Residual Stress Analysis of Cold-drawn Pearlite Steel Wire Using White Synchrotron Radiation

Abstract

Measurement of the residual stresses in cold-drawn pearlitic steel wire was conducted using an energy dispersive X-ray diffraction technique. The residual stresses of the ferrite and cementite phases were determined for different crystal orientations and large residual stresses were found to exist in the cold-drawn pearlitic steel wire. The residual stresses in the ferrite phase were compressive in the axial direction but nearly zero in the hoop and radial directions. In addition, the residual stresses of the reflection indices for the ferrite phase were similar to one another. For the cementite phase, while tensile residual stress existed in the axial direction, compressive residual stress existed in the hoop and radial directions. These stresses in the ferrite phase in the axial direction and cementite phase in all directions decreased along the radial positions. A residual stress state model was proposed on the basis of the aligned lamellar structure along the drawing direction; the model explains the effect of the lamellar direction on residual stress. Reanalysis of the wire sample using the proposed model provided residual strains and stresses in the lamellar direction that were different from the average values estimated using the simple stress analysis method.

1. Introduction

Cold-drawn pearlitic steel wires (steel wires) exhibit high tensile strength and thus are widely used in industrial applications such as steel cords for tire reinforcement and cable wires for suspension bridges.¹⁾ The strength of the steel wire is improved by optimizing the cold-drawing conditions.^2,3,4,5) Residual stress is formed in steel wires mainly because of a mismatch of the plastic strains in the ferrite and cementite phases, which are constituent phases in the pearlite microstructure, during the cold-drawn process.^6,7,8) Because residual stress affects material strength, the influences of residual stress on the mechanical properties of steel wires are of considerable interest. Numerous studies have investigated residual stress in steel wires.^{1,2,3,4,5,6,7,8,9,10,11)} Although X-ray diffraction analysis is a common residual stress measurement method, it is limited to the measurement of stresses in the surface layers of the materials. In addition, the diffraction intensities from the cementite phase are insufficient in measurement using conventional X-ray sources. Therefore, the residual stress in steel wires is not comprehensively understood despite the abundant literature.⁶⁾ In recent years, neutron beam and high-energy synchrotron radiation have been used to characterize stresses in the cold-drawn pearlitic steels using in situ measurement during tensile tests.^2,3,4,5,8) These analytical techniques have provided new information on the residual stresses in steel wires. For instance, Perez et al. revealed the existence of residual stresses in the ferrite and cementite phases in steel wire using neutron and synchrotron radiation,⁹⁾ whereas Kriška et al. focused on the evolution of macro and phase residual stresses in the ferrite phase.¹⁰⁾ However, few studies take the microstructure of the steel wires into account. Therefore, further studies are required to understand the details of residual stress states in cold-drawn pearlitic steel and the mechanisms of their generation.

In this study, measurement of the residual stresses in a steel wire was performed using white synchrotron radiation to investigate the residual stresses of both ferrite and cementite phases, and they were measured along different crystal orientations. In addition, a simple model that considered the aligned lamellar structure along the drawing direction of the steel wire was proposed for understanding residual strains and stresses in detail and their generation mechanism.

2. Experimental

Residual stresses in a steel wire were measured. The chemical composition was 0.73% C, 0.19% Si, 0.5% Mn, 0.021% P, and 0.007% S in mass percentage. Initially, the steel wire was heated to 1223 K to form austenite and then rapidly quenched in lead at 853 K. The structure of this material was empirically estimated to be a fine pearlitic structure. Subsequently, the steel wire was descaled with hydrochloric acid, coated using zinc phosphate, and drawn once from 5.5 mm to 5 mm in diameter at a rate of 20 m/min. The specimen was 17.3% drawn in the cross-section area, and the true strain was 0.19. The mechanical properties of the specimen including the tensile strength, elongation, and elongation decrease ratio were 1194 MPa, 2.41%, and 34.9%, respectively. The specimen was then cut perpendicular to the axial direction into 3 mm lengths.

The residual stresses were measured using high-energy white X-ray radiation via an energy dispersive X-ray diffraction method at BL28B2 of SPring-8, Japan. The diffracted energy dispersive peaks were determined using a germanium solid state detector (Ge-SSD). Energy calibration of the Ge-SSD was performed using the diffraction patterns of LaB₆ powder (SRM 660b, NIST). The diffraction angle 2θ was fixed at 3.2° for all hkl reflection indices (110, 200, and 211). The slit height and width of the incident beam varied between 40 × 600 μm² and 60 × 600 μm², respectively, according to the specimen orientation. The measurements were obtained for three geometric directions (axial, hoop, and radial) at various radius positions r (= 0, 0.63, 1.25, 1.88, and 2.47 mm), as shown in Fig. 1. The strain in each direction was estimated using the following equation:   

$${\epsilon }_i=\frac{d_i-d_0}{d_0}=\frac{E_0}{E_i}-1,$$(1)

where d is the lattice spacing, E is the peak value of the diffracted X-ray energy, and the subscript 0 indicates the unstrained state and subscript i denotes the axial (A), hoop (H), and radial (R) geometric directions of the specimen. The d₀ value for the ferrite phase was calculated from the lattice constant 0.28664 nm,¹²⁾ while the d₀ value (0.2381 nm) for the cementite phase was determined from the measured diffraction peak. The residual stress in each direction was then calculated using the following equation:   

$$⟨{\sigma }_i⟩=\frac{Y_{hkl}}{1+{\nu }_{hkl}}\left\{⟨{\epsilon }_i⟩+\frac{{\nu }_{hkl}}{1-2{\nu }_{hkl}}\left(⟨{\epsilon }_{\text{A}}⟩+⟨{\epsilon }_{\text{H}}⟩+⟨{\epsilon }_{\text{R}}⟩\right)\right\},$$(2)

where 〈σ_i〉 denotes the average value for the measured directions, Y_hkl is Young’s modulus for each reflection plane, and ν_hkl is Poisson’s ratio. The values for the ferrite phase were obtained from the stiffness of the single crystals¹³⁾ using Kröner’s model and those for the cementite phase were obtained from the literature.¹⁴⁾ Table 1 summarizes the Young’s moduli and Poisson’s ratios for the ferrite and cementite phases.

Fig. 1.

Schematic of X-ray analysis in each direction. x–y–z is the laboratory coordinate system. $\overrightarrow{q}$ shows the direction of the scattering vector.

Table 1. Elastic modulus of each hkl index.

Phase	Index	Yhkl, GPa	νhkl
Ferrite	110	223.5	0.273
	200	169.3	0.328
	211	223.5	0.273
Cementite	112, 021	177	0.26(6)

3. Results

3.1. Residual Stress

Figure 2 shows the measured diffraction profiles of the specimen (17.3% drawn steel wire) at the center of the specimen (r = 0) in three directions as examples. Strain and stress analyses were performed for the 110, 200, and 211 reflections of the ferrite phase. The obtained d₀ values for the three indices of the ferrite phase were 0.2027, 0.1434, and 0.1171 nm, respectively. Note that the 112 and 021 doublet reflections of the cementite phase were analyzed as a single peak because they were broadened and overlapped as a result of plastic deformation. The peak positions of ferrite phase and cementite phase diffractions were defined using a Voigt function, because their phase diffraction profiles fit well with the function.

Fig. 2.

Diffraction profiles in each direction from the center of the specimen (17.3% drawn steel wire).

Figures 3(a)–3(c) show the strain distributions of the ferrite phase measured at different positions. Compressive strain existed in the axial direction, and tensile strains existed in the hoop and radial directions (transverse directions). The absolute values of the strains in the transverse directions were much smaller than that in the axial direction. Figures 3(d)–3(f) show the residual stress distributions in the ferrite phase, calculated from the strain data using Eq. (2). These results show that compressive residual stresses existed in the axial direction; however, the tensile residual stresses in the transverse directions were evidently smaller than that of the axial direction.

Fig. 3.

Residual strain and stress profiles in the ferrite phase for each diffraction in each direction. (Online version in color.)

While the axial strains of the 200 reflection of the ferrite phase were greater than those of the other indices, the residual stress of the 200 reflection was smaller than that of the other directions. This is primarily because of the difference in the elastic modulus of each reflection index (Table 1). Typically, the elastic modulus of the 200 reflection of ferrite phase is less than that of the other reflections; therefore, the strain of the 200 reflection of the ferrite phase is greater than that of the other reflections when the stresses are small. However, differences in the residual stresses and strains for the different reflection indices were insignificant although the elastic and plastic anisotropy depended on the hkl directions. This result likely occurred because the reduction rate of the specimen used in this study was low.

Figures 4 and 5 show the measured residual strain and residual stress distributions in the cementite phase, respectively. Unlike in the ferrite phase, a large tensile stress existed in the axial direction of the cementite, whereas large compressive stresses existed in the radial and hoop directions.

Fig. 4.

Residual strains in the cementite phase in all directions. (Online version in color.)

Fig. 5.

Residual stresses in the cementite phase in all directions. (Online version in color.)

Note that in both phases, residual stresses varied depending on the position r from the center of the wire. Large absolute values for stresses existed around the center of the specimen, and the stresses decreased near the circumference in all directions. For example, the axial residual stresses of the 110 reflection of the ferrite phase were −590 MPa at the center and −451 MPa near the surface (r = 2.47 mm). The residual stress profiles in each direction and in the two phases are similar to those reported by Perez et al.⁹⁾ In the axial direction of the ferrite phase, a large compressive residual stress existed, and the absolute value decreased along the radial position. In the radial and hoop directions of the ferrite phase, however, a small compressive residual stress relative to the axial direction existed, and the value shifted toward tensile stress. Notably, while there are differences in the details of the results obtained in the earlier⁹⁾ and present studies, the residual stress profiles are approximately similar.

3.2. Line Profile Broadening

Because microstructures near the surfaces of the drawn wires undergo severe plastic deformation owing to friction with the dies during the drawing process, higher residual stresses are expected to occur near the surface. However, the residual stresses at the surface were less than those in the interior. Here, line profile width qualitatively indicates the amplitude of plastic deformation. Therefore, the full width at half maximum (FWHM) of the measured diffraction profiles was evaluated as a parameter of the line profile width. Figure 6 shows the FWHM distributions of the 110 reflections of the ferrite and cementite doublet peaks, where the FWHMs are expressed as ratios of the averages of the values obtained for all three geometrical directions before and after annealing of the sample. The FWHMs of the ferrite and cementite phases in the wire before annealing were approximately 1.2 and 2.5 times those of the annealed specimen, respectively. In addition, both the FWHMs of the ferrite and cementite phases were greater near the center of the wire than near the surface. The X-ray diffraction profiles are broadened because of the small crystallite size and/or crystal distortion due to dislocations.¹⁵⁾ Therefore, the variation in FWHMs shown in Fig. 6 indicates that there was an amplitude distribution of the heterogeneous plastic deformation, and the wire is deformed more severely at the center than near the surface. Sato et al. reported details of the microstructural characteristics as follows:¹¹⁾ The crystallite size at the specimen surface is somewhat larger compared with the interior of the specimen; the dislocation density decreases with an increase in distance from the center of the specimen. We therefore concluded that the microstructures near the surface dynamically recovered during cold drawing. Consequently, the residual stresses near the surface were less than those in the interior of the specimen.

Fig. 6.

Ratios of the FWHMs of the 110 reflections of the ferrite and cementite phases before and after annealing as a function of r. The FWHMs are the mean values for all directions.

3.3. Texture

To evaluate the texture’s orientation, a rocking curve was measured for the cross-sectional surface of the specimen using the 220 reflection of the ferrite phase and a laboratory X-ray diffractometer with characteristic Co–Kα X-rays. Figure 7 shows the relative intensity diagram against the rocking angle, which is the angle between the normal direction to the specimen surface and scattering vector. The intensity curve had two peaks near 0° and 60°, indicating that the <110> texture of the ferrite phase developed in the axial direction during the cold drawing of the steel wire.

Fig. 7.

Rocking curve for the 220 reflection of the ferrite phase.

4. Discussion

The specimen had the typical <110> texture of the steel wire (section 3.3). According to Zelin, the crystal orientation in the transverse direction is not oriented.¹⁶⁾ Pearlite colonies are known to form by frequently stacking thin layers of ferrite and cementite (Fig. 8). To understand the residual stresses and strains in detail, the thickness and width directions of the thin layers must be considered for determining the strains and stresses in the transverse direction, as well as the results calculated using Eq. (2) in section 3.1.

Fig. 8.

Schematic of the pearlite structure and its crystal orientation. A cross section of the cold-drawn wire and a colony of pearlite are shown on the left and right, respectively.

In Fig. 9, strains in the width and thickness directions of the pearlite are denoted as ε^W and ε^T, respectively, for transverse directions. Because the measured strains are average strains due to random orientation of pearlite colonies around the axial direction, the average strain in the transverse direction, 〈ε_T〉, is expressed as the average of each strain around the axial direction:   

$$\begin{array}{l}⟨{\epsilon }_{\text{T}}⟩=\frac{{{\displaystyle \int }}_0^{\pi /2}\left({\epsilon }^{\text{W}}\text{cos}\phi +{\epsilon }^{\text{T}}\text{sin}\phi \right)d\phi }{\left(\pi /2\right)}\\ \hspace{1em}\hspace{1em}=\left({\epsilon }^{\text{W}}+{\epsilon }^{\text{T}}\right)/\left(\pi /2\right),\end{array}$$(3)

where φ is the rotation angle around the axial direction. The measured strains in the hoop and radial directions, 〈ε_H〉 and 〈ε_R〉, respectively, are ideally equal to 〈ε_T〉. In Figs. 3 and 5, 〈ε_H〉 and 〈ε_R〉 are nearly the same; therefore, 〈ε_T〉 can be calculated as the arithmetic average of 〈ε_H〉 and 〈ε_R〉.

Fig. 9.

Width and thickness directions of the strain and stress components in the pearlite layers used for reanalysis. The superscripts W and T indicate the width and thickness directions, respectively.

It is assumed that the stresses in both phases in the thickness direction are the same because the ferrite and cementite phases serially connect. In addition, the stresses were assumed to be nearly zero because the layers are thin. Hence, we assumed that the stresses in both phases were equal to zero in the thickness direction. Thus, the stress in the thickness direction, σ^T, can be expressed as   

$${\sigma }^{\text{T}}=0=\frac{Y_{hkl}}{1+{\nu }_{hkl}}\left\{{\epsilon }^{\text{T}}+\frac{\nu }{1-2{\nu }_{hkl}}\left(⟨{\epsilon }_{\text{A}}⟩+{\epsilon }^{\text{W}}+{\epsilon }^{\text{T}}\right)\right\}.$$(4)

Consequently, the unknown strains ε^W and ε^T were obtained by solving Eqs. (3) and (4).

Figure 10 shows the recalculated strains for the cementite phase using the proposed equation system. The obtained recalculated strains, ε^W and ε^T, were –7.4×10⁻³ to −1.0×10⁻² in the width direction and −2.6×10⁻⁴ to 1.7×10⁻³ in the thickness direction. Notably, the recalculated strains in the width direction, ε^W, were approximately 1.5 times greater than the average strains in the transverse direction, 〈ε_T〉; whereas the strains in the thickness direction, ε^T, were nearly zero. Thus, the deformed shape of the cementite layers is revealed by the strain analysis. The thin cementite layers stretched toward the axial direction and shrunk toward the width direction, but were unaffected in the thickness direction.

Fig. 10.

Reanalyzed and averaged residual strains for the cementite phase. (Online version in color.)

Figure 11 shows the recalculated strains for the ferrite phase using the proposed equation system, Eqs. (3) and (4). The ferrite phase strains were small in the thickness and width directions. This result indicated that elastic strains did not exist even toward the width direction in the ferrite phase. In the width direction, the cementite and ferrite layers continuously adhered to one another in parallel, and therefore the total amount of deformation in this direction must be equal although the elastic strain in each layer was different. We inferred that deformation of the ferrite phase occurred owing to plastic strain because the yield strength of ferrite is lower relative to cementite.

Fig. 11.

Reanalyzed and averaged residual strains for the ferrite phase. (Online version in color.)

Residual stresses in the width direction can be obtained using the following equation and the obtained strains, ε^W and ε^T:   

$${\sigma }^{\text{W}}=\frac{Y_{hkl}}{1+{\nu }_{hkl}}\left\{{\epsilon }^{\text{W}}+\frac{\nu }{1-2{\nu }_{hkl}}\left(⟨{\epsilon }_{\text{A}}⟩+{\epsilon }^{\text{W}}+{\epsilon }^{\text{T}}\right)\right\}.$$(5)

Figures 12 and 13 show the recalculated residual stresses in the cementite and ferrite phases, respectively. Here, 〈σ_T〉 denotes the residual stress in the transverse direction, which is the arithmetic average of 〈σ_H〉 and 〈σ_R〉. In the cementite phase, the compressive residual stress in the width direction, σ^W, was approximately 130 MPa greater than that of 〈σ_T〉 on average for all positions. In the ferrite phase, the compressive residual stress in the width direction was approximately 120 MPa greater than that of 〈σ_T〉.

Fig. 12.

Reanalyzed and averaged residual stresses for the cementite phase. (Online version in color.)

Fig. 13.

Reanalyzed and averaged residual stresses for the ferrite phase. (Online version in color.)

Residual stresses of the ferrite and cementite phases in the axial direction were compressive and tensile, respectively, (Figs. 3 and 5). The origin of the residual stresses can be simply explained depending on the misfit of the plastic strains between the ferrite and cementite phases, which stretched along the axial direction during deformation. While Young’s moduli of ferrite and cementite are similar, the yield strength of cementite is considerably greater than that of ferrite.¹⁷⁾ Accordingly, although both ferrite and cementite phases shrunk after deformation, the amount of elastic shrinkage in the cementite phase was greater relative to the ferrite phase. Consequently, the ferrite phase was compressed in accordance with the elastic shrinking of the cementite phase, and compressive and tensile stresses occurred in the ferrite and cementite phases, respectively.

In transverse directions, residual stresses in both ferrite and cementite phases in the width direction became compressive, and the absolute value of the compressive stress in the cementite phase was approximately 5 to 17 times greater than that of ferrite phase at the same radius positions. To balance the residual stresses in the ferrite and cementite phases in the width direction, the signs of the two stresses should be opposite (plus/minus); however, the stresses for both phases had the same sign. The difference in the thicknesses of the ferrite and cementite phases can be one reason for this result. The volume of the cementite phase was theoretically calculated from the mass fractions and densities of both phases, which were each 11.2% in the specimen. The lattice constants of cementite, 0.45235, 0.50888, and 0.67431 nm,¹⁸⁾ were used for the calculation. The solubility of carbon in the ferrite phase was ignored owing to its significantly lower percentage compared with the total carbon content.¹⁹⁾ Because the areas of both phases were the same on account of the lamellar structure, the thickness of the ferrite phase was approximately 8 times that of the cementite phase. Therefore, the residual stress of the cementite phase was 8 times that of the ferrite phase in the opposite direction in order to balance the forces. In addition, because the mean residual stress through all the radial positions of the cementite phase in the width direction was −1154 MPa, as indicated in Fig. 12, the estimated stress of the ferrite phase was 144 MPa. In Fig. 13, it can be seen that the average of the analyzed stress σ^W was −116 MPa. Although these values for the residual stresses in the ferrite phase are not exactly the same, if the resolution of the strain in the energy dispersive diffraction analysis is taken into account, they are similar. The fact that only the stresses in the <110> direction were considered is also thought to contribute to the difference.

5. Conclusion

Results of X-ray analysis of stresses in a steel wire using white synchrotron radiation revealed that large residual stresses evolved during the cold drawing process. The residual stresses in the ferrite phase were compressive in the axial direction and nearly zero in the transverse direction. In addition, the residual stresses for the different reflection indices of the ferrite phase were nearly the same. In the cementite phase, while tensile stress existed in the axial direction, compressive residual stresses existed in the transverse directions. In both phases, the stresses decreased along the radial positions, suggesting that the near circumferential structure was thermally recovered during cold drawing.

A simple model was also proposed for understanding the residual strains and stresses obtained in this study. The model indicates that the residual stresses in the transverse directions are different from the average strains and stresses and that the texture of the pearlite phase must be taken into account while considering residual stress and strain formation during cold-drawn of steel wires.

Acknowledgements

We thank Tokyo Rope Mfg. Co., Ltd. for supplying the samples. We also thank Dr. Kentaro Kajiwara of the Japan Synchrotron Radiation Research Institute and Dr. Takahisa Shobu and Ayumi Shiro of the Japan Atomic Energy Agency for their experimental support at SPring-8. We are also grateful to Mr. Takuya Kikuchi and Naoto Yamaguchi of Tokyo City University for their assistance. The synchrotron radiation experiments were performed at BL28B2 of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2012A1062).

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