2021 Volume 61 Issue 11 Pages 2792-2797
We investigated the drawing process with a temperature gradient in the radial direction of the bar to achieve flexible control of the residual stress in the drawn bar with only the drawing process. The obtained results are as follows: (1) A heating-cooling-drawing process was developed to generate a temperature gradient in the radial direction of the bar. The optimum cooling time was determined by heat conduction analysis. A cooling time of 0.54 s is optimal for a steel bar with a diameter of 10 mm. (2) We experimentally confirmed that the proposed method is extremely effective for controlling the residual stress in a bar or wire. (3) The residual stress decreased by increasing the heating temperature up to 400°C. Above 400°C, the control of stress was small. (4) The combination of the proposed method and extremely small reduction drawing is effective for obtaining strong compressive residual stress in the surface layer. For a 0.4% or 0.6% reduction rate of the section area, residual stress reduction of 900 MPa was obtained. (5) It was confirmed that residual stress is reduced when the material is cooled down after drawing by finite element analysis considering thermal strain. The mechanism of residual stress reduction by the proposed method is the loss of thermal stress due to the drawing process and the thermal contraction at the center during cooling.
Bars and wires are used for parts in automobiles, precision instruments, and so on. They are mainly produced by the drawing process. However, due to inhomogeneous deformation during this process, tensile residual stress is generated in the surface layer of the bar and compressive residual stress is generated in its center.1) The residual stresses in the bar or wire cause deformation during secondary processing and heat treatment, and the tensile residual stresses in the surface layer reduces the fatigue strength. Therefore, it is necessary to reduce the residual stress to suppress deformation, and to add compressive residual stress to the surface layer to improve fatigue strength.2)
In a conventional study of residual stress in drawn bar, Kuboki et al. have shown the effectiveness of extremely small reduction drawing.3) Kajino et al. clarified the effects of the die approach shape, bearing length, and protrusion into the bearing area on the residual stress.1) Kuntani et al. clarified the effect of the die half angle, bearing length, die transition radius, friction coefficient, and area reduction on the residual stress by finite element analysis (FEA).4) However, these studies did not achieve a strong compressive residual stress in the surface layer. Further, these studies were related to the drawing conditions and die shape, and did not focus on the use of heat.
There are many previous studies about plastic working using heat. Furushima et al.5,6) studied about the forming behavior of die-less drawing. Sekiguchi et al.,7) Kobatake et al.,8) and Kubota et al.9,10,11,12) studied the forming behavior of tube bending by high frequency induction heating. Studies about the numerical analysis of tube bending by high frequency induction heating were also carried out.13,14,15,16,17,18) However, these studies did not focus on the residual stress. On the other hand, Lee et al.19) compared the residual stress of experiment and numerical analysis in low-carbon steel tube after induction bending, and showed that there was a discrepancy.
Kusakabe et al.20) and Yoshida et al.21) studied the residual stresses in H-shaped steel after hot rolling and found that the cooling rate difference affected the residual stresses. Tani et al.23) reduced the residual stress of TMCP steel sheet by uniform cooling.
In the field of grinding, Onishi et al.24) studied the relationship between temperature distribution during grinding and residual stress. In the field of heat treatment, there are many studies on the relationship between heating-cooling methods and residual stress.25,26,27,28)
As described above there are many studies about heat and residual stress. However, there is no study about controlling residual stress by actively generated temperature gradients during plastic working.
In this study, we investigated the drawing process with a temperature gradient in the radial direction of the bar to achieve flexible control of the residual stress in the drawn bar only by the drawing process. In other words, a new heating-cooling-drawing process was developed. We explain the following points in this paper: the technology concepts that underpin this process,29) the design of the cooling system, clarification of the effect of heating temperature, clarification of the effect of amount of reduction, the method to add a high compressive residual stress to the surface layer, and clarification of the mechanism by FEA.
Figure 1 is a schematic illustration of the proposed drawing process. The surface layer of a uniformly heated bar is rapidly cooled just before drawing. In other words, the bar is drawn with the surface layer in a state of thermal contraction. We thought that the residual stress in the surface layer could be reduced by the delayed thermal contraction of the central part after drawing. This method makes it possible to control the distribution of residual stress by changing the heating temperature and cooling conditions. This method can be applied not only to steel but also to any metal that thermally expands and contracts.
Temperature history of proposed drawing process and residual stress distribution of drawn bar and wire. (Online version in color.)
The key to this technology is the design of the cooling system. We considered that the best effect is obtained when the drawing process is performed when the temperature gradient in the radial direction of the bar is maximized. In other words, if the length of the cooling zone is too short, the bar is not cooled sufficiently, and if it is too long, the bar is cooled to the center and the temperature gradient disappears. Therefore, unsteady heat conduction analysis assuming a one-dimensional cylindrical coordinate system in the radial direction was performed to investigate the cooling zone length.
The governing equation of one-dimensional heat conduction is in the form
| (1) |
| (2) |
| (3) |
With Eqs. (1), (2), (3), the heat conduction analysis is carried out using a finite difference analysis with the Euler method.
In the analysis, the bar diameter d was 0.01 m (10 mm). The thermal properties of the material were assumed to be those of steel. The thermal conductivity λ was 36 W/mK, the density ρ was 7600 kg/m3, and the specific heat c was 731 J/kg·K. The initial temperature of the material T0 was 400°C, and the heat transfer coefficient h was 10000 W/m2·K, which corresponds to pool boiling with literature values.30) The coolant temperature Tw was 25°C.
Figure 2 shows the temperature history obtained from the analysis. The temperature difference between the outer surface and the center is also shown as an index of the temperature gradient. “Position” on the horizontal axis is the distance from the cooling start position when the drawing speed of the drawing bench (31 mm/s) is considered. As a result, the appropriate cooling time is 0.54 s, and the appropriate cooling zone length is about 17 mm. This result indicates that a short cooling zone is necessary.
Surface and center temperature history by heat conduction analysis. (Online version in color.)
As discussed above, for the steel bar with the diameter d=10 mm, the optimum cooling time is 0.54 s. However, this optimum value varies depending on the diameter and thermal conductivity of the bar. Qualitatively, when the bar diameter becomes smaller, the optimal cooling time becomes shorter because the cooling rate is higher. As a result, the length of the cooling zone becomes shorter. When a material with higher thermal conductivity (Ex. Aluminum) is used, the optimal cooling time becomes shorter. As for the drawing speed, in order to maintain a certain cooling time, the cooling zone length must be increased proportionally as the drawing speed increases. The effects of bar diameter, thermal conductivity, and drawing speed on the optimal cooling time can be obtained by the heat conduction analysis described above.
The experimental setup is shown in Fig. 3. The heating unit, cooling unit, and die were arranged in order from the entry side. A curtain made of glass wool was installed at the entrance of the cooling unit to prevent the heating unit from being damaged by splashes of cooling water. The specimen was a 0.45 mass% carbon steel bar (Japan Industrial Standard, JIS G3123, Cold finished carbon and alloy bars, S45C-D). The chemical composition of the material is shown in Table 1. For lubrication, a thin coating of solid graphite lubricant was applied to the entire surface of the material. The drawing was performed by a hydraulic drawing bench at a drawing speed of 31 mm/s.
Experimental setup for heating-cooling-drawing process. (Online version in color.)
| C | Si | Mn | P | S |
|---|---|---|---|---|
| 0.45 | 0.20 | 0.72 | 0.18 | 0.26 |
A ceramic fiber heater with a length of 305 mm and an inner diameter of 25 mm was used as the heating device to ensure uniform heating of the residual stress evaluation area. Cooling was carried out by directly supplying tap water to the cooling system described below. The flow rate was set at 1.8 L/min.
The cooling device used in this experiment is shown in Fig. 4. It has a dual-cavity structure with an internal partition wall. The cooling water outlet is located at the bottom of the bar inlet. The length of the cooling zone was larger than the optimal length of 17 mm obtained in Section 3 due to limitations in the fabrication of the cooling device. In the experimental setup, this length was determined to be 25 mm.
Cooling device (unit: mm). (Online version in color.)
To investigate the effect of heating temperature T0 and reduction on the residual stress, we employed the conditions described in this section.
The initial diameter of the bar was 10 mm, and the die hole diameters were 9.98, 9.97, and 9.48. The reduction rate of section area of bar RA for these die hole diameters were 0.4%, 0.6%, and 10%, respectively. We deliberately included extremely small reduction conditions of less than 1% because it generally results in low residual stress.3) The die half angle of α=6.5° was used. Several heating temperatures from room temperature (conventional method) to 600°C were used.
4.4. Residual Stress Measurement Method (Slit Method)The slit method was used to measure the residual stress of the drawn bar. A schematic illustration of the slit method is shown in Fig. 5. A slit of l=100 mm was made in the center of the bar by wire electrical discharge machining. If tensile stress was in the surface layer of the bar and compressive stress was in the center, the slit was opened by the release of the residual stress. The amount of opening width δ was measured. Here, Young’s modulus is E=206 GPa and the radius of the bar is R=d/2. The longitudinal residual stress in the surface layer σl can be calculated using the following equation:2)
| (4) |
Schematic illustration of slit method.
Because the method assumes a constant stress gradient from the center to the surface, the residual stress values are approximate. Conversely, if the residual stress was compressive in the surface layer and tensile in the center, the slit stayed closed and δ could not be measured. In this case, the slit portion was cut out and the residual stress was completely released to obtain a pseudo δ (negative value) by image analysis.
4.5. Experimental ProcedureThe experimental setup described in section 4.2 was applied with the following procedure:
(1) Apply lubricant and place the bar in the heater.
(2) Heat the bar until it reaches the specified temperature.
(3) Perform the drawing process while cooling water flows.
(4) Allow the bar to cool down to room temperature.
(5) Evaluate the residual stress in the surface layer by the slit method. (Section 4.4)
Figure 6 shows the experimental result. It was confirmed that this process caused a dramatic change in residual stress. For RA=10%, the residual stress was reduced by about 300 MPa compared with the conventional method (room temperature). For RA=0.4% and RA=0.6%, 900 MPa of residual stress reduction was obtained. Little difference was obtained between the results of RA=0.4% and RA=0.6%. Conversely, with a heating temperature above 400°C, the change in residual stress with increasing temperature was small.
Relationship between heating temperature and residual stress on surface of drawn bar. (Online version in color.)
It is clear that the combination of an extremely small reduction condition, less than 1%, and the heating-cooling-drawing process had a very large effect on residual stress reduction. In other words, this condition is suitable for improving the fatigue resistance of drawn bars and wires. However, there is a concern that the extremely small reduction condition less than 1% is not stable in actual industrial operations. In other words, this condition is susceptible to thermal expansion of the die, diameter variation of the bar before drawing, and so on. In this experiment, there was little difference between the results of RA=0.4% and RA=0.6%. This indicates that the effect of this new process is robust under extremely small reduction conditions.
The change in residual stress due to increasing the temperature was small when the heating temperature was 400°C or more. We considered that the reason for this is that the surface temperature of the material rises, causing a film boiling state, which reduces the cooling capability.30) With the cooling system and water flow rate of this experiment, the best condition for minimizing residual stress while minimizing heating energy was 400°C. However, if a cooling system with a larger cooling water flow rate were used, the residual stress reduction effect is expected to be even greater at higher material temperatures. It is necessary to clarify this point in the future.
The mechanism of residual stress reduction by this new process is discussed in the next section using FEA.
To investigate the mechanism of residual stress reduction with the proposed method, the conventional and proposed methods were evaluated by thermo-elastic-plastic analysis using the finite element method. Although this is a simple analysis that does not consider the temperature dependency of flow stress, the thermal strain was taken into account to verify its effect.
The static implicit FEA software MSC Marc 2013 was used for the analysis. An axisymmetric model of a bar 50 mm long and 10 mm in diameter was created, as shown in Fig. 7. Four-node axisymmetric solid elements were used. The element size in the longitudinal direction was less than 1/30 of the die hole diameter. The element size in the radial direction of the surface layer, where deformation was large, was the same as that in the axial direction.3) The flow stress curve of 0.45 mass% carbon steel at room temperature was used31) (Fig. 8). Young’s modulus was 206 GPa, Poisson’s ratio was 0.3, the thermal expansion ratio was 1.12×10−5, the thermal conductivity λ was 36 W/mK, the density ρ was 7600 kg/m3, and the specific heat c was 731 J/kg·K. Heat conduction inside the material, heat transfer from the material to the cooling water, and thermal strain of the material were taken into account. The temperature dependency of the flow stress and the strain rate dependency of the flow stress were ignored. Heat generation by plastic deformation and heat generation by friction were also ignored.
Axisymmetric FEA model for drawing (unit: mm). (Online version in color.)
Flow stress curve of 0.45 mass% carbon steel.
A die half angle of α=6.5° and hole diameter of 9.48 mm were used, as in the experiment. The reduction rate RA was 10%.
The thermal boundary conditions are shown in Fig. 7. In the analysis of the conventional method, the bars were drawn at room temperature without heating and cooling. In the case of the proposed method, the initial temperature of the bar was 600°C, and convection heat transfer boundary conditions were applied to the outer surface [(a) in the figure]. The coolant temperature was 25°C, and the heat transfer coefficient was 10000 W/m2·K.6)
The mechanical boundary conditions were as follows. Forced displacement was applied to the nodes at the front end of the bar [(b) in the figure]. As in the experiment, it was important that the bar was drawn after 0.5 s of cooling. In this analysis, the bar was restrained in the initial position and cooled for 0.5 s, and then the drawing process was completed in 0.05 s. This analysis operation allows the drawing to be carried out using the temperature distribution after 0.5 s of cooling. After drawing, the bar was restrained for about 20 s for cooling analysis.
A friction coefficient of 0.05 between the bar and the die was employed. The evaluation points of longitudinal stress at surface and center are (c) and (d) in figure, respectively.
Figure 9 shows the radial distribution of longitudinal residual stress obtained by FEA. Compared with the conventional method, the proposed method shows a decrease in residual stress in the surface layer and an increase in residual stress at the center. Because this was a simplified analysis, quantitative accuracy is limited, but the results are in agreement with the trend of residual stress change seen in the experiments.
Longitudinal residual stress distribution in radial direction in drawn bar by FEA (RA= 10%). (Online version in color.)
Figure 10 shows the transition of axial stress at the surface and center. In the proposed method, the stress due to cooling is generated before the material reaches the die [(A) in the figure]. At this time, tensile stress is generated in the surface and compressive stress is generated at the center. However, the stress values of the conventional method and the proposed method became the same when the specimen was drawn by the die [(B) in the figure]. After drawing, as the temperature became uniform, the residual stress decreased in the proposed method [(C) in the figure]. In other words, the mechanism of residual stress reduction by the proposed method is the loss of thermal stress due to the drawing process and the thermal contraction at the center during cooling.
Longitudinal stress transition by FEA (RA= 10%). (Online version in color.)
The analysis result of RA=10% was described above. But, we could not perform the analysis with sufficient accuracy in the case of RA=0.4% and RA=0.6%, which are the optimum conditions in the experiment. Because the extremely small contact length causes a problem in the contact analysis between the die and the bar surface. To develop the analysis method for extremely small reduction condition is our future work.
In the experimental results, the residual stress reduction effect of the proposed process was greater for the extremely small reduction condition than for the RA=10% condition. The above FEM analysis of RA=10% condition shows that the loss of thermal stress due to the drawing process and the thermal contraction at the center of the material during cooling are the basic mechanisms of residual stress reduction in this process. If this mechanism can be applied to the extremely small reduction condition, the effect under the extremely small reduction condition should be the same as the effect under the RA=10% condition, since the thermal contraction of the material is determined by the temperature. However, the results of the experiment disprove this.
It is conventionally known that the extremely small reduction drawing induces plastic deformation mainly in the surface layer of the bar.4) In the proposed process, we considered both tensile thermal stress and contact pressure from the drawing die acted on the surface layer, and axial tensile plastic deformation occurred only in the surface layer. We estimate that this characteristic deformation enhanced the effect in the extremely small reduction conditions.
In this study, we confirmed that residual stress can be controlled by the temperature gradient during plastic working. In addition, we clarified the basic principles for controlling the residual stress using FEA. In the future, this principle can be applied to various types of plastic working.
To control residual stress in drawn bars and wires, this study examined the drawing process under the condition of a temperature gradient in the radial direction of a bar. In addition, the mechanism of residual stress reduction was investigated by FEA. The obtained results are as follows:
(1) A heating-cooling-drawing process was developed to generate a temperature gradient in the radial direction of drawn bars. The optimum cooling time was determined by heat conduction analysis. A cooling time of 0.54 s is optimal for a steel bar with a diameter of 10 mm.
(2) It was confirmed that the proposed method is extremely effective for controlling the residual stress of drawn bars and wires.
(3) The residual stress decreased when the heating temperature was increased up to 400°C. Above 400°C, the effect of increasing the temperature was small.
(4) The combination of the proposed method and the extremely small reduction drawing was effective for obtaining strong compressive residual stress in the surface layer. Under the conditions of 0.4% and 0.6% in reduction, 900 MPa of residual stress reduction was obtained.
(5) It was confirmed that the reduction of residual stress occurs when the material is cooled down after drawing by FEA considering thermal strain. The mechanism of residual stress reduction by the proposed method is the loss of thermal stress due to the drawing process and the thermal contraction at the center during cooling.
(6) We confirmed that the residual stress can be controlled by the temperature gradient during plastic working. Moreover, we also clarified the principle by FEA. In the future, this principle can be applied to various types of plastic working.
This research was supported by a “Research Grant for Young Researchers” from the FY2020 fund for the promotion of technology for plasticity by the Japan Society for Technology of Plasticity. The authors express their gratitude for the cooperation of Hatano-seimitsu Co. for implementing the wire electrical discharge machining for slit method.
