Materials Science and Engineering A 393 (2005) 310–314

On-line prediction of carbon equivalent on high-nickelaustenitic ductile iron

Qin Hua∗, Yuhui Zhang, Yongshen Yan

Department of Material Science and Engineering, Shanghai University, Shanghai 200072, People’s Republic of China

Received 14 July 2004; accepted 25 October 2004

Abstract

In this paper, experiments have been made on high-nickel ductile iron for controlling the property by the computer-aided thermal analysissystem. The experimental results have been analyzed with statistics and applied to on-line predicting and controlling carbon equivalent,which obtained satisfying result. The experiments show that the relationship between the carbon equivalent of high-nickel ductile iron and itsliquidus temperature is linear, which can be expressed as: CEL = 15.7826− 0.0096575×TL. In order to ensure the tensile strength greater than400 MPa with the probability up to 99%, the liquidus temperature of high-nickel austenitic ductile iron must be in the range of [1203–1226◦C].©

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2004 Elsevier B.V. All rights reserved.

eywords:Carbon equivalent; High-nickel ductile iron; On-line prediction; Cooling curve

. Introduction

Despite its cost, high-nickel austenitic ductile iron is one ofhe most widely utilized materials in corrosive environmentsue to its excellent heat and corrosive resistance[1]. An ab-ormal type of graphite may occur in high-nickel austeniticuctile iron with nickel contents ranging from 13 to 37%.his type of graphite forms as fine flake-like chunks in theost slowly cooled portions of casting. It was reported that

he carbon, silicon and nickel contents in austenitic ductileron are adjusted according to the formula:[2].

TC%+ 0.2 Si%+ 0.06 Ni% ≤ 4.4

(TC% = total carbon %)

If not, the presence of chuck graphite can be detectedn many cases. According to ANSI/ASTM A439–89, D5-Sigh-nickel austenitic ductile iron contains: C%≤ 2.30; Si%.90–5.00; Ni% 34.0–37.0; the left-side value of formula isasily over 4.4. The lower the carbon content, the longer is the

dendrite arm and castings will exist much shrinkage[3]. So,it is important to control the level of carbon equivalent forhigh quality of high-nickel austenitic ductile iron casting

The thermal analysis used to study Mg-treated nlar graphite iron that can be traced to the early 1970s[4].Computer-aided thermal analysis system can provide imation about the composition of alloy and determine deof modification and grain refining on aluminum alloy agraphite morphology on cast iron[5,6].

The main objective of the research effort presented inpaper has been to set up the relationship between socation model and carbon equivalent, in order to controcomposition and property of high-nickel austenitic duciron castings.

2. Experimental procedures

The composition of metal charge was C%: 1.5–2.0, S4.5–5.0, Mn%: 0.15–0.20, Ni%: 34.0–37.0, Cr%: 1.6–P%≤ 0.02, S≤ 0.02, which was melted by coreless ind

∗ Corresponding author.E-mail address:qhua@mail.shu.edu.cn (Q. Hua).

tion furnace of 150 kg capacity. The melt was superheatedat 1600–1620◦C. After superheating the melt was treated inthe ladle with nodulizing alloys (magnesium–nickel ferrosil-

921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved.

oi:10.1016/j.msea.2004.10.029

Q. Hua et al. / Materials Science and Engineering A 393 (2005) 310–314 311

Fig. 1. Structure of thermal analysis system.

icon) by the trigger method. After the reaction was completedand slagged off, post inoculation was performed with 75%ferrosilicon at 1530–1550◦C.

The shell cup of 50 mm in diameter and 60 mm in height,into which a type of Rt–Rh thermocouple was inserted andpoured and a cooling curve was recorded by computer-aidedanalysis system (Fig. 1). At the same time other samples werepoured for microstructure and mechanical property.

3. Experimental result and discussion

3.1. Typical thermal analysis curve of high-nickelaustenitic ductile iron

Fig. 2shows a cooling curve, a first-derivative curve alsocalled cooling rate curve and a second-derivative curve alsocalled cooling acceleration curve, which contain a great dealof information about solidification of cast iron. Two platformsat the cooling curve,TL (temperature of liquidus arrest) andTEU (temperature of eutectic undercooling), are widely ap-plied at pouring station for quality control[7]. Two peaksat the first-derivative curve, which are called austenite peakand eutectic peak, can be used to calculate the amount ofaustenite and eutectic[8]. Though the cooling acceleration

curve was much undulant, it may help to determine the criticalpoint.

3.2. The effect of carbon equivalent on the character ofcooling curve

As known to all, cast iron with different carbon equiv-alent has a different form of cooling curve. In general, thelower of carbon equivalent the higher the temperature ofaustenite arrest and the lower eutectic action, the same resultalso take place in high-nickel austenitic ductile iron shown inFig. 3.The carbon equivalent of high-nickel austenitic ductileiron can be calculated as the following formula:[9]

CEL = C%+ 0.33(%Si)+ 0.047(Ni%)

−0.0055(%Ni)(%Si)

In this paper, the carbon equivalent was also calculated asthe formula and the data inTable A.1were the result of thisexperiment (seeAppendix A).

3.3. Linear regression

Suppose that the relationship between carbon equivalentand liquidus temperature is linear, by the least squares method

therma

Fig. 2. Typical l analysis curves.

312 Q. Hua et al. / Materials Science and Engineering A 393 (2005) 310–314

Fig. 3. Cooling curves of different carbon equivalent.

a regression linear formula as following is derived from thedata ofTable A.2(seeAppendix A).

CEL = A + B × TL

where

B =∑27

i=1Sxy∑27i=1Sxx

= −9.6575× 10−3

Sxy = (TLi − TL)(CELi − CEL)

Sxx = (TL − TL)2

A = CEL − B × TL = 15.7826

Thus, the first linear regression formula can be described as:

CEL = 15.7826− 0.0096575× TL

In Fig. 4, its shape is shown and the points are the data of thisexperiment.

ature.

3.4. Significant test

According to the theory of statistics, if

B

σ

√Sxx > tα/2(n − 2)

the linear regression is significant, where:

σ =√

Qe/n − 2, a variance of point estimation;

Qe =n∑

i=1

(CEL − CEL)2 − β2 ×

n∑i=1

(TL − TL)2,

a residual sum of squares;

n, times for experiment;tα/2(n− 2), Student’s distribution withn degrees of free-

dom against (1− α), which is a confidence level.Thus,

σ =√

Qe/n − 2 = 3.0106× 10−2,

regarded as the error of carbon equivalent

So,

B

σ

√Sxx = 25.656> tα/2(n − 2) = 2.787

I ence.T ilitypi

3

kela minea liq-u b-ai

P

w

δ

C

I r-ap %.

C

Fig. 4. The regression line for carbon equivalent and liquidus temper

t is clear that the linear regression is considerable confidhetα/2(n − 2) can be resulted from the table of probaboints oft distribution[10] and the confidence level (1− α)

s 0.99.

.5. Carbon equivalent predicting and controlling

In order to predict the carbon equivalent of high-nicustenitic ductile iron accurately, it is necessary to deterreasonable interval of carbon equivalent for a certain

idus temperature,TL0. According to statistical law, the probility of coverage of carbon equivalent against certainTL0

s as follows:

{CEL − δ(TL0) < CEL0 < CEL + δ(TL0)} = 1 − α;

here

(TL0) = tα/2(n − 2)σ

√1 + 1

n+ (TL0 − TL)2

Sxx

;

EL = A + B × TL0.

f 1 − α = 0.99 and 1190◦C <TL0 < 1240◦C, then the covege of CEL0 is shown inFig. 5. WhenTL0 < 1199◦C therobability of carbon equivalent within [4.11, 4.29] is 99

Because,

EL0 = A + B × TL0 ± tα/2(n − 2)σ

×√

1 + 1

n+ (TL0 − TL)2

Sxx

,

Q. Hua et al. / Materials Science and Engineering A 393 (2005) 310–314 313

Fig. 5. Predicting range of carbon equivalent.

If the value ofTL0 is very close toTL0 andn is biggerenough, then√

1 + 1

n+ (TL0 − TL)2

Sxx

≈ 1;

Thus,

CEL0 = A + B × TL0 ± tα/2(n − 2)σ.

In order to guarantee the tensile strength of casting is greaterthan 400 MPa, the carbon equivalent must be controlled in-side [3.86, 4.25%], since the relationship between carbonequivalent and tensile strength is shown asFig. 6 in this ex-periment.

In order to ensure the carbon equivalent within [3.86,4.25%], an interval of liquidus temperature must be deter-mined, so liquidus temperature is controlled inside [TL1,TL2].

Thus,

TL1 = CEL1 − A + tα/2(n − 2)σ/B = 1203

TL2 = CEL2 − A − tα/2(n − 2)σ/B = 1226

here

CEL1 = 3.86% CEL2 = 4.25%.

If the range of liquidus temperature is within [1203–1226◦C],t that

Fig. 6. The relationship between carbon equivalent and tensile strength.

is to say, the tensile strength of high-nickel ductile cast ironis greater than 400 MPa with the probability up to 99%.

4. Conclusions

(1) It is obvious that the relationship between the carbonequivalent of high-nickel ductile iron and its liquidustemperature is linear, which can be expressed as: CEL=15.7826− 0.0096575× TL.

(2) In order to ensure the tensile strength greater than400 MPa with the probability up to 99%, the liq-uidus temperature must be inside the range of [1203–1226◦C].

(3) By the computer-aided thermal analysis system on-lineprediction of carbon equivalent on high-nickel ductileiron is available, the predicting precision of carbon equiv-alent is within 3.01%.

Acknowledgments

The author is grateful to Professor Zhenghua Zhu andZhenghua Pang of Shanghai University, for their encourage-ment and suggestions over the years on the thermal analysisi iminW of-f

he carbon equivalent is certainly inside [3.86, 4.25%],

n the foundry. Much appreciation is also expressed to Yang, Dewei Yao, Gouhua Cai and Liuqian Jiang, who

ered great help in this experiment.

314 Q. Hua et al. / Materials Science and Engineering A 393 (2005) 310–314

Appendix A

SeeTables A.1 and A.2.

Table A.1Composition, carbon equivalent and liquidus temperature

No. of furnace C (%) Si (%) Ni (%) CEL TL

S1 1.60 4.87 34.0 3.89 1234S2 1.77 4.93 34.2 4.08 1211S3 1.57 5.26 38.6 4.00 1218S4 1.50 4.40 34.9 3.75 1245S5 1.41 4.46 34.9 3.67 1250S6 1.48 4.97 35.3 3.81 1236S7 1.73 3.89 36.0 3.94 1230S8 1.54 4.98 35.0 3.87 1234S9 1.97 4.78 34.7 4.27 1187S10 1.78 4.98 34.6 4.10 1209S11 1.91 4.70 35.2 4.21 1198S12 1.82 5.01 34.2 4.14 1209S13 1.53 5.01 36.8 3.90 1229S14 1.80 4.75 34.9 4.10 1208S15 1.90 4.93 35.1 4.22 1199S16 1.81 4.96 34.6 4.13 1209S17 1.74 4.87 35.0 4.05 1218S18 1.60 4.74 34.2 3.88 1232S19 1.82 5.01 34.2 4.14 1208S20 1.69 5.18 34.0 4.03 1215S21 1.76 4.82 35.0 4.07 1208S 07S 03S 23S 08SS

TD

Nf

1234

Table A.2 (Continued)

No. offurnace

CEL TL Syy Sxx Sxy

5 3.666 1250 0.13987 1162.81 −12.75336 3.81427 1236 0.05095 404.01 −4.537087 3.93548 1230 0.01092 198.81 −1.473738 3.86975 1234 0.02899 327.61 −3.081529 4.26604 1187 0.05109 835.21 −6.5324710 4.10191 1209 0.00383 47.61 −0.4271511 4.20548 1198 0.02738 320.41 −2.9620912 4.13832 1209 0.00967 47.61 −0.678413 3.89888 1229 0.01992 171.61 −1.8487214 4.09604 1208 0.00314 62.41 −0.442715 4.22486 1199 0.03417 285.61 −3.1241916 4.12911 1209 0.00794 47.61 −0.6148717 4.05463 1218 2.14E-04 4.41 0.0307118 3.88001 1232 0.0256 259.21 −2.575919 4.13832 1208 0.00967 62.41 −0.7767220 4.02874 1215 1.27E-04 0.81 0.0101321 4.06775 1208 7.70E-04 62.41 −0.2192322 4.1203 1207 0.00645 79.21 −0.7146723 4.19665 1203 0.02454 166.41 −2.0207924 4.0121 1223 7.78E-04 50.41 −0.1980825 4.15858 1208 0.01406 62.41 −0.9367526 4.19684 1195 0.0246 436.81 −3.2778727 4.16341 1206 0.01523 98.01 −1.22172

Average 4.040217 1215.889 0.022936 236.9137 −2.28799

Summation 113.1261 34044.89 0.619259 6396.67 −61.7759

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22 1.78 5.00 35.4 4.12 1223 1.87 5.00 34.7 4.20 1224 1.70 4.98 34.1 4.01 1225 1.88 4.56 35.3 4.16 12

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