Induction heat treatment of a ISO C45 steel bar: Experimental and numerical analysis I. Magnabosco *, P. Ferro, A. Tiziani, F. Bonollo Department of Management and Engineering, DTG University of Padova, Stradella S. Nicola 3, Vicenza 36100, Italy Received 17 May 2004; received in revised form 16 March 2005; accepted 17 March 2005
Abstract An experimental and numerical study of the induction heat treatment applied to ISO C45 steel was carried out. Both normalised and annealed samples were considered. The process parameters were implemented in a numerical code (Sysweld 2000) with an aim of predicting the thermal and metallurgical history of the material. The aim of this work was to create a thermo-metallurgical model of the induction heat treatment validated by experimental results. The experimental results (microstructure and micro-hardness profiles) were compared to the numerical values. A satisfactory agreement was found. 2005 Elsevier B.V. All rights reserved. Keywords: Induction heating; Quenching; Heat treatment; ISO C45 steel; Modelling; Finite element analysis; Metallurgical transformations
1. Introduction The development of numerical codes to calculate thermal histories, phase transformations and stress fields of different materials allow us to develop models which can predict the effects of heat treatment on the metallurgical and mechanical properties of machine components. It is very useful to forecast distortions, residual stresses, phase distributions, hardened depth, thickness of carburized layer, etc. Therefore, the possibility of optimising the process parameters by using numerical simulations rather than experimental tests, could become very advantageous both in design and economic aspects. In literature it is possible to find many works regarding the quenching heat treatment with very encouraging results [1–3]. However, numerical models of more complex heat treatment, as the induction heat-
*
ing and quenching, are still in progress. It is clear that the complexity of the phenomena involved in a generic heat treatment, such as heat exchange, elements diffusion, phase transformations and the consequent Ôtransformation plasticityÕ [4–6], makes the analysis very heavy. Furthermore, it is necessary to take into account the non-linearity of the material laws, functions of temperature and phases. So, the need to experimentally validate these models, and verify their reliability, is still very high. This work describes the numerical and experimental analysis of the induction heat treatment of a C45 steel bar. Experimental data were obtained by hardness tests and optical microscope analysis. The material properties, taken from literature, and the process parameters, were implemented in the numerical code with the aim of determining the thermal and metallurgical history of the material under investigation. The solid–solid phase transformation model, based on the contributions of Leblond and Devaux [7], Johnson-Mehl-Avrami [8–11] and Koistinen-Marburger [12] contribution, was taken into account. A high coupling level was considered
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between thermal metallurgical and magnetic computation. Finally, the simulation results have been compared with experimental values. The finite element numerical model was carried out using the Sysweld 2000 simulation code.
99
Table 2 Layer thickness having micro-hardness values superior to 650 HV0.1 Steel
(mm)
ISO C45 normalised ISO C45 annealed
1.4 1.25
2. Material and experimental tests The material under investigation, ISO C45 steel, has the nominal chemical composition shown in Table 1. The size of the two analysed samples were 20 mm diameter by 200 mm length. One of them, before the quenching process, was subjected to the annealing heat treatment while the other one was left in its normalised state. The process parameters used in the induction treatment were: • Displacement rate: 20 [mm/s] • Frequency: 27 [kHz] • Power: 31 [kW] During the heat treatment the specimens were made to rotate around their axis. The quenching was performed by a ring inductor coaxial with the sample while the cooling shower was applied by another coaxial ring attached to the inductor. The samples were analysed by optical microscope after suitably polishing and etching the surface (Nital 3%); obviously, in both the annealed and normalised state, the microstructure consisted of perlite and ferrite with a coarser form in the case of the annealed metal. After the thermal heat treatment the superficial layer was transformed in martensite. Micro-hardness Vickers (HV0.1) profiles were carried out in the radial direction of the specimen in order to detect the penetration hardening. These analyses were performed after the thermal heat treatment and carried out on a transversal section, placed at the centre of the quenched zone in order to avoid the boundary effects. Table 2 shows the layer thickness having micro-hardness values superior to 650 HV0.1. Fig. 1 shows the zone affected by the treatment, whose thickness is about 2 mm, that may be observed in the normalised ISO C45 steel bar. The obtained micro-hardness profiles are shown in Fig. 2. Figs. 3 and 4 relate to micro-graphs of the C45 normalised steel bar. In particular, they show the metallographic structures at the surface and at the core of the specimen after the heat treatment.
Fig. 1. Macrograph of the normalised ISO C45 steel bar after quenching (6X).
Fig. 2. Vickers micro-hardness (HV0.1) profiles on the middle cross section of the heat treated C45 specimens.
3. Numerical simulation Thermal and magnetic properties of the material under investigation were taken from the literature [13], likewise, the properties of the cooling medium and the
Table 1 Nominal chemical composition of ISO C45 steel (weight %) C
Si
Mn
S
P
Cr
Mo
Ni
Al
Cu
Fe
0.45
0.25
0.65
0.025
0.008
0.4
0.1
0.4
0.01
0.17
Bal.
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Fig. 3. Microstructure at the surface of the normalised C45 steel specimen after the induction treatment (500X).
Fig. 4. Microstructure at the core of the normalised C45 steel specimen after the induction treatment (500X).
inductor (copper). The numerical calculation combines two different analyses: the first one performs a thermal–metallurgical computation and the second one an electromagnetic computation. They are solved by means of fully transient analyses. Each of them requires a geometric model, boundary conditions and material properties. Thermal and metallurgical calculations are coupled by the latent heat of phase transformations. Because of the electrical and magnetic properties laws depend on temperature a high coupling grade between thermal and electromagnetic equations arises. The heat source consists, in facts, of the eddy currents induced by the magnetic field variations (Joule effect). Fig. 5 shows a scheme of thermal and magnetic coupling. Fig. 6 shows a scheme of the coupling grade between thermal and magnetic analyses. The time axis of the thermal calculation is divided into macro step, Dt. When the initial temperature is known, the intensity of the eddy current value can be calculated; this value is then used to compute the heat generated by the Joule effect. For each magnetic sub-step the temperature value is recalculated until a steady state between the heat generated by the Joule effect and the temperature field, resulting from the thermal analysis, is reached. This routine represents the possible maximum coupling level to perform [13]: magnetic and thermal property values at t + 1 * Dt instant are used to calculate those at the same t + 1 * Dt instant. Each thermal macro-step (Dt = 0.1 s) is divided into a lot of sub-steps (dt = 105 s) to create the convenient magnetic time scale and make the convergence of the magnetic calculus, that is strongly not linear, easier.
Fig. 5. Thermal–magnetic coupling.
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Fig. 6. Magneto-thermal coupling level and time scales (magnetic and thermal) [13].
3.1. Geometry and specimen numerical model In Fig. 7 one can see the geometry of the inductor ring with a rectangular section of 10 · 15 mm. For the axisymmetrical conditions, only a half section of the whole geometry was modelled, as shown in Fig. 8. The mesh elements were divided into groups in order to describe the system portions with different properties. Specific mono-dimensional elements were created for modelling the air around the part (‘‘air’’ group), the
Fig. 7. Cylinder-coil geometry.
Fig. 8. Mesh scheme.
101
Fig. 9. Mono-dimensional elements groups.
inductor cooling water (‘‘water’’ group) and the cooling spray on the object (‘‘cooling’’ group). Heat exchange due to water and air was modelled by imposing the respective global heat exchange coefficients on the mono-dimensional elements. The axis of the bar, defined by means of a mono-dimensional element group (named ‘‘axis’’), was used to impose symmetrical conditions. The mesh is the same for each analysis (thermal–metallurgical and electromagnetic). Fig. 9 shows the different groups of elements generated in the model. Finally, isoparametric rectangular elements groups with four nodes were created to model the specimen and the coil (groups ‘‘object’’ and ‘‘inductor’’). Specific heat (C (J/kgK)), thermal conductivity (k (W/mK)) and material density (q (kg/m3)), are functions of phases and temperature and their values are shown in Figs. 10–12 and in Tables 3 and 4 [14]. The heat exchange with the surrounding air and water was modelled by the respective overall heat transfer coefficient assigned to the boundary group elements (Table 3). In particular, the movement of the cooling spray was modelled by means of a FORTRAN function which, connected to the ‘‘cooling’’ group, modifies the global heat exchange coefficient according to the position of the cooling tool. Fig. 13 shows a scheme of the heat treatment with some input data of the numerical model.
Fig. 10. Thermal conductivity k (W/mK) of the C45 steel bar [14].
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(768 C) (Fig. 14). The magnetic permeability (l) associated with the ‘‘object’’ group has been expressed through the above equation. Fig. 15 shows the electric conductivity of steel as a function of temperature. For the axisymmetric conditions, the potential in the specimen axis has been imposed to zero. The function which describes the voltage trend at the extremes of the inductor, represented by Eq. (2), was defined using FORTRAN language and implemented in the numerical code.
Fig. 11. Specific heat C (J/kg K) of the C45 steel bar [14].
VV ðtt; tÞ ¼ V 0 ðttÞ cosðxt þ uÞ
Fig. 12. Density q (kg/m3) of the C45 steel bar [14].
Table 3 Thermal properties of copper inductor [13]
‘‘Inductor’’ group
Specific heat (C) J/kg K
Thermal conductivity (k) W/mK
Density (q) kg/m3
386
400
8930
Table 4 Thermal properties of the thermal exchange medium [15]
‘‘Air’’ group ‘‘Water’’ group ‘‘Cooling’’ group
Emissivity
Heat transfer coefficient W/m2K
0.9 – –
5 10,000 5500
In order to simplify the physical model, all the heat transfer coefficients and the inductor thermal conductivity were considered temperature independent. 3.2. Magnetical properties 1
The values of the electric conductivity (r [(Xm) ]) and permeability (l (Henry/m)) used for the ‘‘inductor’’, ‘‘air’’ and ‘‘water’’ groups are shown in Table 5. The well-known equation: B ¼ lH
ð1Þ
relates the magnetic induction with the magnetic field. For the copper coil this relation (1) is linear while for steel it is non-linear below the Curie temperature
ð2Þ
In Eq. (2), tt is the time on the thermal scale and t is the time on the electromagnetic scale (this diversification is necessary because of the coupling between the two different analyses, the first one for thermal calculus and the second for the electromagnetic computation); x is the pulsation and u is the phase. In particular, x = 2pf, where f is the frequency, VN = VV/2p, because of the geometry of the numerical model (sector of 1 radiant), and u = 0. If t0 is the time (in the thermal scale) related to the beginning of the magneto-thermal analysis, t1 = t0 + a and t2 = t1 + b are respectively the time at the beginning and at the end of the steady-state conditions. Finally, t3 is the time at the end of the magnetothermal coupling. The voltage amplitude V0 (tt), in Eq. (2), assumes the following values: V 0 ¼ VN
ð3Þ
if t1 < tt < t2 ;
V0 ¼
VN tt t1
V0 ¼
VN ðtt t2 Þ þ VN t2 t3
ð4Þ
if tt < t1 ; if tt > t2 .
ð5Þ
The t0, t1, t2, t3 parameters have been fixed during the preliminary phase of the analysis (Table 6). In this case, since it was imposed t3 < t2, the final transient effects were neglected. Fig. 16 shows the trend of the imposed maximum voltage with relation to time. For the axisymmetric condition, the current density (J) in the inductor depends only on the space variables (r, z) in the plane concerned and has only a single out-of plane component (J = J(r, z) eh). 3.3. Metallurgical characteristics The presence of four microstructures were considered in the numerical model: ferrite–perlite, bainite, martensite and austenite. The phase transformations that involve austenite, ferrite–perlite and bainite were realised by means of the Leblond-Devaux formulas (6) [7] while the Koistinen-Marburger formula (7) [12] was used for the austenite–martensite transformations: peq ðhÞ p _ dp ¼ F ðhÞ dt sR ðhÞ
ð6Þ
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103
Fig. 13. Induction hardening process scheme.
Table 5 Electromagnetic properties of air, of inductor cooling water and of copper coil [13,15]
‘‘Air’’ group ‘‘Water’’ group ‘‘Inductor’’ group
Electric conductivity r [(Xm)1]
Permeability (Henry/m)
– – 59 · 106
12.57 · 107 12.57 · 107 12.57 · 107
Fig. 15. Electrical conductivity of the C45 steel bar [14].
Table 6 Time parameters of the magneto-thermal analysis (s) t0
t1 = t0 + a
t2 = t1 + b
t3
2
3
7
6.5
Fig. 14. Magnetisation curves for different temperatures [14].
In Eq. (6) p is the phase proportion, t is the time, h is the temperature, peq(h) is the phase proportion calculated at thermodynamic equilibrium, sR is the delay time of the transformation due to the continuous cooling or heating, and F is a function of the heating or cooling rate. The formulation leading to Eq. (6) is defined for a transformation between only two phases but it can be extended to the transformation of more than two phases. The unknown parameters in Eq. (6)
Fig. 16. Voltage as time function.
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Fig. 17. CCT diagram (temperature in C).
(peq(h), sR, F) can be calculated by comparison with the equilibrium, CCT and austenitisation diagrams [16]. pðhÞ ¼ p ð1 exp ð b ðMs hÞÞÞ with h 6 Ms. ð7Þ In Eq. (7) p is the phase proportion obtained at a very low temperature (in most cases equal to 1), Ms is the temperature of the initial martensitic transformation (325 C [16]) and b is a material coefficient (0.03 [14]). These values were obtained from the CCT diagram of the C45 steel [16]. Fig. 17 shows the calculated CCT diagram obtained by using Eqs. (6) and (7). 3.4. Numerical determination of hardness Knowledge of the thermal and metallurgical history allows us to predict hardness in the heat-altered zone. For this purpose experimental formulas taken from the literature [13,15,17,18] have been implemented in the numerical code (Eqs. (8)–(10)); they take into account the material chemical composition, the final microstructure and the cooling rate at 700 C (VR), while the grain size is neglected. In order to obtain valid results the element proportions must be located within the following chemical composition ranges: 0.1% < C < 0.5%, Si < 1%, Mn < 2%, Ni 6 4%, Cr 6 3%, Mo 6 1%, V < 0.2%, Cu < 0.5%, 0.01% < Al < 0.05%. HVmartensite ¼ 127 þ 949C þ 27Si þ 11Mn þ 8Ni þ 16Cr þ 21 log10 vR
ð8Þ
HVbainite ¼ 323 þ 185C þ 330Si þ 153Mn þ 65Ni þ 144Cr þ 191Mo þ log10 vR ð89 þ 53C 55Si 22Mn 10Ni 20Cr 33MoÞ
ð9Þ
HVferrite ¼ 42 þ 223C þ 53Si þ 30Mn þ 12.6Ni þ 7Cr þ 1Mo þ log10 vR ð10 19Si þ 4Ni þ 8Cr þ 130VÞ ð10Þ In Eqs. (8) and (9) an error with a standard deviation of about 20 Vickers is foreseen [13,15].
4. Simulation results Fig. 18 shows the maximum temperature values achieved in some nodes along a radius of the specimen and their correlation with the corresponding experimental final structures. A good agreement can be observed if one considers the natural inertia of the phase transformations added to the short exposure time of the material to the high temperatures. In spite of the high heating rate at the surface of the specimen, the very high temperatures reached (about 1250 C) in this zone are able to completely transform the external layer in austenite. The subsequent cooling phase induces in the material a complete martensitic micro-structure, as confirmed in Fig. 18 (micrograph A). At 2.5 mm distance from the surface, the temperatures reached are very closed (or lower with respect) to the eutectoidic temperature, and not sufficient to permit the austenitisation of the pre-existing ferritic–perlitic microstructure, which is still present at the end of treatment (micrograph D). At intermediate zones, the maximum temperatures reached are in the A1–A3 interval, so that the transformation from perlite to austenite is almost complete (as well as the consequent austenite to martensite transformation), while the ferritic phase can not transform itself into austenite. As a consequence, we found an increment of not transformed ferritic phase moving toward the specimen axis (Fig. 18, micrographs B and C).
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105
Fig. 18. Maximum temperature profile results from simulation compared with specimen microstructures of normalised steel after induction hardening.
A comparison between the micro-hardness measurement in the two analysed specimens and the values obtained with the numerical model is shown in Fig. 19. The experimental data of the annealed material show a more irregular trend compared to the normalised one. This phenomenon is due to the coarser granular structure of the annealed specimen which results, during the austenitisation process, in a more inhomogeneous carbon distribution compared to the normalised material. Consequently, martensite grains characterised by large hardness differences were found. A fairly good agreement was obtained between numerical and experimental values of micro hardness (Fig. 19) and a good prediction of the maximum value of micro-hardness was obtained. The discrepancies may be due to the empirical character of Eqs. ((8)– (10)), to an inevitable uncertainty of the material law
Fig. 19. Comparison between the micro-hardness measurement in the analysed specimens and the values obtained with the numerical model.
behaviour at high temperature and to the residual stresses arising in the material and not considered in the model. Thus, a more precise calibration of the material low and the modelling of the residual stresses influence seems to be necessary in the future to optimise the model. Finally, some approximations taken in the model can to have negative influence on the results, as well as a thermal exchange coefficient constant with relation to temperature and dimension of cooling tool.
5. Conclusions An experimental and numerical study was carried out on the induction hardening process of type C45 steel. The test pieces have been used both in the annealed and normalised states. The hardened depth and the microstructure of the samples were investigated through conventional microstructure and micro-hardness analyses. A numerical model was used to simulate the heat treatment in order to predict the thermal history, the phase distributions and the micro-hardness profiles. The simulation results were validated by experimental data. It is appropriate to highlight the difficulties and the limits of this procedure needing an accurate knowledge of process and material parameters. The error range observed between the experimental and numerical results can be justified considering approximations admitted upon the model construction. The initial material structure was considered homogeneous without distinction between the perlite and ferrite phases. So the model neglects the heterogeneity effect on electrical and thermal conductivity properties. This hypothesis is verified when the grain dimension is sufficiently fine. Best results could be possible considering also the initial
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grain dimension. Furthermore, thermal exchange coefficient was considered constant with the temperature. Finally, the residual stresses induced by the process were not taken into account in the micro-hardness calculus. Notwithstanding this, numerical results are in satisfactory agreement with experimental observations. Work is in progress about the process parameter influence on metallurgical modifications induced on the steel. A further analysis will take into account the mechanical computation during the entire heat treatment process with a particular attention to the residual stresses prediction and experimental determination by X-ray measurements.
[5]
[6]
[7]
[8] [9] [10]
Acknowledgement [11]
The authors gratefully acknowledge the numerical support provided by Mr. H. Porzner (ESI Group).
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