Trans Indian Inst Met (2015) 68(3):453–463 DOI 10.1007/s12666-014-0476-6
TECHNICAL PAPER
TP 2870
Multi Response Optimization for Processing Al–SiCp Composites: An Approach Towards Enhancement of Mechanical Properties H. Goyal • N. Mandal • H. Roy • S. K. Mitra B. Mondal
•
Received: 29 July 2014 / Accepted: 28 October 2014 / Published online: 27 November 2014 Ó The Indian Institute of Metals - IIM 2014
Abstract The present study illustrates the manufacturing aspects of composite with different wt% of SiC particulates as reinforcement in the aluminum alloy matrix developed through investment casting route. The composites were prepared by varying certain process parameters like preheating temperature of particulates, percentage reinforcement and stirring speed. Detailed micro-structural characterization and estimation of mechanical properties (viz., strength, hardness and porosity measurement) are necessary supplements to this investigation. A mathematical model is developed using regression analysis technique for prediction of optimum process parameters viz. percentage reinforcement, preheating temperature of particulates and stirring speed for producing MMCs with enhanced mechanical properties and adequacy of the model has been validated using analysis of variance techniques. Finally the optimization of parameters has also been done using design expert software. The authors have achieved 81.56 % desirability level using multi-response optimization; the optimum value of process parameters would lead to enhanced mechanical properties of cast component.
H. Goyal S. K. Mitra Dept of Metallurgical & Materials Engineering, National Institute of Technology, Durgapur 713 209, India N. Mandal (&) B. Mondal Centre for Advanced Materials Processing, CSIR-Central Mechanical Engineering Research Institute (CSIR-CMERI), Mahatma Gandhi Avenue, Durgapur 713 209, India e-mail:
[email protected];
[email protected] H. Roy NDT & Metallurgy Group, CSIR-Central Mechanical Engineering Research Institute (CSIR-CMERI), Mahatma Gandhi Avenue, Durgapur 713 209, India
Keywords Metal matrix composites SiC particulates Response surface methodology Central composite design
1 Introduction The increased demand of lightweight materials in the engineering fields like aerospace and automotive industries has led to the development of Al-alloy-based composites (mainly Al-alloy/SiCp composites). Therefore, in the recent past, Al based metal matrix composites (MMC’s) were developed for improvement of specific characteristics such as coefficient of thermal expansion, tensile strength, and wear properties [1–4]. Presently, MMCs are continuously replacing the general lightweight materials such as aluminum alloy in different industrial applications where high strength, low weight and energy savings are the most important criteria [5–7]. Usually, with the introduction of the SiC particulates, elastic modulus and yield stress increases, but at the same time ductility and toughness of the composite decreases. Optimizing the mechanical properties of reinforced composites attracted a lot of interest in the recent past [8–10]. The synthesis of MMCs by casting or solidification process is considered to be the least expensive with respect to other methods such as semisolid processing, solid state processing etc. [11]. Compared to other casting routes, investment casting was chosen for fabrication of MMCs in the present work because of its advantages over other routes. Some of the advantages of investment casting are capability to cast complex and intricate shapes, near net shape production, capability to cast thin walls and low material waste [12– 16]. But as the process is complex and various parameters are involved so modeling and optimization of process parameters to get fine product is very necessary. Several
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researchers are continuously studying in this direction like Gupta et al. [17] have studied influence of process parameters on near net shape synthesis of aluminum based metal MMCs by varying the stirring speed, holding and stirring time and total flight distance and they reported that at stirring speed of 500 rpm and holding time of 15 min better distribution of particle and minimum porosity level was achieved. Shasha et al. [18] have studied the influence of stirring speed on SiC particles distribution in A356 liquid by varying the blade design and stirring speed and they obtained higher concentration of particles at the periphery. Singh et al. [19] have tried to optimize the process parameters like particle size, wt% of reinforcement and stirring time to study their effect on impact strength, tensile strength and hardness and they have reported enhanced mechanical properties with increase in wt% and stirring time and decrease in particle size. Singh et al. [20] developed the Al alloy LM6 based SiC andAl2O3 particulate MMC with stir casting technique. These investigators showed that ductility decreased with increasing particle wt% and the behavior of material changes from ductile to brittle. The UTS and yield strength increased with increase in weight percentage of SiC and Al2O3 particles in the matrix. In another investigative work Muhammed et al. [21] manufactured Al–Si/Al2O3 composite by vortex technique. Different composites were prepared by varying parameters like stirring time, stirring speed and wt% of the reinforcement. Taguchi method was used improve the performance of the product, process design and system. Their experimental and analytical results showed that wt% of the reinforcement was the most influential parameter that gives the highest tensile and hardness properties to the composite. Recently, different evolutionary approaches like Neural Network, Genetic Algorithms etc. are now intensely used in the areas of metallurgy and materials engineering. Giri et al. [22] have tried to model the different parameters for melting in Blast Furnace using BioGP algorithm. It was found that this modeling technique was very effective for complex modeling problem. In another work of Giri et al. [23] a new bi-objective genetic programming (BioGP) technique has been developed for meta-modeling in a chromatographic separation process using a simulated moving bed. The BioGP technique produced acceptable results for data-driven modeling and multi objective optimization studies. However, a survey of the technical literature reveals that limited information is available on the effect of process parameters in investment casting of composites. Information regarding the optimization of various process parameters such as particulate preheating temperature, stirring speed is currently unavailable. In this study an attempt has been made to correlate the effect of process parameters such as percentage reinforcement, pre heating temperature
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of particulates and stirring speed on ultimate tensile strength (UTS), hardness and porosity level of the composite cast by investment casting route. But as the above mentioned mechanical properties is not so conflicting in nature the effect of process parameters is studied through response surface methodology (RSM) utilizing the relevant experimental data obtained through experiments. The adequacy of the developed mathematical model is also tested by the analysis of variance test (ANOVA) [24]. Finally, an attempt is made to obtain optimal process parameters for maximum UTS and hardness keeping the porosity level minimum.
2 Experimental Procedure 2.1 Materials In the present study, commercial grade Al-alloy (Al– Si7Mg) was used as the base matrix of the composite and silicon carbide (SiCp) particulates of average size 15 lm were used as the reinforcement. Details of the composition are shown in Table 1. 2.2 Preparation of Ceramic Mold for Investment Casting Rapid prototyping (RP) technology is utilized for manufacturing the wax patterns of investment casting. The wax patterns were made in vacuum casting machine by pouring the molten wax in the silicon rubber mold and were then gated in the form of tree assembly integrated with pouring cup, central sprue and runner system. The assembled wax patterns were then cleaned and dipped in primary ceramic slurry and left in an environment to dry. After the primary coats had been applied the ‘‘back-up’’ coats were formed with slurry and sprinkled coarser size of zircon sand to build the shell thickness more rapidly. After drying of each layer, the process was repeated with subsequent layers until the required ceramic shell thickness had been achieved. The molds were then air dried and finally de-waxed at autoclave followed by burning at 900 °C for 1–2 h. Then the ceramic shell molds were placed in a furnace to preheat at a temperature of 350–500 °C for an hour and kept in an adjustable horizontal movement trolley for bottom pouring. The stirring was continued throughout the pouring process. 2.3 Melting, Casting and Solidification For synthesizing of different wt% SiCp (i.e. 5, 10, and 15) reinforced aluminum-based MMC vortex stirring method was employed followed by investment casting. Samples were prepared by varying the chosen process parameters.
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Table 1 Composition Element
wt% Element
wt%
Composition of Al-alloy Cu
Mg
Si
Fe
Mn
Ni
Zn
Pb
Sn
Ti
Al
0.1
0.2–0.6
6.5–7.5
0.5
0.3
0.1
0.1
0.1
0.05
0.2
Balance
Composition of SiCp (Purity[ 99 %) Al
Ca
Cr
Fe
Mg
Mn
Ni
Ti
0.2
0.03
0.01
0.15
0.008
0.008
0.03
0.12
About 2–3 kg of Al-alloy was placed in a graphite crucible and heated to 80 °C above the liquidus temperature. After degassing with argon, surface of the melt was cleaned by skimming and SiCp particulates were added manually to the vortex formed using the stirrer. Once the addition of particulates was completed, stirring was done at varying speeds (200–400 rpm), and it was held for a period of 5–15 min before pouring it into the ceramic mold. The effect of stirring speed and preheating temperature of particulates is important for uniform distribution of particulates and for reducing the porosity levels in the cast MMCs. The next step is the solidification of the melt containing suspended particulates into an investment ceramic shell mold to obtain the cast product. The shell temperature was kept around 350–500 °C during pouring and then allowed to conventionally air-cool. 2.4 Micro Structural Characterization Metallographic specimens were cut from the synthesized Al–SiCp composite. The cut specimens were then prepared for microstructural observation by polishing and then finally etching using Keller’s reagent (2.5 % HNO3 ? 1.5 % HCl ? 0.5 % HF). Few representative microstructures were recorded both using an optical microscope and scanning electron microscope (SEM). 2.5 Mechanical Characterization 2.5.1 Measurement of Hardness, Ultimate Tensile Strength and Porosity Hardness was determined using the vickers micro hardness testing machine. Hardness was measured at two loads 0.1 Kgf and 0.2 Kgf. In the present work, authors have also tried to directly cast the tensile specimens as per ASTM E8 standard. The tensile testing was conducted using a 50 kN Universal Testing Machine (M/s. Tinius Olsen). The porosity level of the samples was measured using Archimedes Principle.
3 Statistical Modeling 3.1 Response Surface Methodology RSM is a modeling technique in which the relationship of different parameters with various responses is determined. It is also helpful in finding out the significance of each parameter and the extent of each on the responses. In the present investigation of mechanical properties of composite, percentage reinforcement, preheating temperature of particulates and stirring speeds were identified as process parameters which affect the responses such as UTS (MPa), % porosity (%) and hardness (HV). The effects of the parameters on the responses were tested through a set of planned experiments based on 3 levels 3-factor central composite design to explore the quadratic response surfaces. The results of the trials were reported in the design layout as shown in Table 2. The response function representing the performance can be expressed as Y ¼ wðR; N; T Þ
ð1Þ
where, Y is the desired response and W is the response function. In the present study the CCD based models for tensile strength MPa, hardness (HV) and % porosity (%) have been developed with % reinforcement (%), Stirring speed (N) and preheating temperature (T) The second order regression equation used to represent the response surface for M factors is given by m m m X X X Y ¼ a0 þ a i Xi þ aij Xi Xj þ aii Xi2 ð2Þ i¼1
i;j¼1
i¼1
where, a0 is the free term of the equation, the coefficients a1, a2 ,..., am are linear terms; a11, a22 ,..., amm are quadratic terms; and a12, a13 ,..., am-1,mare the interaction terms. For three factors, the selected polynomial could be expressed as Y ¼ a0 þ a1 R þ a2 N þ a3 T þ a12 RN þ a13 RT þ a23 NT þ a11 R2 þ a22 N2 þ a33 T2 ð3Þ
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Table 2 Experimental run Exp no.
A: % of SiCp
B: Pre heating temp
C: Stirring speed
UTS in MPa
% Porosity
Hardness in Hv
1
15
700
300
112
4.3
124.3
2
10
700
300
154
3.6
112
3
15
800
200
107
4.6
120
4
10
700
300
154
3.7
110.6
5
10
800
300
146
4
110
6
5
800
400
122
2.95
104
7
5
800
200
133
2.6
98
8
10
700
200
156
3.4
109
9
10
600
300
148
4.1
109
10
10
700
400
152
3.8
110
11 12
15 15
600 800
200 400
107 102
4.1 4.7
123 128
13
15
600
400
104
4.9
122
14
5
600
200
137
2.3
95
15
5
700
300
135
2.4
97
16
5
600
400
131
2.65
98
The values of the coefficients of the polynomial of Eq. (3) were calculated by the regression method. The design expert software (version 8.0.1) was used to calculate the coefficient values.
The coefficient values were determined using Eq. 3, and the mathematical model for UTS has been represented as Ultimate Tensile StrengthðUTSÞ
2
29:93 A 6:43 B þ 0:57 C
ð6Þ ð4Þ
The adequacy of the developed models was tested through ANOVA. Then the backward elimination process was applied to automatically eliminate the non-significant terms, and the resulting ANOVA table for the reduced quadratic model for UTS is shown in Table 3. The model Fvalue of 583.16 implies that the model is significant. It was found that the developed models were significant at 95 % confidence level. A ratio of greater than 4 is desirable. And the obtained ratio of 64.87 indicates an adequate signal. So, the present model can be used to navigate the design space. The following developed equations are the final empirical models in terms of coded factors for:
¼ 153:75 12:6 A 1:7 B 2:9 C 29:75 A 6:25 B
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Following the same procedure of modeling as followed for UTS the following equation were obtained as the final empirical model in terms of actual factor for % porosity and hardness respectively: % Porosity ¼ þ 13:38522727 þ 0:490363636 % of SiCp 0:042711 pre heating temp þ 0:008125 stirring speed 0:00000875 pre heating temp stirring speed 0:014818182 % of SiCp2 þ 0:00003295 ð7Þ
Hardness ¼ þ102:85875 þ 2:506 % of SiCp 0:032
þ 1:375 A B þ 1:125 A C 0:87 B C 2
3.3 Modeling of Porosity and Hardness
pre heating temp2
Ultimate Tensile Strength ðUTSÞ
2
þ 0:00275 %of SiCp pre heating temp þ 0:00225 % of SiCp stirring speed 0:0000875 pre heating temp stirring speed 1:19 % of SiCp2 0:000625 pre heating temp2
¼ þ153:62 12:60 A 1:70 B 2:90 C þ 1:38 A B þ 1:13 A C 0:87 B C 2
Ultimate Tensile Strength ðUTSÞ ¼ 218:075 þ 18:68 % of SiCp þ 0:85675 pre heating temp þ 0:00975 stirring speed
3.2 Modeling of Ultimate Tensile Strength (UTS)
2
While, the following equations are the final empirical model in terms of actual factor for:
ð5Þ
pre heating temp 0:088 stirring speed þ 0:00015 pre heating temp stirring speed ð8Þ
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Table 3 ANOVA table for the reduced quadratic model for UTS Sum of squares
Model
5848.225
8
A- % of SiCp
1587.6
1
1587.6
B-pre heating temp
28.9
1
28.9
C-stirring speed
84.1
1
AB
15.125
1
AC
10.125
1
10.125
8.0769231
0.0250
Significant
BC
6.125
1
6.125
4.8860399
0.0628
Not significant
A^2
2596.18333
1
2596.183333
B^2
114.583333
df
1
Mean square
F value
p value prob [F
Source
\0.0001
Significant
\0.0001
Significant
23.054131
0.0020
Significant
84.1
67.088319
\0.0001
Significant
15.125
12.065527
0.0104
Significant
731.028125
583.15634 1266.4615
2071.0294
114.5833333
91.405508
Residual
8.775
7
1.253571429
Lack of fit Pure error
8.775 0
6 1
1.4625 0
Cor total SD Mean CV % PRESS
5857 1.11963004 131.25 0.85305146 72.8756735
\0.0001
Significant
\0.0001
Significant Not significant
15 R-squared
0.9985018
Adj R-squared
0.9967896
Pred R-squared Adeq precision
As can be seen from Tables 4 and 5 that the Model F-values of 103.93 and 173.37 implied that the models are significant. 3.4 Confirmation Run In order to validate the models developed, five confirmations run were performed as depicted in Table 6. Using the point prediction capability of Design Expert software, the results were predicted with 95 % confidence level. The predicted values of tensile strength, % porosity and hardness were calculated from the Eqs. 6, 7 and 8 respectively.The percentage error was also calculated and it varied between 2.98 and 2.45 %.
4 Results and Discussion The observed microstructures for different wt% of SiC are shown in Fig. 1. The microstructures reveal reasonably uniform distribution of SiC particulates in the Al matrix. However, some segregation of SiC particles can be seen in 15 wt% SiC sample. The composites have been characterized in terms of their mechanical properties i.e. porosity, hardness and ultimate tensile strength (UTS). The observed variation of these properties is shown in Fig. 2a, which reveals that both hardness as well as porosity level increase uniformly with increases in wt% of SiCp. However, the
0.9875575 64.872619
variation in UTS shows a point of inflexion at 10 wt% SiCp. The same properties show a different trend with variation in pre-heating temperature. Strength and hardness vary with similar fashion; whereas porosity shows a reverse trend with pre-heating temperature. The possible explanation of the variation of mechanical properties with wt% of SiCp, pre-heating temperature and stirring speed are explained in the subsequent sections. 4.1 Direct effect of Process Parameters Direct and interaction effect of different process parameters i.e. wt% of SiCp, preheating temperature and stirring speed with mechanical properties i.e. porosity, hardness and UTS were computed and plotted in Figs. 2a, 3d. It can be derived from Fig. 2a that value of all the three responses (i.e. hardness, tensile strength and % porosity) increases as the percentage of SiCp increases but after 10 wt% of SiCp, value of tensile strength decreases due to agglomeration of particulates and porosity level increases due to increase in the percentage of the hard and brittle phase of the ceramic body in the alloy matrix. Min et al. [2] also reported increase in the value of yield strength and tensile strength with the increase in volume fraction of SiC. Hang et al. [25] reported the effect of increasing volume fraction of SiC on mechanical properties due to agglomeration of particulates. From Fig. 2b, it can be concluded that with increase in preheating temperature of particulates up to 700 °C, values of tensile strength and hardness increases
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Table 4 ANOVA table for the reduced quadratic model for Porosity Source
Sum of squares
Model
10.42885227
df
Mean square
F value
p value prob [F
6
1.738142045
103.9264
\0.0001
Significant
A-% of SiCp
9.409
1
9.409
562.5795
\0.0001
Significant
B-pre heating temp
0.064
1
0.064
C-stirring speed
0.4
1
0.4
BC
0.06125
1
0.06125
A2
0.402560606
1
0.402560606
3.826665 23.91665 3.662238
B2
0.318560606
1
0.318560606
Residual
0.150522727
9
0.016724747
Lack of fit
0.145522727
8
0.018190341
1
0.005
Pure error
0.005
Cor total SD
10.579375 0.129324195
0.0821
Not Significant
0.0009
Significant
0.0879
Not significant
24.06976
0.0008
Significant
19.04726
0.0018
Significant
0.3857
Not significant
3.638068
15 R-squared
0.985772
Mean
3.63125
Adj R-squared
0.976287
CV %
3.561423621
Pred R-squared
0.944637
PRESS
0.585707454
Adeq precision
29.40148
Table 5 ANOVA table for the reduced quadratic model for Hardness Source
Sum of squares
df
Mean square
Model
1633.809
4
A- % of SiCp
408.45225
1570.009
1
1570.009
B-pre heating temp
16.9
1
16.9
C-stirring speed
28.9
1
28.9
BC
18
1
18
Residual
25.915375
11
Lack of fit
24.935375
10
Pure error
0.98
1
Cor total
1659.724375
15
SD
1.5349082
Mean CV% PRESS
F value
p value prob [F
173.3710105
\0.0001
Significant
666.4035925
\0.0001
Significant
7.173347868
0.0215
Significant
0.0049
Significant
7.640252167
0.0184
Significant
2.54442602
0.4552
Not significant
12.26684931
2.355943182 2.4935375 0.98 R-squared
0.984385736
110.61875 1.387566032
Adj R-squared Pred R-squared
0.978707821 0.960377243
65.7628559
Adeq precision
36.66496724
Table 6 Confirmation run Run Parameters
Stirring speed Predicted value
% of SiCp Pre heating temp
UTS
Experimental value
% Error
% Porosity Hardness UTS % Porosity Hardness UTS
% Porosity Hardness
1
15
800
200
107.47 4.55
121.25
107
4.6
120
0.44 -1.09
2
10
700
200
156.65 3.46
108.92
156
3.4
109
0.42
3
5
600
200
136.57 2.28
96.59
137
2.3
4
7.5
900
300
122.84 4.56
106.95
124
5
7.5
800
100
152.65 3.26
99.25
149
but the porosity level decreases. This phenomenon occurs because of the pretreatment of SiC particles, which helped in achieving better distribution of particulates. Similar
123
1.04
1.76
-0.07
95
-0.31 -0.87
1.67
4.7
105
-0.94 -2.98
1.86
3.3
101
2.45 -1.21
-1.73
observation was made by Zhang et al. [26] but beyond 700 °C the particles developed a layer of SiO2 which decreases the wettability of particulates [27]. On further pre
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heating the particulates, there were chances of aluminum carbide formation as per the following equation: 4Al þ 3SiC ! Al4 C3 þ 3SiC ð9Þ This formation of aluminum carbides has deleterious effect on the mechanical properties of the composite as observed by Yang et al. [27]. From Fig. 2c, it is vividly evident that with increasing stirring speed porosity level increases continuously and at the same time value of hardness and tensile strength varies considerably at different sections. This is due to the reason that with increasing stirring speed centrifugal force continuously increases which in turn forces the ceramic particulates away from the center and in turn the density of particulates increases in the periphery and the central portion is nearly devoid of ceramic particulates. Prabu et al. [28] had found that at lower stirring speed and time, uniform distribution of particles could not be achieved which resulted in variation of hardness values at different points. 4.2 Interaction Effect of Variables
Fig. 1 a SEM image of MMC with 5 wt% SiCp. b SEM image of MMC with 10 wt% SiCp. c SEM image of MMC with 15 wt% SiCp
From Fig. 3a, it can be concluded that among the two parameters pre heating temperature of particulates and wt% of SiCp, the influence of the latter is much more prominent than the former one on UTS. At intermediate wt% of SiCp (10 %) and preheating temperature (700 °C) highest value of tensile strength was obtained and at higher wt% of SiCp, the particles started forming clusters due to which the increase in the value of UTS was limited. Similar observations were made by Hang et al. [25]. From Fig. 3b, it is clearly seen that among the two process parameters stirring speed and % of SiCp, the former shows more or less constant effect on the UTS value while the latter affects UTS in the same way as shown in Fig. 3a i.e. increases up to certain wt% of SiCp and then decreases. From Fig. 3c, it can be concluded that among two process parameters stirring speed and pre heating temperature, porosity level continuously increases with increasing stirring speed. The reason for such a phenomenon could be attributed to the fact that with increasing speed, particulates are forced radially outwards leading to porous region in the core. The variation of porosity in the selected composite with preheating temperature shows an inflexion point at an intermediate value (700 °C). This occurs due to absorbed gases because increasing the preheating temperature reduces the amount of absorbed gases and moisture level of particulates leading to lower porosity and beyond 700 °C a layer of SiO2 is generally created on the SiC particle surface, which reacts with Al and decreases the wettability of the particulates or the particles could react with Al to form aluminum carbides thereby increasing the porosity level. Similar observations
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Fig. 2 a Direct effect of SiCp on UTS, hardness and porosity. b Direct effect of preheating temperature on UTS, hardness and porosity. c Direct effect of stirring speed on UTS, hardness and porosity
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Fig. 3 a Interaction effect of preheating temperature and % of SiCp on UTS. b Interaction effect of stirring speed and % of SiCp on UTS. c Interaction effect of stirring speed and preheating temperature on porosity. d Interaction effect of preheating temperature and stirring speed on hardness Table 7 Conditions for optimization Condition
Goal
Lower limit
Upper limit
% of SiCp
Is in range
5
15
Pre heating temp
Is in range
600
800
Stirring speed
Is in range
200
400
UTS
Maximize
102
156
% Porosity
Minimize
2.3
4.9
Hardness
Maximize
95
128
former has negligible effect on the average hardness value. It is also observed that increasing stirring speed results in increase in average hardness value. The reason could be due to non-uniform distribution of particulates between the circumference and core of the composite at higher stirring speed. Similar observations were made by Prabu et al. [28] while studying the effect of stirring speed and time on distribution of particles. 4.3 Optimization of Parameters
were reported by Zhang et al. [26] and Yang et al. [27]. From Fig. 3d, it is prominent that among the two process parameters pre heating temperature and stirring speed, the
Desirability function optimization of the RSM has been employed for multi-response optimization in the present
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Table 8 Optimization result No.
% of SiCp
Pre heating temp
Stirring speed
UTS (MPa)
Porosity (%)
Hardness (Hv)
Desirability
1
10.17
677.22
200.00
156
3.46843
109.392
0.815627108
2
10.15
674.10
200.00
156
3.46403
109.343
0.815585964
3
10.19
680.78
200.00
156
3.4733
109.436
0.815583856
4
10.20
682.34
200.00
156.001
3.47536
109.45
0.815535012
5
10.21
685.60
200.02
156
3.47974
109.475
0.815375567
6
10.04
674.62
200.00
156.335
3.44376
109.076
0.815033413
study. Employing the optimization process, the target has been fixed to obtain the optimal values of process parameters in order to maximize the hardness and UTS while simultaneously minimizing the porosity level of the composites. The constraints used in the optimization process are summarized in Table 7 and the optimal solutions are reported in Table 8 in order of decreasing desirability level.
Selected
desirability function approach, the values of process parameters were predicted with 81.56 % desirability. Acknowledgments The authors would like to acknowledge Dr. Pijush Pal Roy, Director, CSIR-Central Mechanical Engineering Research Institute, Durgapur for his constant source of inspiration in writing this paper. The authors also acknowledge the financial support from Council of Scientific & Industrial Research, New Delhi to carry out the research work. The authors are also gratefully acknowledged all the staff members of CAMP group for their continuous effort in the experimentation part of the paper.
5 Conclusions In this work, composites were successfully synthesized in varying wt% of SiCp using investment casting route and RSM has been employed to develop the mathematical model for UTS, % porosity and hardness with respect to the process parameters i.e. % of SiCp, pre heating temperature of particulates and stirring speed. Multi-response optimization using desirability function approach has been applied to achieve optimum value of the process parameters for achieving highest UTS and hardness with minimum porosity. From this study, the following conclusion can be drawn: UTS: wt% of SiC and pre heating temperature of particulates has a major effect on the UTS value but with the variation in stirring speed value of UTS varies marginally. % Porosity: with increase in wt% of SiC and stirring speed the porosity level of the composite keeps on increasing while with the variation in pre heating temperature of particulates, minimum level of porosity was achieved at an intermediate temperature of around 700 °C. Hardness: with increase in wt% of SiC the hardness value keeps on increasing but with the variation of stirring speed and pre heating temperature of particulates hardness value remains more or less constant. Among the three studied process parameters wt% of SiC has the major contribution on the hardness and UTS value, and in case of % porosity value of stirring speed has the major effect. Using the multi response optimization with
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