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New Case Hardening Software SimCarb QuenchTemp for the Simulation of Hardness and Microstructure from Carburization Profiles

M. Kaffenberger1,a, J. Gegner1,b

1University of Siegen, Institute of Material Science, Paul-Bonatz-Straße 9-11, 57068 Siegen, Germany.

akaffenberger@lot.mb.uni-siegen.de, bjuergen.gegner@uni-siegen.de

Keywords: Case hardening software, quenching, tempering, simulation of hardness, prediction of microstructure.

ABSTRACT

The SimCarb program package as powerful stand-alone solution provides a user-friendly Windows

expert software suite for computer aided case hardening engineering in industrial heat treatment

and research. In the present paper, a new simulation tool is introduced for the prediction of the

depth distributions of the quenching and tempering hardness as well the microstructure develop-

ment from a given carburization profile by taking into account the process conditions, chemical

steel composition and work piece geometry. SimCarb QuenchTemp offers both an empirical and a

thermophysical model. The functionality and practical application of the software are demonstrated

by means of screenshots and simulation examples. In the empirical model, the quenching hardness

is derived from calculated sets of Jominy curves for the carbon concentrations in the case at the

applicable distance from the quenched end. The representative cylinder diameter characterizes the

influence of the size and shape of the work piece. The cooling ability of the medium is quantified by

the Grossman quench severity. The tempering hardness is calculated by a diminution factor. In the

thermophysical model, the temperature distribution during quenching is simulated by applying the

finite difference method. Fourier’s law is modified to use temperature dependent heat transfer and

conduction coefficients. A simplified approach considers the changing microstructure in the

calculation of heat conduction coefficients from the chemical composition of the steel. Heat transfer

coefficients are taken from the literature for common quenchants and can be selected by the user.

The quenching hardness and the microstructure composition is finally derived by identifying the

simulated cooling curves for each depth in continuous cooling transformation diagrams, which are

implemented for conventional case hardening steels and carbon concentrations of 0.1 to 1.0 wt.%.

The tempering hardness is deduced by experimentally determined Hollomon-Jaffe parameters.

Introduction

Case hardening [1‒ 9], with a world market share of more than one third of the industrial hardening

processes, holds a leading position within the heat treatment technologies of steels. To produce

reliable components cost-effectively, it is important to ensure high accuracy in achieving the target

quantities, particularly the carburizing and case hardening depth and the surface hardness [10].

These process values, however, are not always met precisely enough in practice [4, 11, 12].

The prediction of the resulting hardness distribution is complex both from a metal physics and

material science as well as a mathematical viewpoint. Previous research focuses on quenching of

steels [13‒ 15]. The cooling conditions influence the material characteristics significantly. There-

fore, the mathematic simulation of quenching processes gains increasing interest [16‒ 20]. Finally

low-temperature tempering, moreover, must also be included. The stand-alone SimCarb program

suite, consisting of the base software SimCarb with the add-on tool SimCarb Diffusivity and

SimCarb QuenchTemp, combines the process simulation and the prediction of all relevant target

quantities in one expert system of computational case hardening engineering.

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SimCarb Quench Temp in the Sequence of the SimCarb Software Package

Computer-aided heat treatment support aims for the analysis, design and optimization of industrial

technologies. Since its introduction at the MMT-2006 conference [21], the SimCarb software is

applied internationally by engineers, researchers, and lecturers from industry and academia [6, 12,

21‒ 33]. The graphical user interface in Microsoft Windows with pull-down menus and buttons

offers various functions, high efficiency, and ease of usability with intuitive mouse navigation,

flexible input options and advanced libraries. SimCarb allows the user to calculate carbon profiles

for real multi-stage carburization processes numerically by applying the finite difference method

(FDM) [12, 21, 29, 31‒ 33]. In addition to the relevant library, the extension module SimCarb

Diffusivity provides steel alloy specific carbon diffusion coefficients in austenite in an editable

form. The basic hardness prediction implemented in SimCarb evaluates carbon concentration

relationships and accounts for the retained austenite contents [31].

The present paper introduces the new software SimCarb QuenchTemp developed in a PhD

research at the Institute of Material Science of the University of Siegen. As all parts of the

integrated SimCarb package, it represents a stand-alone Windows program. SimCarb QuenchTemp

calculates the quenching and tempering hardness as well as the microstructure composition of a

case hardened steel component. These simulations involve the given carbon depth distribution after

carburizing, computed by SimCarb or measured, e. g., by secondary ion mass spectrometry [6, 34,

35], as well as the material parameters, component geometry, and process conditions.

The SimCarb QuenchTemp software provides an empirical and a thermophysical model that can

be selected by the user. Each operating mode supports the direct import of carburization profiles as

ASCII files in the .txt format exported from SimCarb for further calculations. Alternatively,

SimCarb QuenchTemp offers a simple subroutine to generate a user-defined carbon depth distribu-

tion and save it in the appropriate ASCII format.

Combined with the precise measurement of the carburization profile and the depth distribution of

the quenching and tempering hardness as well as the accurate knowledge of the process conditions,

application of the SimCarb expert software package permits the methodical analysis, design and

optimization of reliable heat treatments. This computer-aided holistic approach is called case

hardening engineering [6, 27, 33].

Empirical model

In order to predict the hardness distribution after quenching from a given carburization profile, a

practical method of Wyss is recommended in literature [36‒ 39]. On the basis of established works

of Grossman [40, 41], this method is proposed for graphical evaluation [36‒ 39]. The empirical

model of SimCarb QuenchTemp includes this procedure in an engineering software solution.

The carbon profile, which is generated in the surface layer by case carburizing, is basically re-

sponsible for the resulting hardness profile after quenching. The influence of the steel composition

is taken into account by the hardenability that depends on the steel composition. The geometry of

the work piece is specified by the representative cylinder diameter of an equivalent round specimen.

This simple sample describes the cooling characteristic of a relevant cross section of the work piece.

The empirical model of SimCarb QuenchTemp takes the process conditions into account, based on

Grossman’s quenching intensity or severity factor. The surface hardness stems from a hardenability

relationship or user input. The hardness profile is then calculated from Jominy curves, the represen-

tative cylinder bore diameter and Grossman quenching severity factor. A carbon dependent diminu-

tion factor is applied for the calculation of the tempering hardness. The martensite fraction is esti-

mated using a simplified method. These approaches are combined to achieve a practical prediction

of the case hardening depth after both quenching and tempering.

Carbon Depth Distribution. Due to the modular concept of the SimCarb software suite, a

carburization profile simulated by SimCarb (ASCII.txt output format), can be imported directly in

SimCarb QuenchTemp. Alternatively, it is possible to create a user-defined carbon distribution in

SimCarb QuenchTemp. In Fig. 1, the dialog box for the user definition of an arbitrary carburization

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profile is shown. Supporting points for depth and carbon concentration are entered into the input

fields below and are specified in mm and wt.%, respectively. The final data point is identified as the

total carburization depth. The carbon distribution can be displayed as a graphical output by the sub-

routine. For later use the carburization profile can also be exported into an ASCII file (.txt format).

Fig. 1. Dialog box for generating a carburization profile.

Jominy Curves and Surface Hardness. For the prediction of the hardness profile, Jominy

curves for different carbon concentrations are determined. This calculation considers the chemical

composition of the steel and its austenite microstructure, expressed as ASTM grain size number

KASTM. An equation proposed by Just is preset in SimCarb QuenchTemp [37, 38, 42]:

ASTMPVSiNiMoMn

CrC2

81.096391.65.53814

2000276.095898.028.1213

Kcccccc

ccJJJH

(1)

This equation is also recommended by the Association for Heat Treatment and Materials Technol-

ogy (AWT, Bremen, Germany). The concentrations c of carbon the other alloying elements are

inserted in wt.%. The grain size KASTM is dimensionless, typical values range between 5 and 10. The

hardness H and the distance J from the end face are specified in HRC and mm, respectively.

Eq. 1 is limited to distances J from the end face between 8 and 80 mm and carbon concentrations

of 0.6 wt.%. That is why the surface hardness at carbon contents from 0.6 to 0.9 wt.% is calculated

by applying a hardenability relationship for martensite microstructure. SimCarb QuenchTemp offers

the following versions:

Burns-Moore-Archer [43]:

30.66 :5.17.0

42.3189.7832.1486.38 :7.05.0

6020 :5.01.0

21.909.94913.600014.13279 :1.004.0

CC

C2C

3CCC

CCC

C2C

3CCC

cHc

ccccHc

ccHc

ccccHc

(2)

Gegner [44]:

47.66 :5.19.0

65.2561.15086.18557.76 :9.007.0

CC

C2C

3CCC

cHc

ccccHc (3)

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Hodge-Orehoski [45]:

78.65 :5.17.0

49,366,23957,30833,133 :7.06.0

5035 :6,01.0

CC

C2C

3CCC

CCC

cHc

ccccHc

ccHc

(4)

Kell [39]:

85.64 :5.17.0

58.2282,11578.6891.14 :7.06.0

6155.32 :4.01.0

CC

C2C

3CCC

CCC

cHc

ccccHc

ccHc

(5)

Riehle-Simmchen [46]:

64.2478.23209.52472.61036.35975.81 :5.10 C2C

3C

4C

5CCC ccccccHc (6)

Wyss [36]:

33.65 :5.173.0

47.3359.5091.2131.54 :73.01.0 23

CC

CCCCC

cHc

ccccHc (7)

It is well known that the prediction of the face quenching hardness for low alloyed steels per-

forms satisfactorily. However, with increasing alloy content (particularly for higher Cr and Ni con-

centrations), this formula loses accuracy [47]. The limitation must also be considered in Eq. 1. To

simulate specific steels with higher amounts of alloying additions, such as 18CrNiMo7-6, SimCarb

QuenchTemp offers the user the possibility to modify the coefficients of Eq. 1 accordingly.

Steel, Steel Composition and Grain Size. In Fig. 2, the dialog box for the steel grade, steel

composition and grain size is shown. It gives an opportunity to select a steel grade from a list of 45

items. Steel type and material number are indicated. According to the choice of the user the average

chemical composition for the steel is loaded. This data is displayed in the corresponding input field

of each element. Additionally, the chemical composition can be modified manually. The austenite

grain size before quenching is entered in the input field “K-ASTM”.

Fig. 2. Dialog box for selecting a steel grade or manually entering the material composition as well

as for filling in the grain size and opening the dialog box to modify the Jominy equation.

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Quenching Severity and Diameter. The state of motion of a quenchant affects the heat transfer

significantly. One factor is the enforced convection, e. g. in a salt bath. In vaporizing fluid, agitation

speeds up the bursting of the isolating vapor layer (Leidenfrost phenomenon) as well as the separa-

tion of bubbles from the work piece surface [48]. The increasing flow rate is characterized in the

quenching severity library by the conditions of mild, weak, active, strong and stormy agitation.

The distance from the quenched end face, J0=(d0,h), which is used in Eq. 1, is determined by a

function of the representative cylinder diameter, d0, of the round model specimen and Grossman’s

quench(ing) intensity factor h [36‒ 38]. In SimCarb QuenchTemp, the influence of type and state of

motion of a quenchant is described by Grossman’s quenching intensity h, which represents a mean

level of heat withdrawal:

λ2

αh (8)

For the heat transfer coefficient α and the heat conduction coefficient λ, constant effective values

are used. Table 1 shows some values for the quenching intensity h and the associated equations to

calculate the distance from the quenched end face J0=(d0,h) [40, 49, 50].

Table 1. Equations for determining the distance J0 from the quenched end for different h values [3].

Quenchant h Equation

e. g. oil, still 0.25 00003,0755.000

ddJ

e. g. oil, weak motion 0.35 00001.0649.000

ddJ

e. g. oil, active motion 0.45 57.000 dJ

e. g. oil, strong motion 0.60 5.000 dJ

e. g. oil, stormy motion 1.00 000015.047.000

ddJ

In SimCarb QuenchTemp, the user is able to choose a quenchant from a program library of 37

different entries. For each quenchant, the associated quenching severity is stored in a database. The

values of the quenching intensity of each included quenchant stem from data analyses of literature

references [5, 13, 48, 51‒ 62].

The quenching severity can also be entered manually by selecting “manual input” from the list.

Valid values of h range from 0.2 to 2.0 and refer to still water of, per definition, h=1.0. Fig. 3 shows

typical Grossman numbers of various groups of quenchants, depending on the agitation condition.

Fig. 1.

Typical Grossman numbers of various quenchant groups,

depending on the agitation.

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Derivation of the Hardness Profile. In a first step the relevant distance from the end face J0 is

calculated from the diameter d0 and Grossman’s quenching intensity h. In Fig. 4a, the function of

h=0.30 is shown. In this example, the calculation is performed for a diameter of d0=50 mm and a

quenching intensity of h=0.30. The resulting distance J0 from the quenched end face is 15 mm.

In a second step, Jominy curves for carbon concentrations from the basic value to a carbon con-

tent of 0.6 wt.% (full martensite hardness) are calculated by means of Eq. 1, as exemplarily shown

Fig. 4b. The evaluation of the calculated Jominy curves is made for J0=15 mm. The hardness values

of the different carbon concentrations of Fig. 4b can also be expected at the corresponding carbon

content in the quenched surface layer. From the carburization profile in Fig. 4c, the distances from

the surface for every carbon concentration are determined. By transferring the hardness values of all

relevant carbon concentrations of Fig. 4b and the distances where these concentrations occur of Fig.

4c as indicated to Fig. 4d, a hardness profile of the case hardening layer is derived.

In SimCarb QuenchTemp the calculation of Jominy curves occurs in steps of 0.01 wt.% C to

achieve a precise hardness resolution in the surface layer. The carburization profile can be

simulated by SimCarb and imported in SimCarb QuenchTemp. Alternatively, a carburization profile

can be generated directly in SimCarb QuenchTemp by entering supporting points for depth and

carbon concentration, as shown in Fig. 1. Between the supporting points a polynomial interpolation

method is used. The subroutine program allocates the corresponding hardness value and distance

from the surface for every carbon concentration between the basic carbon content and 0.6 wt.% C

and calculates a hardness profile in the case hardening layer. For the determination of hardness

values between the surface hardness value and the hardness value at the carbon concentration of 0.6

wt.%, a polynomial interpolation method is used.

Fig. 2. Graphical representation of the derivation of the quench hardness distribution in the case. a)

determination of the applicable distance from the end face from the representative cylinder

diameter and the quenching intensity; b) calculated Jominy curves for the carbon concentra-

tions in the case; c) carburization profile; d) resulting quenching hardness distribution.

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Tempering. In order to have a satisfying fatigue and abrasion resistance, a minimum hardness of

about 60 HRC after tempering is necessary [63]. That is why a typical tempering temperature and

time combination of 150 to 200 °C and 2 to 4 hours, respectively, is applied [9]. Hence in SimCarb

QenchTemp the user is able to choose a tempering temperature between 150 and 200 °C and a

tempering time between 2 and 4 hours. During tempering, the ductility is increased and the risk of

cracking is reduced. Furthermore, the microstructure of the quenched steel is stabilized and the

dominating hardness mechanisms changes. In the indicvated temperature range, the hardness of the

martensitic structure decreases whereas the other phases do not response accordingly. For the

calculation of the hardness of the martensite microstructure, the diminution factor d is used [64]:

tTcdHH ,,CQT (9)

QH and

TH respectively describe the quenched and tempered hardness of the martensitic

structure. The martensite content is estimated following a method of Hodge and Orehoski [85]. The

used data of the diminution factor d arise from own experiments. The matrix with low carbon

concentrations, cC, around 0.2 wt.% changes hardly during tempering so that in these regions the

quenching hardness is equal to the tempering hardness. For a given tempering temperature and time,

the diminution factor d decreases with increasing carbon concentration cC. Therefore, a higher

initial quenching hardness decreases more than a lower one. The other microstructures like bainite,

perlite, ferrite and retained austenite that can occur in the surface layer are thermally more stable

and do not reveal such tempering reaction in the relevant temperature range. For these constituents,

the quenching hardness may be assumed according to the following equation:

R

T

R

Q HH (10)

In Fig. 5, the tempering dialog box is shown. The user is able to choose a tempering temperature

(150, 170, 185 and 200 °C) and a tempering time (2, 3 and 4 h) from two list boxes. Alternatively, it

is possible to enter a user defined equation by a polynomial of maximum fifth degree (continuous

index i) for the calculation of the diminution factor:

5

0

CC )(i

i

i cAcd (11)

The carbon concentration cC is expressed in wt.%. The diminution factor d of martensite is

dimensionless. The unit of the coefficient Ai, which is entered into the input boxes, is (wt.%)-i.

Thermophysical model

The essential part of the thermophysical model of SimCarb QuenchTemp is also the hardness simu-

lation in the case after quenching and tempering. Moreover, this model simulates the depth distribu-

tion of the quenching microstructure, which is not significantly changed by tempering in the rele-

vant range of maximum 200 °C (retained austenite transformation negligible). As well as in the

empirical model, the carburization profile is imported or user defined to perform the calculation.

A temperature distribution during quenching is simulated by applying the finite difference

method. Fourier’s law is modified to use temperature dependent heat transfer and conduction

coefficients. A simplified approach considers the changing microstructure during quenching in the

calculation of heat conduction coefficients from the chemical composition of the steel. Heat transfer

coefficients are taken from literature for common quenchants and can be selected by the user. Alter-

natively, the generation of user-defined quenchants by entering supporting points for temperature

and heat transfer coefficient is possible.

The quenching hardness and the microstructural composition is derived by identifying the simu-

lated cooling curves for each depth in continuous cooling transformation diagrams which are imple-

mented for conventional case hardening steels and carbon concentrations from 0.1 to 1.0 wt.%. The

tempering hardness is deduced by experimentally determined Hollomon-Jaffe parameters.

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Fig. 5. Dialog box for entering an equation of the carbon dependent diminution factor for martensite or

selecting the tempering conditions (temperature, time) based on stored experimental data.

Modification of Fourier’s Law. The temperature distribution during quenching is described by

Fourier’s law for an ideal round specimen (infinitely long plain cylinder) of diameter of 2R. The

conventional equation of Fourier’s law for one-dimensional radial heat flow in cylinder coordinates

is written as follows [65‒ 67]:

r

Tar

rrt

T 1 (12)

Eq. 12 is a parabolic partial (transport) differential equation of second degree. The temperature

conductibility a is, analogously to Fick’s law, also known as thermal diffusion coefficient:

ρ

λ

pca (13)

The coefficients T, t, , cp and respectively stand for temperature, time, heat conductivity, spe-

cific heat capacity and density. As the heat conduction coefficient λ is considered as dependent

upon the temperature, the temperature conductibility a also becomes temperature dependent:

ρ

λ

pc

TTa (14)

For the temperature dependent temperature conductibility a(T), the Fourier temperature conduc-

tion equation is modified:

r

T

T

a

r

Ta

r

T

r

TTa

t

T2

2

(15)

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The initial condition is given as follows:

0,,H tRrTT (16)

The quenching temperature TH is assumed to be uniformly in the entire work piece. The heat

transfer from quenchant to work piece is described by a boundary condition of third degree:

0,,λ

αF

tRrTT

r

T (17)

The quenchant temperature is denoted TF. The heat transfer coefficient (T) takes the relevant

stages of heat transfer into account. It depends in a complex way on the temperature and flow rate

of the quenchant as well as on the steel grade, geometry and surface condition of the work piece.

This coefficient is well suited for the description of the cooling effect of a quenchants.

Alternatively, a boundary condition of the first degree can be used:

0,, tRrtfT (18)

The surface temperature of the work piece is defined as a function of time during the quenching

process.

Heat Transfer Coefficient and Quenchant Temperature. The heat transfer coefficient has a

significant influence on the simulation of the temperature distribution and is highly dependent on

temperature and type of quenchant [48]. Once a work piece is introduced into a liquid, the occurring

cooling curve is much more complex than suggested by Newton’s law of cooling [13]. Fig. 6 shows

heat transfer coefficients for resting water at 20 and 60 °C as a function of surface temperature [68].

Generally, there are three different key stages of heat transfer during quenching. The first stage

of cooling is characterized by the formation of a vapor blanket around the work piece, which slows

down cooling significantly because it acts as an insulator [69]. Basically, cooling occurs by radia-

tion through the vapor film. The temperature, above which a total vapor blanket is maintained, is

known as the Leidenfrost temperature [55, 70].

The highest cooling rate occurs in the second so-called boiling stage. In this phase, the vapor

blanket disappears and the colder liquid is continuously brought into contact with the hot surface.

High heat extraction rates are the consequence [13, 71].

The third stage begins when the temperature of the steel reaches a point where liquid convection

is sufficient to keep it from boiling. Below this point, boiling stops and cooling takes place by

conduction and convection into the quenchant. The cooling rate thus decreases in the third phase of

quenching [70, 71].

Fig. 3.

Comparison of temperature de-

pendent heat transfer coeffi-

cients for “Water, still” at 20

and 60 °C [68].

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The three quenching stages cannot be taken into account in the calculation by a constant value of

the heat transfer coefficient. Therefore, simulation in SimCarb QuenchTemp is realized by means of

temperature dependent heat transfer coefficients α(T). In Fig. 7, the dialog box for quenchant type

and temperature is displayed. The user can choose a quenchant from a list of totally 12 entries.

Fig. 4. Dialog box for selecting a quenchant, entering a constant heat transfer coefficient manually

or generating a user-defined quenchant, including input field for the quenchant temperature.

Temperature dependent heat transfer coefficients for several quenchants, which can be selected

by the user, are taken from the literature for common quenchants [13, 55, 68, 72‒ 75]. It is also

possible to enter a constant value of the heat transfer coefficient instead of choosing a quenchant.

This value is inserted in Wm–2

K–1

.

Moreover, user-defined quenchants can be created by entering supporting points for temperature

T and heat transfer coefficient α. The way of creating quenchants is comparable with the generation

of carburization profiles. A user-defined quenchant can be saved for further simulations into an

ASCII file.

Heat Conduction Coefficient. The heat conductivity depends on the temperature, microstruc-

ture composition and carbon concentration of each steel [48, 76, 77]. In SimCarb QuenchTemp, a

model for the estimation of the heat conduction coefficient λ(T) is developed. The approach is based

on empirical data of heat conduction of different microstructures and temperatures and is illustrated

in Fig. 8. It is assumed that during quenching there are three different microstructure constituents:

austenite, mixed microstructure region austenite/martensite and martensite. The transition between

the microstructure areas is characterized by the martensite start and finish temperature, Ms and Mf.

Above the martensite start temperature Ms, in principle austenitic microstructure exists. Within

this region, the heat conduction coefficient decreases with decreasing temperature [78]. Between the

Ms and Mf temperature, a mixed microstructure region occurs, where the heat conduction coefficient

increases with decreasing temperature. Below the martensite finish temperature Mf, the martensite

transformation is completed. Within the martensitic microstructure, the heat conduction coefficient

increases slightly with decreasing temperature [79, 80].

This approach for the calculation of the temperature dependent heat conduction coefficients (T)

is implemented in SimCarb QuenchTemp. Here, a simplified linear development as shown in Fig. 8

is assumed.

This calculation method is performed, amongst others, by means of Ms , Mf and Ac1 temperature

of the selected steel. The determination of Ms and Mf temperature considers the alloy composition

and is based on the method of Andrews [81]. For the determination of the heat conductivity at 25 °C

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the so-called ADC (austenite decomposition) model is applied [80]. The heat conductivity at Ms and

Ac1 (723 °C) is calculated by a linear equation for the austenitic region [78]. The heat conductivity

at Mf is determined by using a linear relationship between the heat conduction coefficients at 25 and

723 °C. These main supporting points are connected by linear correlations to compute heat

conduction coefficients at each temperature. The heat conduction coefficients are calculated for

every temperature step during quenching by applying this method.

Fig. 5. Temperature dependency of the heat conduction coefficient for 18CrNiMo7-6.

As an alternative, it is possible to use a constant value of the heat conduction coefficient for the

simulation of the temperature distribution. This value is entered into the corresponding dialog box

of Fig. 9 in Wm–1

K–1

.

Fig. 6. Dialog box for selecting temperature dependent heat conduction or entering a constant value

of the heat conduction coefficient.

Simulation of the Temperature Distribution. The modified Fourier law is solved by using an

explicit finite difference method (FDM) for radial heat flow. Temperature dependent heat transfer

coefficient and heat conduction coefficient can be applied for the simulation of the temperature field

during quenching.

Fig. 10 shows a chart of supporting points nr for the discretization of space in the finite

difference method. To avoid incorrect user input with possible stability problems, the ideal number

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of supporting points nr is automatically calculated by the program, depending on the diameter of the

round specimen and the value of the time increment.

Fig. 10. Scheme of the spatial discretization.

The number of time increments, nt, can be determined automatically for optimized computing

performance or is alternatively entered manually as a cooling time. This cooling time is inserted in s

and subsequently converted into a number of time elements nt. The optimal extension of the time

increments Δt is preset and deduced from a large number of test runs.

If the automatic mode is selected, SimCarb QuenchTemp continuous with the simulation until a

temperature of 500 °C is reached. This is the temperature needed for the calculation of average

cooling rates (see next section). The automatic mode of the program optimizes the computing time

of the simulation and is recommended to the user.

Identification of Quenching Hardness and Microstructure Composition. To identify the

quenching hardness and microstructure composition, the t8/5 cooling time is calculated for each

depth of the simulated temperature distribution. This parameter is known from welding models and

stands for the time that is required to pass through the temperature range from 800 to 500 °C [13,

82]. From this time t8/5, an average cooling rate v is calculated by the following equation:

s

C500800

5/8

tv (19)

This determined cooling rate v is then compared with cooling curves of continuous time-tem-

perature-transformation (TTT) diagrams, which are calculated by means of the JMatPro® software

for more than 35 conventional case hardening steels. The considered carbon concentrations and

cooling rates range from 0.1 to 1.0 wt.% and 1 to 600 °C, respectively. In this way, the quenching

hardness and microstructure composition is derived step by step for every depth.

The user can select case hardening steels from the corresponding dialog box in SimCarb

QuenchTemp. Moreover, there is the possibility to change the chemical composition of each alloy.

This modification influences the simulation of the temperature distribution but has no direct effect

on the subsequent identification of the quenching hardness and the microstructure composition.

Tempering. In the empirical model, the tempering hardness is calculated by a diminution factor

for martensite [64]. In the thermophysical model, the Hollomon-Jaffe parameter, HP, is used to

predict the hardness decrease as an established approach. The application of tempering parameters,

particularly of HP, is proposed in the literature. By this parameter, a satisfying agreement with data

for a large hardness range is achieved [83‒ 85], particularly at higher temperatures [86].

Clog15.273P tTH (12)

In this equation, T, t and C stand for temperature, time and a material dependent constant,

respectively. The material constant C is dimensionless and ranges for unalloyed and moderately

alloyed steels from 14 to 20 [85, 87, 88]. Different combinations of temperature and time can result

in the same Hollomon-Jaffe parameter, which means similar tempering effect as well.

The data, which are used in SimCarb QuenchTemp, are deduced from own experiments for

18CrNiMo7-6, 20MoCr4 and 16MnCr5. For these case hardening steels, tempering experiments at

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temperatures and times from 150 to 200 °C and 2 to 4 h, respectively, are carried out to investigate

the differences in tempering resistance. It is found that the hardness decrease of these steel grades in

the considered temperature range between 150 and 200 °C is identical. At higher temperatures up to

300 and 400 °C, the hardness decrease of the different materials varies: whereas 18CrNiMo7-6 is

rather resistant to tempering and does not lose much hardness, 20MoCr4 and 16MnCr5 reveal

significantly lower tempering resistance.

As the typical temperature range of tempering in case hardening is between 150 and 200 °C,

tempering resistivity of different case hardening steels can be assumed to be equal in SimCarb

QuenchTemp. Therefore, it is not necessary to define different types of tempering resistance groups

with varying Hollomon-Jaffe parameters. One HP set for every temperature-time combination is

evaluated from the experimental data and used for all steels in SimCarb QuenchTemp. In the

thermophysical model, the user can choose a tempering temperature between 150 and 200 °C in

steps of 1 °C and a tempering time between 2 and 4 h in steps of 1 min for the calculation of the

tempering hardness from Hollomon-Jaffe parameters.

Simulation results

In SimCarb QuenchTemp, numerous simulation results are provided to the user. This includes,

besides a summary of the most important simulation results and process information, a graphical

output of the hardness depth distribution after quenching and tempering. Furthermore, the depth

dependent hardness and microstructure composition can be exported as an ASCII file (.txt format)

for further processing with, e. g., Microsoft Excel.

After each simulation, the most significant simulation results and process information like, e. g.,

steel composition, model cylinder diameter, heat transfer, heat conduction, quenchant type and

quenchant temperature, hardening temperature, surface carbon concentration, surface hardness and

case hardening depth are displayed in at a glance SimCarb QuenchTemp. This information can be

printed out and saved as an image file.

The hardness profile after quenching and tempering is displayed as a graphical hardness depth

distribution, as shown in Fig. 11. This diagram can be printed and saved.

Fig. 11. Graphical output representation of the simulated hardness profile.

With the export function of SimCarb QuenchTemp, it is, furthermore, possible to export the

hardness and microstructure composition as a function of depth into an ASCII file for further

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processing with, e. g., Microsoft Excel. The export function for the microstructure composition is

limited to the thermophysical model and includes the microstructures martensite, bainite, ferrite,

perlite and (retained) austenite.

Simulation Examples and Verification by Case Hardening Experiments

In the following section, the practical application of the SimCarb QuenchTemp software is demon-

strated by means of typical simulation examples of the empirical and thermophysical model. In

addition to the quenching hardness distribution, the case hardening depth, CHD, as key process

target parameter is evaluated.

Empirical model With the empirical model, a quenching process of the case hardening steel 15Cr3 with a cylinder di-

ameter of d0=50 mm is simulated. For this quenching process, strongly differing Grossman numbers

h=0.3 and h=1.5 are applied. The used carburization profile with a surface carbon concentration of

0.6 wt.% is simulated during a two-stage gas carburizing process by SimCarb. The austenite grain

size KASTM is 8. The resulting quenching hardness distributions are shown in Fig. 12. Additionally,

the carburization profile and the quenching hardness distribution, which is calculated by SimCarb

with the hardenability relationship of Hodge-Orehoski (see Eq. 4), are plotted in the diagram.

Fig. 12.

Simulated quenching hard-

ness distributions (cylinder

diameter d0=50 mm) of

15Cr3 steel for clearly dif-

ferent Grossman numbers

h=0.3 and h=1.5.

In Fig. 13, the influence of the representative cylinder diameter d0 on the resulting quenching

hardness distribution is demonstrated for the case hardening steel 15Cr3. The applied representative

cylinder diameters d0 amount to 50, 100 and 300 mm. The Grossman number is h=1.0, which corre-

sponds to still water.

Fig. 13.

Simulated quenching hardness

distributions of the case hard-

ening steel 15Cr3 for the indi-

cated representative cylinder

diameters d0. The carburization

profile, which is also plotted in

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Fig.12, is considered in the analysis. The quenching severity factor equals 1.0.

Thermophysical model Applying the thermophysical model, a quenching process on a cylinder of 18NiCrMo14-6 steel of a

diameter of d=40 mm is simulated. The carburization profile with a surface carbon concentration of

0.82 wt.% after a two-stage boost-diffuse gas carburizing process, determined by secondary ion

mass spectrometry (SIMS) [35], is shown in Fig. 14. The carbon content in the near-surface area,

where the measuring accuracy is reduced, is adjusted by means of the alloy factor recommended by

the AWT [3]. For the quenching process, “quenching oil, still” with a fluid temperature TF of 53 °C

is considered as quenchant. The heat transfer coefficient α of this quenchant is shown in Fig. 15 as a

function of the surface temperature T.

Fig. 14.

Measured carbon content after

carburizing of 18NiCrMo14-6.

The carbon concentrations in

the surface zone are adjusted

according to the alloy factor

proposed by the AWT [3].

In Fig. 16, the resulting quenching hardness distribution of the simulation for the thermophysical

model is displayed. Also, the measured quenching hardness profile from identical quenching

experiments is plotted. Both hardness profiles are quite similar, the case hardening depths of 4.02

and 4.24 mm lie close to each other. In the surface area, a retained austenite content of almost 23

vol.% and a martensite fraction of about 77 vol.% are predicted.

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Fig. 15. Heat transfer coefficient of “quenching oil, still” as a function of surface temperature T.

Fig. 16. Simulated and measured hardness profile of 18NiCrMo14-6 steel quenched in “quenching

oil, still“.

Fig. 17 provides a comparison of the simulated and measured retained austenite distribution of

18NiCrMo14-6 steel after the quenching treatment. The computation moderately falls below the

data points, which obviously does not affect the hardness prediction noticeably.

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Fig. 17. Simulated and measured retained austenite distribution after quenching of 18NiCrMo14-6.

Discussion

In the empirical as well as in the thermophysical model of SimCarb QuenchTemp, several simplifi-

cations in the prediction of the hardness from a given carburization profile after quenching and

tempering are made. These assumptions are discussed briefly in the following.

Empirical model The procedure of Wyss to simulate the hardness profile after quenching is established in practice.

Comparisons with measured hardness profiles of carburized steels are available in the literature

[39]. In this procedure the preset equation for the calculation of carbon dependent Jominy curves

stems from regression analyses [37, 38, 42]. This expression proposed by Just achieves good agree-

ment with measured hardness profiles for low alloyed case hardening steels (e. g. 17Cr3). However,

it should be noted that the equation is not applicable to higher alloyed grades (e. g. 18CrNiMo7-6).

The hardenability relationships for the determination of the surface hardness take only the carbon

concentration into account. The influence of the alloying elements is neglected as the maximum

martensite hardness is governed by the carbon content.

The quenching severity factor of Grossman semiquantitatively estimates the cooling rate of a

work piece (model cylinder) achieved by an applied quenchant (e. g. hardening oil) in relation to

still water at 18 °C. This thermophysical parameter can be determined experimentally or taken from

the literature. The chilling effect depends on the quenchant type and its state of agitation and flow.

Furthermore, it depends on the heat conduction of the steel and some other influencing factors, e. g.

bath and hardening temperature, mass of the work piece and wall thickness [48, 55, 89, 90]. The

relevant characteristics for the chilling effect like chemical composition, viscosity and boiling point,

however, cannot be taken into account as a criterion in the empirical model.

The heat conductivity of a steel grade depends on the microstructure, carbon concentration and

temperature [48, 76, 77]. These influencing factors vary with time and position during quenching.

On the contrary, the Grossman number represents a constant effective value. Especially during

nucleate boiling, the heat conduction coefficient is very high and only described insufficiently by

the Grossman number. Actually, many quenchants in industrial heat treatment do not show a

Newtonian cooling [89]. Finally the concept of Grossman is not suitable for discontinuous (e. g.

interrupted) quenching processes [13]: changing quenchants or modified stages of agitation cannot

be treated by this severity factor.

The microstructure analysis, based on the approach of Hodge and Orehoski, provides a practical

but, particularly for small contents, a rough estimation of the martensite fraction. This martensite

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content is required for the carbon, temperature and time dependent diminution factor, which is used

for the prediction of the tempering from the quenching hardness. A direct determination of the

microstructural composition is not possible in the empirical model. That is why the martensite con-

tent is required as a function of carbon concentration or depth.

Only the martensitic phase is sensitive to tempering response by hardness decrease in the tem-

perature range up to 200 °C common in case hardening. With increasing distance from the surface,

the critical cooling rate for reaching the martensite start temperature transformation free depends on

the alloy composition of the steel and the carbon concentration. Here, the simplified microstructure

analysis loses precision and the estimation of the martensite content is too high leading to a reduced

tempering hardness. With decreasing carbon concentration and increasing distance from the surface,

the diminution factor tends toward 1, which limits this deviation in the practical application.

Thermophysical model The simulation of the temperature distribution during quenching is based on a modified Fourier law

that is solved by an explicit finite difference method. It is well know from the literature that an

implicit finite difference method is faster and numerically more stable. To achieve good results with

an explicit method, the time steps Δt should be very small, which results in a large number of time

increments nt. This normally extends the computing time. However, the simulated quenching time

from hardening temperature to 500 °C is less than one minute, which means that the number of time

increments nt is still manageable for an explicit method. Due to this reason and the fact that the

programmability in FORTRAN is more comfortable, the explicit method is a good choice for this

kind of simulation. The results of this numerical technique agree very well with an analytical solu-

tion applied to special conditions as reference [65]. The computing time is less than two seconds.

When it comes to the different stages of heat transfer during quenching (film boiling, nucleate

boiling, convection), the heat transfer coefficient is considered as a function of temperature in

SimCarb QuenchTemp. This means that, for every temperature step, the adequate heat transfer

coefficient is used, which makes the simulation more comparable to industrial heat treatment

processes. Heat transfer coefficients for the most quenchants in SimCarb QuenchTemp are taken

from the literature [13, 55, 68, 72‒ 75]. As the heat transfer coefficients sensitively depend on the

state of agitation, temperature and type of quenchant, little deviations have a great influence on the

simulation and, as a consequence, on the quenching hardness and microstructure composition.

Therefore, the heat transfer coefficients of the used quenchant must be known precisely to achieve

reliable results.

As mentioned above, the heat conductivity of steel depends upon the microstructure, carbon

concentration and temperature [48, 76, 77]. In the empirical model, the heat conductivity is taken

into account only by a constant (effective) value for every stage of the quenching process. In the

thermophysical model, for each temperature step of the finite difference method, a temperature

dependent heat conduction coefficient is used. As shown in Fig. 8, a linear relationship of the heat

conductivity in the martensitic and austenitic structure as well as in the mixed area in between is

assumed. This simplified linear assumption is based on empirical research [78‒ 81].

The cooling time t8/5 is well known from welding and denotes the time that is needed to pass

through a temperature range from 800 to 500 °C during cooling of a weld seam [13, 82]. The choice

of the temperature interval of 800 and 500 °C is proven successfully in welding modeling. In

SimCarb QuenchTemp, this temperature range is used to calculate an average cooling rate for every

depth. Simulation parameter studies reveal that a change of the interval limits especially to lower

temperature results in a lower average cooling rate because the cooling rate decreases at lower

temperatures. However, the good agreement of the simulation results with measurements shows that

the temperature span of 800 to 500 °C is well suited for the calculation of characteristic average

cooling rates in SimCarb QuenchTemp.

Continuous cooling transformation (CCT) diagrams for more than 35 steels, its carbon contents

between 0.1 and 1.0 wt.% and cooling rates from 1 to 600 °C/s are stored in SimCarb QuenchTemp.

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These CCT diagrams are calculated by means of the commercial JMatPro®

software. As the avail-

able CCT diagrams must be calculated in advance, the user is limited to the implemented steels.

The use of time-temperature parameters, especially Hollomon-Jaffe parameters, for tempering is

suggested in the literature [83, 84]. Experiments show that there is no significant difference in

hardness decrease of different steel grades in the temperature range between 150 and 200 °C and for

times from 2 and 4 h typical of tempering in case hardening. That is why the different steel grades

in SimCarb QuenchTemp are not classified into different tempering resistance groups. For the

implemented temperature-time combination, a set of Hollomon-Jaffe parameters is evaluated from

tempering experiments. For deviating temperature-time combinations, a linear interpolation method

is used to calculate the tempering hardness profile. The simulation results for tempering hardness

distributions are found to be in very good agreement with experimental data. This can be attributed

to the use of time-temperature parameters for the calculation of the tempering from the quenching

hardness.

Changes of the microstructure during tempering cannot be predicted by time-temperature param-

eters. The tempering conditions usually applied in case hardening, however, do not cause such

alterations. Noticeable retained austenite transformations starts not before a temperature of 200 °C

is exceeded.

Conclusions

The new simulation tool SimCarb QuenchTemp is developed for the prediction of the depth

distributions of the quenching and tempering hardness as well as the microstructure evolution from

a given carburization profile by considering the process conditions, chemical steel composition and

work piece geometry. It offers the following two approaches to the user of the expert software.

In the empirical model, there are several program libraries for quenchants, steels types and

hardenability relationships. Data like the Grossman quenching intensity factor, alloy composition or

surface hardness can also be entered manually. A formula proposed by Just for the calculation of

Jominy curves is preset. The coefficients of this formula can be modified. The carburization profile

is imported from SimCarb (ASCII file output) or created manually in an integrated subroutine by

entering supporting points for depth and carbon concentration. For tempering simulation, a dimi-

nution factor is used for a temperature range from 150 to 200 °C and tempering periods of 2 to 4 h.

In the thermophysical model, the temperature field during quenching is simulated by applying

the finite difference method. A simplified approach considers the changing microstructure in the

calculation of heat conduction coefficients from the chemical composition of the steel. Heat transfer

coefficients are taken from the literature for common quenchants and are stored in program

libraries. Furthermore, there is the possibility to involve user-defined quenchants by entering

supporting points for depth and heat transfer coefficient. The quenching hardness and the micro-

structure composition are finally derived by identifying the simulated cooling curves for each depth

in continuous cooling transformation diagrams, which are implemented for conventional case hard-

ening steels and carbon concentrations from 0.1 to 1.0 wt.%. The tempering hardness is deduced by

experimentally determined Hollomon-Jaffe parameters for a temperature range from 150 to 200 °C

and tempering periods of 2 to 4 h, as common in case hardening practice.

In the empirical model, the equation proposed by Just is only suitable for low alloyed steels like,

e.g., 17Cr3 or 16MnCr5. A further development of the Jominy equation for higher alloyed case

hardening steels is intended. Moreover, the extension of the implemented values of the Grossman

quenching intensity factor below 0.2 and particularly above 2.0 is desirable.

In the thermophysical model, the user is limited to the steel grades that are already implemented

in the SimCarb QuenchTemp program library. Main future research aims at the implementation of a

CCT calculation tool. So, the quenching process could be simulated unrestrictedly for any alloy

composition of the steel. Although it is possible for the user to define further quenchants, another

improvement is the extension of the quenchant library of the SimCarb QuenchTemp software.

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