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

Transcription

1 New ase Hardening Software Simarb QuenhTemp for the Simulation of Hardness and Mirostruture from arburization Profiles M. Kaffenberger 1,a, J. Gegner 1,b 1 University of Siegen, Institute of Material Siene, Paul-Bonatz-Straße 9-11, Siegen, Germany. a kaffenberger@lot.mb.uni-siegen.de, b juergen.gegner@uni-siegen.de Keywords: ase hardening software, quenhing, tempering, simulation of hardness, predition of mirostruture. ABSTRAT The Simarb program pakage as powerful stand-alone solution provides a user-friendly Windows expert software suite for omputer aided ase hardening engineering in industrial heat treatment and researh. In the present paper, a new simulation tool is introdued for the predition of the depth distributions of the quenhing and tempering hardness as well the mirostruture development from a given arburization profile by taking into aount the proess onditions, hemial steel omposition and work piee geometry. Simarb QuenhTemp offers both an empirial and a thermophysial model. The funtionality and pratial appliation of the software are demonstrated by means of sreenshots and simulation examples. In the empirial model, the quenhing hardness is derived from alulated sets of Jominy urves for the arbon onentrations in the ase at the appliable distane from the quenhed end. The representative ylinder diameter haraterizes the influene of the size and shape of the work piee. The ooling ability of the medium is quantified by the Grossman quenh severity. The tempering hardness is alulated by a diminution fator. In the thermophysial model, the temperature distribution during quenhing is simulated by applying the finite differene method. Fourier s law is modified to use temperature dependent heat transfer and ondution oeffiients. A simplified approah onsiders the hanging mirostruture in the alulation of heat ondution oeffiients from the hemial omposition of the steel. Heat transfer oeffiients are taken from the literature for ommon quenhants and an be seleted by the user. The quenhing hardness and the mirostruture omposition is finally derived by identifying the simulated ooling urves for eah depth in ontinuous ooling transformation diagrams, whih are implemented for onventional ase hardening steels and arbon onentrations of 0.1 to 1.0 wt.%. The tempering hardness is dedued by experimentally determined Hollomon-Jaffe parameters. Introdution ase hardening [1 9], with a world market share of more than one third of the industrial hardening proesses, holds a leading position within the heat treatment tehnologies of steels. To produe reliable omponents ost-effetively, it is important to ensure high auray in ahieving the target quantities, partiularly the arburizing and ase hardening depth and the surfae hardness [10]. These proess values, however, are not always met preisely enough in pratie [4, 11, 12]. The predition of the resulting hardness distribution is omplex both from a metal physis and material siene as well as a mathematial viewpoint. Previous researh fouses on quenhing of steels [13 15]. The ooling onditions influene the material harateristis signifiantly. Therefore, the mathemati simulation of quenhing proesses gains inreasing interest [16 20]. Finally low-temperature tempering, moreover, must also be inluded. The stand-alone Simarb program suite, onsisting of the base software Simarb with the add-on tool Simarb Diffusivity and Simarb QuenhTemp, ombines the proess simulation and the predition of all relevant target quantities in one expert system of omputational ase hardening engineering

2 Simarb Quenh Temp in the Sequene of the Simarb Software Pakage omputer-aided heat treatment support aims for the analysis, design and optimization of industrial tehnologies. Sine its introdution at the MMT-2006 onferene [21], the Simarb software is applied internationally by engineers, researhers, and leturers from industry and aademia [6, 12, 21 33]. The graphial user interfae in Mirosoft Windows with pull-down menus and buttons offers various funtions, high effiieny, and ease of usability with intuitive mouse navigation, flexible input options and advaned libraries. Simarb allows the user to alulate arbon profiles for real multi-stage arburization proesses numerially by applying the finite differene method (FDM) [12, 21, 29, 31 33]. In addition to the relevant library, the extension module Simarb Diffusivity provides steel alloy speifi arbon diffusion oeffiients in austenite in an editable form. The basi hardness predition implemented in Simarb evaluates arbon onentration relationships and aounts for the retained austenite ontents [31]. The present paper introdues the new software Simarb QuenhTemp developed in a PhD researh at the Institute of Material Siene of the University of Siegen. As all parts of the integrated Simarb pakage, it represents a stand-alone Windows program. Simarb QuenhTemp alulates the quenhing and tempering hardness as well as the mirostruture omposition of a ase hardened steel omponent. These simulations involve the given arbon depth distribution after arburizing, omputed by Simarb or measured, e. g., by seondary ion mass spetrometry [6, 34, 35], as well as the material parameters, omponent geometry, and proess onditions. The Simarb QuenhTemp software provides an empirial and a thermophysial model that an be seleted by the user. Eah operating mode supports the diret import of arburization profiles as ASII files in the.txt format exported from Simarb for further alulations. Alternatively, Simarb QuenhTemp offers a simple subroutine to generate a user-defined arbon depth distribution and save it in the appropriate ASII format. ombined with the preise measurement of the arburization profile and the depth distribution of the quenhing and tempering hardness as well as the aurate knowledge of the proess onditions, appliation of the Simarb expert software pakage permits the methodial analysis, design and optimization of reliable heat treatments. This omputer-aided holisti approah is alled ase hardening engineering [6, 27, 33]. Empirial model In order to predit the hardness distribution after quenhing from a given arburization profile, a pratial method of Wyss is reommended in literature [36 39]. On the basis of established works of Grossman [40, 41], this method is proposed for graphial evaluation [36 39]. The empirial model of Simarb QuenhTemp inludes this proedure in an engineering software solution. The arbon profile, whih is generated in the surfae layer by ase arburizing, is basially responsible for the resulting hardness profile after quenhing. The influene of the steel omposition is taken into aount by the hardenability that depends on the steel omposition. The geometry of the work piee is speified by the representative ylinder diameter of an equivalent round speimen. This simple sample desribes the ooling harateristi of a relevant ross setion of the work piee. The empirial model of Simarb QuenhTemp takes the proess onditions into aount, based on Grossman s quenhing intensity or severity fator. The surfae hardness stems from a hardenability relationship or user input. The hardness profile is then alulated from Jominy urves, the representative ylinder bore diameter and Grossman quenhing severity fator. A arbon dependent diminution fator is applied for the alulation of the tempering hardness. The martensite fration is estimated using a simplified method. These approahes are ombined to ahieve a pratial predition of the ase hardening depth after both quenhing and tempering. arbon Depth Distribution. Due to the modular onept of the Simarb software suite, a arburization profile simulated by Simarb (ASII.txt output format), an be imported diretly in Simarb QuenhTemp. Alternatively, it is possible to reate a user-defined arbon distribution in Simarb QuenhTemp. In Fig. 1, the dialog box for the user definition of an arbitrary arburization 1-207

3 profile is shown. Supporting points for depth and arbon onentration are entered into the input fields below and are speified in mm and wt.%, respetively. The final data point is identified as the total arburization depth. The arbon distribution an be displayed as a graphial output by the subroutine. For later use the arburization profile an also be exported into an ASII file (.txt format). Fig. 1. Dialog box for generating a arburization profile. Jominy urves and Surfae Hardness. For the predition of the hardness profile, Jominy urves for different arbon onentrations are determined. This alulation onsiders the hemial omposition of the steel and its austenite mirostruture, expressed as ASTM grain size number K ASTM. An equation proposed by Just is preset in Simarb QuenhTemp [37, 38, 42]: H Mn 38 J J Mo 5.5 Ni J 6.1 Si 39 V P r 0.81K This equation is also reommended by the Assoiation for Heat Treatment and Materials Tehnology (AWT, Bremen, Germany). The onentrations of arbon the other alloying elements are inserted in wt.%. The grain size K ASTM is dimensionless, typial values range between 5 and 10. The hardness H and the distane J from the end fae are speified in HR and mm, respetively. Eq. 1 is limited to distanes J from the end fae between 8 and 80 mm and arbon onentrations of 0.6 wt.%. That is why the surfae hardness at arbon ontents from 0.6 to 0.9 wt.% is alulated by applying a hardenability relationship for martensite mirostruture. Simarb QuenhTemp offers the following versions: Burns-Moore-Arher [43]: : H : H 0.7 : H 1.5 : H Gegner [44]: : H 1.5 : H ASTM (1) (2) (3)

4 Hodge-Orehoski [45]: 0.1 0,6 : H : H 1.5 : H Kell [39]: : H 0.7 : H 1.5 : H , , ,66 115,82 3, Riehle-Simmhen [46]: : H (6) 64 0 Wyss [36]: : H 1.5 : H It is well known that the predition of the fae quenhing hardness for low alloyed steels performs satisfatorily. However, with inreasing alloy ontent (partiularly for higher r and Ni onentrations), this formula loses auray [47]. The limitation must also be onsidered in Eq. 1. To simulate speifi steels with higher amounts of alloying additions, suh as 18rNiMo7-6, Simarb QuenhTemp offers the user the possibility to modify the oeffiients of Eq. 1 aordingly. Steel, Steel omposition and Grain Size. In Fig. 2, the dialog box for the steel grade, steel omposition and grain size is shown. It gives an opportunity to selet a steel grade from a list of 45 items. Steel type and material number are indiated. Aording to the hoie of the user the average hemial omposition for the steel is loaded. This data is displayed in the orresponding input field of eah element. Additionally, the hemial omposition an be modified manually. The austenite grain size before quenhing is entered in the input field K-ASTM. (4) (5) (7) Fig. 2. Dialog box for seleting a steel grade or manually entering the material omposition as well as for filling in the grain size and opening the dialog box to modify the Jominy equation

5 Quenhing Severity and Diameter. The state of motion of a quenhant affets the heat transfer signifiantly. One fator is the enfored onvetion, 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 separation of bubbles from the work piee surfae [48]. The inreasing flow rate is haraterized in the quenhing severity library by the onditions of mild, weak, ative, strong and stormy agitation. The distane from the quenhed end fae, J 0 =(d 0,h), whih is used in Eq. 1, is determined by a funtion of the representative ylinder diameter, d 0, of the round model speimen and Grossman s quenh(ing) intensity fator h [36 38]. In Simarb QuenhTemp, the influene of type and state of motion of a quenhant is desribed by Grossman s quenhing intensity h, whih represents a mean level of heat withdrawal: α h (8) 2λ For the heat transfer oeffiient α and the heat ondution oeffiient λ, onstant effetive values are used. Table 1 shows some values for the quenhing intensity h and the assoiated equations to alulate the distane from the quenhed end fae J 0 =(d 0,h) [40, 49, 50]. Table 1. Equations for determining the distane J 0 from the quenhed end for different h values [3]. Quenhant h Equation ,0003d 0 0 e. g. oil, still 0.25 J d 0 e. g. oil, weak motion 0.35 J d e. g. oil, ative motion 0.45 e. g. oil, strong motion d 0 J 0.5 J0 d d d 0 0 e. g. oil, stormy motion 1.00 J d In Simarb QuenhTemp, the user is able to hoose a quenhant from a program library of 37 different entries. For eah quenhant, the assoiated quenhing severity is stored in a database. The values of the quenhing intensity of eah inluded quenhant stem from data analyses of literature referenes [5, 13, 48, 51 62]. The quenhing severity an also be entered manually by seleting 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 typial Grossman numbers of various groups of quenhants, depending on the agitation ondition. 0 Fig. 1. Typial Grossman numbers of various quenhant groups, depending on the agitation

6 Derivation of the Hardness Profile. In a first step the relevant distane from the end fae J 0 is alulated from the diameter d 0 and Grossman s quenhing intensity h. In Fig. 4a, the funtion of h=0.30 is shown. In this example, the alulation is performed for a diameter of d 0 =50 mm and a quenhing intensity of h=0.30. The resulting distane J 0 from the quenhed end fae is 15 mm. In a seond step, Jominy urves for arbon onentrations from the basi value to a arbon ontent of 0.6 wt.% (full martensite hardness) are alulated by means of Eq. 1, as exemplarily shown Fig. 4b. The evaluation of the alulated Jominy urves is made for J 0 =15 mm. The hardness values of the different arbon onentrations of Fig. 4b an also be expeted at the orresponding arbon ontent in the quenhed surfae layer. From the arburization profile in Fig. 4, the distanes from the surfae for every arbon onentration are determined. By transferring the hardness values of all relevant arbon onentrations of Fig. 4b and the distanes where these onentrations our of Fig. 4 as indiated to Fig. 4d, a hardness profile of the ase hardening layer is derived. In Simarb QuenhTemp the alulation of Jominy urves ours in steps of 0.01 wt.% to ahieve a preise hardness resolution in the surfae layer. The arburization profile an be simulated by Simarb and imported in Simarb QuenhTemp. Alternatively, a arburization profile an be generated diretly in Simarb QuenhTemp by entering supporting points for depth and arbon onentration, as shown in Fig. 1. Between the supporting points a polynomial interpolation method is used. The subroutine program alloates the orresponding hardness value and distane from the surfae for every arbon onentration between the basi arbon ontent and 0.6 wt.% and alulates a hardness profile in the ase hardening layer. For the determination of hardness values between the surfae hardness value and the hardness value at the arbon onentration of 0.6 wt.%, a polynomial interpolation method is used. Fig. 2. Graphial representation of the derivation of the quenh hardness distribution in the ase. a) determination of the appliable distane from the end fae from the representative ylinder diameter and the quenhing intensity; b) alulated Jominy urves for the arbon onentrations in the ase; ) arburization profile; d) resulting quenhing hardness distribution

7 Tempering. In order to have a satisfying fatigue and abrasion resistane, a minimum hardness of about 60 HR after tempering is neessary [63]. That is why a typial tempering temperature and time ombination of 150 to 200 and 2 to 4 hours, respetively, is applied [9]. Hene in Simarb QenhTemp the user is able to hoose a tempering temperature between 150 and 200 and a tempering time between 2 and 4 hours. During tempering, the dutility is inreased and the risk of raking is redued. Furthermore, the mirostruture of the quenhed steel is stabilized and the dominating hardness mehanisms hanges. In the indivated temperature range, the hardness of the martensiti struture dereases whereas the other phases do not response aordingly. For the alulation of the hardness of the martensite mirostruture, the diminution fator d is used [64]: H H d T, t T Q H Q and, H T respetively desribe the quenhed and tempered hardness of the martensiti struture. The martensite ontent is estimated following a method of Hodge and Orehoski [85]. The used data of the diminution fator d arise from own experiments. The matrix with low arbon onentrations,, around 0.2 wt.% hanges hardly during tempering so that in these regions the quenhing hardness is equal to the tempering hardness. For a given tempering temperature and time, the diminution fator d dereases with inreasing arbon onentration. Therefore, a higher initial quenhing hardness dereases more than a lower one. The other mirostrutures like bainite, perlite, ferrite and retained austenite that an our in the surfae layer are thermally more stable and do not reveal suh tempering reation in the relevant temperature range. For these onstituents, the quenhing hardness may be assumed aording to the following equation: H H (10) R Q R T In Fig. 5, the tempering dialog box is shown. The user is able to hoose a tempering temperature (150, 170, 185 and 200 ) 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 (ontinuous index i) for the alulation of the diminution fator: 5 ( ) i0 i d A i (11) The arbon onentration is expressed in wt.%. The diminution fator d of martensite is dimensionless. The unit of the oeffiient A i, whih is entered into the input boxes, is (wt.%) -i. Thermophysial model The essential part of the thermophysial model of Simarb QuenhTemp is also the hardness simulation in the ase after quenhing and tempering. Moreover, this model simulates the depth distribution of the quenhing mirostruture, whih is not signifiantly hanged by tempering in the relevant range of maximum 200 (retained austenite transformation negligible). As well as in the empirial model, the arburization profile is imported or user defined to perform the alulation. A temperature distribution during quenhing is simulated by applying the finite differene method. Fourier s law is modified to use temperature dependent heat transfer and ondution oeffiients. A simplified approah onsiders the hanging mirostruture during quenhing in the alulation of heat ondution oeffiients from the hemial omposition of the steel. Heat transfer oeffiients are taken from literature for ommon quenhants and an be seleted by the user. Alternatively, the generation of user-defined quenhants by entering supporting points for temperature and heat transfer oeffiient is possible. The quenhing hardness and the mirostrutural omposition is derived by identifying the simulated ooling urves for eah depth in ontinuous ooling transformation diagrams whih are implemented for onventional ase hardening steels and arbon onentrations from 0.1 to 1.0 wt.%. The tempering hardness is dedued by experimentally determined Hollomon-Jaffe parameters (9)

8 Fig. 5. Dialog box for entering an equation of the arbon dependent diminution fator for martensite or seleting the tempering onditions (temperature, time) based on stored experimental data. Modifiation of Fourier s Law. The temperature distribution during quenhing is desribed by Fourier s law for an ideal round speimen (infinitely long plain ylinder) of diameter of 2R. The onventional equation of Fourier s law for one-dimensional radial heat flow in ylinder oordinates is written as follows [65 67]: T 1 T r a t r r r Eq. 12 is a paraboli partial (transport) differential equation of seond degree. The temperature ondutibility a is, analogously to Fik s law, also known as thermal diffusion oeffiient: λ a (13) ρ p The oeffiients T, t,, p and respetively stand for temperature, time, heat ondutivity, speifi heat apaity and density. As the heat ondution oeffiient λ is onsidered as dependent upon the temperature, the temperature ondutibility a also beomes temperature dependent: λ T a T (14) ρ p For the temperature dependent temperature ondutibility a(t), the Fourier temperature ondution equation is modified: T t a 2 T T T 2 r r a T r a T T r (12) (15) 1-213

9 The initial ondition is given as follows: T T, r R, t 0 (16) H The quenhing temperature T H is assumed to be uniformly in the entire work piee. The heat transfer from quenhant to work piee is desribed by a boundary ondition of third degree: T r α λ T T, r R, t 0 F The quenhant temperature is denoted T F. The heat transfer oeffiient (T) takes the relevant stages of heat transfer into aount. It depends in a omplex way on the temperature and flow rate of the quenhant as well as on the steel grade, geometry and surfae ondition of the work piee. This oeffiient is well suited for the desription of the ooling effet of a quenhants. Alternatively, a boundary ondition of the first degree an be used: t, r R, t 0 T f (18) The surfae temperature of the work piee is defined as a funtion of time during the quenhing proess. Heat Transfer oeffiient and Quenhant Temperature. The heat transfer oeffiient has a signifiant influene on the simulation of the temperature distribution and is highly dependent on temperature and type of quenhant [48]. One a work piee is introdued into a liquid, the ourring ooling urve is muh more omplex than suggested by Newton s law of ooling [13]. Fig. 6 shows heat transfer oeffiients for resting water at 20 and 60 as a funtion of surfae temperature [68]. Generally, there are three different key stages of heat transfer during quenhing. The first stage of ooling is haraterized by the formation of a vapor blanket around the work piee, whih slows down ooling signifiantly beause it ats as an insulator [69]. Basially, ooling ours by radiation through the vapor film. The temperature, above whih a total vapor blanket is maintained, is known as the Leidenfrost temperature [55, 70]. The highest ooling rate ours in the seond so-alled boiling stage. In this phase, the vapor blanket disappears and the older liquid is ontinuously brought into ontat with the hot surfae. High heat extration rates are the onsequene [13, 71]. The third stage begins when the temperature of the steel reahes a point where liquid onvetion is suffiient to keep it from boiling. Below this point, boiling stops and ooling takes plae by ondution and onvetion into the quenhant. The ooling rate thus dereases in the third phase of quenhing [70, 71]. (17) Fig. 3. omparison of temperature dependent heat transfer oeffiients for Water, still at 20 and 60 [68]

10 The three quenhing stages annot be taken into aount in the alulation by a onstant value of the heat transfer oeffiient. Therefore, simulation in Simarb QuenhTemp is realized by means of temperature dependent heat transfer oeffiients α(t). In Fig. 7, the dialog box for quenhant type and temperature is displayed. The user an hoose a quenhant from a list of totally 12 entries. Fig. 4. Dialog box for seleting a quenhant, entering a onstant heat transfer oeffiient manually or generating a user-defined quenhant, inluding input field for the quenhant temperature. Temperature dependent heat transfer oeffiients for several quenhants, whih an be seleted by the user, are taken from the literature for ommon quenhants [13, 55, 68, 72 75]. It is also possible to enter a onstant value of the heat transfer oeffiient instead of hoosing a quenhant. This value is inserted in Wm 2 K 1. Moreover, user-defined quenhants an be reated by entering supporting points for temperature T and heat transfer oeffiient α. The way of reating quenhants is omparable with the generation of arburization profiles. A user-defined quenhant an be saved for further simulations into an ASII file. Heat ondution oeffiient. The heat ondutivity depends on the temperature, mirostruture omposition and arbon onentration of eah steel [48, 76, 77]. In Simarb QuenhTemp, a model for the estimation of the heat ondution oeffiient λ(t) is developed. The approah is based on empirial data of heat ondution of different mirostrutures and temperatures and is illustrated in Fig. 8. It is assumed that during quenhing there are three different mirostruture onstituents: austenite, mixed mirostruture region austenite/martensite and martensite. The transition between the mirostruture areas is haraterized by the martensite start and finish temperature, M s and M f. Above the martensite start temperature M s, in priniple austeniti mirostruture exists. Within this region, the heat ondution oeffiient dereases with dereasing temperature [78]. Between the M s and M f temperature, a mixed mirostruture region ours, where the heat ondution oeffiient inreases with dereasing temperature. Below the martensite finish temperature M f, the martensite transformation is ompleted. Within the martensiti mirostruture, the heat ondution oeffiient inreases slightly with dereasing temperature [79, 80]. This approah for the alulation of the temperature dependent heat ondution oeffiients (T) is implemented in Simarb QuenhTemp. Here, a simplified linear development as shown in Fig. 8 is assumed. This alulation method is performed, amongst others, by means of M s, M f and A 1 temperature of the seleted steel. The determination of M s and M f temperature onsiders the alloy omposition and is based on the method of Andrews [81]. For the determination of the heat ondutivity at

11 the so-alled AD (austenite deomposition) model is applied [80]. The heat ondutivity at M s and A 1 (723 ) is alulated by a linear equation for the austeniti region [78]. The heat ondutivity at M f is determined by using a linear relationship between the heat ondution oeffiients at 25 and 723. These main supporting points are onneted by linear orrelations to ompute heat ondution oeffiients at eah temperature. The heat ondution oeffiients are alulated for every temperature step during quenhing by applying this method. Fig. 5. Temperature dependeny of the heat ondution oeffiient for 18rNiMo7-6. As an alternative, it is possible to use a onstant value of the heat ondution oeffiient for the simulation of the temperature distribution. This value is entered into the orresponding dialog box of Fig. 9 in Wm 1 K 1. Fig. 6. Dialog box for seleting temperature dependent heat ondution or entering a onstant value of the heat ondution oeffiient. Simulation of the Temperature Distribution. The modified Fourier law is solved by using an expliit finite differene method (FDM) for radial heat flow. Temperature dependent heat transfer oeffiient and heat ondution oeffiient an be applied for the simulation of the temperature field during quenhing. Fig. 10 shows a hart of supporting points nr for the disretization of spae in the finite differene method. To avoid inorret user input with possible stability problems, the ideal number 1-216

12 of supporting points nr is automatially alulated by the program, depending on the diameter of the round speimen and the value of the time inrement. Fig. 10. Sheme of the spatial disretization. The number of time inrements, nt, an be determined automatially for optimized omputing performane or is alternatively entered manually as a ooling time. This ooling time is inserted in s and subsequently onverted into a number of time elements nt. The optimal extension of the time inrements Δt is preset and dedued from a large number of test runs. If the automati mode is seleted, Simarb QuenhTemp ontinuous with the simulation until a temperature of 500 is reahed. This is the temperature needed for the alulation of average ooling rates (see next setion). The automati mode of the program optimizes the omputing time of the simulation and is reommended to the user. Identifiation of Quenhing Hardness and Mirostruture omposition. To identify the quenhing hardness and mirostruture omposition, the t 8/5 ooling time is alulated for eah 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 [13, 82]. From this time t 8/5, an average ooling rate v is alulated by the following equation: v (19) t s 8/ 5 This determined ooling rate v is then ompared with ooling urves of ontinuous time-temperature-transformation (TTT) diagrams, whih are alulated by means of the JMatPro software for more than 35 onventional ase hardening steels. The onsidered arbon onentrations and ooling rates range from 0.1 to 1.0 wt.% and 1 to 600, respetively. In this way, the quenhing hardness and mirostruture omposition is derived step by step for every depth. The user an selet ase hardening steels from the orresponding dialog box in Simarb QuenhTemp. Moreover, there is the possibility to hange the hemial omposition of eah alloy. This modifiation influenes the simulation of the temperature distribution but has no diret effet on the subsequent identifiation of the quenhing hardness and the mirostruture omposition. Tempering. In the empirial model, the tempering hardness is alulated by a diminution fator for martensite [64]. In the thermophysial model, the Hollomon-Jaffe parameter, H P, is used to predit the hardness derease as an established approah. The appliation of tempering parameters, partiularly of H P, is proposed in the literature. By this parameter, a satisfying agreement with data for a large hardness range is ahieved [83 85], partiularly at higher temperatures [86]. P T logt H (12) In this equation, T, t and stand for temperature, time and a material dependent onstant, respetively. The material onstant is dimensionless and ranges for unalloyed and moderately alloyed steels from 14 to 20 [85, 87, 88]. Different ombinations of temperature and time an result in the same Hollomon-Jaffe parameter, whih means similar tempering effet as well. The data, whih are used in Simarb QuenhTemp, are dedued from own experiments for 18rNiMo7-6, 20Mor4 and 16Mnr5. For these ase hardening steels, tempering experiments at 1-217

13 temperatures and times from 150 to 200 and 2 to 4 h, respetively, are arried out to investigate the differenes in tempering resistane. It is found that the hardness derease of these steel grades in the onsidered temperature range between 150 and 200 is idential. At higher temperatures up to 300 and 400, the hardness derease of the different materials varies: whereas 18rNiMo7-6 is rather resistant to tempering and does not lose muh hardness, 20Mor4 and 16Mnr5 reveal signifiantly lower tempering resistane. As the typial temperature range of tempering in ase hardening is between 150 and 200, tempering resistivity of different ase hardening steels an be assumed to be equal in Simarb QuenhTemp. Therefore, it is not neessary to define different types of tempering resistane groups with varying Hollomon-Jaffe parameters. One H P set for every temperature-time ombination is evaluated from the experimental data and used for all steels in Simarb QuenhTemp. In the thermophysial model, the user an hoose a tempering temperature between 150 and 200 in steps of 1 and a tempering time between 2 and 4 h in steps of 1 min for the alulation of the tempering hardness from Hollomon-Jaffe parameters. Simulation results In Simarb QuenhTemp, numerous simulation results are provided to the user. This inludes, besides a summary of the most important simulation results and proess information, a graphial output of the hardness depth distribution after quenhing and tempering. Furthermore, the depth dependent hardness and mirostruture omposition an be exported as an ASII file (.txt format) for further proessing with, e. g., Mirosoft Exel. After eah simulation, the most signifiant simulation results and proess information like, e. g., steel omposition, model ylinder diameter, heat transfer, heat ondution, quenhant type and quenhant temperature, hardening temperature, surfae arbon onentration, surfae hardness and ase hardening depth are displayed in at a glane Simarb QuenhTemp. This information an be printed out and saved as an image file. The hardness profile after quenhing and tempering is displayed as a graphial hardness depth distribution, as shown in Fig. 11. This diagram an be printed and saved. Fig. 11. Graphial output representation of the simulated hardness profile. With the export funtion of Simarb QuenhTemp, it is, furthermore, possible to export the hardness and mirostruture omposition as a funtion of depth into an ASII file for further 1-218

14 proessing with, e. g., Mirosoft Exel. The export funtion for the mirostruture omposition is limited to the thermophysial model and inludes the mirostrutures martensite, bainite, ferrite, perlite and (retained) austenite. Simulation Examples and Verifiation by ase Hardening Experiments In the following setion, the pratial appliation of the Simarb QuenhTemp software is demonstrated by means of typial simulation examples of the empirial and thermophysial model. In addition to the quenhing hardness distribution, the ase hardening depth, HD, as key proess target parameter is evaluated. Empirial model With the empirial model, a quenhing proess of the ase hardening steel 15r3 with a ylinder diameter of d 0 =50 mm is simulated. For this quenhing proess, strongly differing Grossman numbers h=0.3 and h=1.5 are applied. The used arburization profile with a surfae arbon onentration of 0.6 wt.% is simulated during a two-stage gas arburizing proess by Simarb. The austenite grain size K ASTM is 8. The resulting quenhing hardness distributions are shown in Fig. 12. Additionally, the arburization profile and the quenhing hardness distribution, whih is alulated by Simarb with the hardenability relationship of Hodge-Orehoski (see Eq. 4), are plotted in the diagram. Fig. 12. Simulated quenhing hardness distributions (ylinder diameter d 0 =50 mm) of 15r3 steel for learly different Grossman numbers h=0.3 and h=1.5. In Fig. 13, the influene of the representative ylinder diameter d 0 on the resulting quenhing hardness distribution is demonstrated for the ase hardening steel 15r3. The applied representative ylinder diameters d 0 amount to 50, 100 and 300 mm. The Grossman number is h=1.0, whih orresponds to still water. Fig. 13. Simulated quenhing hardness distributions of the ase hardening steel 15r3 for the indiated representative ylinder diameters d 0. The arburization profile, whih is also plotted in 1-219

15 Fig.12, is onsidered in the analysis. The quenhing severity fator equals 1.0. Thermophysial model Applying the thermophysial model, a quenhing proess on a ylinder of 18NirMo14-6 steel of a diameter of d=40 mm is simulated. The arburization profile with a surfae arbon onentration of 0.82 wt.% after a two-stage boost-diffuse gas arburizing proess, determined by seondary ion mass spetrometry (SIMS) [35], is shown in Fig. 14. The arbon ontent in the near-surfae area, where the measuring auray is redued, is adjusted by means of the alloy fator reommended by the AWT [3]. For the quenhing proess, quenhing oil, still with a fluid temperature T F of 53 is onsidered as quenhant. The heat transfer oeffiient α of this quenhant is shown in Fig. 15 as a funtion of the surfae temperature T. Fig. 14. Measured arbon ontent after arburizing of 18NirMo14-6. The arbon onentrations in the surfae zone are adjusted aording to the alloy fator proposed by the AWT [3]. In Fig. 16, the resulting quenhing hardness distribution of the simulation for the thermophysial model is displayed. Also, the measured quenhing hardness profile from idential quenhing experiments is plotted. Both hardness profiles are quite similar, the ase hardening depths of 4.02 and 4.24 mm lie lose to eah other. In the surfae area, a retained austenite ontent of almost 23 vol.% and a martensite fration of about 77 vol.% are predited

16 Fig. 15. Heat transfer oeffiient of quenhing oil, still as a funtion of surfae temperature T. Fig. 16. Simulated and measured hardness profile of 18NirMo14-6 steel quenhed in quenhing oil, still. Fig. 17 provides a omparison of the simulated and measured retained austenite distribution of 18NirMo14-6 steel after the quenhing treatment. The omputation moderately falls below the data points, whih obviously does not affet the hardness predition notieably

17 Fig. 17. Simulated and measured retained austenite distribution after quenhing of 18NirMo14-6. Disussion In the empirial as well as in the thermophysial model of Simarb QuenhTemp, several simplifiations in the predition of the hardness from a given arburization profile after quenhing and tempering are made. These assumptions are disussed briefly in the following. Empirial model The proedure of Wyss to simulate the hardness profile after quenhing is established in pratie. omparisons with measured hardness profiles of arburized steels are available in the literature [39]. In this proedure the preset equation for the alulation of arbon dependent Jominy urves stems from regression analyses [37, 38, 42]. This expression proposed by Just ahieves good agreement with measured hardness profiles for low alloyed ase hardening steels (e. g. 17r3). However, it should be noted that the equation is not appliable to higher alloyed grades (e. g. 18rNiMo7-6). The hardenability relationships for the determination of the surfae hardness take only the arbon onentration into aount. The influene of the alloying elements is negleted as the maximum martensite hardness is governed by the arbon ontent. The quenhing severity fator of Grossman semiquantitatively estimates the ooling rate of a work piee (model ylinder) ahieved by an applied quenhant (e. g. hardening oil) in relation to still water at 18. This thermophysial parameter an be determined experimentally or taken from the literature. The hilling effet depends on the quenhant type and its state of agitation and flow. Furthermore, it depends on the heat ondution of the steel and some other influening fators, e. g. bath and hardening temperature, mass of the work piee and wall thikness [48, 55, 89, 90]. The relevant harateristis for the hilling effet like hemial omposition, visosity and boiling point, however, annot be taken into aount as a riterion in the empirial model. The heat ondutivity of a steel grade depends on the mirostruture, arbon onentration and temperature [48, 76, 77]. These influening fators vary with time and position during quenhing. On the ontrary, the Grossman number represents a onstant effetive value. Espeially during nuleate boiling, the heat ondution oeffiient is very high and only desribed insuffiiently by the Grossman number. Atually, many quenhants in industrial heat treatment do not show a Newtonian ooling [89]. Finally the onept of Grossman is not suitable for disontinuous (e. g. interrupted) quenhing proesses [13]: hanging quenhants or modified stages of agitation annot be treated by this severity fator. The mirostruture analysis, based on the approah of Hodge and Orehoski, provides a pratial but, partiularly for small ontents, a rough estimation of the martensite fration. This martensite 1-222

18 ontent is required for the arbon, temperature and time dependent diminution fator, whih is used for the predition of the tempering from the quenhing hardness. A diret determination of the mirostrutural omposition is not possible in the empirial model. That is why the martensite ontent is required as a funtion of arbon onentration or depth. Only the martensiti phase is sensitive to tempering response by hardness derease in the temperature range up to 200 ommon in ase hardening. With inreasing distane from the surfae, the ritial ooling rate for reahing the martensite start temperature transformation free depends on the alloy omposition of the steel and the arbon onentration. Here, the simplified mirostruture analysis loses preision and the estimation of the martensite ontent is too high leading to a redued tempering hardness. With dereasing arbon onentration and inreasing distane from the surfae, the diminution fator tends toward 1, whih limits this deviation in the pratial appliation. Thermophysial model The simulation of the temperature distribution during quenhing is based on a modified Fourier law that is solved by an expliit finite differene method. It is well know from the literature that an impliit finite differene method is faster and numerially more stable. To ahieve good results with an expliit method, the time steps Δt should be very small, whih results in a large number of time inrements nt. This normally extends the omputing time. However, the simulated quenhing time from hardening temperature to 500 is less than one minute, whih means that the number of time inrements nt is still manageable for an expliit method. Due to this reason and the fat that the programmability in FORTRAN is more omfortable, the expliit method is a good hoie for this kind of simulation. The results of this numerial tehnique agree very well with an analytial solution applied to speial onditions as referene [65]. The omputing time is less than two seonds. When it omes to the different stages of heat transfer during quenhing (film boiling, nuleate boiling, onvetion), the heat transfer oeffiient is onsidered as a funtion of temperature in Simarb QuenhTemp. This means that, for every temperature step, the adequate heat transfer oeffiient is used, whih makes the simulation more omparable to industrial heat treatment proesses. Heat transfer oeffiients for the most quenhants in Simarb QuenhTemp are taken from the literature [13, 55, 68, 72 75]. As the heat transfer oeffiients sensitively depend on the state of agitation, temperature and type of quenhant, little deviations have a great influene on the simulation and, as a onsequene, on the quenhing hardness and mirostruture omposition. Therefore, the heat transfer oeffiients of the used quenhant must be known preisely to ahieve reliable results. As mentioned above, the heat ondutivity of steel depends upon the mirostruture, arbon onentration and temperature [48, 76, 77]. In the empirial model, the heat ondutivity is taken into aount only by a onstant (effetive) value for every stage of the quenhing proess. In the thermophysial model, for eah temperature step of the finite differene method, a temperature dependent heat ondution oeffiient is used. As shown in Fig. 8, a linear relationship of the heat ondutivity in the martensiti and austeniti struture as well as in the mixed area in between is assumed. This simplified linear assumption is based on empirial researh [78 81]. The ooling time t 8/5 is well known from welding and denotes the time that is needed to pass through a temperature range from 800 to 500 during ooling of a weld seam [13, 82]. The hoie of the temperature interval of 800 and 500 is proven suessfully in welding modeling. In Simarb QuenhTemp, this temperature range is used to alulate an average ooling rate for every depth. Simulation parameter studies reveal that a hange of the interval limits espeially to lower temperature results in a lower average ooling rate beause the ooling rate dereases at lower temperatures. However, the good agreement of the simulation results with measurements shows that the temperature span of 800 to 500 is well suited for the alulation of harateristi average ooling rates in Simarb QuenhTemp. ontinuous ooling transformation (T) diagrams for more than 35 steels, its arbon ontents between 0.1 and 1.0 wt.% and ooling rates from 1 to 600 /s are stored in Simarb QuenhTemp

19 These T diagrams are alulated by means of the ommerial JMatPro software. As the available T diagrams must be alulated in advane, the user is limited to the implemented steels. The use of time-temperature parameters, espeially Hollomon-Jaffe parameters, for tempering is suggested in the literature [83, 84]. Experiments show that there is no signifiant differene in hardness derease of different steel grades in the temperature range between 150 and 200 and for times from 2 and 4 h typial of tempering in ase hardening. That is why the different steel grades in Simarb QuenhTemp are not lassified into different tempering resistane groups. For the implemented temperature-time ombination, a set of Hollomon-Jaffe parameters is evaluated from tempering experiments. For deviating temperature-time ombinations, a linear interpolation method is used to alulate the tempering hardness profile. The simulation results for tempering hardness distributions are found to be in very good agreement with experimental data. This an be attributed to the use of time-temperature parameters for the alulation of the tempering from the quenhing hardness. hanges of the mirostruture during tempering annot be predited by time-temperature parameters. The tempering onditions usually applied in ase hardening, however, do not ause suh alterations. Notieable retained austenite transformations starts not before a temperature of 200 is exeeded. onlusions The new simulation tool Simarb QuenhTemp is developed for the predition of the depth distributions of the quenhing and tempering hardness as well as the mirostruture evolution from a given arburization profile by onsidering the proess onditions, hemial steel omposition and work piee geometry. It offers the following two approahes to the user of the expert software. In the empirial model, there are several program libraries for quenhants, steels types and hardenability relationships. Data like the Grossman quenhing intensity fator, alloy omposition or surfae hardness an also be entered manually. A formula proposed by Just for the alulation of Jominy urves is preset. The oeffiients of this formula an be modified. The arburization profile is imported from Simarb (ASII file output) or reated manually in an integrated subroutine by entering supporting points for depth and arbon onentration. For tempering simulation, a diminution fator is used for a temperature range from 150 to 200 and tempering periods of 2 to 4 h. In the thermophysial model, the temperature field during quenhing is simulated by applying the finite differene method. A simplified approah onsiders the hanging mirostruture in the alulation of heat ondution oeffiients from the hemial omposition of the steel. Heat transfer oeffiients are taken from the literature for ommon quenhants and are stored in program libraries. Furthermore, there is the possibility to involve user-defined quenhants by entering supporting points for depth and heat transfer oeffiient. The quenhing hardness and the mirostruture omposition are finally derived by identifying the simulated ooling urves for eah depth in ontinuous ooling transformation diagrams, whih are implemented for onventional ase hardening steels and arbon onentrations from 0.1 to 1.0 wt.%. The tempering hardness is dedued by experimentally determined Hollomon-Jaffe parameters for a temperature range from 150 to 200 and tempering periods of 2 to 4 h, as ommon in ase hardening pratie. In the empirial model, the equation proposed by Just is only suitable for low alloyed steels like, e.g., 17r3 or 16Mnr5. A further development of the Jominy equation for higher alloyed ase hardening steels is intended. Moreover, the extension of the implemented values of the Grossman quenhing intensity fator below 0.2 and partiularly above 2.0 is desirable. In the thermophysial model, the user is limited to the steel grades that are already implemented in the Simarb QuenhTemp program library. Main future researh aims at the implementation of a T alulation tool. So, the quenhing proess ould be simulated unrestritedly for any alloy omposition of the steel. Although it is possible for the user to define further quenhants, another improvement is the extension of the quenhant library of the Simarb QuenhTemp software

20 Referenes [1] Parrish, G. and Harper, G. S.: Prodution Gas arburizing, Pergamon Press, Oxford, [2] Boyer, H. E. (Ed.): ase Hardening of Steel, ASM International, Materials Park, Ohio, [3] Grabke, H. J., Grassl, D., Hoffmann, F., Liedtke, D., Neumann, F., Shahinger, H., Weissohn, K.-H., Wünning, J., Wyss, U. and Zoh, H.-W.: Die Prozessregelung beim Gasaufkohlen und Einsatzhärten, expert publisher, Renningen, Germany, 1997, in German. [4] Parrish, G.: arburizing Mirostrutures and Properties, ASM International, Materials Park, Ohio, [5] Edenhofer, B.: HTM Z.Werkst. Wärmebeh. Fertigung., 56, 2001, 14, in German. [6] Gegner, J.: Komplexe Diffuisionsprozesse in Metallen, expert publisher, Renningen, Germany, 2006, in German. [7] Liedtke, D.: Wärmebehandlung von Eisenwerkstoffen I Grundlagen und Anwendung, expert publisher, Renningen, Germany, 2007, in German. [8] Liedtke, D.: HTM J.Heat. Treat. Mat., 64, 2009, 323. [9] Grosh, J.: Einsatzhärten Grundlagen, Verfahren, Anwendungen, Eigenshaften einsatzgehärteter Gefüge und Bauteile, expert publisher, Renningen, Germany, 2010, in German. [10] Wünning, J.: Grundlagen der rehnergesteuerten Aufkohlung, in: Einsatzhärten, edited by J. Grosh and J. Wünning, Assoiation for Heat Treatment and Materials Tehnology (AWT), Berlin, 1989, pp , in German. [11] Winter, K.-M.: Gaswärme International, 57, 2008, 237, in German. [12] Gegner, J.: HTM J. Heat Treatm. Mat., 64, 2009, 53, in German. [13] Liši, B., Tensi, H. M. and Luty, W. (Ed.): Theory and Tehnology of Quenhing, Springer, Berlin, [14] Tensi, H. M., Totten, G. E. and Kunzel, T.: presented on the 20 th ASM Heat Treat. So. onf., St. Louis, Missouri, 9 th 12 th Otober 2000, pp [15] Tensi, H. M., Totten, G. E. and Kunzel, T.: presented on the 20 th ASM Heat Treat. So. onf., St. Louis, Missouri, 9 th 12 th Otober 2000, pp [16] Lübben, T.: Zahlenmäßige Beshreibung des Wärmeübergangs flüssiger Abshrekmedien am Beispiel zweier Härteöle als wesentlihe Randbedingung für die numerishe Simulation von Wärmebehandlungsprozessen, VDI publisher, Düsseldorf, Germany, 1994, in German. [17] Lainer, K.: PhD Thesis, Munih University of Tehnology, Munih, 1996, in German. [18] Nelle, S.: omputergestützte Simulation von Prozessen der Wärmebehandlung an real gestalteten Bauteilen, VDI publisher, Düsseldorf, Germany, 1996, in German. [19] Tensi, H. M. and Lainer, K.: HTM Z. Werkst. Wärmebeh. Fertigung., 52, 1997, 298. [20] Tensi, H. M. and Totten, G. E.: presented on the 20 th ASM Heat Treatm. So. onf., St. Louis, Missouri, 9 th 12 th Otober 2000, pp [21] Gegner, J. and Bontems, N.: First Purhasable High-End FDM Software for Advaned ase Hardening Tehnology of Steels, Pro. 4 th Int. onf. on Mathematial Modeling and omputer Simulation of Materials Tehnologies (MMT), Ariel, Israel, 11 th 15 th September 2006, ollege of Judea and Samaria, 2006, Vol. 1, hap. 2, pp [22] Gegner, J.: ZWF Z.Wirtsh. Fabrikbetr., 97, 2002, 544, in German. [23] Gegner, J., Öhsner, A.; Wilbrandt, P.-J., Kirhheim, R. and Nierlih, W.: HTM Z. Werkst. Wärmebeh. Fertigung., 58, 2003, 5, in German. [24] Gegner, J.: Konstruktion, 55, 2003, 44, in German. [25] Gegner, J.: Analytial Modeling of arbon Transport Proesses in Heat Treatment Tehnology of Steels, Pro. 3 rd Int. onf. on Mathematial Modeling and omputer Simulation of Materials Tehnologies (MMT), Ariel, Israel, 6 th 10 th September 2004, ollege of Judea and Samaria, 2004, hap. 1, pp [26] Gegner, J.: Mat.-wiss. u. Werkstoffteh., 36, 2005, 56, in German