Abstract
In this study, we used neutron diffraction to analyze in a non-destructive method the distribution of internal residual stress in a free-cutting steel bar processed by cold drawing and straightening. Since a change in lattice-plane spacing occurs in a strain-free standard sample used as a reference due to the cold-drawing and straightening processes, it was necessary for the sake of improving measurement accuracy to prepare strain-free standard samples for each individual process. As a result, the residual stresses were successfully measured with excellent stress balance. The residual stresses generated by the cold-drawing process were reduced by subsequent straightening, and the distribution of residual stresses by finite element method (FEM) simulation was consistent with the measured values by neutron diffraction. As a result of the FEM analysis, it is assumed that the rod was subjected to strong tensile strains in the axial direction during the drawing process, and the residual stresses were generated when the rod was unloaded. Those residual stresses were presumably reduced by the redistribution of residual stresses in the subsequent straightening process.
1. Introduction
Special steel bars with high machinability called free-cutting steel are used for shafts and other parts that are cut for use in precision instruments, electronic equipment, etc. Using wire rod as a raw material, it is formed into bars having a high degree of straightness through complex plastic forming processes such as cold drawing, spinner straightening, and roll straightening. On the other hand, subjecting a bar manufactured with good accuracy to a cutting process generates bending and deformation in the bar material that can lead to problems such as drops in the degree of roundness and straightness. The cause of such bending and deformation is the release during machining of residual stress accumulated within the raw material at the time of plastic forming. Therefore, in the actual manufacturing process, a straightening process is used to reduce the residual stresses generated in the cold-drawing process. Determining the distribution of internal residual stress in products manufactured by plastic forming is considered to play an important role in achieving product accuracy and reliability.1,2)
Methods for measuring residual stress in bars processed by cold drawing are dominated by destructive techniques.3–5) These include the slitting method that calculates the residual stress on the surface of the bar by measuring the width of the opening generated after making an incision in the bar’s axial direction, and the Heyn-Bauer method that determines surface residual stress by measuring changes in the length of the bar material after removing a small portion of the bar’s outer layer and repeating this measurement toward the bar’s interior. Residual stress measurement using X-ray diffraction is a non-destructive method, but it can only provide information near the surface of the material.6,7) On the other hand, the ability of neutron diffraction to penetrate deep into material enables to measure residual stress in the interior portion of steel material. While a number of studies have focused on measuring residual stress caused by cold drawing using neutron diffraction, there are no examples of measuring residual stress in relation to both cold drawing and straightening.8–10) In this study, we exploit the penetrating ability of neutron diffraction to determine in a non-destructive manner the distribution of internal residual stress of a free-cutting steel bar processed by cold drawing and straightening.
2. Residual Stress Measurement by Neutron Diffraction
Neutron sources come in two types: one generates neutrons through continuous reactions in a nuclear reactor and the other generates pulse-shaped white neutrons by nuclear spallation using a pulse proton accelerator.11) In this study, we used the time-of-flight (TOF) method as a neutron diffraction method using pulse-shaped white neutrons. The TOF method irradiates a sample with neutrons and measures the TOF of those neutrons up to a detector. A schematic diagram of this measurement equipment is shown in Fig. 1. Denoting L as the distance from the neutron source to the detector, TOF as the flight time, m as the mass of the neutron and v as the velocity of the neutron, the wavelength λ of the neutron beam can be determined from the following equation.
| \begin{equation*}
\lambda=\mathrm{h}/(\mathrm{m}\times \mathrm{v})=(\mathrm{h}\times \mathrm{TOF})/\mathrm{m}\times \mathrm{L}
\end{equation*}
|
Here, h is the Planck constant. In addition, strain can be determined from the change in neutron flight speed, that is, the change in wavelength, from the following equation.
| \begin{equation*}
\varepsilon=(\lambda-\lambda_{0})/\lambda_{0}=(\mathrm{d}-\mathrm{d}_{0})/\mathrm{d}_{0}
\end{equation*}
|
Here, ε is the strain in the measurement direction, λ is the wavelength of the specimen, λ
0 is the wavelength of the specimen in the strain-free state, d is the lattice strain of the specimen, and d
0 is the lattice spacing in the strain-free state. Therefore, it is necessary to measure d
0 beforehand when the residual stress is to be measured by the neutron diffraction method. The neutron diffraction method measures residual stress by measuring strain in the measurement target and calculating stress. In this study, the target of measurement was a steel bar, so we measured the strain in the axial, radial, and hoop directions. The strain in the axial, radial, and hoop directions are denoted as ε
A, ε
R, and ε
H, respectively. The stresses σ
A in the axial direction, σ
R in the radial direction and σ
H in the hoop direction are given as follows.
| \begin{equation*}
\sigma_{\text{A}}=\mathrm{E}/(1+\nu)[\varepsilon_{\text{A}}+\nu/(1-2\nu)\times(\varepsilon_{\text{A}}+\varepsilon_{\text{R}}+\varepsilon_{\text{H}})]
\end{equation*}
|
| \begin{equation*}
\sigma_{\text{R}}=\mathrm{E}/(1+\nu)[\varepsilon_{\text{R}}+\nu/(1-2\nu)\times(\varepsilon_{\text{A}}+\varepsilon_{\text{R}}+\varepsilon_{\text{H}})]
\end{equation*}
|
| \begin{equation*}
\sigma_{\text{H}}=\mathrm{E}/(1+\nu)[\varepsilon_{\text{H}}+\nu/(1-2\nu)\times(\varepsilon_{\text{A}}+\varepsilon_{\text{R}}+\varepsilon_{\text{H}})]
\end{equation*}
|
Here, E is the elastic constant and ν is Poisson’s ratio. The stress in each direction can be determined from this conversion formula.
3. Material and Experimental Methods
A low-carbon free-cutting steel bar (SUM24L type) with a diameter of 10 mm and a length of 2500 mm was used. The chemical composition of this material is given in Table 1. In the experiment, the bar material underwent a cold-drawing process consisting of drawing, spinner straightening, and roll straightening. A schematic diagram of this overall cold-drawing process is shown in Fig. 2. The rods were drawn in one pass from a 12-mm diameter to a final diameter of 10 mm (31% reduction in section). After that, the lots were subjected to spinner and roll straightening, which are rotary bending straightening processes. The tensile test results for each process are shown in Fig. 3. The true-stress/true-strain curves before the drawing process were obtained by measuring the outside diameter of the bar during the tensile test, as performed in the work of Tsuchida et al.,12) to obtain the true-stress/true-strain curves. The average ferrite grain size measured by optical microscopy was 10 µm.
Table 1 Chemical composition (mass%).
To conduct the measurements, we used the J-PARC/MLF BL19 “TAKUMI” diffractometer shown in Fig. 4 and measured the residual strain at 11 locations in the direction from the material surface to the central axis at 0.5 mm intervals. Additionally, prior to processing, we cut out 1.5-mm cubes from the steel bar by electrical discharge processing and assembled them with no directivity as shown in Fig. 5. We used these cubes as strain-free standard samples for use in measuring d0.
To measure strain in the hoop and radial directions, the incident beam slit was set to 1 mm × 30 mm and the radial collimator width to 1 mm to form a measurement region of 1 mm × 1 mm × 30 mm.
To measure in the axial direction, the incident beam slit was set to 1 mm × 1 mm to form a measurement region of 1 mm × 1 mm × 1 mm. To shorten the measurement time of the neutrons, the measurement area was increased to 30 mm for axial measurements as the change along the axis is considered to be small.
4. Experimental Results and Discussion
4.1 Effects of texture on residual stress measurement
The elastic constant E is required to measure stress from the strain in all three principal directions, and possesses a diffraction plane dependency that differs on the basis of each plane. There are recommended diffraction planes for BCC-Fe, (211) and (110), which have a good linear stress-strain relationship. Except for the recommended planes, the stress-strain relationship may be nonlinear.13) Peak profiles obtained from measurements of the d0 coupon sample and the drawn rods are shown in Fig. 6. Due to the weak strength of the (211) plane, the (110) plane was used, and the Young’s modulus E = 224 GPa and Poisson’s ratio ν = 0.3 for the (110) plane of iron were used. Using the ability of the TOF method to capture multiple diffraction peaks, the lattice constants were calculated from the values of the lattice spacing of all the obtained peaks (nine peaks between 0.65 and 2.3 nm) and the residual stresses were calculated from the changes in the average lattice constant.14) By using all the obtained average lattice constants, macroscopic elastic constants could be used, with E = 206 GPa and Poisson’s ratio ν = 0.3. The axial stresses after pulling out are shown in Fig. 7. The (211) plane has a weak diffraction intensity and a large error. The residual stresses should be balanced between tensile and compressive stresses, but the one using the (110) plane and all the peaks shows that the stress balances are incorrect.
First, sections of the raw material cut out before processing were used as strain-free standard samples. However, it became clear that type-2 stresses existed due to the generation of plastic strain, and it has been pointed out that determining lattice constants with considering type-2 stresses is important.15) On the other hand, in most neutron diffraction experiments, d0 is determined from the stress balance without measuring d0 experimentally.9,10,16) Following the work of Holden et al., in which they prepared strain-free standard samples from the objects being measured and successfully measured them with excellent stress balance,15) samples were prepared in the same manner. The samples fabricated for a second time after each process are shown in Fig. 8. The results of comparing strain in d0 coupons before and after each process are shown in Fig. 9. The peak position before drawing was different from that of each process. Consequently, since change also occurs in strain-free standard samples due to plastic forming, it can be said that preparing samples for each process is necessary to improve measurement accuracy. On the basis of the above results, we decided to calculate residual stress using the lattice-spacing values obtained from the strain-free standard samples of each process.
The results based on the d0 coupons for each process are shown in Fig. 10. These results show that measurements could be performed with good accuracy. In these measurements, (110) planes and all diffraction planes were used, but the results showed that accurate measurements could be performed even with diffraction planes other than the (211) and (110) recommended planes.15) The distribution of residual stress after drawing shows tensile stress at the surface and compressive stress at the center similar to those found by neutron-based studies.8–10) In addition, it was found that the internal residual stress generated by the drawing process tended to decrease by the subsequent straightening processes in all three directions (in the bar’s hoop, radial, and axial directions). This decrease in residual stress by straightening is the same as that found in earlier studies.4,17,18) It is, therefore, clear that devising appropriate plastic forming processes can decrease the internal residual stress in a product.
As described in the previous section, we succeeded in measuring the distribution of residual stress inside a steel bar through neutron diffraction. However, experiments using neutron diffraction are limited to those conducted using special experimental facilities, so increasing the frequency of measurements is difficult. With this in mind, we conducted an analysis using simulations to determine whether a residual stress distribution could be obtained in a similar means to neutron diffraction.
The simulation was done using open source software (integrated structural analysis system DEXCS-WinXistr). The rod and die setup were developed in SALOME and imported to EasyISTR. FrontISTR was used for the calculations and ParaView was used to analyze the results. The calculation was done using the method of Lagrange multipliers. The true-stress/true-strain before the drawing process was used in the analysis, as shown in Fig. 3.
First, the drawing process was simulated using the die geometry shown in Fig. 2(b). The die was fixed and a 12-mm rod with both ends tapered to a 10-mm diameter was pulled out to enable it to be pulled out smoothly. The lot was forced to displace and pass through the die. The mesh was a 0.7-mm hexahedral primary element created to be as close to a regular hexahedron as possible.
In this analysis, the elastic constant and Poisson’s ratio of the raw material were set to E = 206 GPa and ν = 0.3, respectively, using a plastic model, while those of the die were set to E = 600 GPa and ν = 0.22, respectively, using an elastic model. In addition, the coefficient of friction was calculated from the experimental values of drawing force (23.5 kN) and set to 0.05. The drawing stroke was set to 40 mm. The distributions of residual stresses and strains are shown in Figs. 11, 12, and 13. These results show that analysis results exhibited the same trends as experimental results for all three directions. After drawing, strong tensile strains were applied in the axial direction, which are slightly stronger in the center than in the periphery. It is presumed that residual stresses occurred when the rod was unloaded.
Next, finite element method (FEM) of bending back the rod was performed in the same way as the straightening process. After pulling out, both ends were fixed and the center was displaced 0.14 mm up and then down. The amount of displacement was close to the bending curvature of the spinner correction. The results are shown in Figs. 14 and 15. After the rod was bent and unloaded, the residual stresses decreased in all three principal directions. The stresses and strains during bending up are shown in Figs. 16 and 17, where the surface stresses did not vary at 0.84 mm and 1.4 mm bends, but the surface strains were increased at 1.4 mm than at 0.84 mm. Since tensile stresses are already present at the rod surface, these regions deform plastically and the redistribution of residual stresses reduces the original levels.19) The actual straightening process is rotational bending, where the bar is gradually bent and returned multiple times. It is presumed that the strains are applied to the entire bar and the residual stresses are uniformly reduced.
5. Conclusion
The purpose of this study was to determine the internal residual stress distribution of a free-cutting steel bar processed by cold-drawing and straightening processes in a non-destructive method using neutron diffraction, which is known for its penetrating ability. We also investigated a residual stress analysis technique for raw material with textures developed by cold drawing. The results of this study are summarized as follows.
For neutron diffraction, we used the TOF method using pulse-shaped white neutrons.
-
(1)
In addition to the conventional method of calculating the residual stress from the (110) deposition plane, we have also succeeded in calculating the residual stress from changes in the mean lattice constant, taking advantage of the TOF method’s ability to capture multiple diffraction peaks.
-
(2)
Given that the lattice spacing in the strain-free standard samples changes due to the cold-drawing and straightening processes, it was necessary to prepare samples for each individual process to improve measurement accuracy. The residual stresses were calculated using the values of lattice spacing obtained by measuring the strain-free standard samples prepared for each process, and were successfully measured with excellent stress balance.
-
(3)
The residual stresses generated by the cold-drawing process were reduced by subsequent straightening, and the distribution of residual stresses by FEM simulation was consistent with the measured values by neutron diffraction.
-
(4)
As a result of the FEM analysis, it is assumed that the rod was subjected to strong tensile strain in the axial direction during the drawing process, and the residual stresses were generated when the rod was unloaded. Those residual stresses were presumably reduced by the redistribution of residual stresses in the subsequent straightening process.
Acknowledgments
The neutron diffraction experiments at the Materials and Life Science Experimental Facility of J-PARC were performed under a user program (Proposal No. 2017A0100). We would like to extend our deep appreciation to Kiyotaka Kashiwa and Takahiro Maeshima of the Industrial Technology Innovation Center of Ibaraki Prefecture for their kind cooperation during the residual stress simulations. A part of this research was supported by Hitachinaka Techno Center, Inc.
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