Modeling of numerical simulation and experimental verification for carburizing-nitriding quenching p

Available online at www.sciencedirect.comsCIENCE(s @oInEoT.Transactions of、Nonferrous MetalsSociety of ChinaScienceTrans. Nonferrous Met. Soc. China 16(2006)s566-s571Presswww.csu.edu.cn/ysxb/Modeling of numerical simulation and experimental verificationfor carburizing-nitriding quenching processR. MUKAI', T. MATSUMOTO, JU Dong-ying', T. SUZUKI, H. SAITO2, Y. ITO41. High-Tech Research Center Special Researcher, Saitama Institute of Technology, Fukaya 369-0293, Japan;2. Department of Mechanical Engineering, Saitama Institute of Technology, Fukaya 369-0293, Japan;3. Research Center of High Technology, Anshan University of Science and Technology, Anshan 1 14044, China;4. Department of Technology Development, Tobuyakin Ltd, JapanReceived 10 April 2006; accepted 25 April 2006Abstract: A model considering quantitative efects of diffused carbon and nitrogen gradients and kinetics of phase transformation ispresented to examine metallo-thermo-mechanical behavior during carburized and nitrided quenching. Coupled simulation ofdiffusion, phase transformation and stres/train provides the final distribution of carbon and nitrogen contents as well as residualstress and distortion. Effects of both transformation and lattice expansion induced by carbon and nitrogen absorption wereintroduced into calculating the evolution of the internal stress and strain. In order to verify the method and the results, the simulateddistributions of carbon and nitrogen content and residual stress/strain of a ring model during carburized and nitrided quenching werecompared with the measured data.Key words: carburizing; nitriding; quenching; numerical simulation; metallo-thermo-mechanical behaviorimprovement are ascribed to the compound layers1 Introductioncomposed of fine nitrides or carbides of alloyingelements, and residual surface stresses are also attributedThe present authors have carried out, for theseto this process. As a known fact, residual stresses aredecades, to construct the fundamental framework ofalways accompanied by changes in shape and size of“metallo-thermo-mechanics [1, 2] relevant to describingwork-piece, which often results in significant distortionthe coupled fields of metallic structure, temperature andof the machine parts. This also leads to undesired effectsstress/strain occurring in the engineering processsuch as increasing noise from transmission gears. Itincorporating phase transformation such as quenching,order to improve such kind of defects, manufacturingwelding and casting, and developed some computerengineers need to have a thorough understanding hovsimulation codes, HEARTS [1, 3], COSMAP [4] andvarious process parameters influence the final profiles ofunder developing. Effect of difused carbon during thecarbon/nitrogen, stress/distortion and microstructures ofcarburized quenching is also possible to be simulated byheat-treated components. To do this, in recent years,these codes, and the results were presented elsewherethere have been a great number of experimental andtheoretical interests in mathematical description ofNitriding is known as another important process ascarburizing and/or nitriding processes [5]. Numericalwell as the carburizing among the thermo-chemicalsimulation by the finite element method (FEM), due tosurface treatments in engineering practice [6- -9]. Theits beneft in reducing consuming time and trial- and-errortechnology is widely applied to machine parts such asexperiments that plague engineers, is looking forward toautomotive gears, shafts and so on due to the beneficialbeing used widely in engineering problems. However, ineffects on fatigue resistance, tribological andmany commerc中国煤化工solve someanti-corrosion properties. The reasons for the propertyproblems on theYHCNMHGgenorsimul-Corresponding author: JU Dong-ying; Tel: +81 -48- 595-6826; Fax: +81-48-585-5928; E-mail: dyju@sitac.jip.R. MUKAI, et al/Trans. Nonferrous Met. Soc. China 16(2006)s567taneous difusion of carbon and nitrogen on theDxv(N)= Dv,of(C,N)h(gradC, gradN)-.following thermo-mechanical simulation still remainimperfect.(4)With respect to this, the numerical modeling forexpRT )simulating the metallo-thermo-mechanical behaviorduring carburized and nitrided quenching is developed inwith the functions f(C, N) and h(gradC, gradN) of carbonthis paper. The purpose of the modeling aims to make itand nitrogen concentrations and the gradients,capable to calculate not only diffusion of multi-elementrespectively. And Qr in Eqn.(4) is the activation energyduring chemical treatment but also the evolution offor diffusing nitrogen, and DN, 0 and R are materialconstants. The coefficient of surface reaction rate βv inmicrostructure, stress and distortion during carburizedEqn.(2) of nitriding process under partial pressure p(H2)and nitrided quenching by considering the effect of CNof hydrogen in the mixed gas is given bydiffusion on distortion and phase transformation kinetics.QIn order to verify the numerical method, the simulatedβN = Bop(H2)exp|RT(5)distributions of carbon and nitrogencontents,temperature and variation of microstructure as well aswhere Po is a constant [5].The equation governing carbon diffusion kineticsresidual stress/strain of a ring during carburized annitrided quenching are compared with the measuredcan be simply obtainable by exchanging N and C in Eqns.results.(1)-(4). When the coefficient of surface reaction rate βcfor carbon is decided by using experimental method [6],2 Modelingthev carbon diffusion in steel can be expressed by thefollowing boundary condition,The modeling developed by the authors can be usedDn;=βc(C-Cw)(6)to predict the evolution of temperature, microstructure,0x;stress/distortion and profiles of chemical componentsuch as carbon and nitrogen and so on during some2.2 Heat conductionprocesses of thermochemical treatment and heatTheheat conduction equation govemingtreatment. The models involved in the FEM proceduretemperature field Tiscan be divided into four categories of analysis: heatconduction, diffusion of C/N, transformation kinetics and8(paTr,=0(7)stress/strain analysis by use of elasto-plastic constitutiveequations. When the boundary conditions are involved, .Here, the coupled term rv with mechanical work andthe prescribed flux boundary conditions are employed.latent heat generation is2.1 Diffusion of nitrogen and carbonr,=σi +Eprl,与(8)Diffusion equation for nitrogen in nitriding processis simply described by normal diffusion type equation:This term is taken into account in the case ofquenching，but not for the carburizing or nitridingDv oNIrN =0process.0t 0xax;The heat conduction in Eqn.(7) is possibly solvedwith heat transfer boundary conditionwith boundary condition-k9n;=h(T-Tw)(9)-Dv-n, = Bv(N-Nw)(2where P, c and k denote density, specific heat and heatwhere N, Nw and I'N respectively stand for difusedconductivity, respectively. rv is internal heat source, hmass percent, environment potential and internal sourceand Tw mean heat transfer coefficient and environmentalof nitrogen. Global diffusivity DN is also assumed to be .temperature on the boundary and n; is u nit normal. Thegiven by the mixture law asvalue ofρ, c and k should be calculated according to themixture ruleDv= 2 Dwv(N)片,(3x=Ex5中国煤化工Each constituent Dv(N) is designed to be calculatedYHCN MH G,is volumeby the formula asfraction of the I-th phase..s568R. MUKAI, et al/Trans. Nonferrous Met. Soc. China 16(2006)2.3 Phase transformation kineticsThe microstructures involved in the present端=Za1T8j(19)simulation are assumed to be composed of threeconstituents; austenite, pearlite or bainite and martensite.j=ZBJ215j8j(20)The diffusion type transformation from austenite tcpearlite is calculated based on the modified Johnson-where E and v are elastic modulus and Poisson ratio,Mehl relation [10]. In this case of carbon steel SCM420,T is temperature, andBj. +/ is the dilatation due to themicrostructure change from the Jth to Ith phase. a, isthe volume fraction of pearlite Sp is expressed asthermal expansion coefficient of the Ith phase.(10)Compared with the previous constitutive equationsof the authors, a new term ij in Eqn.(15) due tocarbon or nitrogen diffusion is introduced in this paper.f(7)=a(a2°)”(15(11)When carbon or nitrogen is absorbed as interstitial atoms,the lattice parameters change to induce the volumetricf2(C)= exp{- a,(C -C)}(12)dilatation. Some researchers proposed formulas of thelattice parameters depending on carbon and nitrogenf3(σ)= exp(agσm)(13)contents. If transformation (a- →β) occurs betweenwhere σm is mean stress, C and Co denote current andtime interval to and t due to the diffusion of carbon andinitial carbon contents and a;(i= 0,1,2.,.-,8) are some .nitrogen, the strain sif istransformation kineticsparameters.Diffusionless(vp(Cr,N,).transformation is controlled by(21)i=-ξM =1-exp{中qT +φ2(C -C)+v&(C,N。φ:(N- No)+φ4σm +0sσe +φ6}/ nT~a,Fewhere n/.Fe means the number of Fe atoms inby modified Magee S rule [11], where 5M is the volumefraction of martensite, φ;(i = 1,2,... ,6) are materialsingle unit cell of certain microstructure. Vd and Vjparameters. N and N。 mean the current and itialdenote the al and a'" lattice parameter before and aftera→β transformation, while C and N, are the carbonnitrogen contents (%) in the nodes, respectively.In the above equations, the effects of CIN profile onand nitrogen contents at time 1.If no transformation occurs during diffusion 0transformation kinetics are considered. Due to the smallpenetrating depth of N atoms and high contents of C incarbon and nitrogen, the microstructure is onlythe nitrogen diffusion layer, lttle pearlite transformationcomposed of austenite. Thus, the strain rate i simplyoccurs in this layer. It should not matter greatly evendepends on the diffusion rate of carbon and nitrogen inthough no effect of nitrogen is taken into account inthe form asdiffusion type transformation kinetics.{a'(C,N,)5{aC,Nn) jC.-C. N,-N%2.4 Constitutive equationsTotal strain rate Eij is assumed to be sum of rates(22)of elastic strain Ei， plastic strain g, thermal strainwhere a is the lattice parameter of austenite, which is ai，transformation strain ei and diffusion inducedfunction of current carbon and nitrogen contents.strain of carbon and nitrogen which is newlyintroduced in this paper.3 Materials and condition of experimentsen=ej +唱+en +i" +igfand simulationHere the four terms are given byThe steel used in this paper is the carbon steel1+ v(JIS- SCM420). The heat pattern is composed of 5 steps,eg=Eσi- Eσkijas shown in Fig.l. In the first step, the specimen isheated up to 930 °C from room temperature and then唱=GJ 0F8F，KaF:| 0F(17)mixed C/N gas is provided with certain carbon and[δσk旨051 J δσjnitrogen pot中国煤化工1% . andw(N)=0.3% in .bd step is forwith yield fiunctioncarburizing anYHcNMHGfterthat,theF=. F(o,,后)(18).R. MUKAI, et al/Trans. Nonferrous Met. Soc. China 16(2006)s569930 C1 000- A(Measured)- B(Measured)850 C800_ CMeasured)s- A(Calculated)CAB|600-B(Calculated)Carburizing 1.1%Nitriding 0.3%C(Calculated)400Holding200Heating" nitriding Difusioh上120160一” 80“30"0-)15202530Tim/minTime/sFig.1 Heat pattern of cartbon steelFig.3 Cooling curves of ring specimen3.5-specimen is cooled to 850 C for 10 min and then isheld at this temperature for 30 min as diffusion period.0一◆一Inside■- Top bottomto decrease the gradients of carbon and nitrogen. The.5▲- Outsidefinal step is for quenching of the specimen into oilquenchant of 60 C..0The sizes of the ring specimen are shown in Fig.2,in which the holes (No.1- 3) are drilled to insertthermocouples for temperature measurement duringquenching. Due to the symmetry, the one-fourth of the0.5-cross section is used for meshing by 1 809 nodes and1 716 elements by use of quadrilateral iso-parameter5001 500elements with four nodes. The thermal and diffusionTemperature/Cboundary conditions are both the flux type, and hardnessFig.4 Heat transfer cofficient curves of ring specimenand residual stresses are measured after experiments, theresults of which are used to compare with the calculatedas mainly originated from surface heat transfer boundaryones.condition. The discrepancy could be decreased byimproving the heat exchange coefficient on the surface.d30Fig.5 and 6 show the calculated microstructureevolution during quenching with temperature change,which follows that the volume fraction of martensite ishigher at certain depth (0.5 mm) than that on the surfacein spite of the decrease in cooling rate from surface tocenter. This is due to the different carbon and nitrogenFig.2 Dimension of carbon steel specimen(mm)contents at the corresponding positions.Fig.7 represents the profile of residual stresses on4 Results and discussionthe middle section of the specimen.The data on thesurface agree qualitatively with the measured values byThe cooling curves on measured points are shownX-ray diffaction method on the surface. The value ofin Fig.3. Using of identifying method based on measuredaxial stress almost equals to that of tangential stress.cooling curves and simulation, the heat transferFig.8 displays the calculated results of final distortion,coefficients in the surface to near the measured points arewhich also agree well to the measured displacements inidentified and shown in Fig.4. .the radial direction. The small discrepancy between themeasured and calculated values may be caused by thecoefficient of the ring specimen during quenchingfollowing factors. Constitutive equations should be theprocess are shown in Figs.3 and 4. Temperaturesfunctions of carbon and nitrogen contents, and Fig.7calculated by the program at the same positions in centerrepresents the profile of residual stresses on the middleand near surface as that in the measurement experimentsection of the specimen. The data on the surface agreeare compared with the measured values. We could seequalitatively with the measured values by X-raythe calculated temperatures agree well with the measureddiffraction method on the surface. The value of axialresults.stress almost中国煤化工stress. Fig.8There is a lttle discrepancy on surface betweendisplays the caYHCNMHGortion, whichboth the calculated and measured data, which is regardedalso agree wellments in the ..s570R. MUKAI, et al/Trans. Nonferrous Met. Soc. China 16(2006)w/%a)0.952(b)0.5000.9050.4690.8580.4380.8110.4060.764 .0.37507170344067003130.6700.3130.6230.2810.5760.2500.5290.2190.4820.1880.4350.1560.3880.1250.3410.093 8↑)0. 291↑}0.062 507470.031 30.2470.2005.5X 10-Fig.5 Distribution of content of carbon and nitrogen: (a) Carbon; (B) Nitrogen0.89900.106 0-| 0.843 00.099 :。 79700.092 80.78700.08620.731 0心0700.674 00.079 (0.618 00.072 90.562 00.066 3-0.50600.059 70.0530-0.45000.393 o0.04640.33700.039 80.28100.033 20750.0260.01Y0.013 30.11201 .006 60.056 24.653X 103Fig.6 Distribution of content of martensite (a) and bainite (b)5007.5 r6.0-▲一Outside No.1250 t4.5(measured)_3.0个Outside No.28 1.5个(measured)0◆- Outside(culclated)-250t-1.55■- Inside-3.0-500--4.5 tM台-6.0- σH:(Calculated)-7502一oz(Calculated)-8.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05- σR(Calculated)Change of radius/mm-1 0001Distance from center/mmFig.8 Comparison of distortionFig.7 Stress profiles on middle sectionneglected at present in the first approximation. But dueradial direction. The small discrepancy between theto the lack of related experimental results about themeasured and calculated values may be caused by theeffects of carb中国煤化工n the relatedfollowing factors: Constitutive equations should be theparameters usecCNMH Gons, they arefunctions of carbon and nitrogen contents, and transfor- neglected at pre.ww ..“considered inmation plasticity should be added while both effectshereafter research and calculations..R. MUKAI, et al/Trans. Nonferrous Met. Soc. China 16(2006)s571[2] INOUE T. Inelastic constitutive relationships and applications to5 Conclusionssome thermo-mechanical processes involving phase transformation,[A]. Hetnarski R B. Thermal Stresses[C]. North-Holland, 1988.[3] JU D Y, LIU C C. Overview on the microstructure evolution andA mathematical model to predict the carbon andinduced stesses in nitrided chromium steels [A]. Nakonieczny A.nitrogen contents as well as residual stresses anNitriding Technology [C]. Institute of Precision Mechanics, 2003,distortions after carburized and nitrided quenching are209- 309.JU D Y, LIU C C, INOUE T. Numerical modeling and simulation ofproposed in this paper， and finite elementcarburized and nitrided quenching process, []. Journal of Materialsimplementation is carried out to identify the profiles. TheProessing Technology, 2003, 143: 880 885.predicted results agree well with the experimental results. [S] METIN E, OSMAN T Kinetics of layer growth and muliphasediffusion in ion-itrided titanium[J]. Metall Trans A, 1989, 20A:This proves that the program can be used effectively to1819-1832.calculate the metallo-thermo-mechanical behavior duringSUN Y, BELL T. A numerical model of plasma nitriding of low alloyheat treatment and chemical treatment. Of course, theresteels []. Mater Sci Eng A, 1997, A224: 33-47.are some aspects to be improved, which can be realizedCHRISTAIN J W. The Theory of Transformation in Metals andAlloys: Equlibrium and General Kinetic Theory [M]. 2nd ed.by considering the effects of carbon and nitrogenPergamon: Oxford, 1975: 542- -546.contents on constitutive equations. The models about theBONGARTZ K. QUADAKKERS W J, SCHULTEN R, NICKEL H.interactions between diffusion of nitrogen and carbonA mathematical model describing carburization in multielement alysystem []. Metall Trans A, 1989, 20A: 1021-1027.also need to be established.[9] ROZENDAL H C, MITTERMEIJER E J, COLJIN PF, VANDER PJ. The development of nitrogen concentration profiles on nitridingAcknowledgementsiron [J]. Metall Trans A, 1983, 9A: 395.The support provided by High Technology Research10] JOHOSON W A, MEHL R F Reation kinetics in processes ofCenter in Saitama Institute of Technology for this worknucleation and growth[]. Trans AIME，1939, 135: 416- 458.is gratefully acknowledged.11] MAGEE C L. Nucleation of Martensite [M]. New York: 1968.(Edited by YANG Hua)References[1] INOUE T, JU D Y, ARIMOTO K. Metallo-thermo -mechanicalsimulation of quenching process-theory and implementation ofHEARTS [A1 Proc 1st IntConfOuenchingandcomputer code HEARTS [A]. Proc lst Int Conf Quenching andControl of Distortion, ASM International[C]. Chicago, 1992.中国煤化工MYHCNMH G.