DETERMINATION OF STRESSES IN THE STEEL PIPE DURING THE SUPERFICIAL HEAT TREATMENT PROCESS WITH HELICAL PATH

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1 Journal of Appled Mathematcs and Computatonal Mechancs 2016, 15(1), p-issn DOI: /jamcm e-issn DETERMINATION OF STRESSES IN THE STEEL PIPE DURING THE SUPERFICIAL HEAT TREATMENT PROCESS WITH HELICAL PATH Adam Kulawk, Norbert Sczygol, Joanna Wróbel Insttute of Computer and Informaton Scence, Czestochowa Unversty of Technology Częstochowa, Poland Abstract. In the paper a numercal model for the quench hardenng process wth the movng heat source of steel ppe made of medum carbon steel have been presented. The constant speed rotaton and movng of the ppe was assumed to obtan the path of the heat source n the shape of the helcal lne. In ths model the relatonshp occurrng between thermal phenomena, phase transformaton n the sold state and mechancal phenomena have been taken nto account. The temperature and stress felds are determned usng the copyrght software based on the fnte element method (three-dmensonal tasks). To calculate the phase content n the sold state, the macroscopc model based on the analyss of the CTP dagrams s used. The range of the martenste transformatons depends on the value of stresses. In the model the temperng phenomena s also taken nto account. In the model of mechancal phenomena the elastc, thermal, structural, plastc strans and transformatons plastcty are consdered. Keywords: numercal analyss, superfcal heat treatment, phase transformatons n the sold state, stresses, steel ppe 1. Introducton The optmzaton of producton costs of the machne parts at the desgn stage requres proper selecton of materal propertes, not always the same n the entre area of the workpece. In the producton of machne parts the more cheaper materals are used. In the load area the materal propertes are mproved by usng the treatment processes. Therefore, the smulaton tools for optmzaton of ndustral processes are used. One of the basc process, whch ams to mprove the mechancal propertes of the steel part, s quench hardenng. In some processes, n whch prevously the volumetrc hardenng has been used, often the heat treatment wth the movng heat source s appled. The use of ths technology allows for more precse control of materal parameters and reduces the energy ntensty of the process.

2 80 A. Kulawk, N. Sczygol, J. Wróbel 2. Numercal model For modellng of the quench hardenng process the complex numercal model takng nto account thermal phenomena, phase transformatons n the sold state and mechancal phenomena are used. Couplng between elements of the model (see Fg. 1) such as: latent heat of phase transformatons (unmportant phenomena durng the superfcal hardenng process), structural and thermal strans as well as transformaton plastcty should also be taken nto consderaton. The nfluence of temperature and phase composton on the propertes of hardened materal (heat transfer coeffcent, thermal capacty, Young's modulus and yeld pont for the approprate phase) and nfluence of the stress state on the range of phase transformatons should also be presented on ths model. Fg. 1. The dagram of numercal model for quench hardenng process To determne the temperature felds, n the next tme steps, the soluton of the heat transfer equaton based on the fnte element method s used T ( λ T) ρc = 0 (1) t where: T s temperature [K], t s tme [s], λ = λ(t) s the thermal conductvty [W/(m K)], ρ s the densty [kg/m 3 ], C s the effectve thermal capacty [J/(kg K)]. The superfcal heat source (Neumann boundary condton) n the smulaton of the heatng process s determned by the functon q( s, z) ( s z s exp 0 2 Q z = 2 2 2π R ) + ( z z0) 2R 2 (2) where: Q s the power of the source [W], R s the radus of the source, 0 s z = P( x0( ϕ), y0( ϕ)), s= z r z (ϕ ), ϕ the angle of the poston of the source, r z s the external radus.

3 Determnaton of stresses n the steel ppe durng the superfcal heat treatment process wth helcal path 81 To calculate the knetc of phase transformatons n the sold state durng the heatng and coolng processes, the macroscopc model based on the analyss of CTP dagrams s used. The fracton of the austente phase durng heatng s determned on the bass of modfed Kostnen-Marburger equaton [1] ~ η γ 4,60517 T T ( T, t) = 1 exp ( T T) sγ fγ sγ (3) The phase transformatons durng the coolng process are calculated by the Johnson-Mehl-Avram-Kolmogorov equaton ( ) ( ) n T T t = ~ 0,01005 η( ), mn η ( %), ηγ η j 1 exp t n( T ) (4) j ts where: η (%) s the fnal fracton of phase estmaton on the bass of CCT dagrams for consdered steel, n(t) the functons dependng on the start and fnsh tmes of transformaton (t s and t f ), T sγ and T fγ are the temperature of start and fnsh of austente transformaton. Increment of martenste phase s descrbed by the Kostnen-Marburger equaton [1, 2] ηm( T, t) = η ~ γ η ( 1 exp( ( M S T + AM( σ ) / 3 + BMσ eff ) (5) M where: σ eff s effectve stress, M S s the start temperature of martenste transformaton, A M and B M are materal coeffcents. The martenste tempered fracton resultng from temperng s descrbed by formula ( ) ( ) 0,01005 = n T η ( ) T, t ηm 1 exp t n( T) (6) ts The curves of start and fnsh of the temperng transformatons were determned on the bass of equatons dependent on the heatng speed [3]. The thermal and structural strans are calculated by the followng equatons ε TPh = ε where: ( T) T + ε Ph T Ph Ph ( T) η T, ε = sgn( T ) ε ( T) η, ε = α (7) α s a thermal expanson coeffcents for phase, ε (T) s a stran expanson coeffcent for transformaton. Ph

4 82 A. Kulawk, N. Sczygol, J. Wróbel In the model of mechancal phenomena the equlbrum equaton was used wthout mass forces. The equlbrum equatons are supplemented by the consttutve relatons n the form σ = D o ε e + D o ε e, ε e = ε ε T ε ph ε pl ε tp (8) where: εe, ε, εpl, εtp are respectvely the elastc, total, plastc and transformaton stran tensors, D s tensor of materal constants. The plastc strans (εpl) are determned by usng the assocated plastc flow law wth sotropc hardenng [4]. To calculate transformatons plastcty (εtp) the model based on the Greenwood-Johnson mechansm s used [4, 5]. The temporary yeld pont s dependent on the temperature and the phase composton. 3. Numercal smulaton The numercal smulaton of the quench hardenng process was performed for the ppe made of C45 steel. It was assumed that the consdered object s only a part of a larger steel element whch was assumed by approprate condtons on the edge ΓB. The dmensons of the medum carbon steel ppe are followng: the length of the element 0.05 m, nternal radus rw = m and external radus rz = m (Fg. 2). Fg. 2. Graphcal nterpretaton of the descrbed example The followng condtons to modellng of the quench hardenng process were assumed: the ntal temperature (T0) n the whole area s equal to 293 K, the thermophyscal propertes such as: heat transfer coeffcent, thermal capacty, Young s modulus and yeld pont for the approprate phase depends on the temperature and phase composton [6],

5 Determnaton of stresses n the steel ppe durng the superfcal heat treatment process wth helcal path 83 the parameters of the heat source: poston z = 0.02 m, superfcal heat source R = m, Q = 1800 W, hardenng speed Vφ = 0.02 m/s (0.8 rad/s), on boundares ΓF, ΓO, ΓI the Newton boundary condton (coolng n the ar) wth Tar = 293 K, (αar) [7], on boundary ΓB the Drchlet boundary condtons Ux = Uy = Uz = 0, T = 293 K. a) b) Fg. 3. Changes of temperature and phase fractons (austente, bante, martenste, tempered martenste) n control nodes: a) frst control node, b) second control node Results of numercal calculatons showng the knetc of phase transformatons, dstrbuton of temperature n two control nodes: p1(0.0077, , ) and p2(0.0077, , ) are depcted n Fgures 2 and 3. The path of the heat source n the shape of the helcal lne caused the nfluence of temperature on the next waveforms to be greater wth the ncreasng of the temperature of element. Due to the gradual heatng of the element the wdth of the heat affected zone s ncreasng. On the next paths the partcular mportance has the temperng process. Because of the shape of the path, the temperng process takes place only n the areas between the paths.

6 84 A. Kulawk, N. Sczygol, J. Wróbel a) b) c)

7 Determnaton of stresses n the steel ppe durng the superfcal heat treatment process wth helcal path 85 d) e) Fg. 4. Dstrbutons of: a) martenste fracton, b) tempered martenste fracton, c) structural strans, d) resdual effectve plastc stran, e) resdual effectve stresses [MPa] 4. Conclusons The characterstcs of the results occurrng n such smple technologcal process ndcates on the very complex stress state. The use of heat source wth constant power caused the ncrease of the martenste phase range n the followng waveforms. The changes of heat source power should be used to obtan unform zones of martenste. Due to the use of a helcal lne of the heat source, the stress state s much more unform than n the case of usng crcular paths (see Fg. 4) [8]. All calculatons were performed on the copyrghted software mplemented n C++ language.

8 86 A. Kulawk, N. Sczygol, J. Wróbel References [1] Kostnen D.P., Marburger R.E., A general equaton prescrbng the extent of the austentemartenste transformaton n pure ron-carbon alloys and plan carbon steels, Acta Metallca 1959, 7, [2] Gejselaers H.J.M., Numercal smulaton of stresses due to sold state transformatons. The smulaton of laser hardenng, Thess, Unversty of Twente, The Netherlands [3] Wnczek J., Kulawk A., Dlatometrc and hardness analyss of C45 steel temperng wth dfferent heatng-up rates, Metalurgja 2012, 51 (1), [4] Bokota A., Modelowane hartowana stal narzędzowych. Zjawska ceplne, przemany fazowe, zjawska mechanczne, Monografe nr 233, Wydawnctwo PCz, Częstochowa [5] Fscher F.D., Rensner G., Werner E., Tanaka K., Calletaud G., Antretter T., A new vew on transformaton nduced plastcty (TRIP), Internatonal Journal of Plastcty 2000, 16, [6] Coret M., Combescure A., A mesomodel for numercal smulaton of the multphasc behavor of materals under ansothermal loadng (applcaton to two low-carbon steels), Internatonal Journal of Mechancal Scences 2002, 44, [7] L C., Wang Y., Zhan H., Han T., Han B., Zhao W., Three-dmensonal fnte element analyss of temperatures and stresses n wde-band laser surface meltng processng, Materals and Desgn 2010, 31, [8] Kulawk A., Wróbel J., The determnaton of the strans for the multpath heat source of the hardenng process, Modelowane Inżynerske 2013, 47(16), (n Polsh). [9] Mochnack B., Nowak A., Pocca A., Numercal model of superfcal layer heat treatment usng the TIG method, Polska metalurga w latach , t. 2, Komtet Metalurg PAN, WN AKAPIT, Kraków 2002,