# Optimization and Prediction of Thermal Conductivity and Electrical Conductivity of Vacuum Sintered Ti-6Al-4V-SiC(15 Wt.%) Using Soft Computing Techniques

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## Abstract

**:**

_{3}SiC

_{2}) is a novel composite material that has found a multitude of uses in the aerodynamics, automobile, and marine industries due to its excellent properties such as high strength and modulus, high thermal and electrical conductivity, high melting point, excellent corrosion resistance, and high-temperature oxidation resistance. These properties are strongly associated with physical properties and microstructural features. Due to difficulties in the synthesis of this material, there have been very few investigations on the relationship between microstructure and physical characteristics of titanium silicon carbide composites processed through powder metallurgical process. However, the importance of thermal conductivity and electrical conductivity of titanium silicon carbide composites in various potential applications has led to keen attention from several researchers. Hence, in this paper, optimization, and prediction of process input parameters during processing under vacuum sintering for achieving maximum electrical and thermal conductivity of Ti-6Al-4V-SiC(15 Wt.%) has been presented. Using Taguchi’s L

_{9}Orthogonal Array, it has been observed that aging temperature (1150 °C), aging time (four hours), heating rate (25 °C/min), and cooling rate (5 °C/min) result in optimum input parameters for achieving the highest electrical conductivity values during the processing of Ti-6Al-4V-SiCp composites. Further, for maximum thermal conductivity values during the processing of Ti-6Al-4V-SiCp composites, aging temperature (1150 °C), aging time (four hours), heating rate (5 °C/min), and cooling rate (5 °C/min) are preferred. A second-order response surface model generated can be effectively used for predicting the electrical conductivity and thermal conductivity during the processing of Ti-6Al-4V-SiCp composites with an accuracy of 99.28% (electrical conductivity) and 99.14% (thermal conductivity). By comparing the experimental results along with the results of the mathematical model and the BPANN model results for nine trials, it was observed that the estimated value is accurate for all tests with an error of 0.39% (electrical conductivity) and 0.48% (thermal conductivity). Further, from X-ray diffraction studies and microstructural analysis, it has been observed that aging at 1150 °C for four hours resulted in the formation of a ternary carbide phase of titanium silicon carbide (Ti

_{3}SiC

_{2}), which resulted in maximum electrical conductivity (4,260,000 Ω

^{−1}m

^{−1}) and thermal conductivity (36.42 W/m·K) of the Ti-6Al-4V-SiC (15 Wt.%) composite specimen.

## 1. Introduction

_{3}SiC

_{2}) is a novel composite material that has found a multitude of uses in the aerodynamics, machining, and marine industries due to its excellent properties such as high strength and modulus, high thermal and electrical conductivity, high melting point, excellent corrosion resistance, and high-temperature oxidation resistance. These properties are strongly associated with physical properties and microstructure features. Due to difficulties in the synthesis of this material, there have been very few investigations on the relationship between microstructure and physical characteristics. Titanium silicon carbide (Ti

_{3}SiC

_{2}) has attracted a lot of attention in the last ten years as a “representative compound of the ternary Mn+1AXn phases (or MAX phases)”, where M is denoted as metal that transitions early with examples like Ti, Cr, Al, and Si, X is denoted by either carbon or nitrogen (some exceptions with both carbon and nitrogen), and n represents a number (1,2,3, etc) [1,2,3]. Its crystal structure consists of three relatively tightly packed Ti layers that contain C atoms in the octahedral positions between three hexagonal nets of Si atoms [4]. This material, which has a density of 4.52 g/cm

^{3}, is a potential material for structural and functional materials used in high-temperature applications. It has a hardness value of HV 4 GPa, making it comparatively soft with a strong thermal shock resistance [1]. The first account of the synthesis of Ti

_{3}SiC

_{2}via chemical reaction was noted in 1967 by Jeitschko and Nowotny [5]. Goto and Hirai [4] analyzed the processing of Ti

_{3}SiC

_{2}following the(CVD) chemical vapor deposition route in 1987. Barsoum et al. (2,3) successfully processed a composite material with a relatively high Ti

_{3}SiC

_{2}content (almost 98 vol%) from mixtures of Ti-SiC-C following the hot-isostatic pressing (HIP) method.

_{9}orthogonal array. Further, response surface methodology and back propagation artificial neural networks have been used to predict the optimum process input parameters. Finally, microstructure analysis along with X-ray diffraction confirms the formation of ternary carbide phase (Ti

_{3}SiC

_{2}) which increased the electrical and thermal conductivity of Ti-6Al-4V-SiC (15 Wt.%) composites, has also been discussed.

## 2. Methodology

- ρ = Resistivity of the sample,
- V = voltage,
- I = current,
- t = thickness of the sample,
- s = distance between the probes

- σ = electrical conductivity of the sample.

^{+}/

_{−}2%. Thermal diffusivity is related to thermal conductivity as shown in Equation (3).

- k = thermal conductivity;
- ρ = density;
- C
_{p}= specific heat capacity.

_{9}orthogonal array was used. Further, this experiment employs response surface methodology to predict the process output parameters using a second-order equation. Powder X-ray diffraction analysis of sintered Ti-6Al-4V-SiC (15 Wt.%) composite powders was performed using Rigaku Miniflex 600 X-ray Diffractometer for 0–80° 2θ value. Microstructure and elemental mapping of the samples were conducted using an Olympic System Optical Microscope and an EVO MA18 Scanning Electron Microscope with Oxford EDS (X-act).

#### 2.1. Taguchi’s Design of Experiments (TDOE)

_{9}orthogonal array has been used to identify the optimal vacuum sintering process parameters. The levels and factors used for vacuum sintering (TDOE) are shown in Table 5. The orthogonal array with factors and levels is shown in Table 6.

#### 2.2. Response Surface Methodology

#### 2.3. Back Propagation Artificial Neural Network

_{p}= “error for the pth presentation vector”, t

_{pj}= “desired value for the jth output neuron” and O

_{pj}= “desired output of the jth output neuron”;

## 3. Results and Discussions

_{9}Orthogonal Array is explored. In addition, the response surface methodology and back propagation artificial neural network technique have been modified to anticipate the optimal process input parameters to optimize electrical and thermal conductivity. Finally, the microstructural investigation of Ti-6Al-4V-SiC (15 Wt%.) under various processing parameters has been discussed.

#### 3.1. Electrical Conductivity

_{9}orthogonal array for electrical conductivity we can observe that the electrical conductivity decreased at 1050 °C and 1250 °C aging temperatures, compared to 1150 °C, which is considered the optimum aging temperature for the formation of ternary carbides of titanium silicon carbide (Ti

_{3}SiC

_{2}). At 1150 °C aging temperature, highly dense Ti

_{3}SiC

_{2}structures are formed due to the higher diffusion rates compared to 1250 °C aging temperature where a less electrically conductive TiSi

_{2}phase is formed. Further aging time of four hours is the optimum aging time allowing for the complete transformation of Ti

_{3}SiC

_{2}. Heating and cooling rates during processing did not show much difference in electrical conductivity compared to aging temperature and aging time. However, with an 1150 °C aging temperature and four hours of aging time with a 25 °C/min heating rate and a 5 °C/min cooling rate, the lowest porosity was observed (Figure 8) However, the electrical conductivity of a material is affected by the percentage of porosity due to the hindered flow of free electrons [34]. Therefore, the highest electrical conductivity of 4,260,000 Ω

^{−1}m

^{−1}has been observed with the samples with the lowest percentage of porosity.

_{3}SiC

_{2}phase under aging temperature (1150 °C), aging time (four hours), heating rate (25 °C/min), and cooling rate (5 °C/min) resulted in increased thermal and electrical conductivity [35].

^{−1}m

^{−1}) = 3,825,280 + 134,444A + 153,333B + 16,667C + 321,667D − 774,773A

^{2}+ 305,227B

^{2}+ 75,227C

^{2}+ 80,227D

^{2}+ 26,250AB − 18,750AC + 53,750AD − 18,750BC + 13,750BD − 18,750CD

_{0.05,14,16}= 59.57), indicating that the generated second-order response function is fairly sufficient.

^{−1}m

^{−1}) presented in Figure 12a, clearly indicate that maximum electrical conductivity (<44,766,021 Ω

^{−1}m

^{−1}) has been achieved with aging temperature (1150 °C), aging time (four hours), heating rate (25 °C/min), and cooling rate (5 °C/min).

#### 3.2. Thermal Conductivity

_{9}orthogonal array, in Figure 13 it is observed that the thermal conductivity decreased at 1050 °C and 1250 °C aging temperature, compared to 1150 °C. Aging temperature and aging time determine the density of the Ti-6Al-4V-SiC composites and facilitate the proper formation of Ti

_{3}SiC

_{2}. At 1150 °C aging temperature and four hours of aging time, minimum porosity corresponding to maximum thermal conductivity (36.15 W/m·K) has been observed. Further, with a heating rate of 25 °C/min and a rapid cooling rate of 5 °C/min, delocalized electrons were formed which improved the thermal conductivity of the Ti-6Al-4V-SiC (15 Wt.%) composite. Furthermore, strong localized bonds of Ti-C and Ti-Si were formed at 1150 °C compared to the 1250 °C aging temperature, improving the thermal conductivity of the Ti-6Al-4V-SiC (15 Wt.%) composite specimen.

^{2}+ 1.356B

^{2}+ 0.156C

^{2}+ 0.521D

^{2}+ 0.2075AB − 0.0637AC + 0.0875AD − 0.0637BC − 0.0225BD − 0.0638CD

_{0.05,14, 14}= 30.69), indicating that the generated second-order response function is fairly sufficient.

^{−1}m

^{−1}) presented in Figure 16a, clearly show that maximum thermal conductivity (36.7214–37.2107 W/m·K) can be achieved with aging temperature (1150 °C), aging time (four hours), heating rate (25 °C/min), and cooling rate (5 °C/min).

#### 3.3. Validation of Electrical and Thermal Conductivity

_{9}orthogonal array with second-order response surface model and BPANN model for nine sets of trials, it was noted that the value estimated is very accurate for all the conducted tests with a minimal error of 0.72% and 0.86% with RSM and 0.39% and 0.48% with BPANN estimated values for electrical conductivity and thermal conductivity, respectively. However, BPANN has been trained with 27 nodes in the hidden layer. The performance of BPANN while testing all the patterns (training and testing) was found to be excellent with a minimal error (1.47%). The BPANN model has been rigorously tested utilizing the training data and corresponding graphs that have been plotted using predicted and tested values (Figure 17) (Table 14). The results indicate that the BPANN model has been successfully applied with an error percentage of 0.39% for electrical conductivity (Ω

^{−1}m

^{−1})and 0.48% for thermal conductivity (W/m·K), respectively. The calculated error is considered reasonable and shows that the BPANN model has been successfully applied for predicting the electrical and thermal conductivity of vacuum-sintered Ti-6Al-4V-SiC (15 Wt.%).

#### 3.4. Microstructural Analysis

_{9}orthogonal array using an Olympus IMS BX53M system optical microscope. Different grades of porosity characterized as black spots can be observed depending on the process input parameters of the vacuum sintering process i.e., aging temperature (°C), aging time (hours), heating rate (°C/min), and Cooling Rate (°C/min). The lowest porosity corresponding to the highest electrical and thermal conductivity has been observed with the sample produced at an aging temperature (1150 °C), aging time (four hours), heating rate (25 °C/min), and cooling rate (5 °C/min).

_{3}SiC

_{2}can be identified along with void spaces and un-transformed SiC particulates embedded in the Ti-6Al-4V matrix alloy. From the elemental mapping (Figure 20) of the Ti-6Al-4V-SiC(15 Wt.%) specimen, the distribution of elements (titanium, silicon, and, carbon) can be seen. The homogenous distribution of carbon indicates the isotropic presence of ternary carbide phases of titanium, ascertaining the formation of Ti

_{3}SiC

_{2}.

## 4. Conclusions

_{9}orthogonal array, response surface methodology (RSM), and back propagation artificial neural network (BPANN). Based on the results, the following conclusions are drawn:

- Using Taguchi’s L
_{9}Orthogonal Array it has been observed that, aging temperature (1150 °C), aging time (four hours), heating rate (25 °C/min), and cooling rate (5 °C/min) result as optimum input parameters for achieving the highest electrical conductivity values during the processing of Ti-6Al-4V-SiCp composites. Furthermore, for maximum thermal conductivity values during the processing of Ti-6Al-4V-SiCp composites, aging temperature (1150 °C), aging time (four hours), heating rate (5 °C/min), and cooling rate (5 °C/min) are preferred; - A second-order response surface model generated can be effectively used for predicting the electrical conductivity and thermal conductivity during the processing of Ti-6Al-4V-SiCp composites with an accuracy of 99.28% (electrical conductivity) and 99.14% (thermal conductivity);
- By comparing the experimental results along with the results of the mathematical model and BPANN model results for nine trials, it was observed that the estimated value is accurate for all tests with an error of 0.39% (electrical conductivity) and 0.48% (thermal conductivity);
- Furthermore, from X-ray diffraction studies and microstructural analysis, it has been observed that, aging at 1150 °C for four hours resulted in the formation of a ternary carbide phase of titanium silicon carbide (Ti
_{3}SiC_{2}) which resulted in maximum electrical conductivity (4,260,000 Ω^{−1}m^{−1}) and thermal conductivity (36.42 W/m·K) of Ti-6Al-4V-SiC (15 Wt.%) composite specimen.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Flowchart of Titanium Silicon Carbide composite processing [20].

**Figure 8.**Experimental results of electrical conductivity (Ω

^{−1}m

^{−1}) under different aging temperatures (°C) and aging times (h) with the constant heating rate (°C/min), and cooling rate (°C/min).

**Figure 9.**Electrical conductivity versus temperature for Ti-6Al-4V-SiC (15 Wt.%) specimen processed at aging temperature (1150 °C), aging time (four hours), heating rate (25 °C/min), and cooling rate (5 °C/min) while cooling from 360–13 °C.

**Figure 11.**XRD Peaks of Ti-6Al-4V-SiC(15 Wt.%) processed under aging temperature (1150 °C), aging time (four hours), heating rate (5 °C/min), and cooling rate (5 °C/min).

**Figure 12.**Contour and surface plots for electrical conductivity (Ω

^{−1}m

^{−1}) (

**a**) Heating Rate (25 °C/min); Cooling Rate (5 °C/min) (

**b**) Heating Rate (15 °C/min); Cooling Rate (3 °C/min) (

**c**) Heating Rate (5 °C/min); Cooling Rate (1 °C/min).

**Figure 14.**Thermal conductivity versus temperature plot of Ti-6Al-4V-SiC(15 Wt.%) processed under aging temperature (1150 °C), aging time (four hours), heating rate (5 °C/min), and cooling rate (5 °C/min).

**Figure 16.**Contour and surface plots for thermal conductivity (W/m·K) (

**a**) Heating Rate (25 °C/min); Cooling Rate (5 °C/min) (

**b**) Heating Rate (15 °C/min); Cooling Rate (3 °C/min) (

**c**) Heating Rate (5 °C/min); Cooling Rate (1 °C/min).

**Figure 17.**Experimental versus RSM versus BPANN prediction values of (

**a**) electrical conductivity and (

**b**) thermal conductivity.

**Figure 19.**Scanning Electron Microscope images of Ti-6Al-4V-SiC(15 Wt.%) processed under aging temperature (1150 °C), aging time (four hours), heating rate (25 °C/min), and cooling rate (5 °C/min).

**Figure 20.**Elemental Mapping of Ti-6Al-4V-SiC(15 Wt.%) composite processed under aging temperature (1150 °C), aging time (four hours), heating rate (25 °C/min), and cooling rate (5 °C/min) from electron dispersive X-ray analysis.

**Table 1.**Composition (Wt%) of Ti-6Al-4V alloy [20].

Element | Aluminium | Vanadium | Iron | Oxygen | Carbon | Nitrogen | Titanium |
---|---|---|---|---|---|---|---|

Wt (%) | 6.1063 | 4.103 | 0.1675 | 0.1124 | 0.0235 | 0.0193 | Balance |

**Table 2.**Composition (Wt%) of SiC reinforcement particle [20].

Element | Carbon | Iron | Nitrogen | Aluminum | Calcium | Oxygen | Potassium | Silicon |
---|---|---|---|---|---|---|---|---|

Wt (%) | 1.172 | 0.664 | 1.4353 | 0.2557 | 0.1454 | 0.8642 | 0.3243 | Balance |

**Table 3.**Thermal properties and Mechanical Properties of Ti-6Al-4V alloy [20].

Properties | Values (Units) |
---|---|

Density | 4.43 g/cm^{3} |

Melting Point | 1604–1660 °C |

Beta Transitional Temperature | 980 °C |

Tensile Strength, Ultimate | 1170 Mpa |

Tensile Strength, Yield | 1100 Mpa |

Compressive Strength | 1070 Mpa |

Modulus of Elasticity | 114 Gpa |

Brinell Hardness | 379 BHN |

**Table 4.**Thermal properties and Mechanical Properties of SiC [20].

Properties | Values (Units) |
---|---|

Density | 3.1 g/cm^{3} |

Melting Point | 2730 °C |

Beta Transitional Temperature | 2000 °C |

Tensile Strength, Ultimate | 390 Mpa |

Compressive Strength | 2000 Mpa |

Modulus of Elasticity | 410 Gpa |

Vicker’s Hardness | 2720 Hv |

**Table 5.**Levels and Control factors for vacuum sintering (TDOE) [20].

Control Factors | Levels | ||
---|---|---|---|

1 | 2 | 3 | |

Aging Temperature (°C) | 1050 | 1150 | 1250 |

Aging time (h) | 2 | 3 | 4 |

Heating Rate (°C/min) | 5 | 15 | 25 |

Cooling Rate (°C/min) | 1 | 3 | 5 |

Trial No. | Factors and Levels | |||
---|---|---|---|---|

Aging Temp (°C) | Aging Time (h) | Heating Rate (°C/min) | Cooling Rate (°C/min) | |

1 | 1 | 1 | 1 | 1 |

2 | 1 | 2 | 2 | 2 |

3 | 1 | 3 | 3 | 3 |

4 | 2 | 1 | 2 | 3 |

5 | 2 | 2 | 3 | 1 |

6 | 2 | 3 | 1 | 2 |

7 | 3 | 1 | 3 | 2 |

8 | 3 | 2 | 1 | 3 |

9 | 3 | 3 | 2 | 1 |

Test No. | Blocks | A | B | C | D |
---|---|---|---|---|---|

1 | 1 | −1 | −1 | −1 | −1 |

2 | 1 | 1 | −1 | −1 | −1 |

3 | 1 | −1 | 1 | −1 | −1 |

4 | 1 | 1 | 1 | −1 | −1 |

5 | 1 | −1 | −1 | 1 | −1 |

6 | 1 | 1 | −1 | 1 | −1 |

7 | 1 | −1 | 1 | 1 | −1 |

8 | 1 | 1 | 1 | 1 | −1 |

9 | 1 | −1 | −1 | −1 | 1 |

10 | 1 | 1 | −1 | −1 | 1 |

11 | 1 | −1 | 1 | −1 | 1 |

12 | 1 | 1 | 1 | −1 | 1 |

13 | 1 | −1 | −1 | 1 | 1 |

14 | 1 | 1 | −1 | 1 | 1 |

15 | 1 | −1 | 1 | 1 | 1 |

16 | 1 | 1 | 1 | 1 | 1 |

17 | 1 | −1 | 0 | 0 | 0 |

18 | 1 | 1 | 0 | 0 | 0 |

19 | 1 | 0 | −1 | 0 | 0 |

20 | 1 | 0 | 1 | 0 | 0 |

21 | 1 | 0 | 0 | −1 | 0 |

22 | 1 | 0 | 0 | 1 | 0 |

23 | 1 | 0 | 0 | 0 | −1 |

24 | 1 | 0 | 0 | 0 | 1 |

25 | 1 | 0 | 0 | 0 | 0 |

26 | 1 | 0 | 0 | 0 | 0 |

27 | 1 | 0 | 0 | 0 | 0 |

28 | 1 | 0 | 0 | 0 | 0 |

29 | 1 | 0 | 0 | 0 | 0 |

30 | 1 | 0 | 0 | 0 | 0 |

31 | 1 | 0 | 0 | 0 | 0 |

Control Factors | Levels | |
---|---|---|

−1 | +1 | |

Aging Temperature (°C) | 1050 | 1250 |

Aging time (h) | 2 | 4 |

Heating Rate (°C/min) | 5 | 25 |

Cooling Rate (°C/min) | 1 | 5 |

Itinerary | Description |
---|---|

Configuration of the network | 4-27-2 |

Hidden Layer | 1 |

Hidden neurons | 27 |

Applied transfer function | “Logsig (sigmoid)” |

Training pattern count | 9 |

Testing pattern count | 9 |

Epoch count | 8000 |

(η) Factor for learning | 0.6 |

(α) Factor of momentum | 1 |

Term | Coef | SE Coef | T | P |
---|---|---|---|---|

Constant | 3,825,280 | 22,155 | 172.660 | 0.000 |

A | 134,444 | 17,603 | 7.637 | 0.000 |

B | 153,333 | 17,603 | 8.710 | 0.000 |

C | 16,667 | 17,603 | 0.947 | 0.358 |

D | 321,667 | 17,603 | 18.273 | 0.000 |

A*A | −774,773 | 46,361 | −16.712 | 0.000 |

B*B | 305,227 | 46,361 | 6.584 | 0.000 |

C*C | 75,227 | 46,361 | 1.623 | 0.124 |

D*D | 80,227 | 46,361 | 1.730 | 0.103 |

A*B | 26,250 | 18,671 | 1.406 | 0.179 |

A*C | −18,750 | 18,671 | −1.004 | 0.330 |

A*D | 53,750 | 18,671 | 2.879 | 0.011 |

B*C | −18,750 | 18,671 | −1.004 | 0.330 |

B*D | 13,750 | 18,671 | 0.736 | 0.472 |

C*D | −18,750 | 18,671 | −1.004 | 0.330 |

**A**; Aging Time (h)—

**B**; Heating Rate (°C/min)—

**C**; Cooling Rate (°C/min)—

**D**.

Source | DF | Seq SS | Adj SS | Adj MS | F | P |
---|---|---|---|---|---|---|

Regression | 14 | 4.65159 × 10^{12} | 4.65159 × 10^{12} | 3.32257 × 10^{11} | 59.57 | 0.000 |

Residual Error | 16 | 89,244,311,111 | 89,244,311,111 | 5,577,769,444 | 0.000 | |

Total | 30 | 4.74084 × 10^{12} |

Term | Coef | SE Coef | T | P |
---|---|---|---|---|

Constant | 33.8480 | 0.09255 | 365.719 | 0.000 |

A | 0.4628 | 0.07354 | 6.293 | 0.000 |

B | 0.5256 | 0.07354 | 7.147 | 0.000 |

C | 0.0567 | 0.07354 | 0.771 | 0.452 |

D | 0.8506 | 0.07354 | 11.566 | 0.000 |

A*A | −2.5590 | 0.19367 | −13.213 | 0.000 |

B*B | 1.3560 | 0.19367 | 7.002 | 0.000 |

C*C | 0.1560 | 0.19367 | 0.805 | 0.432 |

D*D | 0.5210 | 0.19367 | 2.690 | 0.016 |

A*B | 0.2075 | 0.07800 | 2.660 | 0.017 |

A*C | −0.0637 | 0.07800 | −0.817 | 0.426 |

A*D | 0.0875 | 0.07800 | 1.122 | 0.278 |

B*C | −0.0637 | 0.07800 | −0.817 | 0.426 |

B*D | −0.0225 | 0.07800 | −0.288 | 0.777 |

C*D | −0.0638 | 0.07800 | −0.817 | 0.426 |

**A**; Aging Time (h)—

**B**; Heating Rate (°C/min)—

**C**; Cooling Rate (°C/min)—

**D**.

Source | DF | Seq SS | Adj SS | Adj MS | F | P |
---|---|---|---|---|---|---|

Regression | 14 | 41.822 | 41.8222 | 2.98730 | 30.69 | 0.000 |

Residual Error | 16 | 1.5574 | 1.5574 | 0.09734 | ||

Total | 30 | 43.3796 |

**Table 14.**Electrical conductivity and thermal conductivity of Ti-6Al-4V-SiC(15 Wt.%) specimen processed under various processing conditions.

Trial No. | Electrical Conductivity (Ω^{−1} m^{−1}) | Error (%) | Thermal Conductivity (W/m·K) | Error (%) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

TDOE | RSM | BPANN | RSM | BPANN | TDOE | RSM | BPANN | RSM | BPANN | |

1 | 2,880,000 | 2,641,592 | 2,611,491 | 9.025 | 1.152 | 31.41 | 32.59844 | 33.1425 | 3.645 | 1.641 |

2 | 2,850,000 | 2,567,891 | 2,415,789 | 10.98 | 6.296 | 30.22 | 31.11954 | 30.95 | 2.89 | 0.547 |

3 | 3,840,000 | 3,769,585 | 3,825,495 | 1.867 | 1.461 | 33.95 | 34.05957 | 35.6830 | 0.321 | 4.549 |

4 | 4,180,000 | 4,305,898 | 4,413,895 | 2.923 | 2.446 | 35.46 | 36.07785 | 36.5815 | 1.712 | 1.376 |

5 | 3,640,000 | 3,812,258 | 3,764,822 | 4.518 | 1.259 | 33.41 | 33.64925 | 32.5512 | 0.711 | 3.373 |

6 | 4,260,000 | 4,393,699 | 4,452,174 | 3.042 | 1.313 | 36.15 | 37.88915 | 38.4951 | 4.59 | 1.574 |

7 | 3,590,000 | 3,745,102 | 3,862,733 | 4.141 | 3.045 | 33.46 | 33.99454 | 34.1920 | 1.572 | 0.577 |

8 | 3,390,000 | 3,508,955 | 3,605,897 | 3.390 | 2.688 | 33.49 | 33.24958 | 32.0552 | 0.723 | 3.726 |

9 | 3,460,000 | 3,577,488 | 3,498,621 | 3.284 | 2.254 | 33.51 | 31.01259 | 31.4586 | 8.052 | 1.417 |

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## Share and Cite

**MDPI and ACS Style**

Hegde, A.; Shetty, R.; Naik, N.; Murthy, B.R.N.; Nayak, M.; Kumar, M.; Shanubhogue, D.
Optimization and Prediction of Thermal Conductivity and Electrical Conductivity of Vacuum Sintered Ti-6Al-4V-SiC(15 Wt.%) Using Soft Computing Techniques. *J. Compos. Sci.* **2023**, *7*, 123.
https://doi.org/10.3390/jcs7030123

**AMA Style**

Hegde A, Shetty R, Naik N, Murthy BRN, Nayak M, Kumar M, Shanubhogue D.
Optimization and Prediction of Thermal Conductivity and Electrical Conductivity of Vacuum Sintered Ti-6Al-4V-SiC(15 Wt.%) Using Soft Computing Techniques. *Journal of Composites Science*. 2023; 7(3):123.
https://doi.org/10.3390/jcs7030123

**Chicago/Turabian Style**

Hegde, Adithya, Raviraj Shetty, Nithesh Naik, B. R. N. Murthy, Madhukar Nayak, Mohan Kumar, and Deepika Shanubhogue.
2023. "Optimization and Prediction of Thermal Conductivity and Electrical Conductivity of Vacuum Sintered Ti-6Al-4V-SiC(15 Wt.%) Using Soft Computing Techniques" *Journal of Composites Science* 7, no. 3: 123.
https://doi.org/10.3390/jcs7030123