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

Abstract

In this work, optimization of hardness, wear and impact strength of antimony modified CADI using Taguchi method was carried out. Carbidic Austempered Ductile Iron is a type of wear resistant ferrous metal having alloyed carbides inside an ausferritic matrix with an evidence of few graphite nodules in most cases. The alloy carbides which are mostly of primary coarse carbides are detrimental to its mechanical properties. The need for improvement of these mechanical properties (hardness, wear, and impact strength) in CADI has led to the usage of micro-addition of antimony to modify the carbides size which has given birth to Antimony Modified CADI. In a bid to get the optimum production factors on the mechanical properties, signal-to-noise (S/N) ratio was computed based on the design of experiments and the Straight graph of Minitab 17. The analysis of variance was computed to know the quantities of the contribution of factors on each mechanical property including its significance. From Taguchi analysis of the hardness, wear resistance and impact toughness, the signal-to-noise ratio using larger is better revealed that antimony content in the antimony modified CADI is the most important factor, followed by the austempering time in terms of improving the hardness and wear resistance of this material, while in the case of impact toughness, antimony content and austempering temperature are the most important factors, and that increasing these parameters would greatly improve the impact toughness of this CADI. The experimental values compared suitably with the results from Taguchi.

Keywords:

• Antimony
• carbidic ADI
• wear resistance
• impact toughness
• hardness
• Taguchi method

PUBLIC INTEREST STATEMENT

The Agricultural-industrial sector has discovered a material (Carbidic austempered ductile iron) that is economical and technically efficient. This material can replace Hadfield steel which is usually used for making agricultural implement like; cultivator, ploughshare and soil tiller. As a result of the difficulty in producing this hadfield steel, that is used in making this agricultural implement, and the high cost procuring this hadfield steel, the new material (carbidic austempered ductile iron) has effectively proven its potential for been used as a material for producing agricultural implement, except that it is brittle compared to hadfield steel. To achieve improvement in the properties of this material, an optimization tool like Taguchi modeling tool help in upgrading the property of this material mathematically. The essence of this optimization tool is to reduce design error, reduce time wastage, reduce the cost of producing this material and to get the maximum obtainable improvement of this new material.

1. Introduction

Optimization is the main step to improving the performance and finding the optimal process parameters of products based on the responses involve. There are several optimization tools such as the gradient search method (GSM), the finite element method (FEM), neural network method and Taguchi method. Taguchi method is a problem-solving tool which is capable of improving the performance of the product, process design and system in a short development cycle with reduced cost. This method combines the experimental and analytical concepts to determine the most influential parameter on the result response for the significant improvement in the overall performance. To solve this task, the Taguchi method uses a special design of orthogonal array to study the entire process parameter space with a small number of experiments. Many of the researchers have attempted to analyze and optimized single and multi-performance responses of foundry process using Taguchi methodology. Among them are; multiple progressive tools by Surace (2010) and utility concept by Sun, Hu, and Chen (2008). The effect of factors on the responses were separately studied by Muhammed (2009); Jadoun, Kumar, and Mishra (2009); Dhanapal and Muhammed (2010). Carbidic Austempered Ductile Iron (CADI) which is a wear resistant austempered ductile iron with alloyed carbide in its matrix has been found to be a very useful material for the production of Agricultural implement (ploughshare). Austempered ductile iron (ADI) is known for its high tensile strength, ductility, wear resistance and toughness qualifying it as a possible replacement for forged steels in many areas of applications Seshan, (1998) and Hayrynen (1995). High toughness of austempered ductile iron is owing to ausferrite matrix which is produced by the austempering process. The high carbon austenite presents in the ausferrite matrix of ADI has a tendency to cause strain hardening effect on its surface. This gives this material high wear resistance Trudel and Gagne (1997). This material is used as agricultural implements Brezina, Filipek, and Senberger (2004), Barnabas, Oyetunji, Seidu, and Adediran (2019). Wear resistance of CADI is better compared than that of forged steel. As a result of this quality, the CADI can stand in for forged steels Zimba, Simbi, and Navara (2003). Alloying elements like copper, nickel and molybdenum improve mechanical properties of ADI Batra, Ray, and Prabhakar (2004); Eric, Rajnovic, Sidjanin, Zec, and Jovanovic (2005); and Rao and Putatunda (2003).

Carbides are the known strong wear resistance compounds which can be produced easily. The availability of carbides in the ausferrite matrix can reduce the toughness of cast iron. The available literature on CADI material shows its application, microstructure and the abrasive resistance of CADI Rimmer (2006); Hayrynen and Brandenberg (2003) and Keough and Hayrynen (2000). The literature Laino, Sikora, and Dommarco (2008) shows the unified effect of high cooling rate with copper chills and the use of carbide stabilizing elements. Carbide stabilizing agents (Mn, Mo) possess the ability to separate into the grain boundaries, which decreases the mechanical characteristics of the ADI Hayryen, Brandenberg, and Kough (2002). The analysis of variance looks at the variability, it includes the calculation of many measures of variability. The concept underlying the analysis of variance is that the total variation of scores can be given to two sources – variance between groups (caused by the treatment), and variance within the groups (error variance). As with t-test, a ratio is formed (the F ratio) with group differences as the number for variance between groups and an error term as the denominator (variance within groups). If at the end of a study, the treatment variance is larger than the error variance, a significant F ratio results, the null hypothesis is rejected. If on the other hand, the treatment variance and error variance are essentially the same, the resulting F ratio is not significant and the null hypothesis is not rejected. The greater the difference, the larger the F ratio. There are two main types of ANOVA: One-way ANOVA and Two-way ANOVA.

1.1. Two-way analysis of variance

This is a step that determines the effect of two independent variables simultaneously. This helps in reducing cost by allowing you to look at two things for the price of one. It also permits one to know whether the two independent variables interact with respect to the effect of the dependent variables. Table 1 shows the source of variance and degree of freedom formulae used in the work. While Table 2 shows the formulae for calculating the analysis of variance (ANOVA). The condition for interpreting the correlation coefficient is as presented in Table 3.

(1) $\mathrm{S}{\mathrm{S}}_{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=\sum X^2=\frac{\sum X^2}{N}$(1)

(2) $\text{mathop {{rm{S}}{{rm{S}}\_{{rm{Row}}}} = ,sum }nolimits left({mathop sum nolimits {{{X^2}} over N}} right){ - \_ }{left({{{mathop sum nolimits X} over N}} right)^2}}$(2)

(3) $\mathrm{S}{\mathrm{S}}_{\mathrm{C}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n}}=\sum \left(\frac{\sum \left(X\right)2}{Column}\right)-{\frac{\sum \left(X\right)}{N}}^2$(3)

(4) $\mathrm{S}{\mathrm{S}}_{\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}=}\mathrm{S}{\mathrm{S}}_{\mathrm{G}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{s}}-\mathrm{S}{\mathrm{S}}_{\mathrm{C}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n}}+\mathrm{S}{\mathrm{S}}_{\mathrm{R}\mathrm{o}\mathrm{w}}$(4)

(5) $\mathrm{S}{\mathrm{S}}_{\mathrm{G}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}}=\sum \left(\frac{\sum \left(X\right)2}{nGroup}\right)-{\left(\frac{{\sum }^X}{Ntotal}\right)}^2$(5)

(6) $\mathrm{S}{\mathrm{S}}_{\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{i}\mathrm{n}}=\mathrm{S}{\mathrm{S}}_{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}-(\mathrm{S}\mathrm{S}\mathrm{R}\mathrm{o}\mathrm{w}+\mathrm{S}{\mathrm{S}}_{\mathrm{C}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n}+}\mathrm{S}{\mathrm{S}}_{\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}})$(6)

(7) $\mathrm{C}\mathrm{F}=\frac{{\left({\sum }_{i=1}^p{\sum }_{j=1}^v{\sum }_{k=1}^{t}Xijk\right)}^2}{n}$(7)

(8) $\mathrm{S}{\mathrm{S}}_{\mathrm{T}}={\sum }_{i=1}^p{\sum }_{j=1}^v{\sum }_{k=1}^t{\left(Xijk\right)}^2-CF$(8)

(9) $\mathrm{S}{\mathrm{S}}_{\mathrm{A}\mathrm{T}}={\sum }_{i=1}^{AT}\frac{({\sum }_{j=1}^v{\sum }_{k=1}^{t}Xijk)2}{nAt\times nsb}-\mathrm{C}\mathrm{F}$(9)

(10) $\mathrm{S}{\mathrm{S}}_{\mathrm{s}\mathrm{b}}={\sum }_{j=1}^{sb}\frac{\left({\sum }_{i=1}^p{\sum }_{k=1}^{t}Xijk\right)2}{nAT\times nAt}-\mathrm{C}\mathrm{F}$(10)

(11) $\mathrm{S}{\mathrm{S}}_{\mathrm{A}\mathrm{T}}\mathrm{s}\mathrm{b}={\sum }_{i=1}^{AT}{\sum }_{j=1}^{sb}\frac{({\sum }_{k=1}^{At}Xijk)2}{nAt}-SSAT-SSsb-CF$(11)

(12) $\mathrm{S}\mathrm{S}\mathrm{s}{\mathrm{b}}_{\mathrm{A}}\mathrm{t}={\sum }_{j=1}^{sb}{\sum }_{k=1}^{At}\frac{\left({\sum }_{i=1}^{AT}Xijk\right)2}{nAT}-SSsb-SSAt-CF$(12)

13 $\mathrm{S}\mathrm{S}\mathrm{E}=\mathrm{S}\mathrm{S}\mathrm{T}-(\mathrm{S}\mathrm{S}\mathrm{s}\mathrm{b}+\mathrm{S}{\mathrm{S}}_{\mathrm{A}\mathrm{T}}+\mathrm{S}{\mathrm{S}}_{\mathrm{A}\mathrm{t}})$13

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

1.2. Signal-to-noise (S/N) ratio

Signal means the desirable value while the noise represents the undesirable value. Therefore, the S/N ratio consolidates many repetitions into one value, which reflects the amount of variation present. Signal-to-noise (S/N) ratio is used to measure the amount of deviation from the desired value. The lower-the-better (LB), the higher-the-better (HB), and the nominal-the-better (NB) are the three types used to analyze the S/N ratio.

The equations associated with signal-to-noise ratios are stated as follows:

Smaller—the—better: S/Ns = —10$log\left(\frac{1}{n}\left({\sum }_{i=1}^n{y}^2\right)\right)$

Larger—the—better: S/N_L = —10$log(\frac{1}{n}({\sum }_{i=1}^n\frac{1}{y2}$))

Nominal—the—best: S/N_T = 10log ($\frac{\bar{y}}{s{y}^2}$)

2. Materials and methods

The flow chart showing the work approach is as presented in Figure 1.

Figure 1. Flow chart of the work approach

2.1. Design of experiment

Two major steps were used in the production of the antimony modified carbidic austempered ductile iron, one of these steps is the casting, while another step is austempering heat treatment operation. In terms of the heat treatment process; austenitization temperature, austenitization time, austempering temperature and austempering time are the controllable parameters. Three major factors which have more effects on the production of the CADI were considered: antimony content, austempering temperature and austempering time. Five levels of the antimony content, two levels of the austempering temperature and three levels of austempering time were selected (shown in Table 5) as factor levels.

2.2. Foundry considerations for the production of CADI

The composition of the antimony modified carbidic ductile iron (CDI) used, was of hypereutectic composition, where the carbon and silicon contents are 3.6 and 2.4, respectively [C.E = 4.44]. Grey cast iron scraps were used as raw material been charged and melted in an indirect electric arc furnace, computed amount of heated ferro-chrome was added to the melt to increase the chromium level in the pouring ladle and also to get alloyed carbides in the melt. The melt was heated up to 1400°C. The melt was then tapped into ladle, the magnesium alloy consisting of Mg-Fe-Si with 9 wt. % of Mg was introduced into the melt for nodularization, and later inoculated with FeSi (75 wt. % Si), varying amount of pulverized antimony (0.3 μm) were added. Sand mold was prepared using silica, bentonite and water. The composition of the samples was analyzed using spectrometer and the results are shown in Table 4.

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

2.3. The austempering process

The produced antimony modified CDI was heated to the temperature of 910°C (austenitization), followed by cooling in a salt bath (Sodium and Potassium Nitrates mix) that is already heated to austempering temperatures of 300°C, and 325°C, respectively. Salt bath has the ability to share the heat uniformly on the samples compared to the atmospheric heating (Dhanapal et al., 2009). The austempering time was varied between 1 and 3 h in a time interval of 1 h. After austempering, the specimens were cooled to room temperature in air.

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

2.4. Characterization of the samples

2.4.1. Microstructure examination

The chemical compositions of the alloys were determined using Spark Emission Optic Spectrometer of model Spectro-pro MAXx-LMM06 with a DV6 excitation source. The surface of the test piece was ground to ensure flatness and then, mounted on the sparking point of the spectrometer. The operation was performed for a period of 30–40 s. Then, the chemical composition of the specimen was displayed on the monitor of the machine (Ashby, Shercliffe, & Cebon, 2007).

2.4.2. Hardness

The hardness test for both as-cast and the heat-treated samples was conducted using Digital Rockwell Hardness Tester Scale C of model Indentec, following standard test method for Rockwell hardness of metallic materials (ASTM E18-19). Three points hardness was measured and the average of the three measurements was taken (Callister, 2000).

2.4.3. Wear

Wear test was carried out using Taber’s method. This was done by attaching each sample to a rotating disc of 25 cm radius and pressure of a specified load was applied according to Friedrich, Edwald, and Martin (2009). The samples used were 12 mm diameter by 40 mm long. The grit used was 220 rough with a revolution of 150 rpm. Exposing time for each sample on the wear test machine was 5 min, density of the CADI was taken to be 7.86 g/cm³. After running through a fixed distance, the samples were removed, the weight loss due to wear was measured. Also, wear rate and wear resistance were recorded in line with the work of Marinov (2007).

3. Orthogonal array

3.1. Taguchi orthogonal array design

The Taguchi method provides a layout of the experimental conditions using specially designed tables called orthogonal array (OA). The choice of the orthogonal array depends upon the degrees of freedom. The factors and levels obtained for this design are L₃₀(5¹ × 3¹ × 2¹) as shown in Table 5. This work has an array of 30 rows, each row represents an experiment, and the columns were assigned to the factor levels. The design of experiments was made of 30 tests in which the first column was assigned to antimony content (Sb), the second column was assigned to austempering temperature (AT) and the third column for the austempering time (At).

Factors and Levels = L₃₀ (5¹ × 2¹ × 3¹)

3.2. Signal-to-noise ratio analysis

Table 6, shows the signal-to-noise ratio for hardness, impact toughness and wear resistance for the produced CADI. Experiment number 18, corresponds to CADI sample with 0.288 wt.% Sb that was subjected to austempering temperature of 325°C held for 3 h gave the highest signal-to-noise ratio of 33.7873 in terms of hardness values, while experiment number 4 corresponding to CADI sample of antimony content of 0.096 wt. % austempered at the temperature of 325°C and held for 3 h has signal-to-noise ratio of 34.829 in terms of impact toughness and for the wear resistance signal-to-noise ratio, experiment 10 gives the highest value of 188.303 as shown in Table 6 (Nalbant, Gokkaya, & Sur, 2007).

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

3.3. Data analysis

The average effects of the factors were calculated and shown in Tables 7, 8 and 9. These Tables includes the ranks based on the delta statistics, which compare the relative value of the effects. It is the difference between the highest and the lowest averages for the factor chosen. Antimony content appears as the first controlling factor for all the responses. The Taguchi analysis of hardness value versus austempering temperature, austempering time and antimony content reveals that delta statistics of the antimony content is 1.87, that of austempering temperature is 0.45 and delta statistics of austempering time is 0.82. This shows that the most important factor for hardness property of the CADI is antimony content, followed by austempering time and the austempering temperature is the least factor (Table 10). In case of the impact toughness of the CADI, the delta statistics of the antimony content is 1.02, austempering temperature has a value of 0.31, while that of austempering time is 0.16. This means that the most important factor for the CADI is antimony, followed by austempering temperature and the least in this case is austempering time. For the wear resistance, the delta statistics of the antimony content is 12.6, that of the austempering temperature is 1.8, while that of austempering time is 4.6, this implies that the most important factor here is antimony content, followed by austempering time and the least factor here is austempering temperature, this is in conformity with Dhanapal and Muhammed (2010).

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

3.4. Analysis of variance (ANOVA)

F-ratio is the ratio between variance due to the effect of the factor and variance due to the error term. This ratio was used to measure the significance of factor at the desired level. F-statistics of factors – antimony content and austempering temperature are significant up to 95% confidence in all the responses. From Table 7, the percentage contribution of antimony content to the antimony modified CADI is higher in both the impact toughness, hardness and wear resistance values. A maximum value of 96%, 57% and 51% contributions of antimony content were gotten for the impact toughness, hardness and wear resistance, respectively, from the ANOVA tables (Tables 11-18). This shows that antimony content greatly influenced the impact toughness, and moderately influenced the hardness and wear resistance of the Sb-modified CADI under this experimental condition. Table 10 shows the variation in CADI production information. Also, the ANOVA data is as presented in Table 11; showing values for impact toughness of antimony modified CADI, the F critical values from the F distribution table with one, two and four degrees of freedom in the numerator and 22 degrees of freedom in the denominator are 4.30, 3.44 and 2.82, respectively; while their F-test from Table 11, are 32.92, 3.41 and 42.38, respectively. Comparing their F-critical values obtained from F-distribution table and their F-test values obtained from the ANOVA together, at a confidence interval of 0.05. The F-test values of antimony content and austempering temperature are far higher than their F-critical values, while that of austempering time are almost the same. This implies that antimony content and austempering temperature highly influenced the impact toughness of the Sb-modified CADI. Table 13 & 14 shows the factors of production of CADI for the ANOVA for wear resistance values. Table 15 shows the factors of production of CADI for the ANOVA hardness value in Table 16. The ANOVA Table 16 for hardness and wear resistance of CADI, the F-critical values for all the factors (antimony content, and austempering time) at both austempering temperature of 300°C and 325°C are higher than their F-test values meaning no significant influence of these factors on hardness and wear resistance of the antimony modified CADI in accordance with Man, Ng, Lawrence, and Yue (2009). The factors of production of CADI for the ANOVA for impact toughness values are as presented in Table 17, while the ANOVA is shown in Table 18.

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

4. Model equation for the impact toughness of the produced CADI

The model equation for quick estimation of impact toughness value of the produced CADI is as expressed in equation (14) with the correlation value of 0.91, which can be interpreted as very highly correlated with reference to Table 3 (Oyetunji & Barnabas, 2012).

4.1. Model equation

14 $\mathrm{I}\mathrm{m}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{T}\mathrm{o}\mathrm{u}\mathrm{g}\mathrm{h}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}\left(\mathrm{J}\mathrm{o}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\right)=28.80+0.0720\mathrm{A}\mathrm{T}+0.350\mathrm{A}\mathrm{t}-8.40\mathrm{S}\mathrm{b}$14

4.2. Model validation of the impact toughness values of the produced CADI

Table 19 shows the validation table that compares the experimental data with the theoretical data of the produced CADI. Judging from values shown in Table 19, experimental data favorably compare with the calculated values of the impact toughness of the CADI.

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)

4.3. Interaction plots for the factors

At the initial stage of the plot, it steeps down from 1 to 2 h and steeps up to 3 h. Increase of austempering time led to increase in the hardness value of the antimony modified CADI. The line of austempering temperature is not steep when compared to other factors; this shows a less effect on the hardness value of the CADI. Comparing the three factors the antimony content line steeps more; which means this affects the hardness of the antimony modified CADI most.

Among the plots in Figures 2, 3 and 4, the gradients of the antimony content plot had the highest value. The same trend is followed in all the graphs. The gradient of austempering temperature line was less when compared with the chromium content. So, the next controllable parameter is austempering temperature and the least is the austempering time.

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

5. Conclusions

The factor that affected the performance of the antimony modified CADI has been determined using Taguchi analysis method. Based on the fact that there is a need for optimizing the three responses (hardness values, impact toughness values and wear resistance values), larger is better (LB) signal-to-noise ratio was applied in this study. Antimony content in the CADI was the most significant factor for all the responses. In terms of hardness value, antimony content and austempering time were the most important factors, while in terms of impact toughness, austempering temperature and antimony content were the most important factors. Regarding the wear resistance of the CADI, the most important factors are the antimony content, the austempering temperature and austempering time have nearly equal contribution to this property (wear resistance).

Acknowledgements

Authors acknowledge the valuable contributions of anonymous reviewers towards this work. AAA appreciates the support from Landmark University Centre for Research, Innovation and Development (LUCRID) towards this work.

Additional information

Funding

The authors received no direct funding for this research.

Notes on contributors

Abel A. Barnabas

Abel A. Barnabas is a Principal technologist in the Department of Metallurgical and Materials Engineering, Federal University of Technology Akure. His research interest has been modelling and simulation, cast irons improvement, corrosion and design and fabrication.

A. Oyetunji

A. Oyetunji has been working as Associate Professor in the Department of Metallurgical and Materials Engineering, Federal University of Technology Akure. His interest is mechanical/production engineering (Cast-irons development, modelling and simulation, design and fabrication of metallurgical equipment).

S. O. Seidu

S. O. Seidu Is a Senior Lecturer in the Department of Metallurgical and Materials Engineering, Federal University of Technology Akure. His interest has also been cast-irons production, modelling and simulation.

Adeolu A. Adediran

Adeolu A. Adediran is a Lecturer in the Department of Mechanical Engineering, Landmark University, Omu-Aran, Kwara State. His research interest evolves around mechanical behaviour of materials under stress, harsh environments, contact, and vibrations. Physical metallurgy, composite design and modelling. He has supervised under graduates students and published both in local, international journals and conference proceedings.