jai103525.1272762-1

Nikolai Kobasko1 and Sharif Guseynov2

Microstructure and Hardness Prediction at the Core of SteelParts of Any Configuration during Quenching

ABSTRACT: In this paper we discuss the standard Jominy curve method, which is used for hardness andmicrostructure prediction at the core of steel parts of different shapes. It is shown that the simplified methodof calculation needs verification by an exact analytical solution of the problem connected with the Jominyend-quench method. For this purpose, an exact analytical method of calculations is proposed. It is estab-lished that the cooling rate at the core of steel parts can differ by up to 12 % as compared with the self-regu-lated boiling process and extremely forced convection. The results of the investigations can be used forJominy standard end-quenched method improvement and analyses of quenching processes. They also canbe used for the development of new technologies.

KEYWORDS: microstructure and hardness prediction, Jominy curves, standard, cooling rate, analyticalsolution, steel parts of any configuration, new technologies

Introduction

Quenching processes are widely used in the heat treating industry to improve the mechanical properties of

materials. Because transient nucleate boiling processes are rather complicated, they have not been widely

or deeply investigated yet. The empirical data and simplified calculations are mostly used when designing

heat treatment technologies. This paper tries to knit together previous experience in making simplified cal-

culations and an up-to-date analytical approach that allows us to establish a correlation between the data

achieved by testing a Jominy standard specimen and the data that are needed for real steel parts. The

developed method of calculation can optimize cooling conditions to receive an optimal microstructure dis-

tribution in real steel parts during quenching.

Jominy Standard Curves

In this paper, Jominy standard end-quench hardenability and microstructure distribution curves are used to

predict the hardness and microstructure at the core of steel parts of any configuration. The Jominy test for

determining the hardenability of steel has been standardized and is described in SAE J406 and ASTM

A225 specifications. A 100 mm (4 in.) long by 25 mm (0.5 in.) diameter bar is austenitized at the proper

temperature and dropped into a fixture, and one end is rapidly cooled with 24�C (75�F) water issuing from

a 13 mm (0.5 in.) orifice under prescribed conditions [1]. The standard test piece is heated to a pre-deter-

mined temperature (815�C–925�C, or 1500�F–1700�F). When the specimen is cold after being quenched

intensively from one end, hardness measurements are made at intervals along the test piece from the

quenched end, and the results are plotted on a standard chart from which the hardenability curve and

microstructure distribution are derived. Figures 1, 2, and 3 illustrate Jominy end-quench curves for AISI

8630 steel, AISI 1060 steel, and AISI 4140 steel (see Table 1) [2,3].

Note that there could be tensile residual stress at the core that decreases hardness; when this is the

case it looks like the amount of martensite has no effect on the measured hardness. In order to analyze this

phenomenon more precisely, the temperature field and residual stress distribution should be measured or

calculated. This means that the Jominy standard end-quenched method can be further improved. The first

step is taken below by providing an exact analytical solution suitable for the Jominy end-quenched probe.

Manuscript received October 25, 2010; accepted for publication June 21, 2011; published online July 2011.1 IQ Technologies Inc., Akron, Ohio 44311 and Intensive Technologies Ltd., Kyiv, Ukraine.2 Institute of Mathematical Sciences and Information Technology, Transport and Telecommunication Institute, Riga, Latvia.

Copyright VC 2011 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959.

Journal of ASTM International, Vol. 8, No. 8Paper ID JAI103525

Available online at www.astm.org

Copyright by ASTM Int'l (all rights reserved); Wed Mar 28 17:38:06 EDT 2012Downloaded/printed byUniversidad Autonoma Del Caribe SB pursuant to License Agreement. No further reproductions authorized.

FIG. 1—Jominy end-quenched hardenability and microstructure distribution for AISI 8630 steel [2]: M,martensite; B, bainite; F, ferrite; P, pearlite.

FIG. 2—Jominy end-quenched hardenability and microstructure distribution for AISI 1060 steel [2]: M,martensite; B, bainite; F, ferrite; P, pearlite.

FIG. 3—Jominy end-quenched hardenability and microstructure distribution for AISI 4140 steel [2]: M,martensite; B, bainite; F, ferrite; P, pearlite. The minimum unit on the x scale is equal to 1=16 in., or1.5875 mm.

2 JOURNAL OF ASTM INTERNATIONAL


Table 2 shows the cooling rate at a temperature of 705�C (1300�F) depending on the distance of the

quenched end [1,3]. The further the distance from the quenched end of the standard specimen, the less

hardness, and the less martensite that is formed in steel, as the cooling rate significantly decreases with dis-

tance. It should be noted that cooling rates within the range of 705�C–450�C are the most important due to

the intermediate phases that form within this range and the fact that the stability of the supercooled austen-

ite is at its minimum. Figure 4 shows how the cooling rate can affect the microstructure formation and

hardness distribution along the standard Jominy specimen. When the cooling rate within the range of

450�C–705�C is very high, as a rule, a martensite microstructure is formed (see line 1 of Fig. 4). When the

cooling rate decreases, intermediate phase bainite can be formed (see line 2 of Fig. 4). When the cooling

rate is rather low, pearlite can be formed (see line 3 of Fig. 4).

The thermal properties of steels during quenching do not depend on their chemical composition

because alloying elements are solved in austenite. The thermal conductivity and thermal diffusivity of aus-

tenite versus the temperature are presented in Tables 3 and 4.

Taking this fact into account, it can be assumed that the cooling rate of the Jominy test specimen as a

function of the distance from the quenched end depends only on the mentioned distance and does not

depend on the chemical composition of steel. Such a function can be used to predict the hardness and

microstructure at the core of steel parts of any shape. The main idea of the calculations consists in the

equality of the microstructures and the hardness if the cooling rate in the Jominy specimen and at the core

of any steel part are the same [3]. In this case there is a need to calculate the cooling rate at the core of a

steel part of any configuration. It is possible to make such calculations if the theory of regular thermal con-

dition is used [4,5]. The cooling rate at the core of a steel part of any shape can be calculated by well-

known Eq 1

� ¼ aKn

KðT � TmÞ (1)

where:

�¼ cooling rate, �C=s,

a¼ thermal diffusivity,

TABLE 1—Chemical composition of AISI 8630, AISI 4140, and ASTM 1060 steels.

Steel C Mn Si Cr Ni Mo

AISI 8630 0.28–0.33 0.70–0.90 0.15–0.35 0.40–0.60 0.40–0.70 0.15–0.25

AISI 4140 0.38–0.43 0.75–1.00 0.15–0.35 0.80–1.10 0.15–0.25

ASTM 1060 0.55–0.66 0.60–0.90 0.15–0.40

TABLE 2—Typical cooling rate along the Jominy specimen as a function of the distance from thequenched end at a temperature of 705�C (1300�F).

Distance from Water Quenched End, 1=16 in. Cooling Rate, �C=s

1 270

2 170

3 110

4 70

5 43

6 31

7 23

8 18

9 14

10 11.9

12 9.1

14 6.9

16 5.6

18 4.6

20 3.9

KOBASKO AND GUSEYNOV ON MICROSTRUCTURE AND HARDNESS PREDICTION 3


Kn¼Kondratjev number (dimensionless value),

T¼ temperature, �C,

Tm¼ bath temperature, �C, and

K¼Kondratjev form factor.

There is a universal relationship between the Kondratjev number Kn and the generalized Biot number

BiV ½BiV ¼ ða=kÞKðS=VÞ�, which can be presented as Kn ¼ f ðBiVÞ [3,4], i.e.,

Kn ¼ wBiV ¼BiVffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Bi2V þ 1:437BiV þ 1

p

In the theory of regular heat conditions [4], the characteristic size is determined as a value L that includes

three parameters, S, V, and K, that is

L ¼ S

VK

where:

K¼Kondratiev form factor,

V¼ volume of the body, m3, and

S¼ surface area, m2.

In this case the generalized Biot number BiV is

BiV ¼ak

L ¼ ak

KS

V

Links between the generalized Biot number BiV, the criterion of temperature field nonsmoothness w, and

the Kondratjev number Kn are provided in Table 5. The Kondratjev form factors for different shapes are

available in Table 6.

The existence of a regular thermal process in steel parts with complicated configurations was some-

times questionable. However, it was proved that for the cores of steel parts, a regular thermal process

TABLE 3—Thermal conductivity of supercooled austenite versus temperature.

T, �C 100 300 500 700 800

�k;W=mK 17.5 19.6 23 26.3 28�k;W=mK 17.5 18.55 20.2 21.90 22

FIG. 4—Affect of cooling rates upon microstructure formation during end-quench standard specimen test-ing. Ac1 is the temperature at which pearlite transforms into austenite (723�C); Ms is the martensite starttemperature; Mf is the martensite finish temperature; 1, 2, and 3 are different cooling rates; bainite andpearlite are intermediate phases.



TABLE 5—Links between the generalized Biot number BiV, the criterion of temperature field non-smoothness w, and the Kondratjev number Kn.

BiV w Kn

0.00 1 0.00

0.10 0.93 0.09

0.20 0.88 0.17

1.00 0.54 0.539

2.00 0.356 0.713

3.00 0.264 0.793

4.00 0.210 0.840

5.00 0.174 0.868

6.00 0.148 0.888

7.00 0.129 0.903

8.00 0.114 0.914

9.00 0.103 0.924

10.0 0.093 0.931

20.0 0.048 0.965

30.0 0.033 0.976

1 0.000 1

TABLE 6—Kondratjev form factors K for bodies of a simple configuration (results of analytical calculations), S=V, and K(S=V) values.

Shape of the Part K, m2 SV ;m

�1 K SV ;m

Plate of thickness L L2

p2

2

L

2L

p2

Cylinder of radius R R2

5:784

2

R

0.346R

Square infinite prism with equal sides L L2

2p2

4

L

2L

p2

Cylinder of radius R and height Z 15:784

R2 þ p2

Z2

2

Rþ 2

Z

� �2RZðRþ ZÞ

5:784Z2 þ p2R2

Finite cylinder, R¼Z R2

15 � 65

4

R

0:256R

Finite cylinder, 2R¼ Z R2

8:252

3

R

0:364R

Cube with sides L L2

3p2

6

L

0:203L

Finite square plate with sides L1, L2, L3 1

p2 1L2

1

þ 1L2

2

þ 1L2

3

� � 2ðL1L2 þ L1L3 þ L2L3ÞL1L2L3

2ðL1L2 þ L1L3 þ L2L3ÞL1L2L3

p2ðL21L2

2 þ L21L2

3 þ L22L2

3Þ

Sphere R2

p2

3

R

0:304R

TABLE 4—Thermal diffusivity a of supercooled austenite versus temperature.

T, �C 100 300 500 600 800

a � 106, m2=s 4.55 4.70 5.34 5.65 6.19

�a � 106;m2=s 4.55 4.625 4.95 5.10 5.37

Note: k and �k at 500�C (and analogously at other temperatures) mean average values for the range of 100�C–

500�C.



always exists (see Fig. 5) [5–7]. The samples (a wedge and a gear are shown in Fig. 5) were made of epoxy

material and cooled in a temperature-controlled tank by agitated water with ice [6,7]. Because of the low

thermal conductivity and thermal diffusivity of the epoxy material, the condition Bi!1 always was

met, which allowed us to calculate the Kondratjev form coefficients for steel parts with complex configu-

ration, such as wedges and gears. The results of calculations based on finite-element method (FEM) nu-

merical calculations and experimental data are presented in Table 7.

Along with the Kondratjev form coefficients K, the Kondratjev numbers Kn are needed in order to cal-

culate correctly the cooling rate at the cores of steel parts. It has been proved that during the nucleate boil-

ing process, when a self-regulated thermal process is established, the Kondratjev numbers change

insignificantly with changing size and configuration. The reason for such behavior is discussed in Refs 8–

10. Some results of experiments and calculations are provided in Tables 8 and 9.

Comparison of the Results of Calculations

Comparison of an Intensive Self-Regulated Thermal Process with Intensive Direct Convection

For practice, it is very important to know the difference between the intensive transient nucleate boiling

process (including the self-regulated thermal process) and intensive direct convection. To make such a

comparison, let us consider two conditions of quenching:

1. Quenching is produced in a tank where film boiling is absent and only nucleate boiling takes

place. The surface temperature during the immersion of steel parts into the quenchant drops almost

instantly to the saturation temperature and then is kept at the level of the boiling point, slightly

decreasing during the entire process of boiling. In this case Eq 1 can be used to calculate the cool-

ing rate at the core within the range of 705�C–450�C if Kn ¼ 1 and the temperature Tm is replaced

by the saturation temperature Ts.

FIG. 5—Shape and size of wedge and gear used in the study of the regular process: (a) wedge; (b) gear;(c) temperature versus time in semi-logarithmic coordinates for wedges; (d) the same for gears;# ¼ T � Tm; Tm, medium temperature.



2. Quenching is produced in a tank where film and nucleate boiling processes are eliminated and

only direct convection takes place (Fig. 6). The surface temperature during the immersion of steel

parts into the quenchant drops almost instantly to a medium temperature Tm. In this case Eq 1 can

be used to calculate the cooling rate at the core within the range of 705�C–450�C if Kn ¼ 1 and

the quenching temperature is Tm.

For both cases, cooling rates at the cores of different steel parts are presented in Table 10.

The calculations show that the difference between the nucleate boiling process and direct convection

is about 12 %. That is not a big difference from the point of view of cooling rate evaluation at the core of

TABLE 7—Kondratjev form factors K achieved on the basis of FEM calculations and experimentswith the epoxy material [5–7].

Steel Part K, m2

73� 10�6

3.94� 10�6

171� 10�6

TABLE 8—Kondratjev numbers Kn for Houghton K oil at a temperature of 110�F (43.3�C), with noagitation, depending on the sizes of cylindrical probes made of AISI 4140 steel.

Probe Diameter,

in. (mm)

Kn at

Kn1300�F (704�C) 650�F (343�C) 400�F (204�C)

0.5

(12.7)

0.230 0.073 0.026 0.106

0.206 0.073 0.026

1

(25.4)

0.142 0.120 0.046 0.102

0.139 0.121 0.046

1.5

(38.1)

0.392 0.136 0.071 0.213

0.407 0.139 0.071

2

(50.8)

0.420 0.158 0.084 0.218

0.414 0.150 0.084



steel parts. However, from the point of view of martensite transformation, it could be a radical difference,

depending on the martensite start temperature MS. As is known, the martensite start temperature for high

carbon steels could be 100�C to 120�C. During the transient nucleate boiling process, the surface tempera-

ture will maintain also at the level of 100�C to 120�C. This means that martensite transformation will be

completely delayed. With intensive direct convection, the surface temperature will be at the level of Tm

(20�C), at which martensite transformation will be almost finished. Such a big difference will cause radical

changes in the residual stress distribution and crack formation. That is why this aspect should be taken

into account.

Based on the data obtained, it is possible to predict the hardness and microstructure at the cores of

steel parts of different configurations.

Comparison of Intensive Quenching with Oil Quenching for Different Steel Parts

In the heat treating industry, often there is a need to measure the hardness at the cores of steel parts and to

investigate whether a microstructure at the core is allowable. The developed simplified method of calcula-

tions can easily predict the hardness and microstructure at the cores of steel parts of any configuration. In

this section of our paper, a simplified method of calculation is illustrated by quenching the gear, bearing,

and shaft in intensive water flow and oil. As is well known, intensive quenching is fulfilled under the con-

dition of 0.8<Kn< 1 [10]. When quenching in oil, the Kondratjev number Kn is about 0.2 to 0.3 (see

FIG. 6—Temperature versus time during intensive quenching of a cylindrical specimen 30 mm in diame-ter: (a) intensive transient nucleate boiling process; (b) intensive direct convection.

TABLE 9—Kondratjev numbers Kn for Houghton K oil at a temperature of 110�F (43.3�C) and agita-tion of 100 fpm (0.508 m=s), depending on sizes of cylindrical probes made of AISI 4140 steel.

Probe Diameter, in. (mm)

Kn at

Kn1300�F (704�C) 650�F (343�C) 400�F (204�C)

0.5

(12.7)

0.257 0.198 0.170 0.20

0.244 0.174 0.148

1

(25.4)

0.325 0.287 0.229 0.28

0.304 0.301 0.227

1.5

(38.1)

0.410 0.275 0.231 0.31

0.414 0.278 0.226

2

(50.8)

0.424 0.277 0.235 0.31

0.422 0.273 0.226



Tables 8 and 9). This means that for oil Kn¼ 0.25, and for intensive quenching Kn¼ 0.9. The cooling rate

at the cores of steel parts during intensive quenching is 4 to 5 times faster as compared with that during oil

quenching. To be more specific, let us predict the hardness and microstructure at the core of a gear, bear-

ing ring, and shaft that are quenched in oil and intensively in water. The gear is made of AISI 8630 steel,

the bearing is made of AISI 1060 steel, and the shaft is made of AISI 4140 steel (see Table 1). Jominy

standard curves for these are shown in Figs. 1, 2, and 3.

Using Eq 1, one can calculate easily the cooling rate at the core of the gear when quenching in oil

� ¼ 5:4� 10�6 m2=s� 0:25

73� 10�6 m2705�C� 20�Cð Þ ¼ 12:7�C=s

A cooling rate of 12.7�C=s is observed at the distance between units 9 and 10 (see Table 2). According to

Fig. 1, between units 9 and 10 at the core of the gear the hardness will be 20 HRC and the percentage of

martensite will be 5 % when quenching in oil. According to these specifications, the minimum hardness at

the core of the gear should be 28 HRC. This means that more intensive quenching is needed in order to

provide a hardness of 28 HRC at the core of the gear. Let us see what is happening during intensive

quenching of the gear when the Kondratjev number Kn¼ 0.9.

Using the same Eq 1, we can calculate the cooling rate at the core of the gear when quenching inten-

sively in water

� ¼ 5:4� 10�6 m2=s� 0:9

73� 10�6 m2705�C� 20�Cð Þ ¼ 45:7�C=s


Fig. 1, between units 4 and 5 there will be a hardness of 28 HRC and a percentage of martensite of 20 %.

This means that the gear should be quenched intensively in order to provide a hardness of 28 HRC and 20

% martensite.

Similarly, one can predict the hardness and microstructure at the core of a bearing ring made of AISI

1060 steel (see Table 7 and Fig. 2). When intensive quenching in water is applied, the cooling rate at the

core of the bearing ring is

� ¼ 5:4� 10�6 m2=s� 0:9

3:94� 10�6 m2705�C� 20�Cð Þ ¼ 845�C=s

This means that the bearing ring will be quenched through, having almost 100 % martensite through all

cross sections.

One can predict also the hardness and microstructure at the core of a shaft made of AISI 4140 steel

(see Table 7 and Fig. 3). When intensively quenched in water (Kn¼ 0.9), the cooling rate at the core of

shaft is

� ¼ 5:4� 10�6 m2=s� 0:9

171� 10�6 m2705�C� 20�Cð Þ ¼ 19:5�C=s

TABLE 10—Cooling rate at the cores of different steel parts cooled from 875�C in water based salt solutions at 20�C.

Shape of Steel Part

Cooling Rate at 700�Cwith Nucleate Boiling

Process, �C=s

Cooling Rate at 700�Cwith Direct

Convection, �C=s Difference, %

Plate, 30 in thickness 35.6 40.3 11.7

Cylinder, 30 mm in diameter 83.3 94.4 11.7

Sphere, 30 mm in diameter 142.1 161 11.7

Cube, 30 mm 106.6 120.8 11.7

Round plate, 30 mm in thickness and 60 mm in diameter 56.35 63.85 11.7

Round plate, 30 mm in thickness and 120 mm in diameter 40.7 46.16 11.7

Cylinder, 30 mm in diameter and 60 mm in height 92.2 104.5 11.7

Cylinder, 30 mm in diameter and 120 mm in height 85.5 96.9 11.7




Fig. 3, between units 7 and 8, at the core of shaft there will be a hardness of 52 HRC and a percentage of

martensite of 70 %. This means that the shaft is quenched through and can be made from less alloy steel to

provide the optimal quenched layer and optimal residual stress distribution after intensive quenching [9].

These simple calculations could be very useful if the appropriate experimental Jominy curves, contain-

ing detailed information on the microstructures and mechanical properties versus the cooling rate, are

available. It should be noted that the Jominy standard method is a powerful tool for getting useful informa-

tion needed for the optimizing of quenching processes, especially those depending on the chemical com-

position of the steel.

Also, the Jominy standard method should be improved on the basis of accurate experiments and ana-

lytical calculations, which are provided below.

Statement of the Direct Initial-Boundary Problem for the Transient Nucleate Boiling Process

Suitable for Improving Jominy Standard

The goal of the direct problem is to find the function uðx; tÞ 2 Cf½0; l� � ½0; T�g, which is the solution of

the classic heat equation [11,12]

@u x; tð Þ@t

¼ a@2u x; tð Þ@x2

þ F x; tð Þ; 0 < x < l <1; 0 < t � T <1 (2)

with the initial condition

u x; tð Þjt¼0¼ u0 xð Þ; 0 � x � L (3)

with two boundary conditions

@u x; tð Þ@x

��x¼l�0

¼ 0; 0 � t � T (4)

�k@u x; tð Þ@x

��x¼0þ0

þbm u x; tð Þjx¼0þ0�h tð Þ� m¼ 0; 0 � t � T (5)

and with the consistency constraints

u00 l� 0ð Þ ¼ 0

� ku00 0þ 0ð Þ þ bm u00 0þ 0ð Þ � h 0þ 0ð Þ� m¼ 0 (6)

Here 0 < a ¼ k=cq; where all parameters k; c; q are positive constants, m ¼ 10=3; b � a constant > 0;and the right-hand side of Eq 2 is a continuous function at the domain ½0; l� � ½0; T� : Fðx; tÞ ¼ f ðx; tÞ=cq2 Cf½0; l� � ½0; T�g; where the function f ðx; tÞ is the intensity of the external source.

It has been shown that Eqs 2–6 can be reduced to a nonlinear Volterra integral equation of the second

kind

h uð Þ ¼ g uð Þ 1�ðu

0

G u;wð Þh wð Þdw

�m

(7)

Here

u ¼ bma

kt



w ¼ bma

ks

g uð Þ ¼ Vm kbma

u

� �

V tð Þ ¼ðl

0

G x; n; tð Þjx¼0 � #0 nð Þdnþðl

0

dnðt

0

G x; n; t� sð Þjx¼0� F n; sð Þ � h0 sð Þð Þds

G u;wð Þ ¼G x; n;

kbma

u� wð Þ� ��

n¼0; x¼0

Vk

bmau

� �

G x; n; tð Þ ¼ 1

lþ 2

l�X1n¼1

e� p�n�ffiffiffiatp

=lð Þ2 � cosp � n � x

l

� �� cos

p � n � nl

� �

Equation 7 can be solved using the recurrence formula

h0 uð Þ ¼ 0

hn uð Þ ¼ g uð Þ 1�Ð u

0G u;wð Þhn�1 wð Þdw

� m; n ¼ 1; 2; 3;…

(8)

Moreover, having designated the exact solution of Eq 7 as the function hexactðuÞ; one can obtain

g uð Þ 1�ðu

0

G u;wð Þ � hn wð Þdw

�m

)n!1

g uð Þ � 1�ðu

0

G u;wð Þ � hexact uð Þdw

�m

i.e., the functional sequence hnðuÞ converges uniformly to the desired solution hexactðuÞ:hnðuÞ )

n!1hexactðuÞ:

After finding the solution of Eq 7 using Eq 8, we can determine the solution of the original problem

[Eqs 2–6] by using Eq 9

u x; tð Þ ¼ h tð Þ þðl

0

@G x; n; tð Þ@t

u0 nð Þ � h 0þ 0ð Þ½ �dnþðt

0

dsðl

0

G x; n; t� sð Þ F n; sð Þ � h0 sð Þ½ �f gdn

� abm

k

ðt

0

G x; n; t� sð Þjn¼0þ0habm

ks

� � �ds

(9)

On the basis of the developed approach [11,12], the monograms can be designed to be used by engineers

in the heat treating industry.

Summary

1. In the paper, the hardness and microstructure at the cores of different steel parts are predicted by

using Jominy standard curves, which contain information about the microstructure and hardness

depending on the cooling rate of the quenching.

2. Because at the core of a steel part with a complex configuration a regular thermal process is

always established, Eq 1 can be used to calculate the cooling rate at the core of any steel part.

3. The developed approach cannot be used to predict the microstructure and hardness in other areas

of a cross section of a steel part, because the regular thermal process in these areas can be absent

or delayed.



4. In order to predict correctly the microstructure and hardness at the cores of steel parts of any con-

figuration, the appropriate Jominy standard curves and Kondratjev form factors should be

available.

5. At the cooling end of a Jominy standard probe, a direct convection or transient nucleate boiling

process can take place during testing. The difference between the two modes is 12 %.

6. An analytical method for the verification of the standard Jominy method is developed.

7. A simplified method of calculation can be used for recipe development and the designing of new

quenching technologies.

References

[1] Totten, G. E., Bates, C. E., and Clinton, N. A., Handbook of Quenchants and Quenching Technology,

ASM International, Materials Park, OH, 1993.

[2] American Society for Metals, Atlas for Isothermal Transformation and Cooling Transformation Dia-grams, The American Society for Metals, Metals Park, OH, 1977.

[3] Kobasko, N., “Hardness and Structure Prediction at the Core of Any Steel Part using Jominy Stand-

ard Test,” Proceedings of the Fifth WSEAS Conference on Heat and Mass Transfer (HMT ’08), Aca-

pulco, Mexico, January 25–27, 2008, pp. 116–121.

[4] Kondratjev, M., Heat Measurements, Mashgiz, Moscow, 1957.

[5] Kobasko, N. I., Aronov, M. A., Powell, J. A., and Totten, G. E., Intensive Quenching Systems: Engi-neering and Design, ASTM International, West Conshohocken, PA, 2010.

[6] Kobasko, N. I., Steel Quenching in Liquid Media under Pressure, Naukova Dumka, Kyiv, 1980, p.

206.

[7] Kobasko, N. I., “Self-regulated thermal processes,” Heat and Mass Transfer, Vol. 8, Nauka i Tekh-

nika, Minsk, 1968, pp. 363–368.

[8] Kobasko, N. I., “Self-Regulated Thermal Processes during Quenching of Steels in Liquid Media,”

International Journal of Microstructure and Materials Properties, Vol. 1, No. 1, 2005, pp. 110–125.

[9] Kobasko, N., “Transient Nucleate Boiling as a Law of Nature and a Basis for Designing of IQ Tech-

nologies,” Proceedings of the Seventh IASME=WSEAS International Conference on Heat Transfer,Thermal Engineering and Environment (THE’09), Moscow, Russia, August 22–23, 2009, pp. 67–75.

[10] N. I. Kobasko, “Quenching Apparatus and Method for Hardening Steel Parts,” U.S. Patent No.

6,364,974 BI (April 2, 2002).

[11] Guseynov, Sh. E., 2003, “Methods of the Solution of Some Linear and Nonlinear Mathematical

Physics Inverse Problems,” Ph.D. thesis, University of Latvia, Riga.

[12] Guseynov, Sh. E. and Kobasko, N. I., “On One Nonlinear Mathematical Model for Intensive Steel

Quenching and its Analytical Solution in Closed Form,” Proceedings of the Fifth WSEAS Interna-tional Conference on Heat and Mass Transfer (HMT ’08), Acapulco, Mexico, January 25–27, 2008.



http://dx.doi.org/10.1504/IJMMP.2005.008135

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