Numerical simulation as a tool for prediction of material behavior during induction quenching.

Behulova, Maria ; Taraba, Bohumil

Abstract: Induction heating followed by water quenching is widely used for hardening of complex-shaped parts when hard surface and tough part core are required. In this paper, the process of induction hardening of a flanged plug from the steel C45E is analysed using numerical simulation of coupled electro-magnetic, temperature and stress fields. On the base of obtained results, the critical areas of possible material failure are predicted.

Key words: induction heating, water spray cooling, numerical simulation, temperature fields, stress-strain fields, crack.

1. INTRODUCTION

Induction quenching is widely used in industry. The main advantages of this method include very accurate control of heated surface and depth, fast heating rates, high efficiency, good reproducibility, cleanness and low energy consumption.

Processes of induction quenching are mostly designed using engineering experience and a trial-and-error procedure. In connection with advance in computational technique and numerical methods, computer simulation is ever more exploited to support design and optimisation of induction heat treatment processes (H'omberg, 2004, Magnabosco, I. et al., 2006).

2. PROBLEM DESCRIPTION

A flanged plug (Fig. 1) made from the steel C45E is under operation subjected to the combined loading. In order to increase the hardness of surface layers along with keeping relatively high core toughness, the flanged plug is quenched using induction heating followed by water spray cooling. During quenching, the plug is supported in centres and it is rotating around its axis to achieve uniform through-hardening. The hardened depth from 2 mm to 3.5 mm is required in the upper and middle parts of a shaft. In the bottom conical part, the chill depth should be from 2 mm to 5 mm, while the minimal hardened layer of 1.5 mm is desired at the plug bottom. Designed shape of inductor coil was adapted to the shape of plug bottom. Inductor is created by a copper single-turn coil with dimension according to Fig. 1.

[FIGURE 1 OMITTED]

Technological process of induction quenching consists of several steps. First, the inductor coil in off-state is fed down along the shaft to the plug bottom. In this position, pre-heating of the area of plug bottom is performed with the generator output of 23.8 kW and the frequency of 20 kHz for a period of 6.9 seconds. Then, generator is switch-off for the dwell time of 2 seconds. In the next step, inductor coil is moving up along the shaft in the vertical direction with the speed of 13.3 mm.[s.sup.-1] and generator output of 33.8 kW during 5.1 seconds. In the time of 9.9 sec., the process of cooling starts with the water mass flow of 50 kg.[min.sup.-1] and temperature of 24 [degrees]C.

The paper deals with numerical simulation of the process of induction quenching of a flanged plug using the finite element program code ANSYS 10.0 in order to analyse electromagnetic, temperature and stress-strain fields in a quenched part. The main aim of the paper is to predict material behavior during induction quenching including the analysis of the possibilities of heat treatment cracks and material failure.

3. PRINCIPLE OF INDUCTION HEATING

In induction heating process, an alternating current is passed through a conductor creating an alternating magnetic field. In a part placed into this magnetic field, eddy currents are induced and material is heated up due to the resistive and hysteresis looses. The induced current and consequently the generated heat are not uniformly distributed throughout the workpiece. Around 63 % of induced current and 87 % of generated heat is concentrated in the outer region called skin depth depending on electric and magnetic properties and mainly on the frequency of current in the coil (Haimbaugh, 2001). In the processes of surface quenching of steels, the surface layer is heated very fast using the high-frequency inductor whereby the internal parts are practically unaffected. Rapid oil or water quenching results in the development of thin hardened surface layers.

4. SIMULATION MODEL

The material behavior during induction heating and quenching is very complex. It can be described by coupled sets of partial differential equations, complicated boundary conditions for electro-magnetic, thermal and stress-strain fields and nonlinear material properties (Behulova & Taraba, 2006). The coupling between electro-magnetic and temperature fields is given by the dependence of electro-magnetic properties on temperature. On the other hand, the temperature field is influenced by the Joule heat generation. In addition, the magnetic permeability depends on the magnetic field density and thermal properties are temperature dependent. The boundary conditions, particularly the heat transfer coefficient varies very strongly with the temperature. The temperature fields are further influenced by movement of inductor and cooler. Moreover, a heated part is deformed during induction heating due to the thermal expansion and plastic deformation occurrence, i. e. the distance between inductor and heated part is changed. The dependence of mechanical properties on temperature must be taken into account as well. All these facts were considered in simulation model and solution procedure using the finite element program code ANSYS 10.0.

Based on the technical documentation of a flanged plug, the axisymmetric geometrical model was prepared. The density of generated FE mesh is considerably higher along quenched surfaces (Fig. 2) in order to take into account the skin effect. Initial position of inductor is illustrated in detail in Fig. 2b.

[FIGURE 2 OMITTED]

Material properties of the C45E steel for electro-magnetic, thermal and static analyses were considered as functions of temperature. Temperature dependent B-H curves were given by special user subroutine. Initial and boundary conditions were defined in compliance with described technological process of induction quenching. The initial temperature of a plug was supposed 20 [degrees]C. The heat extraction from the plug surface to the surroundings with the temperature of 20 [degrees]C is realised by free convection and radiation. The combined heat transfer coefficient was calculated in the dependence on plug surface temperature (Incropera & DeWitt, 1996). During water spray cooling with temperature of 24 [degrees]C, the value of the heat transfer coefficient of 5000 W.[m.sup.-2].[K.sup.-1] for was supposed (Specht, 1992).

5. RESULTS AND DISSCUSION

Results of numerical simulation were analysed and evaluated with the aim to predict the material behavior during induction quenching and to examine critical regions of possible plug failure. In the phase of pre-heating of a plug bottom, the maximum heating rates are reached in the areas with the highest intensity of magnetic field. The maximum temperatures at the end of pre-heating in the time of 6.9 sec. exceed 1100 [degrees]C (Fig. 3a). The maximum stresses at this time are localised at the outer side of a plug under structural element called a "cup" (Fig. 3b). The maximum displacements along the cup circumference reach the values up to 0.34 mm. In the node 1, the equivalent elastic Mises stresses ([[sigma].sub.M] = 430 MPa) exceed the yield strength of the C45E steel ([R.sub.e,min] = 390 MPa) indicating possibility of the occurrence of plastic deformations in the area of the plug root.

During the holding time, temperatures in the critical parts of a cup slightly decrease (Fig. 3d) mainly due to the heat conduction to the inner parts of a plug and also the heat extraction to the surroundings. In the time of 9.9 sec., the plug surface started to be water spray quenched. Rapid temperature drop in the area of a cup results in the enhacement of equivalent Mises stresses (Fig. 3d). Tensile stresses rise in the superficial plug areas while compression stresses act inside the plug. The maximum values of equivalent Misses stresses are moving from cimcumference parts of the plug to the inner cup area attaining values more than 1000 MPa (Fig. 3c). As these values exceed the ultimate strength of the C45E steel ([R.sub.m] = 785 MPa), appearance of cracks and material failure can be awaited with a high probability in the cup area.

[FIGURE 3 OMITTED]

6. CONCLUSIONS

From the construction point of view, the analysed flanged plug represents a complicated part comprising of different cross-sections with variously specified hardened depths. Based on numerical simulation, the area of a cup seems to be the most critical place of the possible plug failure during induction quenching or later on operating conditions. In this region, equivalent Misses stresses exceed the ultimate strength of the C45E steel during quenching. Moreover, the cup is hardened through the whole thickness what was proved experimentally as well. This fact increase brittle damage ability of the cup.

The higher level of structural analysis represents the application of elastic-plastic material model which enables to evaluate plastic deformations and residual stresses. However, according to the author's experience, the elastic model provides sometimes better information on critical regions with potential occurrance of maximum stresses and possible initiation of material damage during and/or after heat treatment.

Nevertheless, the numerical simulation is a powerful tool for examination of material behavior as well as for analysing and optimisation of technological processes. In this case, the next work will be focused particularly on the optimisation of inductor shape and the process of induction heating.

The research has been supported by VEGA MS SR and SAV within the projects No. 1/2073/05 and VEGA 1/2101/05.

7. REFERENCES

H'omberg, D. (2004). A mathematical model for induction hardening including mechanical effects. Nonlinear Analysis: Real World Applications 5, 2004, pp. 55-90.

Magnabosco, I. et al. (2006). Induction heat treatment of a ISO C45 steel bar: Experimental and numerical analysis. Computational Materials Science 35, 2006, pp. 98-106.

Haimbaugh, R. E. (2001). Practical Induction Heat Treating, ASM International, Materials Park, Ohio.

Behulova, M. & Taraba, B. (2006) Analysis of temperature and stress fields by induction hardening. In: 21st Int. Conf. on Heat Treatment. ATZK, Jihlava, pp. 305-312.

Incropera, F. P. & DeWitt, D. P. (1996). Fundamentals of heat and mass transfer, John Wiley & Sons, New York.

Specht, E. & Jeschar, R. (1992). Heat transfer in continuous casting during spray-water cooling. Heat and Mass Transfer in Materials Processing, pp. 535-547.