PSI - Issue 81

Jesús Toribio et al. / Procedia Structural Integrity 81 (2026) 54–57

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With regard to the materials-science relationship between microstructure and strength, it is now well known that the pearlite interlamellar spacing governs the yield strength of eutectoid pearlitic steels, as thoroughly explained by Embury and Fisher (1966), Langford (1977), Porter et al. (1978), Hyzak and Bernstein (1976), Lewandowski and Thompson (1986), Dollar et al. (1988) and Alexander and Bernstein (1989). The Hall-Petch equation, based on the classical research works by Hall (1951) and Petch (1953), has been proposed by Choi and Park (1996) and Nam et al. (2002) to correlate interlamellar spacing and material strength. However, the specific dependence between yield strength and pearlite interlamellar spacing is not so clear, and variations in the exponent of the Hall-Petch equation can be found, and even contradictions — that cannot be physically justified — do exist in the definitions of the fitting constants and these facts confirm the recommendation by Dieter (1988) of using the Hall-Petch equation with some caution. Apart from the sort of functional relationship used to describe the influence of microstructural variables on the macroscopic behaviour, there is general agreement that the interlamellar spacing effectively controls mechanical properties such as the yield strength of the steel, at least in isotropic (randomly-oriented) microstructures. The final aim of this paper is to elucidate the relationship between anisotropic microstructure and strength in heavily cold drawn pearlitic steels supplied in the form of prestressing steel wires for prestressed concrete. Furthermore, as pearlitic steel wires with different cold drawing degrees are analyzed (taken form a real cold-drawing manufacturing chain), the effective relationship is studied between the progressively anisotropic (oriented) microstructure and the increasing yield strength at each stage of the manufacturing process by repetitive cold drawing to ascertain the effect of cumulative straining on the pearlitic interlamellar spacing and its consequences in the matter of a relevant mechanical property such as the yield strength, a very Materials were high-strength pearlitic steels with different degree of plastic strain ( different cold drawing level ), named with digits 0 to 6 indicating the number of drawing steps undergone, from the initial hot rolled bar (not cold drawn at all) to the final commercial product (commercial prestressing steel wire). 2.1. Strength evolution during progressive (multi-step) cold drawing One important issue in cold-drawn pearlitic steel wires is the relationship between microstructure and strength, i.e., the effect of microstructural evolution on the (macroscopic) mechanical properties, since the final aim of the manufacture process by cold drawing is the improvement of mechanical properties (increase of strength) by a strain hardening mechanism. Fig. 1 (left) plots the stress-strain curves for the progressively cold-drawn pearlitic steels from A0 (hot rolled steel, not cold drawn at all, 0 drawing steps) to the commercial prestressing steel wire A6 (heavily cold drawn pearlitic steel that has undergone 6 drawing steps). A strain-hardening behaviour is observed, i.e., both the yield strength  Y and the UTS  max increase with the drawing degree. 2.2. Hierarchical microstructural evolution during progressive (multi-step) cold drawing Progressive cold drawing of pearlitic steel affects the microstructural arrangement in the form of slenderizing of the colonies, decrease of interlamellar spacing and orientation in the direction of cold drawing (wire axis) of both colonies and lamellae (Toribio and Ovejero, 1997, 1998a, 1998b, 1998c), i.e., inducing microstructural anisotropy, as shown in Fig. 1 (right) in the most heavily cold drawn pearlitic steel wire. important design parameter in structural materials. 2. Effect of cold drawing of the pearlitic steel wires

2.0

1.5

1.0

0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 A6 A5 A4 A3 A2 A1 A0  (GPa)  0.5

Fig. 1. Stress-strain curves of the progressively drawn pearlitic steels A0 to A6 (from 0 to 6 steps of cold drawing; left) and microstructure of the cold drawn wire A6 (right). Vertical side of the micrograph is parallel to the wire axis or drawing direction and horizontal side is associated with the radial direction.