## Abstract

Near eutectoid fully pearlitic wire rod (5.5 mm diameter) was taken through six stages of wire drawing (drawing strains of 0 to 2.47). The as-drawn (AD) wires were further laboratory annealed (LA) to re-austenitize and reform the pearlite. AD and LA grades, for respective wire diameters, had similar pearlite microstructure: interlamellar spacing (*λ*) and pearlite alignment with the wire axis. However, LA grade had lower hardness (for both phases) and slightly lower fiber texture and residual stresses in ferrite. Surprisingly, essentially identical tensile yield strengths in AD and LA wires, measured at equivalent spacing, were found. The work hardened AD had, as expected, higher torsional yield strengths and lower tensile and torsional ductilities than LA. In both wires, stronger pearlite alignment gave significantly increased torsional ductility.

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## ACKNOWLEDGMENTS

Support from Tata Steel and DST (Department of Science and Technology, India) are acknowledged. The authors would also like to express their appreciation for the usage of the National Facility of Texture and OIM (at IIT Bombay), the Nano-Indention facility (a central facility of IIT Bombay), and the TEM laboratory (of SAIF, IIT Bombay). Support from CoEST (center of excellent in steel technology) IIT Bombay is also acknowledged.

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Manuscript submitted April 1, 2017.

## APPENDIX

### APPENDIX

Assuming uniaxial plastic strain,

It has been suggested[5] that strong 〈110〉 ferrite fiber texture makes it a plain strain deformation. In that case,

However, data from Langford[4] as well as Zelin[5] indicate that for *ε* > 1 measured spacings follow Eq. [AII]. Toribio’s[11] observation on a slower spacing reduction for *ε* ≤ 1 is a clear contradiction. Langford[3] originally proposed, although the argument was not described and it does not appear to be widely remembered/acknowledged, that a slower spacing reduction is expected in misaligned pearlite. This is exactly what is seen, qualitatively in Figure 12(a). This appendix makes an attempt to quantify this effect.

For this, a unit cube of eutectoid cementite, Figure 12(b), was considered. Using Langford’s nomenclature[3] the cementite is on the “LK” plane, where wire axis is “L”. The original lamellar spacing (before deformation) is *λ*
_{i} with an initial orientation angle *α*
_{i} (with ‘L’). Other important dimensions are the sides of the triangle: *A*
_{i}, *H*
_{i} and *O*
_{i}. After drawing to a strain\( { \in = }0.693 \left( {{ \in = }\ln \left( {\frac{{A_{\text{f}} }}{{A_{\text{i}} }}} \right)} \right) \), the triangle dimensions (Figure 12(b)) changes to: *α*
_{f}, *H*
_{f}, *A*
_{f} (*A*
_{f} = *A*
_{i}*2) and *O*
_{f} (=*O*
_{i}/√2). Following parameters can be geometrically estimated,

Equation [AVI] is for \( { \in} \, = \, 0.693 \). The same can be extended for any given strain (*ε*) as,

Thus, *α*
_{f} can be related to \( \alpha_{\text{i}} \) and strain (*ε*) as,

The Equation [AVIII] thus predicts the rotation of misaligned lamellae to the wire axis “L.” Assuming constant volume,

where *t* is the thickness of the lamella.

Since \( \sin \alpha_{\text{i}} = \frac{{A_{\text{i}} }}{{H_{\text{i}} }} \) and \( \sin \alpha_{\text{f}} = \frac{{A_{\text{f}} }}{{H_{\text{f}} }} \), it can be shown that

And also in terms of interlamellar spacing (*λ*),

From Eqs. [AVIII] and [AXI] and a given strain (*ε*), *α*
_{f} and \( \frac{{\lambda_{\text{f}} }}{{\lambda_{\text{i}} }} \) can be calculated. These are shown for *ε* = 0.693 in Figure 12(c). The figure demonstrates, quantitatively, the effect of *α*
_{i} on *α*
_{f} and \( \frac{{\lambda_{\text{f}} }}{{\lambda_{\text{i}} }} \). For example, at *α*
_{i} = 90 deg and 0 deg the \( \frac{{\lambda_{\text{f}} }}{{\lambda_{\text{i}} }} \) will be 2 and 0.707, respectively.

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Durgaprasad, A., Giri, S., Lenka, S. *et al.* Microstructures and Mechanical Properties of as-Drawn and Laboratory Annealed Pearlitic Steel Wires.
*Metall Mater Trans A* **48**, 4583–4597 (2017). https://doi.org/10.1007/s11661-017-4269-5

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DOI: https://doi.org/10.1007/s11661-017-4269-5