Prediction of Tempered Martensite Hardness Incorporatingthe Composition-Dependent Tempering Parameterin Low Alloy Steels

Singon Kang1 and Seok-Jae Lee2,+

1Advanced Steel Processing and Products Research Center, Department of Metallurgical and Materials Engineering,Colorado School of Mines, Golden, CO 80401, USA2Division of Advanced Materials Engineering, Research Center for Advanced Materials Development,Chonbuk National University, Jeonju 561-756, Republic of Korea

We investigated a composition-dependent tempering parameter for more accurate prediction of tempered martensite hardness in low alloysteels. The proposed composition-dependent tempering parameter decreased with the addition of alloying elements related to the activationenergy for tempering. The tempered martensite hardness calculated using the composition-dependent tempering parameter showed a reliableaccuracy compared with experimental data. [doi:10.2320/matertrans.M2014004]

(Received January 6, 2014; Accepted April 10, 2014; Published May 23, 2014)

Keywords: tempered martensite hardness, tempering parameter, alloying element effect, time-temperature-hardness (TTH) diagram, low alloysteels

1. Introduction

The primary purpose of the tempering process is toimprove the insufficient toughness of quenched martensiticsteels, but deteriorating hardness generally accompanies theprocess. It arises from the complex evolution of micro-structures such as the precipitation of transition carbide,decomposition of retained austenite into ferrite and cemen-tite, precipitation and spheroidization of cementite, and therecovery and recrystallization of martensite.1)

To address the complexity, Hollomon and Jaffe2) proposeda parameter representing the extent of tempering to predictthe hardness of tempered martensite. The tempering parame-ter (TP) is a function of tempering temperature and time asgiven by

TP ¼ T ðlog tþ CÞ ð1Þwhere T is the tempering temperature in Kelvin, t is theholding tempering time in hour for an isothermal condition,and C is a constant. Even though it is known that theevolution of microstructure is mainly dependent on thetempering conditions as expressed in eq. (1), the chemicalcomposition also affects the hardness of tempered martensite.The appropriate C value for experimental steel data isdetermined, e.g., the value of C for low-carbon boron steelreported by Säglitz et al.3) was 11.8 whereas Kamp et al.4)

used a C value of 20.0 for dual phase steels. While the valueof C in eq. (1) is relevant to the chemical composition ofmartensitic steel, quantitative analysis of the C valueconsidering the effect of alloying element addition has notbeen reported. Therefore, in the present study, we investigatea composition-dependent tempering parameter for predictingthe hardness of tempered martensite with enhanced accuracy.

2. Experimental Data from Literature

The experimental hardness values of tempered martensite

with various tempering temperature and time in low alloysteels were obtained from the literature.2,5­21) The alloyingelements considered in this work are C, Mn, Si, Ni, Cr, andMo. Data from the literature including alloying elementsother than the above six elements were excluded. Table 1summarizes the ranges of chemical composition, temperingtemperature, holding time, and hardness values from theadopted literature data. The alloy composition range waslimited to avoid the effect of secondary hardening from alloycarbides which is observed in high alloy steels. A total of1926 data points were used in the present study.

3. Formulation of Composition-Dependent TemperingParameter

The tempering parameter was derived by assuming thatthe softening of virgin martensite is a diffusion-controlledphenomenon during tempering of steels.2) Hollomon andJaffe confirmed that the hardness of tempered martensitevaries with a simple parameter as follows:

t0 ¼ t exp � Q

RT

� �ð2Þ

where t is the isothermal tempering time, T is the absolutetempering temperature, R is the gas constant, and Q is theactivation energy for tempering. According to the analysisof experimental data by Hollomon and Jaffe,2) t0 can beassumed to be constant and eq. (2) is rewritten as follows:

Q

R¼ T ðlog t� log t0Þ ð3Þ

Thus, eq. (3) induces the tempering parameter of eq. (1).This means that the hardness of tempered martensite isexpressed as a function of the activation energy for temper-ing. This activation energy changes based on both thetempering condition associated with different temperingstages and alloy composition related to carbide formation.22)

A constant C value of 20 is commonly used for carbon andlow alloy steel. There are a few reports that C varies with+Corresponding author, E-mail: seokjaelee@jbnu.ac.kr

Materials Transactions, Vol. 55, No. 7 (2014) pp. 1069 to 1072©2014 The Japan Institute of Metals and Materials

carbon content in carbon steels. Hollomon and Jaffe2) found alinear decrease in C for the change of carbon content from0.3 to 1.1mass%. In addition, Tamaki and Suzuki15) observedthat not only the carbon content but also amounts of otheralloying elements changed both the activation energy and Cvalue. Tamura et al.23) also reported that C is determinedbased on experimental hardness data. Thus, the compositiondependency of the tempering parameter can be taken intoaccount by using a fluctuating C value relying on thechemical composition of alloy steels instead of a constant Cvalue. We propose the tempering parameter taking intoaccount the composition-dependent C function as follows:

TP ¼ log tþ k0 þXi

kiXi

! !ð4Þ

where ki is the coefficient for the alloying element i, Xi is theamount of alloying element i in mass%, and k0 is a constantrelated to the tempering of pure iron. Table 2 lists the optimalvalues of ki and k0 which are determined from theexperimental data in Table 1.

By comparing several types of empirical equations for therelationship between the proposed tempering parameter ineq. (4) and the hardness of tempered martensite, we suggestan exponential expression as given.

TMH ¼ 1542:97� 25:31

XC

� �� expð�1:23� 10�4TPÞ ð5Þ

where TMH is the tempered martensite hardness in Vickersand the carbon dependent pre-exponent is used. Thecoefficients in eq. (5) were determined to minimize thedifference between the experimental hardness values oftempered martensite in Table 1 and the calculated hardnessvalues by using eq. (5).

4. Verification with Discussion

Figures 1(a) and (b) show the measured hardness oftempered martensite with the tempering parameter using aconstant C (= 20) and the composition-dependent temperingparameter from eq. (4), respectively. The measured hardnessvalues commonly decrease as the tempering parameterincreases. The use of the constant C causes relatively widedata scattering. This proves that the tempering parameterdepending only on both tempering temperature and time islimited to express the variation of the hardness of temperedmartensite accurately for alloy steels with wide ranges ofchemical composition as shown in Table 1. On the other hand,the use of the composition-dependent tempering parametereffectively reduces data scattering, because the hardness oftempered martensite is affected by the addition of alloyingelements even though the tempering condition is identical.

Figure 2 shows the variation of the composition-dependentC with the measured hardness in different temperatureranges. Typically the addition of alloying elements increasesthe hardness of steels, but decreases the composition-dependent C (all ki values are negative). The tendency to

Table 2 Parameters of eq. (4) for the alloying element effect.

Parameter Value

k0 17.396

kC ¹6.661

kMn ¹1.604

kSi ¹3.412

kNi ¹0.248

kCr ¹1.112

kMo ¹4.355

Fig. 1 Effect of alloying element on the tempering parameter com-pared with measured hardness values: (a) tempering parameter using aconstant C (= 20) and (b) tempering parameter using the composition-dependent C.

Table 1 Ranges of chemical composition, tempering temperature, holdingtime, and hardness for the experimental data used in the present study.

Parameter Min Max

C (mass%) 0.12 1.15

Mn (mass%) 0.00 1.75

Si (mass%) 0.00 0.90

Ni (mass%) 0.00 3.50

Cr (mass%) 0.00 2.00

Mo (mass%) 0.00 0.50

Tempering temperature (°C) 145 716

Holding time (s) 30 3500000

Hardness (HV) 105 899

S. Kang and S.-J. Lee1070

decrease the composition-dependent C as hardness increasesis observed clearly for all temperature ranges. It seems thatthe increase of hardness due to the addition of alloyingelements can be expressed by using the composition-dependent C regardless of tempering stages.

Recently, Mukherjee et al.21) suggested a regressedequation to predict the tempered martensite hardness foralloy steels considering various alloying elements. Theyselected the best combination of tempering temperature,tempering time, and composition term with no considerationof the tempering parameter. Figure 3 compares the predictionaccuracy by using three different equations: regressedequation,21) eq. (5) with a constant C value of 20, andeq. (5) with the composition-dependent tempering parameter.The tempered martensite hardness calculated by the proposedeq. (5) considering the composition-dependent temperingparameter in eq. (4) shows higher accuracy (R2 = 0.941)than the two other calculations (R2 = 0.927 for regressedequation; and R2 = 0.904 for eq. (5) with constant C).

It is possible to predict the time-temperature-hardness(TTH) diagram of low alloy steels using the combination ofeqs. (4) and (5). For example, Fig. 4 compares the predictedTTH diagrams of AISI 1040 carbon steel and AISI 4340 lowalloy steel. The composition-dependent C of AISI 1040(common chemical composition: Fe­0.4C­0.75Mn­0.23Siin mass%) is 12.7, while that of AISI 4340 (commonchemical composition: Fe­0.4C­0.75Mn­0.23Si­1.85Ni­0.8Cr­0.25Mo in mass%) is 10.3 due to the addition of Ni,Cr, and Mo comparing with the composition of AISI 1040. Itis anticipated that the predicted TTH diagram will be used todetermine the tempering condition of low alloy steels toobtain a desired hardness of tempered martensite.

5. Conclusions

An empirical equation for a composition-dependenttempering parameter has been proposed in low alloy steels.

Fig. 2 Relationship between the composition-dependent C function andmeasured hardness. Ranges of tempering temperature are T < 300°C forlow tempering temperature, 300°C < T < 500°C for mid temperingtemperature, and T > 500°C for high tempering temperature.

Fig. 3 Calculated hardness of tempered martensite compared withexperimental data in Table 1. Different equations were adopted:(a) regressed equation,21) (b) eq. (5) with constant C (= 20), and(c) eq. (5) with composition-dependent C in eq. (4).

Prediction of Tempered Martensite Hardness Incorporating the Composition-Dependent Tempering Parameter in Low Alloy Steels 1071

The composition-dependent tempering parameter decreaseswith the addition of alloying elements such as C, Mn, Si, Ni,Cr, and Mo. The hardness of tempered martensite wascalculated using the composition-dependent tempering pa-rameter, and it decreased as the tempering parameterincreased. The accuracy of the calculated hardness has beenimproved with the composition-dependent tempering pa-rameter from both that with a constant parameter and thatwith a regression equation. The time-temperature-hardnessdiagram of respective alloy compositions can be calculatedusing the composition-dependent tempering parameter.

Acknowledgement

This work was supported by grant from Jeon-DaeMemorial Fund.

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Fig. 4 Predicted TTH diagram for AISI 1040 and 4340 steels by using theproposed composition-dependent equation.

S. Kang and S.-J. Lee1072