Numerical Simulation of Thermal Stress Fields in the Magnetic Quenching Process of 45 Steel

J. Mater. Sci. Technol, Vol.19 Suppl.1, 2003153(3) Finite element method in that contex belongs to theuniversal technique of stress control and is very computer ap(4) The proposed finite element generation is very modernand suitable tool for mentioned type of stress analysis.AcknowledgementThis work was supported by the Ministry of Science and Tech-nology of Republic of Croatia under grant No.0069-006.REFERENCES[1. ] LN.G ,Rozvany: Structural Design viaOptimality Criteria,'Kluwer Acadermic Publ, London, 1989.Fig.4 Beam loaded by transversal force[2] K.J.Bathe: Finite Element Procedure, Prentice Hall, New Jer-sey, 1994. Conclusions[3] T.Kawai and Y.Fugitani: Some Considerations on the Mod-ern Beam Theory, Inst. of Industrial Science, Univ. of Tokyo,Tokyo, 1986.(1) Any design as well as manufacturing philosophy long[4 ] J.Brmid: Elastomechanics and Plastomechanics, Skolska knjiga,for optimal solutions(6.Zagreb, 1996.(in Croatian)(2) Stress analysis, as an interactive process, is very im-; ] D.E.Smith: Design Optimization, (in ASM Handbook, Volportant part of design procedure.20), ASM International, USA, 1997.Numerical Simulation of Thermal Stress Fields in the MagneticQuenching Process of 45 SteelZiliang Lt, Junruo CHEN, Miao ZHANG and Yihong GUANT| AFaculty of Mechanical and Electrical Engineering, Kunming University of Science & Technology, Kunming 650093, China[ Manuscript received November 4, 2003)Based on a transient temperature distribution of a 45 steel cylinder workpiece during magnetic quenching, which was obtainedby solving the governing equations with nonlinear boundary on the condition of coupling effects of heat-magnetism. Accordingto the theory of thermal non-elasticit, computational mechanics, ferromagnetism and phase transformation, a nevv constitutiveequation considering effects of phase transformation is proposed and solved by means of finite element method. The transientthermal stress and residual stress are obtained and the infuencing factors on the thermal stress of magnetic field are analyzedand discussed.KEY WORDS: Numerical simulation, Thermal stress, Magnetic quenching, FEM1. Introduction2. Infuence of Magnetic Field on the Physical Prop-erties of FerromagneticWith the development of science and technology, the tech-niques of heat treatment ways have been advanced and the2.1 Abrupt change of heat expansion coficientnew methods are more and more, such as laser heat treat-It is the basic feature of ferromagnetic that there existsment, the nitrogen treatment of metal material and so on.abrupt change of volume expansion and heat expansion co-At present, it is a very important developing direction to addefficient at Curie temperature. According to the theory ofmagnetic field in the heat treatment process of ferromagneticferromagnetism4, the calculating expression of the magneticmaterial, which can well improve the mechanical propertiesmaterial heat expansion coefficient aH as follows:of material. In this respect, some scholars have utilized thequenching by additional magnetic field to change the orga-nization and capability of the metal. But it merely limitsan=a-(%)(唱),to experiments, the theoretical study on this new heat treat-ment method is very little. In this paper, on the basis ofIn this formula, the sign a; means common heat expan-earlier paper(1], the transient temperature field of a 45sion coefficient. w stands for volume contraction induced byaneartierpaper'steel cylinder during magnetic quenching was obtained. Themagnetic feld which is the function of temperature T and thethermal elastoplastic constitutive equation, including variablemagnetic field intensity H, a8 H is the function of spontaneousphysical properties and phase transformation, is put forwardmagnetization intensity I and temperature T.and solved by means of finite element method (FEM)[. Thetransient thermal stress field and the residual stress field of2.2 Maeneto-elasticitv effectthe cylinder are obtained and the infuencing factors on the中国煤化工f frromagnetic materialthermal stress of magnetic field are discussed. The results arewill:ed by the magnetic fieldsatisfying.anHCNMHG↑Lecturer, to whom correpondence should be adesed,E-mail: liliang@public.km.yn.cn.Bn= Bo-OE= Bo[I- Eo(%0)](2)154J. Mater. Sci. Technol, Vol.19 Suppl.1, 2003In which, Eo is the Young' s modulus without magnetized,component, respectively. Their expresions can be witten as:μo is the initial magnetic permeability, and H4o = , whereI。is saturated intensity of magnetization, σi is internal stress,d{}.= DH{o}dT + [D]h'd{}; d{e}p = dep品入。is the saturated magnetostriction.de)r+={a)dr; de}. =号(兰F1({lu).Jr2.3 Variable physical propertiesDuring magnetic quenching, the physical properties of fer-romagnetic material are not only the nonlinear function of(J= F,P,B,M)temperature but also effected by the magnetic field. Put(7)phase transformation conditions and phase compositions intcIn which, {a} is the column matrix of heat expansion. Asthe physical properties, and considering formula (1) and (2),to the axisymmetric problem, because of the isotropic heatwe can get the expressions of physical properties of carbonexpansion, so {a}=aμ[1 1 1 0]T, whereis the heat ex-Dansioncoefcientdetersteel as follows:rmined by Eq.(3). [D]H is the elasticrectangular matrix, for the axisymmetric problem, it may beexpressed as: .an(I,i,H)=.总Es[,[), (器).(路)]+步却品0](1-总Ft5)a.4)[D]u=EH(8)1+μ品却器0El(,H)=点Brf{E(T)[1- Ev(T(鶚:)]}+0告」(- PR5t)B:.) (V=PB.).where, Eu is the Young's modulus determined by Eq:(3), μis Poisson's ratio.(3According to the mobile criteria and generalized Hooke'slaw, we can get: .where, qg and En are the heat exexpansion coficient and theYoung's modulus influenced by magnetic field, a, (T) andEA(T) are the heat expansion coefficient and the Young'sd{} = (DInd{e}. = [D]n(d{e} - d{e}p - d{e}r - d{e}w)modulus of austenite under the corresponding temperaturerespectively, FJ and fs are the phase transformation condi-tion and the phase volume fraction of phase J, as well asF, B, P, M respectively stand for ferrite, bainite, pearlite andmartensite.= D)(de-adep -d{e}r -d{}.)(9)For other physical properties, such as heat conductioncoficient and specific heat, the expressions are similar toEq.(3).Through formula (5) and (9), we can gain the incrementsform of thermal elastoplastic constitutive equation duringmagnetic quenching process as follows:3. Thermal Elastoplastic Constitutive Equation dur-ing Magnetic QuenchingAdopt the Mises' yield criteria of isotropic strengtheningd()=Dnd{dt}-- [" (0)+ (o]ar - den}-model as this3):;元[D]a路导dTo-F({ dep,T)=0 .(D]n 6{可] +器+{緔} [D]u器(10)where, Ep and a represent equivalent plastic strain and equiv-where, [D]epH is the thermal elastoplastic matrix during mag-alent stress, respectively. Different from the Eq.(4), we can netic quenching process that may be expressed as fllws:get:(DIu(3T) do=;F.dep + dT(5[D]epH = [D]u(11)站+(路) (In尚」According to incremental theory, let d{e} stands for theincrements form of the total strain, thus:4. Calculation Results and Discussiond{e} =d{e}e +d{e}p +d{e}r + d{e}.. .(6中国煤化工cin Fig.1. It is a 45 steelcylinMHC N M H Ghing nital teperature .In which, d{e}e, d{e}p, d{e}r and d{e}u are the incre-is 860°C, and the magnetic field intensity is 4.4x10* A/m. Itments form of the elastic strain, plastic strain, thermal strain is continuously cooled in water with an initial temperature ofand the united expression of all phase transformation strain 21°C.J Mater. Sci. Technol, Vol.19 Suppl.1, 2003155sults of transient stress distribution. Considering restrictionzof extent, we only take section I into account.In Fig.2, the transient stress distribution during magneticquenching and normal quenching process50 s on the section I are given. Through Fig.2, we can makeou(1) During magnetic quenching, σz, σr, σe all are smallerthan the normal quenching process. It indicates that usingmagnetic quenching can decrease the internal stress of thesample due to the following reasons: First, additionel m8gnetic field may reduce the workpiece cooling rate, and lightenits temperature difference between surface and innerl1. Sothe thermal stress is small. Second, the heat expansion coefficient of magnetized material takes place abrupt change atFig.1 SampleCurie temperature, wwhich is about 7550°C, and infuences theprocess of phase transformation, then leads to the lttle ther-a)mal stress. Third, under the effect of additional magneticfield, the Young's modulus of 45 steel becomes smaller andmakes the elastic matrix and the thermal elastoplastic matrixchange and result in the lttle thermal stress.x(2) Through the calculation results we can see that themaximum of stress component is σr. This is consilient to thepractical fact that quenching crack of axisymmetric workpieceis readily formed as ring fissure.00 9(3) After 10 s, the changingrange of stress descends grad-200↓ually. After 50 s, the changes will tend to stability astress distribution tends to the residual stress distribution.00 !5. Conclusions咖[(C)(1) It is feasible to solve the transient stress distribu-Sr/mmtion and the residual stress distribution of the cylinder byEq.(9) based on the known transient temperature distribu-tion of workpiece during magnetic quenching. Moreover, theresults are in good satisfaction.(2) The calculation results verifies when using magneticquenching, internal texture stress low, deformation less andmechanical properties better. So the study of magneticquenching has much extensive perspective.一olmom ourching --- .。ormapnotce auntrREFERENCESFig.2 Thermal stress at various instant on sec-tionI (a) 0.78, (b) 10s, (c) 50 sMeihong LIU: Proceedings EPMESC VII, 2001, 6.Yicheng GUO: Ferromagnetism, Higher Education Press, Bei-Based on the known transient temperature distribution ofjing, 1965. (in Chinese)a 45 steel cylinder workpiece during magnetic quenching',[3] Beichen LIU: Engineering Computational Mechanics, Mechan-Eq.(10) is solved by means of FEM and we can get the reical Industry Pres, Beijing, 1990. (in Chinese)中国煤化工MYHCNMHG