Application of Direct Resistance Heating in Hot Forging and Analysis of Processing Parameters based on Thermo-electro-mechanical Coupling FEM

Experimental apparatus

The experimental setup used in this study is shown in Figure 1. The copper electrode having a thickness of 2.0 mm was placed in the groove of the die holder to prevent deformation of the electrode. The cylindrical billet was sandwiched between the dies. The billet, dies, electrodes and power supply formed a series circuit. When the DC current flowed through the dies and the billet, they were heated due to the Joule heating effect.

Figure 1:

(a) Scheme and (b) photo of the experimental setup.

The entire device was set at the Zwick /z150 testing machine (maximum load of 150kN) to provide a certain pressure. The insulator was positioned between the setup and the testing machine to protect the test machine from current, as shown in Figure 1(b). The die made of heat-resistant molybdenum alloy (TZM) had a diameter of 120 mm and a height of 30 mm. All the experiments carried out in the air. To measure the temperature distribution of the device, two NiCr-NiSi thermocouples (diameter 0.5 mm) were used. As shown in Figure 1(a), the thermocouple No. 1 was located at the center of the billet (diameter 1 mm, depth 3 mm), indicating the temperature of the billet. The thermocouple No. 2 was located on the die surface and represented the temperature of the die.

Materials

The billet material is 42CrMo4, and the thermoforming temperature field is 850~1200 °C. Due to the power supply limitation, a cylindrical billet with a diameter of 6 mm and a height of 8 mm was used in the heating and upsetting experiments. The chemical composition of 42CrMo4 is shown in Table 1.

Heating experiments

The resistance heating was controlled by current intensity. DC power was supplied by the TSQLG 400-8 /2000 (maximum output of 8 v×2000 A), resulting in a constant current. The initial conditions for the heating and upsetting experiments were made up of the initial temperature and the contact pressure. In all experiments in this study, the initial temperature of the billet and the dies was room temperature. The initial contact press can be manually changed.

Upsetting experiments

In the upsetting experiments, the billet was heated to above 1000 °C in the dies, then kept at that temperature for about 5 s, and subsequently formed at a constant speed. After the upsetting, the billet was cooled down in the dies until it reached room temperature. Due to the relatively small size of the billet and the high cooling rate, the speed of the upper die was set at 1 mm/s to avoid excessive cooling during forming. When the maximum forming force reached 30 kN, the upsetting process stopped.

In order to determine the effect of the resistance heating during forming, two types of upsetting experiments were performed: (a) the resistance heating stopped before upsetting (case a) and (b) the constant resistance heating was applied during heating and upsetting (case b).

Analyses of heating process

It is one of the key issues of the system, whether the billet can be heated to the forming temperature in a short time or not. According to the Joule’s laws, the heat generated in the billet depends on the current intensity, resistance and heating time. In addition, the heating dissipation of the billet depends on the conduction to the dies on the contact area and the radiation to the environment.

To improve the understanding of the heating process, a typical heating and cooling process under a current intensity at 400 A using the above described system was shown in Figure 2 (initial contact pressure: 5.3 MPa). The whole process can be divided into three stages, namely preheating, holding and cooling. During the preheating stage, the temperatures of the billet and the die rapidly increased to 262 °C and 63 °C in about 10 s at a current intensity of 400 A. The temperature of the die was much lower than that of the billet due to the larger volume and lower resistance of the die. Therefore, it was apparent that the temperature gradient between the billet and the die was steep. In addition, the minimum temperature of the billet occurred at the edge as a result of the heat loss through conduction and radiation.

Figure 2:

Time history of temperature in the resistance heating process.

At the holding stage, the temperature of the billet and the die was stabilized so as to strike a balance between the heating generation and dissipation. It can be observed that the heating temperatures cannot increase with the heating time at the holding stage. When the current was stopped during the cooling stage, the temperature of the billet rapidly reduced at a rate of about 60 °C/s due to the high thermal conductivity of the billet and the die.

Effects of the initial contact pressure on the heating process

The billet holding temperature at a current intensity of 400 A for different initial contact pressures was shown in Figure 3. The experiments show the heating temperature decreases as initial contact pressure increases. The effect of the initial contact pressure on the heating temperature can be explained as follows: Increasing the contact pressure consequently decreases the contact resistance and increases the heat transfer between the billet and the die due to the increase in the contact area.

Figure 3:

Effect of initial contact pressure on the billet holding temperature.

It can be observed that the heating temperature is rapidly reduced as the initial contact pressure increases until the pressure reaches about 50 MPa. As the initial contact pressure increases above 50 MPa, the heating temperature tends to change slightly. This indicates that the smaller initial contact pressure is favorable for obtaining high temperature at the same current intensity. In addition, it can be said that due to the larger forming pressure, it is difficult to heating the billet during the upsetting process. Although the smaller initial contact pressure improves the heating temperature, it tends to result in an increase of local contact, which causes a rapid increase in the temperature of the surface. In this study, the initial contact pressure of about 3 to 15 MPa is optimal for good contact and higher heating temperature.

Effects of the current intensity on the heating process

The heating temperature for different current intensities is shown in Figure 4 (initial contact pressure 5.3 MPa). As can be observed in the graph, the heating temperature was significantly increased by increasing the current intensity. Figure 5 shows the relationship between the rise of the billet temperature at the holding stage and the square of the current intensity. It is clear that the rise in temperature is proportional to the square of the current intensity. Therefore, the heating temperature can be adjusted by changing the current intensity.

Figure 4:

Effect of current intensity on temperature variation.

Figure 5:

Relationship between the billet heating temperature and the square of current intensity.

Based on the above results, it can be concluded that the final heating temperature depends on the initial contact pressure, the current intensity during the heating process. The smaller initial pressure favors a higher heating temperature at the same current intensity. The heating temperature is proportional to the square of the current intensity at a certain initial contact pressure.

Analyses of upsetting process

The temperature history of the billet directly affects the forming process and the final shape of the billet. Two types of upsetting experiments were examined (see Figure 6). In case a, the resistance heating stopped before upsetting. In case b, the resistance heating continued during heating and upsetting to investigate the effect of the resistance heating during forming. In both cases, the current intensity was 1000 A and the initial pressure was 3.5 MPa. It can be observed that the billet can be heated to above 1000 °C in about 10 s.

Figure 6:

The forming process for (a) upsetting without resistance heating, (b) upsetting with resistance heating.

After keeping the temperature for about 5 s, the upsetting test began and the temperature of the billet decreased significantly during the upsetting process. When the maximal forming force reached 30 kN, the upsetting process stopped. It was reported that the contact resistance was very sensitive to the interfacial conditions including roughness, oxide, pollution, hardness [19], and hence different heating temperatures were obtained in case of using the same heating parameters for different billets. As can be seen in the figures, the cooling rate was about 334 °C /s and 290 °C /s during the upsetting process in two cases. The final billet height values after upsetting were 5.2 mm and 4.5 mm respectively. This finding means that the continuous application of resistance heating during forming results in a significant reduction in the cooling rate, which extends the forming time as shown in Figure 7.

Figure 7:

Forming time and forming force of different cases.

Effect on the forming quality

Many surface cracks and non-contact areas were observed on the formed billet surface (see Figure 8). The reason of the cracks was that the surface suffered from a large pressure at a relatively low temperature. In the experiments, the phenomenon of the non-contact areas is unavoidable because the surfaces of the billet are roughened and the hardness of two materials is large. In addition, the die’s plastic deformation happened at the contact area because of the low temperature and large forming pressure. Higher current intensity and lower forming speed are considered to improve the forming quality.

Figure 8:

The billet face quality in the experiment of case b.

Based on the results of both upsetting experiments described above, it is obvious that the billet can be heated to a forming temperature in about 10 s by using this system and the resistance heating during forming reduces the cooling rate and increases the forming time.

Finite element model

As shown in Figure 9, the two-dimensional axis-symmetric model to simulate the hot-forging process with direct resistance heating was developed. For the analysis, several assumptions are adopted to simplify the calculation and reduce the calculation time: (1) direct current (DC) is applied directly at the top of the upper die, and the electric potential is zero at the bottom of the lower die instead of the function of the electrodes; (2) the die external diameter is changed to 18 mm and the height is changed to 10 mm. The outer surfaces of the dies are always kept at room temperature during the simulation; (3) the mechanical deformation of the die is neglected during the resistance heating process; (4) the decrease of the contact resistance with temperature is considered during the resistance heating prior to forming, and the contact resistance is constant during forming process.

Figure 9:

Finite element model of the experimental setup.

Procedure of the simulation

Since the process is a thermo-electro-mechanical system, the corresponding modeling deals with a complex coupling of thermal, electric and mechanic phenomena. However, the true thermo-electro-mechanical model has not been reported at present. An incrementally coupled thermo-electro-mechanical model was used in the paper, which was composed with several electrical-thermal analyses and one thermal-mechanical analysis. The heating process prior to forming was first calculated by the electrical-thermal analysis, and the calculated temperature field was transferred to the thermal-mechanical analysis in order to calculate the displacement and the stress in a small increment. Afterwards, the displacement and the temperature of every node were transferred to another electrical-thermal analysis, which was used to calculate the temperature development after the increment. The updated temperature field was then transferred to the thermal-mechanical analysis for the calculation of the displacement and the temperature. This process continued until the forming process was finally completed.

The electrical-thermal and thermal-mechanical analyzes were implemented by the coupled thermal-electrical modeling and the coupled temp-displacement modeling in ABAQUS, respectively. 643 nodes and 550 elements were employed in the analysis. The thermal-mechanical analysis is divided into several parts in order to input and output the temperature field and displacement at every increment. The data transfer between the two analyses was carried out by the self-compiling programs. In this study, the heating time prior to forming was 17 s and the forming time was 4 s. The time increment during forming was 0.2 s.

Contact resistance model

The contact resistance at the interface has a dominant effect on the heating temperature during the resistance heating. Several models have been developed to deal with the contact resistance [4]. However, the availability of these models is limited because the parameters in the models are difficult to confirm. In the paper, a simple model of the contact resistance has been proposed in which the electric conductance of the contact resistance (σ_c) is proportional to the heating temperature, which can be expressed as follows:

where a₁ and a₂ are the parameters signifying the interface quality, material and contact pressure, T represents the interface temperature. For the resistance heating process under a certain initial contact pressure, the contact pressure increases with the increase of the temperature due to the thermal expansion, this suggests that the increment of the contact pressure is a function of the heating temperature. As a result, the contact resistance at a certain initial contact pressure can be expressed with a temperature-dependent model. Finally, the contact resistance can be obtained by the following equation:

where R_c represents the contact resistance and A represents the contact area. In the simulation, the interface between the die and the billet is ideal. In the approach, the parameters a1 and a2 are generated by comparing the simulated and experimental heating temperatures at different currents and a certain initial contact pressure. The parameter a1 is 0.87 and a2 is 132 by the heating and forming process of Figure 6(b).

Figure 10 shows the holding temperature distribution and the temperature history at different locations by the contact resistance model at the current intensity of 1000 A. Three locations in the system are: (1) the center of the billet, (2) the center of the billet edge and (3) the lower edge of the billet. As can be seen in Figure 10(a), the temperature distribution of the billet was non-uniform. The highest temperature occurred at the middle range of the billet and the lowest temperature of the billet occurred at the edge of the billet at the end of the heating stage. As shown in Figure 10(b), the contact region between the billet and the die (point 2, 3) reached the stable stage more quickly during the heating stage. Then, the temperature of the billet center (point 1) increased slowly until the holding stage was reached.

Figure 10:

Predicted heating temperature during heating stage: (a) temperature distribution at the end of the heating stage and (b) temperature history at different points.

Simulation of the forming process

Figure 11 shows the comparison of temperature distribution at the billet center between the experimental and modeling results. Although the conformity between the simulation and the experiment was good, the model tended to overestimate the temperature in the heating stage. One possible reason is that the reduction of the contact resistance in the simulation is slower than that in the experiment. The comparison of the cross-section shape between the experiment and the simulation is performed in Figure 12, and it is found that the simulation result is highly corroborated with the experimental result.

Figure 11:

Time dependence of the temperature in the center of the billet in the experiment and the simulation.

Figure 12:

Comparison of the section shape between the experiment and the simulation.