.: DETERMINATION OF SUBSTRATE LOG-NORMAL DISTRIBUTION IN THE AZ91/SICP COMPOSITETo obtain the cooling curves of the samples, a four-channel data-logging system with an acquisition rate of five readings per second was used to record the change in temperature vs. time from a K-type thermocouple po-sitioned in the centre of each plate (approx. 50 mm above the base plate shown in Figure 1). A number of cuboid samples with a cross section of 35  35 mm2 and height of 45 mm. The thermocouple was located in the centre of the cuboid crucible.Metallographic specimens, taken from the cast plates at a distance of 3 mm from the hot junction of the embedded thermocouples, were ground and polished using conventional preparation methods, and then etched at room temperature. The specimens for grain density measurement were etched for about 90 s in a solution containing 50 ml distilled water, 150 ml etha-nol and 1 ml ethanoic acid [1]. The etched specimens were examined in white polarized light (using crossed polars and a first-order retardation plate). The planar grain density was measured using the image-analysis software NIS-Elements 3.0. The planar grain density NA was obtained from a population of 100 grains, and the volumetric density NV is calculated from NA using equa-tion (2).  (2)where: (1/l)mean is the mean value of the inverse diame-ters of all observed grain intercepts.COMPUTATIONAL ALGORITHMThe developed algorithm is based on next input data: experimental values characterizing the composite (maximal supercooling, grain densities), thermodynam-ic parameters of the composite (volumetric entropy of fusion and interfacial energy at the boundary liquid/crystallite) and assumed total number of nucleation sub-strates (N0), interval of substrate size (Dmin - Dmax), with-in which a value of geometric mean will be looking for, interval of a standard deviation, integration step, maxi-mal number of integration steps and the assumed toler-ance for integral calculations accuracy.The supercooling at which a nucleation substrate be-comes active is that at which there can be free growth of the nucleated grain from the substrate. Greer et al. sug-gested that this critical supercooling is inversely pro-portional to the nucleation substrate diameter [2]:  (3)where: ΔTfg - free growth supercooling, K, σl/c - interfa-cial energy on the boundary, Jm-2, ΔSV - entropy of fu-sion per unit volume, Jm-3K-1.Thus, on cooling an alloy containing nucleation sub-strates, nucleation occurs first on the largest substrates. The equation (3) allows determining the minimal di-mension of the substrate dmini and can be described by:  (4)Basing on equation (1), value of misfit functional J(σi, d0k) can be calculated:  (5)where: NVi – experimental grain density, m-3, NVti – theo-retical grain density calculated by numerical integration of equation (1), m-3:  (6)In other words, the computational algorithm gener-ates a sequence of distribution depended on the distri-bution geometrical mean, on the standard deviation and on the previously assumed N0, and then allows to deter-mine the theoretical density of active nucleation sub-strates (integral of lower limit dmin). The misfit function-al (5), enabling the selection of the distribution the best resembling the actual distribution of the heterogeneous nucleation substrate in the given composite. The graph-ical diagram of the developed algorithm was presented by Gracz [7] and show in the Figure 2.Figure 2 Diagram of the computational algorithm [7]RESULTSThe input data for presented computational algo-rithm are ΔSV = 6,51∙105 Jm-3K-1 and σl/c = 0,115 Jm-2 [8] and obtained resulted from the experimental investiga-tion, Table 2.Table 2  The volumetric grain density and maximal supercooling obtained from experimental investigationPlate thicknes / mm Maximal supercool-ing / KGrain density,/ m-310 8,259 1,493∙101115 7,680 1,235∙101120 6,876 0,787∙101130 6,367 0,442∙1011206  METALURGIJA 54 (2015) 1, 204-206J. LELITO et al.: DETERMINATION OF SUBSTRATE LOG-NORMAL DISTRIBUTION IN THE AZ91/SICP COMPOSITEThese data allowed determining the nucleation sub-strate size distribution for the AZ91 / 1 % SiCp compos-ite described by equation (7).  (7)The final effect of the representation were showed in Figures 3 and 4.Figure 3  Diagram of nucleation substrat size distribution for the AZ91 / 1 % SiCp composite on the base of eqution (7)Figure 4  Diagram of nucleation substrat size distribution for the AZ91 / 1 % SiCp composite on the base of eqution (7) with minimal substrate dimension for experimental dataBasing on the equation (4) the minimal active sub-strate, which took part in heterogeneous nucleation pro-cess, was calculated for different condition (Table 2) and showed as diagram in the Figures 5 and 6.CONCLUSIONSUsed algorithm allowed determining the nucleation substrate size distribution for the composite and de-scribed by equation (7). Equation (7) and given cooling rate used in the free-growth model allowed to calculat-ed grain density of magnesium primary phase in the AZ91 / 1 % SiCp.Applying the inverse modelling allows not only tak-ing into account active nucleation particles but also to consider the situation when the nucleation occurs on more than one surface of a particle.AcknowledgementThe authors acknowledge financial support from the National Science Center grant No. UMO-2011/03/B/ST8/05217 (AGH no. 18.18.170.459).REFERENCES[1] J. Lelito, P. L. Zak, A. A. Shirzadi, A. L. Greer, W. K. Kra-jewski, J. S. Suchy, K. Haberl, P. Schumacher, Acta Mate-rialia, 60 (2012), 2950-2958.[2] A. L. Greer, A. M. Bunn, A. Tronche, P. V. Evans, D. J. Bristow, Acta Materialia, 48 (2000), 2823-2835.[3] T. E. Quested, A. L. Greer, Acta Materialia, 52 (2004), 3859-3868.[4] A. Luo, Scripta Metall. Mater., 31 (1994), 1253-1258.[5] J. Dańko, R. Dańko, M. Holtzer, Metalurgija, 42 (2003) 3, 173-177.[6] R. Dańko, Metalurgija, 50 (2011) 2, 93-96.[7] B. Gracz, Wydawnictwo Naukowe AKAPIT (2013), 364-368.[8] R. Gunther, Ch. Hartig, R. Bormann, Acta Meterialia, 54 (2006), 5591-5597.Note:  The responsible translator for English language: “ANGOS” Translation Office, Poland, Kraków.Figure 5  The minimal dimension of the active substrate as a function of supercoolingFigure 6  The minimal dimension of the active substrate as a function of experimental grain density

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Determination of substrate log-normal distribution in the AZ91/SICP composite

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204   METALURGIJA 54 (2015) 1, 204-206J. LELITO, P. L. ŻAK, B. GRACZ, M. SZUCKI, D. KALISZ, P. MALINOWSKI, J. S. SUCHY, W. K. KRAJEWSKIDETERMINATION OF SUBSTRATE LOG-NORMAL DISTRIBUTION IN THE AZ91/SICP COMPOSITEReceived – Prispjelo: 2014-02-29Accepted – Prihvaćeno: 2014-07-15Preliminary Note – Prethodno priopćenjeISSN 0543-5846METABK 54(1) 204-206 (2015)UDC – UDK 669.715.5.782.784: 539.12=111J. Lelito, P. L. Żak, B. Gracz, M. Szucki, D. Kalisz, P. Malinowski, J. S. Suchy, W. K. Krajewski. AGH University of Science and Technology, Faculty of Foundry Engineering, Kraków, PolandThe aim in this work is to develop a log-normal distribution of heterogeneous nucleation substrates for the compos-ite based on AZ91 alloy reinforced by SiC particles. The computational algorithm allowing the restore of the nuclea-tion substrates distribution was used. The experiment was performed for the AZ91 alloy containing 1 % wt. of SiC particles. Obtained from experiment, the grains density of magnesium primary phase and supercooling were used to algorithm as input data.Key words: The AZ91/SiCp composite, particle, heterogeneous nucleation, log-normal distribution of substrate.INTRODUCTIONThe AZ91/SiCp composites, with their lower densi-ty and good mechanical properties, are more attractive material for automobile and aerospace industries. The grain size of magnesium primary phase in these com-posites substantially affects their mechanical properties. The effect of the SiC particles in refining the grain size in the matrix phase is not attributed only to enhanced nucleation. There are other effects such as restriction of grain growth arising from the pushing of particles. Par-ticles being pushed could, for example, impede solute redistribution at the solid-liquid interface [1].The literature offers many examples of the applica-tion of the simulation method for the heterogeneous nu-cleation. One of this method is based on the hemispher-ical cap model proposed by Greer et al. [2, 3]. It allows a prediction of the grain size as a function of the particle size log-normal distribution, the volumetric content of ceramic inoculants, the cooling rate and the alloy con-stitution. Because used size of SiC particles (45 μm) and fact that these particles are not good inoculants for AZ91 alloy, the aim in this work is to develop a log-normal distribution of heterogeneous nucleation sub-strates and given by the following formula:   (1)where: N0 – total population of nucleation substrate / m-3; d0 – geometric mean of log-normal distribution / m; σ – geometric standard deviation of log-normal distri-bution; d – mean diameter of nucleation substrate / m.EXPERIMENTAL METHODSThe magnesium alloy AZ91 was selected as the ma-trix for this work, Table 1.Table 1 The chemical composition of AZ91Chemical composition / wt. %Al Zn Mn Si Fe Cu Ni9,0 0,6 0,2 0,03 0,002 0,003 0,001The sample contained 1 wt % sharp SiC particles (from Polmineral) with nominal arithmetic mean diam-eters of 45 μm. The AZ91 alloy was melted in a steel crucible, using an electric resistance furnace filled with SF6 / CO2 shielding gas, and kept at 700 °C for one hour before adding the SiC particles pre-heated to 450 °C. The melt was mechanically stirred for two minutes to ensure a uniform distribution of the SiC particles (simi-lar to the procedure of Luo [4]), and then cast into a resin-hardened sand mould [5, 6]. The mould was de-signed to produce four 100 x 100 mm plates with a thickness of 10, 15, 20 or 30 mm, giving a range of cooling rates.Figure 1   Gating system and model of four plates used for casting four 100 x 100 mm2 composite plates with thicknesses of 10, 15, 20 or 30 mm205 METALURGIJA 54 (2015) 1, 204-206J. LELITO et al.: DETERMINATION OF SUBSTRATE LOG-NORMAL DISTRIBUTION IN THE AZ91/SICP COMPOSITETo obtain the cooling curves of the samples, a four-channel data-logging system with an acquisition rate of five readings per second was used to record the change in temperature vs. time from a K-type thermocouple po-sitioned in the centre of each plate (approx. 50 mm above the base plate shown in Figure 1). A number of cuboid samples with a cross section of 35  35 mm2 and height of 45 mm. The thermocouple was located in the centre of the cuboid crucible.Metallographic specimens, taken from the cast plates at a distance of 3 mm from the hot junction of the embedded thermocouples, were ground and polished using conventional preparation methods, and then etched at room temperature. The specimens for grain density measurement were etched for about 90 s in a solution containing 50 ml distilled water, 150 ml etha-nol and 1 ml ethanoic acid [1]. The etched specimens were examined in white polarized light (using crossed polars and a first-order retardation plate). The planar grain density was measured using the image-analysis software NIS-Elements 3.0. The planar grain density NA was obtained from a population of 100 grains, and the volumetric density NV is calculated from NA using equa-tion (2).   (2)where: (1/l)mean is the mean value of the inverse diame-ters of all observed grain intercepts.COMPUTATIONAL ALGORITHMThe developed algorithm is based on next input data: experimental values characterizing the composite (maximal supercooling, grain densities), thermodynam-ic parameters of the composite (volumetric entropy of fusion and interfacial energy at the boundary liquid/crystallite) and assumed total number of nucleation sub-strates (N0), interval of substrate size (Dmin - Dmax), with-in which a value of geometric mean will be looking for, interval of a standard deviation, integration step, maxi-mal number of integration steps and the assumed toler-ance for integral calculations accuracy.The supercooling at which a nucleation substrate be-comes active is that at which there can be free growth of the nucleated grain from the substrate. Greer et al. sug-gested that this critical supercooling is inversely pro-portional to the nucleation substrate diameter [2]:   (3)where: ΔTfg - free growth supercooling, K, σl/c - interfa-cial energy on the boundary, Jm-2, ΔSV - entropy of fu-sion per unit volume, Jm-3K-1.Thus, on cooling an alloy containing nucleation sub-strates, nucleation occurs first on the largest substrates. The equation (3) allows determining the minimal di-mension of the substrate dmini and can be described by:   (4)Basing on equation (1), value of misfit functional J(σi, d0k) can be calculated:   (5)where: NVi – experimental grain density, m-3, NVti – theo-retical grain density calculated by numerical integration of equation (1), m-3:   (6)In other words, the computational algorithm gener-ates a sequence of distribution depended on the distri-bution geometrical mean, on the standard deviation and on the previously assumed N0, and then allows to deter-mine the theoretical density of active nucleation sub-strates (integral of lower limit dmin). The misfit function-al (5), enabling the selection of the distribution the best resembling the actual distribution of the heterogeneous nucleation substrate in the given composite. The graph-ical diagram of the developed algorithm was presented by Gracz [7] and show in the Figure 2.Figure 2 Diagram of the computational algorithm [7]RESULTSThe input data for presented computational algo-rithm are ΔSV = 6,51∙105 Jm-3K-1 and σl/c = 0,115 Jm-2 [8] and obtained resulted from the experimental investiga-tion, Table 2.Table 2   The volumetric grain density and maximal supercooling obtained from experimental investigationPlate thicknes / mm Maximal supercool-ing / KGrain density,/ m-310 8,259 1,493∙101115 7,680 1,235∙101120 6,876 0,787∙101130 6,367 0,442∙1011206   METALURGIJA 54 (2015) 1, 204-206J. LELITO et al.: DETERMINATION OF SUBSTRATE LOG-NORMAL DISTRIBUTION IN THE AZ91/SICP COMPOSITEThese data allowed determining the nucleation sub-strate size distribution for the AZ91 / 1 % SiCp compos-ite described by equation (7).   (7)The final effect of the representation were showed in Figures 3 and 4.Figure 3   Diagram of nucleation substrat size distribution for the AZ91 / 1 % SiCp composite on the base of eqution (7)Figure 4   Diagram of nucleation substrat size distribution for the AZ91 / 1 % SiCp composite on the base of eqution (7) with minimal substrate dimension for experimental dataBasing on the equation (4) the minimal active sub-strate, which took part in heterogeneous nucleation pro-cess, was calculated for different condition (Table 2) and showed as diagram in the Figures 5 and 6.CONCLUSIONSUsed algorithm allowed determining the nucleation substrate size distribution for the composite and de-scribed by equation (7). Equation (7) and given cooling rate used in the free-growth model allowed to calculat-ed grain density of magnesium primary phase in the AZ91 / 1 % SiCp.Applying the inverse modelling allows not only tak-ing into account active nucleation particles but also to consider the situation when the nucleation occurs on more than one surface of a particle.AcknowledgementThe authors acknowledge financial support from the National Science Center grant No. UMO-2011/03/B/ST8/05217 (AGH no. 18.18.170.459).REFERENCES[1]  J. Lelito, P. L. Zak, A. A. Shirzadi, A. L. Greer, W. K. Kra-jewski, J. S. Suchy, K. Haberl, P. Schumacher, Acta Mate-rialia, 60 (2012), 2950-2958.[2]  A. L. Greer, A. M. Bunn, A. Tronche, P. V. Evans, D. J. Bristow, Acta Materialia, 48 (2000), 2823-2835.[3]  T. E. Quested, A. L. Greer, Acta Materialia, 52 (2004), 3859-3868.[4]  A. Luo, Scripta Metall. Mater., 31 (1994), 1253-1258.[5] J.  Dańko, R. Dańko, M. Holtzer, Metalurgija, 42 (2003) 3, 173-177.[6] R.  Dańko, Metalurgija, 50 (2011) 2, 93-96.[7]  B. Gracz, Wydawnictwo Naukowe AKAPIT (2013), 364-368.[8]  R. Gunther, Ch. Hartig, R. Bormann, Acta Meterialia, 54 (2006), 5591-5597.Note:   The responsible translator for English language: “ANGOS” Translation Office, Poland, Kraków.Figure 5   The minimal dimension of the active substrate as a function of supercoolingFigure 6   The minimal dimension of the active substrate as a function of experimental grain density

Determination of substrate log-normal distribution in the AZ91/SICP composite

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