Optimization of parameters of antimony modified carbidic austempered ductile iron (CADI) using Taguchi method

Figures & data

Table 1. source of variance and degree of freedom

Source of variance	Degree of freedom (df)
Rows	Number of Rows $-$1
Column	Number of Columns $-$1
Interaction	(Columns $-$1) (Rows $-$ 1)
Within	Number of Subject $-\mathrm{R}\mathrm{o}\mathrm{w}\mathrm{s}\times \mathrm{N}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}-1$
Columns
Total

$\bar{y}$ is the average of observed data, Sy² is the variance of y, n is the number of observations, and y is observed data

Table 2. Information on ANOVA

Source	DF	SS	MS	F-test	% Contribution
Aust. Temp. (AT)	NAT—1	SSAT	MSAT—$\frac{SSAT}{\mathrm{N}AT-1}$	FAT—$\frac{MSAT}{MSE}$	$\frac{SSAT}{SST}$ $\times$100$\mathrm{\%}$
Antimony (Sb)	Nsb—1	SSsb	MSsb—$\frac{SSsb}{nsb-1}$	Fsb—$\frac{MSsb}{MSE}$	$\frac{SSsb}{SST}$ $\times$100$\mathrm{\%}$
AT–Sb Interaction	(NAT—1) (Nsb—1)	SSATSb	MSATSb—$\frac{SS\mathrm{A}\mathrm{T}\mathrm{S}\mathrm{b}}{\left(NAT-1\right)\left(Nsb1\right)}$	FATSB—$\frac{MS\mathrm{A}\mathrm{T}\mathrm{S}\mathrm{B}}{MSE}$	$\frac{SSpv}{SST}$ $\times$100$\mathrm{\%}$
At–Sb Interaction	(NAt—1) (Nsb—1)	SSATsb	MSATsb—$\frac{SS\mathrm{A}\mathrm{T}\mathrm{s}\mathrm{b}}{\left(NAt-1\right)\left(Nsb-1\right)}$	FATsb—$\frac{MS\mathrm{A}\mathrm{T}\mathrm{s}\mathrm{b}}{MSE}$	$\frac{SS\mathrm{A}\mathrm{T}\mathrm{s}\mathrm{b}}{SST}$ $\times$100$\mathrm{\%}$
AT–At Interaction	(NAT—1) (NAt—1)	SSATAt	MSATAt—$\frac{SSATAt}{\left(T-1\right)\left(NAt1\right)}$	FATAt—$\frac{MSATAt}{MSE}$	$\frac{SSATAt}{SST}$ $\times$100$\mathrm{\%}$
Error	$e^{\ast }$	SSE	MSAT—$\frac{SSE}{e^{\ast }}$		$\frac{SSE}{SST}$ $\times$100$\mathrm{\%}$

e is total number of df – (Sum of the other df) $\left(n1\right)\left(df1+df2+df3+\dots dfm\right)$

n is total number of observations and m is the total number of sources for ANOVA calculation Dhanapal, Premkumar, and Mohamed Nazirudeen (2009).

Table 3. Conditions for interpreting the correlation coefficient (R) (Oyetunji & Barnabas, 2012)

Value of R	Interpretation
0.90–1.00	Very high correlation
0.70–0.90	High correlation
0.40–0.70	Moderate correlation
0.20–0.40	Low correlation
0.00–0.20	Slight correlation

Figure 1. Flow chart of the work approach

Table 4. Chemical composition of the produced alloys (wt. %)

No	Fe	C	Si	Mn	Cr	Ni	Cu	Mg	Sb	S	P	C.E
1	89.39	3.62	2.42	0.58	2.6	0.60	0.69	0.06	-	0.004	0.040	4.43
2	89.33	3.62	2.40	0.57	2.61	0.61	0.65	0.07	0.096	0.005	0.041	4.43
3	89.24	3.62	2.41	0.57	2.62	0.62	0.61	0.07	0.192	0.005	0.042	4.44
4	89.19	3.63	2.40	0.56	2.60	0.60	0.62	0.07	0.288	0.005	0.042	4.44
5	89.10	3.62	2.41	0.56	2.63	0.61	0.62	0.06	0.384	0.005	0.040	4.44
6	88.97	3.62	2.40	0.58	2.62	0.60	0.63	0.06	0.480	0.004	0.041	4.43

Table 5. Orthogonal array for the samples

Factors	Levels
Antimony Content (%)	0.096	0.192	0.288	0.384	0.480
Austempering Temperature, AT (°C)	300		325
Austempering Time, At (hrs)	1		3		2

Plate 1: Optical Micrographs of samples: (a) CADI without Sb showing blocky carbide, graphite and ausferrite; (b) CADI with 0.096 wt.% Sb showing less blocky carbide, graphite and ausferrite; (c) CADI with 0.192 wt.% Sb showing granular carbide, graphite and ausferrite; (d) CADI with 0.288 wt.% Sb showing more granular carbide, graphite and ausferrite; (e) CADI with 0.384 wt.% Sb showing granular carbide, graphite and ausferrite; and (f) CADI with 0.48 wt.% Sb showing cellulose carbide, graphite and ausferrite

Table 6. Signal-to-noise-ratio

						Signal-to-noise-ratio
AT (°C)	At (h)	Sb content	Hardness (HRc)	Impact toughness (Joules)	Wear resistance (cm^−2)	Hardness	Impact toughness (J)	Wear resistance (cm^−2)
300	1	0.096	49	50	556,000,000	32.2106	34.4044	179.532
300	2	0.096	44	51	529,000,000	31.6849	34.3656	174.912
300	3	0.096	43	53	815,000,000	32.5032	34.5222	176.919
325	1	0.096	32	55	1,030,000,000	32.6634	34.7112	181.321
325	2	0.096	43	56	970,000,000	32.1377	34.6724	176.7
325	3	0.096	40	57	1,060,000,000	32.956	34.829	178.708
300	1	0.192	32	48	1,980,000,000	32.0636	33.5042	186.515
300	2	0.192	42	47	1,870,000,000	31.5379	33.4654	181.894
300	3	0.192	35	49	2,210,000,000	32.3562	33.622	183.901
325	1	0.192	49	49	2,810,000,000	32.5164	33.8109	188.303
325	2	0.192	40	48	398,000,000	31.9907	33.7721	183.683
325	3	0.192	50	49	3,450,000,000	32.809	33.9287	185.69
300	1	0.288	57.6	47	283,000,000	33.0419	33.3835	179.502
300	2	0.288	32	47	257,000,000	32.5162	33.3447	174.881
300	3	0.288	51	47	1,050,000,000	33.3345	33.5014	176.888
325	1	0.288	51	48	3,740,000,000	33.4947	33.6903	181.29
325	2	0.288	35	48	2,920,000,000	32.969	33.6515	176.67
325	3	0.288	54	49	298,000,000	33.7873	33.8081	178.677
300	1	0.384	37	48	3,290,000,000	31.1758	33.623	180.811
300	2	0.384	30	48	288,000,000	30.6501	33.5842	176.19
300	3	0.384	35	49	336,000,000	31.4684	33.7408	178.197
325	1	0.384	35	50	1,450,000,000	31.6285	33.9297	182.599
325	2	0.384	51	49	1,090,000,000	31.1028	33.8909	177.979
325	3	0.384	36	50	1,220,000,000	31.9211	34.0476	179.986
300	1	0.489	45	49	724,000,000	31.6694	33.6529	173.948
300	2	0.489	30	48	670,000,000	31.1437	33.6141	169.327
300	3	0.489	43	49	747,000,000	31.962	33.7707	171.334
325	1	0.489	32	50	258,000,000	32.1221	33.9596	175.736
325	2	0.489	45	50	244,000,000	31.5964	33.9208	171.116
325	3	0.489	42	49	235,000,000	32.4147	34.0774	173.123

Table 7.: Taguchi analysis: hardness values versus austempering temperature, austempering time, and antimony content. Response table for signal-to-noise ratios larger is better

	Austemp.	Austempering	Antimony
Level	Temperature	Time	Content
1	31.95	32.26	32.36
2	32.41	31.73	32.21
3		32.55	33.19
4			31.32
5			31.82
Delta	0.45	0.82	1.87
Rank	3	2	1

Table 8. Taguchi analysis: impact toughness versus austempering temperature, austempering time, and antimony content. Response table for signal-to-noise ratios, larger is better

	Austemp.	Austempering	Antimony
Level	Temperature	Time	Content
1	33.74	33.87	34.58
2	34.05	33.83	33.68
3		33.98	33.56
4			33.80
5			33.83
Delta	0.31	0.16	1.02
Rank	2	3	1

Table 9. Taguchi analysis: wear resistance versus austempering temperature, austempering time, and antimony content. Response table for signal-to-noise ratios, larger is better

	Austemp.	Austempering	Antimony
Level	Temperature	Time	Content
1	177.7	181.0	178.0
2	179.4	176.3	185.0
3		178.3	178.0
4			179.3
5			172.4
Delta	1.8	4.6	12.6
Rank	3	2	1

Table 10. Factors of CADI production information

Factor	Type	Levels	Values
Austemp. temperature	Fixed	2	300, 325
Austempering time	Fixed	3	1, 2, 3
Antimony content	Fixed	5	0.096, 0.192, 0.288, 0.384, 0.489

Table 11. Analysis of variance for response

Source	DF	Adj SS	Adj MS	F-test	F-Value (at p ‹ 0.05)
Austemp. temperature	1	19.653	19.6532	32.92	4.30
Austempering time	2	4.075	2.0376	3.41	3.44
Antimony content	4	101.195	25.2989	42.38	2.82
Residual	22	13.133	0.5969
Total	29	138.057

Table 12. Model summary for transformed response

S	R-sq	R-sq (adj)	R-sq (pred)
0.772623	90.49%	87.46%	82.31%

Table 13. General linear model: wear resistance versus austempering time, antimony content. Method factor information

Factor	Type	Levels	Values
Austempering time	Fixed	3	1, 2, 3
Antimony content	Fixed	5	0.096, 0.192, 0.288, 0.384, 0.480

Table 14. Analysis of variance for response

Source	DF	Seq SS	Contribution	Adj SS	Adj MS	F- test	F-Value
Austempering time	2	0.8895	6.42%	0.8895	0.4447	0.60	4.46
Antimony content	4	7.0720	51.05%	7.0720	1.7680	2.40	3.84
Residual	8	5.8923	42.53%	5.8923	0.7365
Total	14	13.8538	100.00%

General Linear Model: Hardness Values (HRc) versus Austempering Time, Antimony Content at 325°C

Table 15. General linear model: Hardness versus austempering time, antimony content. Factor information

Factor	Type	Levels	Values
Austempering Time	Fixed	3	1, 2, 3
Antimony content	Fixed	5	0.096, 0.192, 0.288, 0.384, 0.489

Table 16. Analysis of variance for transformed response

Source	DF	Seq SS	Contribution	Adj SS	Adj MS	F-test	F-Value
Austempering Time	2	0.8895	6.42%	0.8895	0.4447	0.60	4.46
Antimony content	4	7.0720	51.05%	7.0720	1.7680	2.40	3.84
Error	8	5.8923	42.53%	5.8923	0.7365
Total	14	13.8538	100.00%

Austempering Temperature, At of 300°C

Table 17. General linear model: Impact toughness values (J) versus austempering time, antimony content. Factor information

Factor	Type	Levels	Values
Austempering Time	Fixed	3	1, 2, 3
Antimony Content	Fixed	5	0.096, 0.192, 0.288, 0.384, 0.480

Table 18. Analysis of variance for impact toughness value

Source	DF	Seq SS	Contribution	Adj SS	Adj MS	F-test	F-Value
Austempering Time	2	0.1166	20.30%	0.1166	0.05830	1.89	4.46
Antimony content	4	0.2114	36.80%	0.2114	0.05284	1.72	3.84
Residual	8	0.2464	42.89%	0.2464	0.03079
Total	14	0.5743	100.00%

Table 19. Fits and diagnostics for all observations. Original response

	Impact
	Toughness
Obs	(Joules)	Fit	95% CI
1	55.00	55.94	(54.79, 57.12)
2	56.00	55.69	(54.54, 56.86)
3	57.00	56.35	(55.19, 57.53)
4	49.00	48.62	(47.62, 49.64)
5	48.00	48.40	(47.40, 49.42)
6	49.00	48.97	(47.97, 50.00)
7	48.00	48.29	(47.29, 49.30)
8	48.00	48.07	(47.08, 49.08)
9	49.00	48.64	(47.64, 49.66)
10	50.00	49.62	(48.60, 50.66)
11	49.00	49.39	(48.38, 50.43)
12	50.00	49.98	(48.95, 51.03)
13	50.00	49.62	(48.60, 50.66)
14	50.00	49.39	(48.38, 50.43)
15	49.00	49.98	(48.95, 51.03)

Figure 2. Interaction plot for hardness values (HRc) of the antimony modified CADI

Figure 3. Interaction plot for wear resistance of the antimony modified CADI

Figure 4. Interaction plot for impact toughness of the antimony modified CADI

Dhanapal, P., Premkumar, R., & Mohamed Nazirudeen, S. S. (2009). A study on the influence of heat treatment on the wear resistance of alloyed austempered ductile iron. Indian Foundry Journal, 55(3), 32–38.

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Oyetunji, A., & Barnabas, A. A. (2012). Development of martempered ductile iron by step -quenching method in warm water. Journal of Emerging Trends in Engineering and Applied Sciences, 3(3), 470–474.

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