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Volume 59, Issue 9, May 2011, Pages 3422-3430

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Volume 59, Issue 9, May 2011, Pages 3422-3430 in st iao gin ch D et, School of Materials Science and Engineering, Chongqing University, Chongqing 400030, People’s Republic of China � 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. divided by fine and closely spaced cementi...

Volume 59, Issue 9, May 2011, Pages 3422-3430
in st iao gin ch D et, School of Materials Science and Engineering, Chongqing University, Chongqing 400030, People’s Republic of China � 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. divided by fine and closely spaced cementite and ferrite lamellae extending almost parallel to the drawing direction. The thickness of these lamellae can be as fine as 10–20 and 1–2 nm for the ferrite and cementite lamellae, respectively. Studies of deformation mechanisms and microstructure in drawn pearlitic wires date back to the 1960s and 1970s, ⇑ Corresponding author at: Danish–Chinese Center for Nanometals, Materials Research Division, Risø National Laboratory for Sustainable Energy, Danmarks Tekniske Universitet, DK-4000 Roskilde, Denmark. Tel.: +45 46775859. E-mail address: xzha@risoe.dtu.dk (X. Zhang). Available online at www.sciencedirect.com Acta Materialia 59 (2011) 3422–34 Keywords: Microstructure; Strengthening mechanisms; Pearlitic steel wire 1. Introduction Cold-drawn high-carbon steel wires of approximately eutectoid composition have the highest strength of all steel products, up to 5–6 GPa. They have wide industrial appli- cations, including cables for suspension bridges, steel cords for automobile tyres and springs. The high strength is also of interest in new applications, for example where steel wires may be used as reinforcement in windmill wings for cleaner energy production. Technological interest has led to numerous scientific studies over the years of the struc- tures and properties [1–3]. However, with the advancement of microscopical techniques, also encompassing the devel- opment of atom probe field ion microscopy [4,5], new opportunities have been created which have led to the pres- ent study, which focuses on the strengthening mechanisms which cause the exceptional high strength. These mecha- nisms occur in a structure with nanoscale dimensions sub- Received 11 January 2011; received in revised form 8 February 2011; accepted 10 February 2011 Available online 17 March 2011 Abstract Strengthening mechanisms and strength–structure relationships have been analyzed in a cold-drawn pearlitic steel with a structural scale in the nanometer range and a flow stress of about 3.5 GPa. The wires have been drawn up to a strain of 3.7 and the structures analyzed and quantified by transmission electron microscopy and high resolution electron microscopy. The mechanical properties have been determined by tensile testing. It is found that the interlamellar spacing and the thickness of the cementite lamellae are reduced in accordance with the changes in wire diameter up to a strain of 2.5. At a higher strain enhanced thinning of the cementite lamellae points to decomposition of the cementite and carbon enrichment of the ferrite lamellae. Dislocations are stored in the interior of the ferrite lamellae and their density increases to about 2 � 1016 m�2. A high dislocation density is also observed at the ferrite/cementite interface. Three strengthening mechanisms have been analyzed: (i) boundary strengthening, (ii) dislocation strengthening and (iii) solid solution hardening. The individual and combined contributions, based on an assumption of linear additivity, of these mechanisms to the wire strength have been estimated. Good agreement has been found between the estimated and the measured flow stresses, which is followed up by a discussion of structure and strengthening mechanisms with a view to extrapolation to larger strains, finer structures and larger stresses. Microstructure and strengthen pearlitic Xiaodan Zhang a,b,⇑, Andy Godfrey a, X aAdvanced Materials Laboratory, Department of Materials Science and En bDanish–Chinese Center for Nanometals, Materials Resear Danmarks Tekniske Universit c 1359-6454/$36.00 � 2011 Acta Materialia Inc. Published by Elsevier Ltd. All doi:10.1016/j.actamat.2011.02.017 g mechanisms in cold-drawn eel wire xu Huang b, Niels Hansen b, Qing Liu c eering, Tsinghua University, Tsinghua 100084, People’s Republic of China ivision, Risø National Laboratory for Sustainable Energy, DK-4000 Roskilde, Denmark www.elsevier.com/locate/actamat 30 rights reserved. and seminal papers have been published by Embury and Fisher [1] and Langford [2]. These authors primarily related the high strength to the close spacing between the cementite lamellae (or fragments) on the assumption that the cementite acts as a barrier to dislocation glide, as do grain boundaries in polycrystalline iron. They therefore introduced the Hall–Petch relationship and related the flow stress of the wires to the reciprocal square root of the spacing between the cementite lamellae (the interlamellar spacing or ILS). It was found by transmission electron microscopy (TEM) examination that this spacing decreases in accordance with the reduction in wire diameter and a relationship between the flow stress (r) and the strain (e) also including Kikuchi diffraction analysis and spot indexing by collecting nanobeam diffraction patterns by field emission gun (FEG-)TEM. The wires have been drawn up to a strain of 3.7 giving a flow stress around 3.7 GPa. It is found that all three mechanisms contribute significantly to the wire strength and that their sum agrees well with the measured flow stress. This agreement leads to a more general discussion of strengthening mechanisms in nanoscale structures. 2. Experimental Five samples at five cold-drawing strains covering the X. Zhang et al. / Acta Materialia 59 (2011) 3422–3430 3423 was formulated [1]: r ¼ r0 þ k1 expðe=4Þ ð1Þ where r0 is the friction stress of the ferrite and k1 is a con- stant which can be derived from the Hall–Petch slope. This equation is a good approximation of the evolution in flow stress with increasing drawing strain, as has been shown in many studies [1,6–8]. An illustration is given in Fig. 1. However, this figure also shows significant deviation from a linear relationship, especially at large strains, which points to other strengthening mechanisms in addition to the barrier resistance of cementite. Such mechanisms could be legion, as the wire structure is complex, but this paper will focus on dislocation strengthening and solid solution hardening. Our approach follows that of previous studies where strengthening of drawn pearlitic wires has been con- sidered as the additive effect of more than one microstruc- tural mechanism [1,6–11]. The reason is that it has been observed that a dislocation structure with a high density of dislocations evolves in the ferrite lamellae [12] and that these lamellae can be enriched by carbon in solution, espe- cially at high strains at which the cementite lamellae start to decompose [7,13–18]. It follows that the following three strengthening mechanisms will be analyzed: (i) barrier or boundary strengthening; (ii) dislocation strengthening; (iii) solid solution hardening. The analysis will be based on characterization of structural morphology and structural parameters by TEM and high resolution electron microscopy (HREM) Fig. 1. Summary of mechanical data relating the flow stress to the drawing strain. different strain hardening stages in Fig. 1 of high strength, near-eutectoid composition steel with a carbon content of 0.8 wt.% (supplied by NV Bekaert SA (Zwevegem, Belgium) Technology Center Laboratory) were investigated. These samples represent intermediate steps of the manufac- turing process from the as-patented wire (1.26 mm) to the final drawn filament (0.2 mm). The sample details are listed in Table 1. The structural analysis based on the ferrite and cement- ite phases will focus on the evolution of structural param- eters during wire drawing. They are the ILS, the thickness of cementite and dislocation configurations and density in the ferrite lamellae. Standard grinding and electro- polishing (10% perchloric acid in ethanol) procedures were used to prepare specimens for investigationa by scanning electron microscopy (SEM) and TEM. The wires were examined in the longitudinal section. For the SEM obser- vations specimens were additionally etched in 4% Nital. The ILS and cementite thickness were measured by TEM, taking care to ensure edge-on conditions to deter- mine the cementite thickness. Additionally, the ILS of wires deformed to low strains (e < 1.51) was measured by SEM using the method of Gensamer et al. [19]. For each sample data were collected from 30 measurements on ran- domly chosen areas. Dislocation configurations and densi- ties were examined using a JEOL 2000FX TEM at 200 kV and a JEOL 3000 FEG–TEM at 300 kV. The stress–strain curves have been determined directly on as-received drawn wires using standard tensile tests Fig. 2. True stress–true strain curves for the wires. Table 1 Summary of wire samples used in this study. Sample 1 2 3 4 5 Diameter (mm) 1.26 0.899 0.591 0.332 0.2 Strain 0.00 0.68 1.51 2.67 3.68 3424 X. Zhang et al. / Acta Materia for wires. The strain rate was 2.5 � 10�3 s�1 and the 0.2% proof stress is taken as the flow stress. The ultimate tensile stress (UTS) and total elongation have also been deter- mined (see Table 2). The stress–strain curves for the drawn wires are shown in Fig. 2, together with the curve for the initial pearlitic sample. None of the specimens show a yield point and parabolic hardening has been observed up to the UTS. 3. Results 3.1. Morphology and structural parameters The evolution of the cementite morphology as a func- tion of the drawing strain has been reported in a previous paper [20]. In agreement with previous findings [21], it was found that the cementite plates align with increasing strain to the extent that about 97% are realigned parallel to the drawing direction when the drawing strain reached 1.5 with an angular spread of 30�. The reduction in thickness of the ferrite lamellae (F) and thickness of the cementite lamellae (T) have been measured and related to the drawing strain, shown in Fig. 3 and Table 3. On the assumption that T is reduced in accordance with the wire diameter, T can be related to the true strain, which is expressed as: e ¼ lnðA0=AÞor lnðD0=DÞ2 ð2Þ where A0 and D0 relate to the cross-sectional area and the diameter of the initial wire and A and D refer to those of a drawn wire. T can then be expressed by the relationship [1]: T ¼ T 0 expð�e=2Þ ð3Þ where T0 is the original thickness of about 19 nm. The cal- culated value for T is plotted in Fig. 3, illustrating good correspondence between the measured and calculated val- ues of T. In addition to measuring T, the ILS has been determined as a function of strain (see Fig. 3b). It can be Area reduction (%) 0 49 78 93 98 seen that there is good agreement between the measured and the calculated ILS, in support of the assumption leading Table 2 UTS and elongation of wire samples used in this study. Strain 0.00 1.51 2.67 3.68 UTS (MPa) 1386 1904 2674 3640 Total elongation (%) 9.0 2.7 1.9 2.1 to Eq. (1), namely that this spacing decreases in accordance with the reduction in wire diameter. In the low strain part of the curve (up to approximately e = 1.5) it is recognized that there are a number of complications with such an analysis. These include the fact that the wire center is likely to deform by plane strain rather than an axisymmetric deformation mode (as indicated by the characteristic curling seen in the transverse sections of drawn wires [22]) and also the fact that significant reorientation of the pearlitic struc- ture takes place as the microstructure evolves towards one where the ferrite and cementite lamellae are parallel to the drawing axis [23,24]. It is believed that these factors are reflected in the larger scatter seen in thickness measure- ments at the lowest investigated strain (e = 0.68). Overall, however, cementite evolution (and ILS) follows the predic- tion from the assumption of simple axisymmetric deforma- tion. However, for a strain above 3 the calculated thickness of cementite is 2.9 nm, whereas the measured thickness is about 2.1 nm. This difference points to a decomposition of about 30 wt.% cementite with about 1.1 at.% carbon enriching the ferrite based on the original concentration of 3.63 at.% (0.8 wt.%) carbon. 3.2. Dislocation configuration and density The mechanical properties of deformed metals are dom- inated by dislocation storage, and the dislocation density in the ferrite lamella is an important factor in understanding the strain hardening and its contribution to the flow stress of drawn pearlitic steel wires. Since little systematic data is available this study has focused on the storage of disloca- tions and their configurations in the ferrite lamellae as observed by TEM. However, at very large strains where the fineness of the ferrite lamellae makes it difficult to quantify the dislocation density the density at a strain of 3.68 has been determined in the JEOL 3000 microscope in high resolution mode. Fig. 4 shows the dislocations in the ferrite lamellae in the initial structure, with a dislocation density of 7.5 � 1013 m�2. The random dislocation lines can be observed as a result of the phase transformation. Disloca- tion configurations in the ferrite lamellae parallel to the drawing direction at a strain of 0.68 are shown in Fig. 5. Most of the dislocations are spread in the ferrite lamellae, with the two ends of the line located at the steps in the ferrite/cementite boundaries. Calculation of the dislocation density gives a value of 7 � 1014 m�2, which is in accordance with the results of crystallographic orientation measurements [12]. Fig. 6 shows a TEM micrograph and a sketch of the dislocation configuration in the ferrite lamellae at a strain of 2.67. Note that the dislocations in the ferrite lamellae are distributed very regularly with a spacing of 10–20 nm. Calculation of the dislocation density gives a value of 8.8 � 1015 m�2. The TEM and HREM investigations of the wire at a lia 59 (2011) 3422–3430 strain of 3.68 show that the dislocation density is 2 � 1016 m�2. teria X. Zhang et al. / Acta Ma 3.3. Structural heterogeneities The observation of morphological changes and the detailed analysis show that the structural evolution is not homogeneous during wire drawing, At small and medium strains the cementite reorients, a process which involves shear banding and grain curling [2,21,22,25,26]. Such heter- ogeneities change the structural morphology but may also affect the density and arrangement of dislocations in the ferrite lamellae. However, the characterization of such het- erogeneities is for further research, as it will require a fairly detailed characterization of microstructural parameters at Fig. 3. (a) Thickness of the cementite lamellae and (b) ILS vs. drawing strain cementite lamellae of the same area at a strain of 0.6. The thickness of the c reduction in thickness of the cementite lamellae and ILS, assuming that they d also given in (a) and (b). The error bars represent the standard deviation for Table 3 ILS and thickness of ferrite (F) and cementite (T). Strain 0.00 0.68 1.51 2.67 3.68 ILS (nm) 89 70 55 28 20 F (nm) 70 56 45 23 18 T (nm) 19 14 10 5 2 lia 59 (2011) 3422–3430 3425 different positions in the wire. The following analysis will therefore be based on the assumption of a fibrous structure where the ferrite and cementite lamellae are parallel to the and TEM micrographs showing the (c) edge-on and (d) inclined state of ementite lamellae was measured in the edge-on condition. The calculated eform in accordance with the macroscopic changes in wire dimensions, is the data at each strain. The data presented in the box is magnified. Fig. 4. TEM micrograph of an undeformed sample showing the disloca- tions in the ferrite lamellae with black arrows. The dislocation density is 7.5 � 1013 m�2. eria 3426 X. Zhang et al. / Acta Mat drawing direction and values for the interlamellar spacing and the dislocation density will be the average values for all structures. This averaging also allows the present data to be compared with data reported in the literature. 4. Analysis of structure and strength The relationship between microstructure and strength will be analyzed on the basis of the structural observations Fig. 5. (a) TEM micrograph of a sample deformed to a strain of 0.68 and (b) a sketch of the dislocation structure in the ferrite lamellae. The dislocation density is 7 � 1014 m�2. Fig. 6. (a) TEM micrograph of a sample deformed to a strain of 2.67 and (b) a sketch of the dislocation structure in the ferrite lamellae. The dislocation density is 8.8 � 1015 m�2. pointing to three strengthening mechanisms contributing to the wire strength: � boundary strengthening related to the distance between the cementite lamellae (r(b)); � dislocation strengthening related to the dislocation den- sity in the ferrite lamellae (r(q)); � solid solution hardening related to the carbon concen- tration in the ferrite lamellae (r(ss)). It is assumed that these strength contributions are line- arly additive, thus the flow stress of the wire can be expressed as: rðeÞ ¼ r0 þ rðbÞ þ rðqÞ þ rðssÞ ð4Þ where r(e) is the flow stress at a given drawing strain and r0 is the friction stress of pure ferrite. The contributions from the three strengthening mechanisms will be analyzed separately. 4.1. Boundary strengthening The contribution of cementite lamellae to the strength is estimated based on the Hall–Petch equation relating the yield stress (ry) to the distance between barriers which can act as obstacles to dislocation glide. This relationship had been shown to be valid in the case of polycrystalline metals where the barrier distance is equal to the grain size [27]. In applying this equation to pearlite the barrier spac- ing is taken to be equal to the mean free path of disloca- tions, which is estimated to be twice the width of the ferrite lamellae (d), i.e. [19]. ry ¼ r0 þ kð2dÞ�0:5 ð5Þ Eq. (5) has in previous studies been shown to give a sat- isfactory description of the relationship between wire strength and barrier distance. Early examples are Embury and Fisher [1], where the barriers are characterized as tan- gled walls and cementite fragments, and Langford [2], where the barriers are characterized as cementite lamellae. In these studies values for the constants r0 = 40–70 MPa, k = 0.62 [1] and k = 0.58–0.68 [2] were reported from mea- surements over a wide strain range. In these studies it was also noted [1,2] that these constants correspond to those obtained for polycrystalline ferrite, indicating similar bar- rier strengths for grain boundaries and for cementite lamellae. Eq. (5) is also applied in the present analysis. However, as other strengthening mechanisms than barrier spacing may be operative and as the contributions of such mecha- nisms may depend on the drawing strain, Eq. (5) is applied separately for corresponding values of stress (r0.2%) and spacing on the assumption of a constant r0, which is taken to be 60 MPa. Values for k are given in Table 4, showing a significant increase in k with increasing strain, which to a lia 59 (2011) 3422–3430 certain degree follows the relationship r � exp (0.25e) in Fig. 1. This strain dependence of k points to contributions decomposition of the cementite, which has been found [16] to increase with increasing strain in the large strain region. This contribution will be analyzed in the next section. 4.3. Solid solution hardening A contribution by solid solution hardening (r(ss)) is esti- mated based on Eqs. (4) and (7) by taking k(e) = 0.31. The results are given in Table 6. The value for r(ss) shows that this contribution to the total flow stress is not important for strains up to about 2.67. However, for e = 3.67 r(ss) is significant. This contribution r(ss) = 478 MPa relates to the observation of decomposition of about one-third of the cementite, enriching the ferrite with a carbon con- centration of 1.1 at.%. Based on literature values [32], the Table 4 Hall
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