Prediction of Phase Composition and Nitrogen Concentration During the Nitriding Process in Low-Alloy Steel

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1 Materals Research. 2016; 19(2): DOI: Predcton of Phase Composton and Ntrogen Concentraton Durng the Ntrdng Process n Low-Alloy Steel Xaohu Deng a *, Dongyng Ju b a anjn Key Laboratory of hgh speed cuttng and precson machnng, anjn Unversty of echnology and Educaton UE, anjn, , Chna b Department of Mechancal Engneerng, Satama Insttute of echnology SI, Satama, , Japan Receved: February 26, 2015; November 26, 2016, 2015; Accepted: December 21, 2015 A dffuson/transformaton coupled model has been developed whch combnes fnte dfference (FD) model wth a phenomenologcal model. he composton of the dfferent ron-ntrogen(fe-n) hardenng phase can be regard as a functon of ntrdng tme and ntrogen concentraton. he dffuson model and transformaton model are lnked by the lmtng ntrogen solubltes and the effectve dffuson coeffcents. he effect of alloy elements (Cr, Mo, Mn, V, N etc.) s consdered by ntroducng an alloy coeffcent for lmtng ntrogen solubltes and dffuson coeffcent. he dffuson/transformaton model can predct ntrogen concentraton, phase composton and hardness dstrbuton. he model s employed to smulate the ntrdng process of SCr420H low-alloy steels. he smulated ntrogen concentraton and hardness profles are consstent wth the measured ones. In addton, the predcted depth dstrbutons of ron-ntrogen phase agree well wth the avalable expermental results. herefore, the comparson shows the relablty of the coupled model. It can be appled to mprove the ntrdng process parameters. Keywords: Ntrdng, Low-alloy steel, Fe-N phase composton, Ntrogen concentraton, Modelng Introducton he ntrdng process s one of the most mportant thermochemcal treatment processes n metallurgy for the producton of case-hardened surface layers n low-alloy steel. he dffuson of ntrogen nto steel leads to the formaton of a ntrde layer, whch comprses a thn outer compound layer (whte layer) and thck nner dffuson layer. he compound layer conssts of the epslon phase (ε) and the gamma prme phase (γʹ). he dffuson layer s composed of ntersttal sold soluton of ntrogen dssolved n the ferrte lattce (α) 1. he mprovement of corroson and wear propertes can be attrbuted to the construct of compound layer. herefore, t s benefcal to predct the ntrogen concentraton profle and phase composton of the compound layer n the ntrdng process. o further understandng the ntrdng process, numercal smulatons have been employed to calculate the ntrde layer growth and the ntrogen concentraton profles snce 1990s Sun and Bell 2 developed a mathematcal model to smulate the plasma ntrdng process of low alloy steel. her model consdered the dffuson of ntrogen n ferrte and development of ron ntrde layer on the surface smultaneously. hen, Goune et al., 3 and Belmont et al., 4 constructed a realstc dffuson-precptaton model to descrbe the volume dffuson of ntrogen n ferrte and the smultaneous precptaton of fne scale alloyng element ntrdes n the dffuson zone. Furthermore, Kammnga, Janssen 8,9 presented a model for the calculaton of ntrogen depth profles n ntrded steel *e-mal: dengxh@tute.edu.cn based on precptaton and trappng, and the calculatons agreed well wth expermental ntrogen depth profles for ntrded Fe Mn (1.62 wt.% Mn) and Fe V (0.55 wt.% V) alloy. Keddam 10 and Cavalere et al., 11 modeled the ntrdng process by couplng the knetcs data of ntrogen n α, γʹand ε phases to the thermodynamc descrpton of the ron-ntrogen (Fe-N) phase dagram respectvely. Recently, Yang et al., 12,13 presented a ntrdng process model ncludng the knetcs of compound layer growth and the determnaton of the ntrogen dffusvty n the dffuson zone. However, the predcton of Fe-N phase composton and the hardness n the ntrde layer have receved less attenton. he man purpose of ths paper s to smulate the ntrogen concentraton, (Fe-N) phase composton and hardness n the ntrdng process of low alloy steel. A dffuson/transformaton coupled model s developed to predct the phase compostons at the thnner compound layer by consderng smultaneous the thermodynamc data and knetcs theory n the ntrdng process. he smulated results are compared wth the expermental ones and theoretcal descrptons. 2. Model descrpton he knowledge of both thermodynamc and knetcs data s requred n modelng the ntrdng process. A large number of thermodynamc and dffuson knetcs data can be found n Iron-ntrogen (Fe-N) bnary phase dagrams are the base to understand the phase evoluton durng the ntrdng process. In the past decades, the ron-ntrogen phase dagram

2 354 Deng & Ju Materals Research and Fe-N system has been nvestgated extensvely 14,15. Moreover, Lakhtn 16 revewed the dffuson foundatons of the ntrdng process n carbon steel and alloy steel. Because the bondng energy n α-phase s lower than that n the lattce of γʹ and ε-phases, the coeffcent of ntrogen dffuson n α-phase should exceed the coeffcents n the γʹ and ε by many tmes 17. Furthermore, the phase composton of a compound zone and growth knetcs of a dffuson zone durng the ntrdng of steel was nvestgated quanttatvely 18,19. Recently, Somers 20 revewed the development of the compound layer durng gaseous ntrdng of Fe-based materals. In the development of the ntrdng model, n order to smplfy model, the followng assumptons are made: Frstly, the dffuson process follows Fck s second law n a sem-nfnte medum; Secondly, the surface ntrogen concentraton does not vary wth the ntrdng tme; hrdly, a unform temperature s assumed throughout the sample; Lastly, local thermodynamc equlbrum s reached quckly at every pont n the materal Ntrogen dffuson model he dffuson of ntrogen nto ferrte phase s consdered to obey Fck s second law N N ( N = D t 2 x ) (1) where, Ns ntrogen concentraton, χ s the depth, t s ntrdng tme, D n denotes the effectve dffuson coeffcent of ntrogen. he numercal method s appled to solve the dffuson equaton. In the present model, an alternatng-drecton mplct (ADI) fnte-dfference formulaton s used to solve equaton (1). t+ 1 t t t t t+ 1 t+ 1 Cn = Cn + F (0.5 ( Cn 1+ Cn+ 1+ Cn 1 + Cn+ 1) t t+ 1 Cn Cn ) where, F t = D t * D / t DX2, D t s the dffuson coeffcent of locaton at tme t, Dt s tme step, Cn t s the ntrogen concentraton of locaton at tme t. he boundary condtons s the followng S Cxt (, ) x= 0 = (3) where, C S s the surface ntrogen concentraton. N 2.2. Fe-N phase composton predcted model By employng the Fe-N phase dagram (Fg. 1 (a)) 14,15, t s feasble to predct the dfferent Fe-N phases accordng to the lmt solublty values 10,11. In Fg. 1 (b), t s presented the composton of the dfferent Fe-N phase as a functon of ntrdng tme and ntrogen concentraton. Based on the lever rule, a phenomenologcal model s developed to calculate the volume fracton of ron-ntrogen phase. he ntrdng parameters are connected wth the mechansms of the (2) Fg. 1 a Fe-N phase dagram; b schematc llustraton of Fe-N phases composton n the ntrdng process. ntrdng process. he volume fracton of ron-ntrogen phases s defned as t, α/ γ t, γ / ε γ =,, / / ε = γ α α γ γ ε/ γ γ / ε ξα = 1 ξγ ξε ξ ξ ξ where, C,t N (4) s ntrogen concentraton, Cα/γʹ N, Cγʹ/α N, Cγʹ/ε N, C ε/γʹ N are the lmtng ntrogen solubltes n Fe-N phase, as a functon 10,11, 16 of temperature can be calculated by α/ γ 4575 γ AE = exp( + 3) 10 γ / α = ( 1.925) γ / ε = ( 2.455) ε/ γ γ AE = ( ( ) ( )) 10 (5)

3 2016; 19(2) Predcton of Phase Composton and Ntrogen Concentraton Durng the Ntrdng Process n Low-Alloy Steel 355 where, γ AE s the actvty coeffcent of ntrogen, whch can be calculated by γ = -( AE Cmo Ccr Cmn + Cw + Cn Cal ) where, C s the wt.% of element Hardness regresson model he hardness could be calculated by the expermental regresson equaton 5,7 n1 n2 n3 HV = HVst + axcx + byξcy + czξnz x= 1 y= 1 z= 1 (6) (7) where, HV s the Vckers Hardness, HV st s the Vckers Hardness of the substrate, C x s the chemcal compostons, ξ cy s the ron-carbon phase compostons, ξ nz s the Fe-N phase compostons, and ax(x = S, Mn, N and Cr), by(y = M, B, A and F), cz (z = ε, γʹ) are the correspondng weghtng coeffcents, whch obtaned by lterature and expermental data. he values of coeffcents are lsted n able Dffuson/ransformaton coupled program he dffuson equaton and transformaton equaton were lnked by the effectve dffusonal coeffcents, whch could be gven by the mxture law 5,6 DN DNξ = (8) where, for each sngle phase, = 1(ε), 2(γʹ), 3(α), D N s dffusvty n varous Fe-N phases, ξ s volume fracton of varous Fe-N phase. he dffusvty of ntrogen n dfferent Fe-N phase could be approxmately expressed n an Arrhenus form 10,11,16,17 ( R ) ( R ) ( R ) α α 7 DN = ηal exp γ γ 9 DN = ηal exp ε ε 8 DN = ηal exp where, η α, ηγʹ and al al ηε are the alloy coeffcents, whch can al be determned by the formula 16 n η = exp [ B (% AE) ] (10) al (9) where (%AE) s the concentraton of the alloyng element n the steel, B and n, are coeffcents determned on the bass of expermental data on the thckness of the ntrded layer n bnary alloys. he flowchart of coupled program s shown n Fg. 2. In the present program, the dffuson and transformaton are calculated respectvely. On the one hand, the effectve dffuson coeffcents are changed wth the ron-ntrogen phase fracton by equaton (8); On the other hand, the ron-ntrogen fracton can be recalculated by equaton (4). 3. Results and dscussons In order to valdate model, the dffuson/transformaton coupled model s appled to predct the ntrdng process of SCr420H steel. he chemcal compostons of specmens are lsted n able 2. he ntrdng process parameters are shown n Fg. 3. Hardness measurements on cross sectons and the surfaces of ntrded specmens were carred out wth a Vckers hardness tester. For the determnaton of ntrogen contents, Electron Probe X-ray Mcroanalyss (EPMA) was performed on cross-sectons of the specmens. Fg. 4 depcts the evolutons of the ntrogen concentraton profles versus depth for ntrdng of SCr420H steel. he profles show the comparson between the smulated and expermental data. Although there are detaled dscrepances, t can be seen that good agreement s acheved between the numercal results and Wavelength Dspersve (WDS) measured results. It appears that the ntrogen concentraton of dffuson layer s underestmated. In the present model, the dstrbutons of ntrogen concentraton depend on the effectve dffusonal coeffcents, whch are relevant to the concentraton of the alloyng element (equaton (9) and (10)). herefore, the assumpton that the chemcal elements are unform dstrbuton may result n naccurate dffusonal coeffcent and ntrogen concentraton dstrbuton. It s found that the ntrogen concentraton gradent adjacent to the surface s very steep, whle away from the surface s flat. It s ndcated the dffusvty of ntrogen greatly change n dfferent depth of sample. In Fg. 5, the volume fractons of the dfferent hardenng phase are shown n SCr420H steel. It can be seen that the ntrde layer s composed of the thnner compound layer (γʹ + ε) and nner dffuson layer (α + γʹ). he smulated depth dstrbutons of γʹ and ε Fe 2 3 N phases are reasonable consstent wth the X-ray dffracton (XRD) phase analyss results 19 and optcal mcrograph. he formaton of γʹ phase subzone n the nner part of the compound zone may able 1 - he values of coeffcents for hardness calculaton Coeffcents HV st a s a Mn a N a Cr b M b F b B b A C ɛ C γʹ Values (HV) able 2 - Chemcal composton of SCr420H steel Chemcal elements Fe C S Mn Cr P S N Mo Wt.%

4 356 Deng & Ju Materals Research upset the balance of the ntrogen concentraton between the dffuson zone and the compound zone, and may as a consequence have an nfluence upon the knetcs of the dffuson zone growth. he volume fracton of Fe-N phases s correspondng to the ntrogen concentraton (Fg. 4). At the outer secton, the ntrogen concentraton s relatvely hgh. At the nner secton, ntrogen concentraton s decreased rapdly to a lower value. he hardness profles after ntrdng are calculated by expermental regresson equaton (4) and shown n Fg. 6 for SCr420H steel. he calculated hardness data result n good agreement wth the measured ones. However, there are dscrepances between calculatons and observatons for the maxmum hardness. he problem probably les n the estmated hardness value of alloy ntrde n regresson equaton, whch can nfluence hardness n dffuson layers sgnfcantly. As shown as n Fg. 4-Fg. 6, t can be concluded that the coupled model can be employed to predct the hardenng phase composton n the ntrdng process quanttatvely. Fg. 2 he flowchart of the dffuson/transformaton coupled program.

5 2016; 19(2) Predcton of Phase Composton and Ntrogen Concentraton Durng the Ntrdng Process n Low-Alloy Steel 357 Fg. 3 A schematc llustraton for ntrdng process n SCr420H steel. Fg. 4 Ntrogen concentraton smulated results n SCr420H steel.

6 358 Fg. 5 Volume fracton of the Fe-N phase n SCr420H steel. Fg. 6 Hardness dstrbutons n SCr420H steel Deng & Ju Materals Research

7 2016; 19(2) Predcton of Phase Composton and Ntrogen Concentraton Durng the Ntrdng Process n Low-Alloy Steel Conclusons In ths paper, a dffuson/transformaton coupled model has been developed to smulate ntrogen concentraton dstrbutons, ron-ntrogen phase formaton and hardness by combnng ntrogen dffuson and Fe-N phase composton calculaton. he model s mplemented to smulate ntrdng process of SCr420H steel. he smulated results ndcate the ntrogen concentraton profles, volume fracton of Fe-N phases and hardness dstrbutons can be predcted quanttatvely by ths model. Moreover, the smulated results are n reasonable agreement wth the expermentally measured ones and theoretcal analyss. It shows the possblty of utlzng the model to mprove the ntrdng process parameters. Acknowledgements hs research receves ongong support from the Hgh tech Research Center and Open Research Center at the Satama Insttute of echnology, and sponsored by Natural Scence Foundaton of anjn (No. 13JCYBJC38900), Natonal Natural Scence Foundaton of Chna (Project ), Scentfc Research Startng Foundaton of anjn Unversty of echnology and Educaton (No. KYQD12008) and Innovaton eam ranng Plan of anjn Unverstes and colleges (Grant No. D ). References 1. Pye D. Practcal ntrdng and ferrtc ntrocarburzng. Materals Park, OH: ASM Internatonal; Sun Y, Bell. A numercal model of plasma ntrdng of low alloy steels. Materals Scence & Engneerng A. 1997;224(1): do: /S (96)10561-X 3. Goune M, Belmonte, Foran JM, Chomer S, Mchel H. Modellng of dffuson precptaton n ntrded alloyed ron. hn Sold Flms. 2000; : do: /S (00) Belmonte, Gouné M, Mchel H. Numercal modelng of ntersttal dffuson n bnary systems: Applcaton to ron ntrdng. Materals Scence & Engneerng A. 2001;302(2): Lu CC, Ju DY, Inoue. A numercal modelng of metallothermo-mechancal behavor n both carburzed and carbontrded quenchng processes. ISIJ Internatonal. 2002;42(10): do: /S (03) Ju DY, Lu CC, Inoue. Numercal modelng and smulaton of carburzed and ntrded quenchng process. Journal of Materals Processng echnology. 2003; : do: / S (03) Krukovch MG. Smulaton of the ntrdng process. Metal Scence and Heat reatment. 2004;46(1): Kammnga JD, Janssen GC. Calculaton of ntrogen depth profles n ntrded Fe-Mn and Fe-V. Surface & Coatngs echnology. 2006;200(20): Kammnga JD, Janssen GC. Calculaton of ntrogen depth profles n ntrded mult-component ferrtc steel. Surface & Coatngs echnology. 2006; 200(20-21): do: /j. surfcoat Keddam M. Surface modfcaton of the pure ron by the pulse plasma ntrdng: Applcaton of a knetc model. Materals Scence & Engneerng A. 2007;462(1): do: /j. msea Cavalere P, Zavarse G, Perllo M. Modelng of carburzng and ntrdng processes. Computatonal Materals Scence. 2009;46(1): Yang M, Yao B, Sohn YH, Ssson Jr RD. Smulaton of the ferrtc ntrdng proces. Internatonal Heat reatment and Surface Engneerng. 2011;5(3): DOI: org/ / x Yang M, Zmmerman C, Donahue D, Ssson Jr RD. Modelng the gas ntrdng process of low alloy steels. Journal of Materals Engneerng and Performance. 2013;22(7): Wredt HA, Gokcen NA, Nafzger RH. he Fe-N (Iron-Ntrogen) system. Bulletn of Alloy Phase Dagrams. 1987;8: Voorthuysen EH, Boerma DO, Chechnn NC. Low-temperature extenson of the lehrer dagram and the ron-ntrogen phase dagram. Metallurgcal and Materals ransactons A. 2002;33(8): Lakhtn YU. Dffuson foundatons of the ntrdng process. Metal Scence and Heat reatment. 1995;37(7): Somers MA, Mttemejer EJ. Layer-growth knetcs on gaseous ntrdng of pure ron: Evaluaton of dffuson coeffcents for ntrogen n ron ntrdes. Metallurgcal and Materals ransactons A. 1995;26(1): Hernandez M, Staa MH, Puch-Cabrera ES. Evaluaton of mcrostructure and mechancal propertes of ntrded steels. Surface & Coatngs echnology. 2008;202(10): do: /j.surfcoat Ratajsk J. Relaton between phase composton of compound zone and growth knetcs of dffuson zone durng ntrdng of steel. Surface & Coatngs echnology. 2009; 203(16): DOI: /j.surfcoat Somers MA. Development of compound layer durng ntrdng and ntrocarbursng; current understandng and future challenges. Internatonal Heat retament and Surface Engneerng. 2011;5(1): Crank J. he mathematcs of dffuson. Oxford: Clarendon Press; Lakhtn YU, Kogan YA, Bulgach AA. Effect of alloyng elements on the thermodynamc actvty and solublty of ntrogen n phases of a ntrded case. Metal Scence and Heat reatment. 1982;24(4): Yakhnna VD, Nktn VV. Development of the hardness of the ntrded case. Metal Scence and Heat reatment. 1975;17(1-2): Lakhtn YU, Kogan YA, Sharlat ES. Ntrdng of low- and medum-carbon steels surface-alloyed wth ntrde-formng elements. Sovet Materals Scence. 1976; 13(5): Glushchenko VN, Goryushn VV, Kondrashova GA, Duka ME. Effect of alloyng on the structure and propertes of the ntrded case on medum-carbon steels. Metal Scence and Heat reatment. 1980;22(9):