Modelling tensile behaviour of stir cast aluminium matrix composites (am cs) using factorial design of experiments
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This document presents a study that uses factorial design of experiments to develop mathematical models for predicting the tensile behavior of stir-cast aluminum matrix composites (AMCs) reinforced with alumina particles. Specifically, models were developed to predict the ultimate tensile strength and percentage elongation based on the size and weight fraction of alumina particles, holding temperature during casting, and holding time. The models showed that ultimate tensile strength was positively influenced by weight fraction, temperature, and time, while percentage elongation was reduced. Ultimate tensile strength of the composites was found to be 20% higher than the aluminum alloy matrix, while percentage elongation decreased by around 30%.
![Chemistry and Materials Research www.iiste.org
ISSN 2224- 3224 (Print) ISSN 2225- 0956 (Online)
Vol 2, No.1, 2012
Modelling Tensile Behaviour of Stir-cast Aluminium Matrix
Composites (AMCs) Using Factorial Design of Experiments
Indumati B. Deshmanya, Dr. GK Purohit
Department of Mechanical Engineering, PDA College of Engineering Gulbarga, India
E-mail: *indu_bd@yahoo.co.in, geeke_purohit@rediffmail.com
Abstract
Aluminium based metal matrix composites (MMCs) with ceramic reinforcement are finding extensive
applications in aerospace, automobile, agricultural farm machinery and other areas which demand
combination of properties such as high strength, stiffness, wear resistance, high temperature resistance, etc.
In particular, components comprising Al7075 alloy matrix, reinforced with alumina (Al2O3) particulates, are
reported to excel their monolithic counterparts. Liquid metal route and powder metallurgy are the most
widely used fabrication techniques to produce these MMCs. The former has advantages such as easy
adaptability, low cost and possibility of subjecting the cast components to secondary processes like forging,
rolling and extrusion for producing the final components. This paper presents the details of developing a
mathematical model to predict the tensile behavior like ultimate tensile strength (UTS) and percentage
elongation of the as-cast Al7075/Al2O3 in terms of size and % fraction of Al2O3, holding temperature and
holding time; using factorial design of experiments (DoE). Adequacy of the models was tested using
Fisher’s F-test. UTS of the composite was increased by 20%compared to that of matrix and % elongation
was reduced by around 30%.
Keywords: MMC, UTS, % elongation, Design of experiments, Modelling.
1. Introduction
Aluminium metal matrix composites (MMCs) with 7xxx alloy as matrix reinforced with ceramic particles
are finding application in aerospace, automobile and farm machinery equipment because of their improved
mechanical and tribological properties [1-6]. In particular, Al2O3 particles mixed with Al7075 matrix in
appropriate proportions are reported to exhibit improved tensile properties because of the higher modulus
of elasticity and strength of the alumina [7]. Out of the available methods of producing these composites,
stir casting route is most promising and economical for synthesizing the particle reinforced AMCs and is
not only simple, but is easy to obtain shape castings [8,9]. It is important to understand the process
parameters that bring about the enhancement in their behaviour. However, conventionally, this requires
conducting costly and time consuming experiments. Alternately, we can predict the influence of process
parameters accurately, and to develop composites possessing desirable mechanical properties various
modelling methods are available [10-13]. This paper presents one such methodology called rotatable central
composite design (CCD), which is a multi-parameter based, multiple response analysis modelling
technique [14]. It is not only fast, economical and very effective in assessing the effect of individual
parameters, but also helps in predicting the interaction effects of the parameters. Hence, in this work an
attempt is made to predict the effect of reinforcement size, %weight fraction of reinforcement, holding
temperature and holding time on the ultimate tensile strength and %elongation of a stir-cast Al7075/Al2O3
composite system using CCD. The adequacy of the models is checked by Fisher’s-F ratio and the analysis
of variance is employed to evaluate the effect of parameters.
2. Materials
Al7075 matrix reinforced with varying sizes of Al2O3 particles were used to produce composites using stir
casting. Tables 1 and 2 present the important properties of the matrix material. Table 3 gives the range of
the four most influential process parameters, viz. size of reinforcement particles (D), weight fraction of
reinforcement (W), holding temperature (T) and holding time (t).
5](https://image.slidesharecdn.com/modellingtensilebehaviourofstir-castaluminiummatrixcompositesamcsusingfactorialdesignofexperiments-120126065432-phpapp02/85/Modelling-tensile-behaviour-of-stir-cast-aluminium-matrix-composites-am-cs-using-factorial-design-of-experiments-1-320.jpg)
![Chemistry and Materials Research www.iiste.org
ISSN 2224- 3224 (Print) ISSN 2225- 0956 (Online)
Vol 2, No.1, 2012
3. Experimental Program
Rotatable central composite design was used to produce the castings [15-17]. Figs. 1 and 2 show the
schematic diagram and close-up view of stir casting process. The details of the process are explained
elsewhere [18]. A total of 31 castings comprising 16 (=24) factorial points, 8 star points and 7 central points
were produced by adapting the CCD as per Table 4. The castings were produced using randomness to avoid
the entry of systematic errors in experimentation. Tensile tests were performed on samples extracted from
defect-free regions of the castings at a rate of 8.33×10-4 s-1 as per [19] and a minimum of 3 specimens were
tested in each case. The average values of UTS and %E are presented in Table 4.
4. Results and Discussion
The maximum value of UTS obtained was 289MPa; minimum was 262MPa and the mean was at 273MPa,
whereas %E obtained was in the range of 14.8% to 9.25% with the average at 11.3%. It is noticed that
introduction of Al2O3 particulates could result in 20% increase in matrix UTS and decreased the %E by
around 30%; implying that composites with enhanced strength can be produced by stir-casting. However,
one has to sacrifice the ductility. Similar observations have been made by many researchers [9,19-20].
Second order relations were obtained by regression analysis and are presented in equations (1) and (2) for
UTS and %E, respectively.
UTS=270.29-3.63D+3.21W+2.36T+3.126t+0.768D2+2.643W2+0.518T2-0.106t2-0.437DW-0.313DT+
0.563Dt-0.063Wt+0.937Tt (1)
%E=10.508+0.396D-0.421W-0.0413T-0.453t+0.386D2+0.220W2+0.126T2+0.301t2-0.049DW-0.093DT
+0.056Dt-0.21WT+0.363Wt+0.277Tt (2)
Table 5 shows the result of the analyses of variance and it is noticed that, in both the cases, experimental
values of F-ratios are higher than that from the table; indicating that the two models are adequate. Also, R2
and Radj2 values indicate that the models can be used to predict the responses with 99% confidence level.
Hence, the models can be effectively used in predicting the UTS and %E, knowing the composition of
Al7075/Al2O3 MMCs.
It is observed from equation (1) that as the size of reinforcement (D) increases UTS decreases. D affects
UTS independently as well as in combination with weight% and holding temperature. On the other hand, W,
T and t contribute positively. Interestingly, the effect of these parameters on elongation is exactly reversed
as shown in equation (2). Thus UTS of composites is observed to be 20% enhanced and elongation reduced
by nearly 30% compared to the matrix material. Similar observations are recorded by many researchers
[19-22]. Leisk and Saigal [23] have shown that further enhancement in tensile strength is possible by
subjecting the composites to heat treatment. However, this claim is to be confirmed for Al7075/Al2O3
composites. All these aspects can be systematically exploited in developing the AMCs possessing desired
tensile strength and %elongation.
5. Conclusion
Based on the experimental work, following conclusions are drawn.
1 Rotatable, central composite design can be successfully used to model the tensile behaviour of AMCs
2 Mathematical models for UTS and %elongation are adequate and will predict the values with 99%
confidence.
3 UTS and %elongation show reverse trends as far as influence of the process parameters are concerned.
4 UTS of the Al7075/Al2O3 MMCs increased by 20%compared to that of matrix and % elongation was
reduced by around 30%.
6. References
[1] Surappa M.K. (2003). Aluminium matrix composites: Challenges and Opportunities. Sadhana, 28 Parts
1 & 2, 319-344.
6](https://image.slidesharecdn.com/modellingtensilebehaviourofstir-castaluminiummatrixcompositesamcsusingfactorialdesignofexperiments-120126065432-phpapp02/85/Modelling-tensile-behaviour-of-stir-cast-aluminium-matrix-composites-am-cs-using-factorial-design-of-experiments-2-320.jpg)
![Chemistry and Materials Research www.iiste.org
ISSN 2224- 3224 (Print) ISSN 2225- 0956 (Online)
Vol 2, No.1, 2012
[2] Ibrahim I.A, Mohamed F.A, Lavernia E.J. (1991). Particulate reinforced metal matrix composites- a
review. Journal of Material Science, 26, 1137-1156.
[3] Nikhilesh Chawla, Yu-Lin Shen. (2001). Mechanical behaviour of particulate reinforced metal matrix
composites. Advanced Engineering Materials, 3, 6, 357-370.
[4] Daoud A, Reif W, Rohatgi P. (2003). Microstructure and tensile properties of extruded 7475 AL-Al2O3
particulate composites. ECCM13, Sweden, 1201.
[5] Ceschini L, Minak G, Morri A. (2009). Forging of the AA2618/20 Vol. % Al2O3p composite: Effects on
microstructure and tensile properties. Composites Science and Technology, 69, 1783-1789.
[6] Mallik, B., et al (2006). Effect of particle content on the mechanical behaviour of aluminium-based
metal matrix composites (AMMC). Indian Foundry Journal, 52, 35-42.
[7] Hashim J, Looney L, Hashmi M. S. J. (1999). Metal matrix composites: production by the stir casting
method. Journal of Materials Processing Technology, 92-93, 1- 7.
[8] Ceschini L, Minak G, Morri A. (2006). Tensile and fatigue properties of the AA6061/20 vol. % Al2O3p
and AA7005/10 Vol. % Al2O3p composites. Composites Science and Technology, Vol. 66, 333-342
[9] Gupta M, Lai M.O, Lim C.Y.H. (2006). Development of a novel hybrid aluminium-based composite
with enhanced properties. Journal Material Processing Technology, Vol. 176, No. 1-3, 191-199.
[10] Sahin Y. (2003). Wear behavior of aluminium alloy and its composites reinforced by SiC particles
using statistical analysis. Materials and Design, 24, 95-103.
[11] Yilmaz O, Buytoz S. (2001). Abrasive wear of Al2O3-reinforced aluminium-based MMCs. Composite
Science and Technology, 61, 2381-2392.
[12] Mondal D.P, Das S. (2006). High stress abrasive wear behavior of aluminium hard particle composites:
Effect of experimental parameters, particle size and volume fraction. Tribology International, 39,
470-478.
[13] Chawla N, Chawla K.K. (2006). Microstructural e-based modeling of the deformation behavior of
particle reinforced metal matrix composites. Journal of Material Science and Technology, (41)
913-925.
[14] Deshmanya Indumati B, Purohit G.K. (2011). Studies on modelling of aluminium matrix composites
(AMCs)-A Review. ICAM 2011, Joint International Conference on Advanced Materials. 144-145.
[15] Cochran W.G, Cox G M. (1992). Experimental Design, John Wiley, New York.
[16] Montgomery D. C. (2009). Design and Analysis of Experiments. John Wiley, New York.
[17] Adler Y.P, Markov E. V, Granovsky Y.V. (1975). The design of experiments to find optimal conditions.
MIR Pub., Moscow.
[18] Deshmanya, Indumati B, Purohit G.K. (2011). Modelling of impact strength and hardness of Al2O3 –
reinforced Al-7075 composites. International Journal of Industrial Engineering Practice, Vol. 3, Issue
1, 61-66.
[19] Doel T. J. A, Bowen P. (1996). Tensile properties of particulate-reinforced metal matrix composites.
Composites Part A: Applied Science and Manufacturing, 27, 655-665.
[20] Srivatsan T.S. (1996). Microstructure tensile properties and fracture behaviour of Al2O3
particulate-reinforced aluminium alloy metal matrix composites. Journal of Materials Science, 31,
1375.
[21] Seah K. H. W, Sharma S. C, Girish B.M. (2001). Mechanical properties of as- cast and heat-treated
ZA-27/graphite particulate composites. Composite: part A. 28A 251-6 Composites Science and
Technology, 61, 2381.
[22] Abis S. (1989). Characterization of an aluminium alloy/alumina metal matrix composites. Journal of
Composite Science and Technology, 35, 1-19.
[23] Leisk G, Saigal A. (1995). Taguchi analysis of heat treatment variables on the mechanical behaviour
7](https://image.slidesharecdn.com/modellingtensilebehaviourofstir-castaluminiummatrixcompositesamcsusingfactorialdesignofexperiments-120126065432-phpapp02/85/Modelling-tensile-behaviour-of-stir-cast-aluminium-matrix-composites-am-cs-using-factorial-design-of-experiments-3-320.jpg)
Modelling tensile behaviour of stir cast aluminium matrix composites (am cs) using factorial design of experiments
- 1. Chemistry and Materials Research www.iiste.org ISSN 2224- 3224 (Print) ISSN 2225- 0956 (Online) Vol 2, No.1, 2012 Modelling Tensile Behaviour of Stir-cast Aluminium Matrix Composites (AMCs) Using Factorial Design of Experiments Indumati B. Deshmanya, Dr. GK Purohit Department of Mechanical Engineering, PDA College of Engineering Gulbarga, India E-mail: *indu_bd@yahoo.co.in, geeke_purohit@rediffmail.com Abstract Aluminium based metal matrix composites (MMCs) with ceramic reinforcement are finding extensive applications in aerospace, automobile, agricultural farm machinery and other areas which demand combination of properties such as high strength, stiffness, wear resistance, high temperature resistance, etc. In particular, components comprising Al7075 alloy matrix, reinforced with alumina (Al2O3) particulates, are reported to excel their monolithic counterparts. Liquid metal route and powder metallurgy are the most widely used fabrication techniques to produce these MMCs. The former has advantages such as easy adaptability, low cost and possibility of subjecting the cast components to secondary processes like forging, rolling and extrusion for producing the final components. This paper presents the details of developing a mathematical model to predict the tensile behavior like ultimate tensile strength (UTS) and percentage elongation of the as-cast Al7075/Al2O3 in terms of size and % fraction of Al2O3, holding temperature and holding time; using factorial design of experiments (DoE). Adequacy of the models was tested using Fisher’s F-test. UTS of the composite was increased by 20%compared to that of matrix and % elongation was reduced by around 30%. Keywords: MMC, UTS, % elongation, Design of experiments, Modelling. 1. Introduction Aluminium metal matrix composites (MMCs) with 7xxx alloy as matrix reinforced with ceramic particles are finding application in aerospace, automobile and farm machinery equipment because of their improved mechanical and tribological properties [1-6]. In particular, Al2O3 particles mixed with Al7075 matrix in appropriate proportions are reported to exhibit improved tensile properties because of the higher modulus of elasticity and strength of the alumina [7]. Out of the available methods of producing these composites, stir casting route is most promising and economical for synthesizing the particle reinforced AMCs and is not only simple, but is easy to obtain shape castings [8,9]. It is important to understand the process parameters that bring about the enhancement in their behaviour. However, conventionally, this requires conducting costly and time consuming experiments. Alternately, we can predict the influence of process parameters accurately, and to develop composites possessing desirable mechanical properties various modelling methods are available [10-13]. This paper presents one such methodology called rotatable central composite design (CCD), which is a multi-parameter based, multiple response analysis modelling technique [14]. It is not only fast, economical and very effective in assessing the effect of individual parameters, but also helps in predicting the interaction effects of the parameters. Hence, in this work an attempt is made to predict the effect of reinforcement size, %weight fraction of reinforcement, holding temperature and holding time on the ultimate tensile strength and %elongation of a stir-cast Al7075/Al2O3 composite system using CCD. The adequacy of the models is checked by Fisher’s-F ratio and the analysis of variance is employed to evaluate the effect of parameters. 2. Materials Al7075 matrix reinforced with varying sizes of Al2O3 particles were used to produce composites using stir casting. Tables 1 and 2 present the important properties of the matrix material. Table 3 gives the range of the four most influential process parameters, viz. size of reinforcement particles (D), weight fraction of reinforcement (W), holding temperature (T) and holding time (t). 5
- 2. Chemistry and Materials Research www.iiste.org ISSN 2224- 3224 (Print) ISSN 2225- 0956 (Online) Vol 2, No.1, 2012 3. Experimental Program Rotatable central composite design was used to produce the castings [15-17]. Figs. 1 and 2 show the schematic diagram and close-up view of stir casting process. The details of the process are explained elsewhere [18]. A total of 31 castings comprising 16 (=24) factorial points, 8 star points and 7 central points were produced by adapting the CCD as per Table 4. The castings were produced using randomness to avoid the entry of systematic errors in experimentation. Tensile tests were performed on samples extracted from defect-free regions of the castings at a rate of 8.33×10-4 s-1 as per [19] and a minimum of 3 specimens were tested in each case. The average values of UTS and %E are presented in Table 4. 4. Results and Discussion The maximum value of UTS obtained was 289MPa; minimum was 262MPa and the mean was at 273MPa, whereas %E obtained was in the range of 14.8% to 9.25% with the average at 11.3%. It is noticed that introduction of Al2O3 particulates could result in 20% increase in matrix UTS and decreased the %E by around 30%; implying that composites with enhanced strength can be produced by stir-casting. However, one has to sacrifice the ductility. Similar observations have been made by many researchers [9,19-20]. Second order relations were obtained by regression analysis and are presented in equations (1) and (2) for UTS and %E, respectively. UTS=270.29-3.63D+3.21W+2.36T+3.126t+0.768D2+2.643W2+0.518T2-0.106t2-0.437DW-0.313DT+ 0.563Dt-0.063Wt+0.937Tt (1) %E=10.508+0.396D-0.421W-0.0413T-0.453t+0.386D2+0.220W2+0.126T2+0.301t2-0.049DW-0.093DT +0.056Dt-0.21WT+0.363Wt+0.277Tt (2) Table 5 shows the result of the analyses of variance and it is noticed that, in both the cases, experimental values of F-ratios are higher than that from the table; indicating that the two models are adequate. Also, R2 and Radj2 values indicate that the models can be used to predict the responses with 99% confidence level. Hence, the models can be effectively used in predicting the UTS and %E, knowing the composition of Al7075/Al2O3 MMCs. It is observed from equation (1) that as the size of reinforcement (D) increases UTS decreases. D affects UTS independently as well as in combination with weight% and holding temperature. On the other hand, W, T and t contribute positively. Interestingly, the effect of these parameters on elongation is exactly reversed as shown in equation (2). Thus UTS of composites is observed to be 20% enhanced and elongation reduced by nearly 30% compared to the matrix material. Similar observations are recorded by many researchers [19-22]. Leisk and Saigal [23] have shown that further enhancement in tensile strength is possible by subjecting the composites to heat treatment. However, this claim is to be confirmed for Al7075/Al2O3 composites. All these aspects can be systematically exploited in developing the AMCs possessing desired tensile strength and %elongation. 5. Conclusion Based on the experimental work, following conclusions are drawn. 1 Rotatable, central composite design can be successfully used to model the tensile behaviour of AMCs 2 Mathematical models for UTS and %elongation are adequate and will predict the values with 99% confidence. 3 UTS and %elongation show reverse trends as far as influence of the process parameters are concerned. 4 UTS of the Al7075/Al2O3 MMCs increased by 20%compared to that of matrix and % elongation was reduced by around 30%. 6. References [1] Surappa M.K. (2003). Aluminium matrix composites: Challenges and Opportunities. Sadhana, 28 Parts 1 & 2, 319-344. 6
- 3. Chemistry and Materials Research www.iiste.org ISSN 2224- 3224 (Print) ISSN 2225- 0956 (Online) Vol 2, No.1, 2012 [2] Ibrahim I.A, Mohamed F.A, Lavernia E.J. (1991). Particulate reinforced metal matrix composites- a review. Journal of Material Science, 26, 1137-1156. [3] Nikhilesh Chawla, Yu-Lin Shen. (2001). Mechanical behaviour of particulate reinforced metal matrix composites. Advanced Engineering Materials, 3, 6, 357-370. [4] Daoud A, Reif W, Rohatgi P. (2003). Microstructure and tensile properties of extruded 7475 AL-Al2O3 particulate composites. ECCM13, Sweden, 1201. [5] Ceschini L, Minak G, Morri A. (2009). Forging of the AA2618/20 Vol. % Al2O3p composite: Effects on microstructure and tensile properties. Composites Science and Technology, 69, 1783-1789. [6] Mallik, B., et al (2006). Effect of particle content on the mechanical behaviour of aluminium-based metal matrix composites (AMMC). Indian Foundry Journal, 52, 35-42. [7] Hashim J, Looney L, Hashmi M. S. J. (1999). Metal matrix composites: production by the stir casting method. Journal of Materials Processing Technology, 92-93, 1- 7. [8] Ceschini L, Minak G, Morri A. (2006). Tensile and fatigue properties of the AA6061/20 vol. % Al2O3p and AA7005/10 Vol. % Al2O3p composites. Composites Science and Technology, Vol. 66, 333-342 [9] Gupta M, Lai M.O, Lim C.Y.H. (2006). Development of a novel hybrid aluminium-based composite with enhanced properties. Journal Material Processing Technology, Vol. 176, No. 1-3, 191-199. [10] Sahin Y. (2003). Wear behavior of aluminium alloy and its composites reinforced by SiC particles using statistical analysis. Materials and Design, 24, 95-103. [11] Yilmaz O, Buytoz S. (2001). Abrasive wear of Al2O3-reinforced aluminium-based MMCs. Composite Science and Technology, 61, 2381-2392. [12] Mondal D.P, Das S. (2006). High stress abrasive wear behavior of aluminium hard particle composites: Effect of experimental parameters, particle size and volume fraction. Tribology International, 39, 470-478. [13] Chawla N, Chawla K.K. (2006). Microstructural e-based modeling of the deformation behavior of particle reinforced metal matrix composites. Journal of Material Science and Technology, (41) 913-925. [14] Deshmanya Indumati B, Purohit G.K. (2011). Studies on modelling of aluminium matrix composites (AMCs)-A Review. ICAM 2011, Joint International Conference on Advanced Materials. 144-145. [15] Cochran W.G, Cox G M. (1992). Experimental Design, John Wiley, New York. [16] Montgomery D. C. (2009). Design and Analysis of Experiments. John Wiley, New York. [17] Adler Y.P, Markov E. V, Granovsky Y.V. (1975). The design of experiments to find optimal conditions. MIR Pub., Moscow. [18] Deshmanya, Indumati B, Purohit G.K. (2011). Modelling of impact strength and hardness of Al2O3 – reinforced Al-7075 composites. International Journal of Industrial Engineering Practice, Vol. 3, Issue 1, 61-66. [19] Doel T. J. A, Bowen P. (1996). Tensile properties of particulate-reinforced metal matrix composites. Composites Part A: Applied Science and Manufacturing, 27, 655-665. [20] Srivatsan T.S. (1996). Microstructure tensile properties and fracture behaviour of Al2O3 particulate-reinforced aluminium alloy metal matrix composites. Journal of Materials Science, 31, 1375. [21] Seah K. H. W, Sharma S. C, Girish B.M. (2001). Mechanical properties of as- cast and heat-treated ZA-27/graphite particulate composites. Composite: part A. 28A 251-6 Composites Science and Technology, 61, 2381. [22] Abis S. (1989). Characterization of an aluminium alloy/alumina metal matrix composites. Journal of Composite Science and Technology, 35, 1-19. [23] Leisk G, Saigal A. (1995). Taguchi analysis of heat treatment variables on the mechanical behaviour 7
- 4. Chemistry and Materials Research www.iiste.org ISSN 2224- 3224 (Print) ISSN 2225- 0956 (Online) Vol 2, No.1, 2012 of alumina /aluminium metal matrix composites. Composites Engineering, 5, 2, 129-142. Table 1: Chemical Composition of Al7075 Cr Cu Mg Zn Al Density g/cc at 20°C 0.22 1.60 2.80 5.50 Balance 2.89 Table 2: Details of other important properties of Al7075 UTS Yield Strength Elongation Hardness Thermal Conductivity Elect. Resistivity 2 MPa MPa % VHN Cal/Cm /Cm/°C at 25°C µΩ-Cm at 20°C 228 103 17 79 0.29 5.74 Table 3: Coded values of as-cast input variables at different levels Coded Input Units Lower level Middle Upper level values parameters Notation -2 -1 0 +1 +2 X1 Size of Al2O3 D µm 36 45 54 63 72 X2 % Wt of W --- 5 7.5 10 12.5 15 Al2O3 X3 Holding T 150 237 325 413 500 °C Temperature X4 Holding Time t Hrs 1 2 3 4 5 8
- 5. Chemistry and Materials Research www.iiste.org ISSN 2224- 3224 (Print) ISSN 2225- 0956 (Online) Vol 2, No.1, 2012 Table 4: Design matrix for preparation of tensile test samples by stir casting along with responses Input Parameters Responses Trial No. X1 X2 X3 X4 UTS Elongation Size of Al2O3 Wt. fraction Holding Holding Time, MPa % D (µm) of Al2O3 Temperature, t (Hrs) %W T (°C) 1 -1 -1 -1 -1 268 13.54 2 +1 -1 -1 -1 264 14.80 3 -1 +1 -1 -1 273 11.35 4 +1 +1 -1 -1 267 13.20 5 -1 -1 +1 -1 275 12.80 6 +1 -1 +1 -1 262 14.50 7 -1 +1 +1 -1 277 10.63 8 +1 +1 +1 -1 275 11.25 9 -1 -1 -1 +1 274 11.54 10 +1 -1 -1 +1 271 13.15 11 -1 +1 -1 +1 278 10.22 12 +1 +1 -1 +1 273 12.12 13 -1 -1 +1 +1 280 11.35 14 +1 -1 +1 +1 276 13.05 15 -1 +1 +1 +1 288 11.12 16 +1 +1 +1 +1 284 12.23 17 -2 0 0 0 285 11.10 18 +2 0 0 0 262 9.98 19 0 -2 0 0 273 9.25 20 0 +2 0 0 289 10.50 21 0 0 -2 0 270 9.00 22 0 0 +2 0 275 10.00 23 0 0 0 -2 267 11.10 24 0 0 0 +2 273 9.30 25 0 0 0 0 270 10.25 26 0 0 0 0 271 10.50 27 0 0 0 0 272 10.55 28 0 0 0 0 270 10.61 29 0 0 0 0 273 10.45 30 0 0 0 0 268 10.70 31 0 0 0 0 268 10.50 9
- 6. Chemistry and Materials Research www.iiste.org ISSN 2224- 3224 (Print) ISSN 2225- 0956 (Online) Vol 2, No.1, 2012 Table 5: Analysis of Variance (ANOVA) Particulars Source DF SS MS F R2 Radj2 I & II 14 455.438 32.531 Order Terms UTS Lack of Fit 10 885.07 3.571 9.11 98.42 98.18 Residual Error 6 21.427 Total 30 1361.935 36.102 9.11 98.42 98.18 2 Source DF SS MS F R Radj2 I & II 23.489 1.677 14 Frame Order Terms Driving motor Lack of Fit 42.54 Stirrer Rod 0.0198 84.52 99.81 99.79 % Elongation 10 Ball Bearing Residual Error 0.1191 6 Stirrer Blade Total 30 66.148 1.6968 84.52 99.81 99.79 Crucible Note: From Table; F14,6,0.05 = 4.07 (i.e. Fmodel > Ftable). Hence the model is adequate. Holding Furnace Figure 1: Schematic diagram showing components of stir-casting process. The stirrer is a servomotor operated ceramic coated stainless steel rod. 10
- 7. Chemistry and Materials Research www.iiste.org ISSN 2224- 3224 (Print) ISSN 2225- 0956 (Online) Vol 2, No.1, 2012 Figure 2:Close-up view of the stir-casting set-up. Al2O3 particulates of various sizes are added to the melt at 730°C which is continuously stirred using a motorized stirrer made of ceramic coated stainless steel rod. 11