Materials and Design 59 (2014) 397–405

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Materials and Design

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Hardening and softening mechanisms of pearlitic steel wire undertorsion

http://dx.doi.org/10.1016/j.matdes.2014.03.0290261-3069/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Address: 72 Wenhua Road, Shenyang 110016, China.Tel.: +86 024 83978266; fax: +86 24 23891320.

E-mail address: shzhang@imr.ac.cn (S.-H. Zhang).

Tian-Zhang Zhao a, Shi-Hong Zhang a,⇑, Guang-Liang Zhang b, Hong-Wu Song a, Ming Cheng a

a Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, Chinab School of Mechanical Engineering, Taizhou University, Taizhou 318000, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 12 November 2013Accepted 13 March 2014Available online 19 March 2014

Keywords:Pearlitic steel wireHardeningSofteningTorsion

The mechanical behaviors and microstructure evolution of pearlitic steel wires under monotonic sheardeformation have been investigated by a torsion test and a number of electron microscopy techniquesincluding scanning electron microscopy (SEM) and transmission electron microscopy (TEM), with anaim to reveal the softening and hardening mechanisms of a randomly oriented pearlitic structure duringa monotonic stain path. Significantly different from the remarkable strain hardening in cold wire draw-ing, the strain hardening rate during torsion drops to zero quickly after a short hardening stage. Themicrostructure observations indicate that the inter-lamellar spacing (ILS) decreases and the dislocationsaccumulate with strain, which leads to hardening of the material. Meanwhile, when the strain is largerthan 0.154, the enhancement of dynamic recovery, shear bands (SBs) and cementite fragmentationsresults in the softening and balances the strain hardening. A microstructure based analytical flow stressmodel with considering the influence of ILS on the mean free path of dislocations and the softeningcaused by SBs and cementite fragmentations, has been established and the predicted flow shear curvemeets well with the measured curve in the torsion test.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The ultra-high strength has brought a particular attention to thecold-drawn pearlitic steel wire. In order to improve its quality andexpand its commercial applications, there is an urgent requirementfor an advanced wire drawing technology. It is very significant tohave a fundamental understanding of mechanical behaviors anddeformation mechanisms of this dual-phase material. Extensiverelated studies have been done over the past few decades [1–11].

For thin steel wires, only a few methods can be used to measurethe mechanical behavior due to its geometry limitation. Tensiletest becomes a widely used method to examine the mechanicalproperty of steel wires. de Castro [8] used the tensile strength toshow the influence of die angles on steel wires’ mechanical proper-ties. Languillaume [10] applied tensile tests on heavily cold drawnand annealed pearlitic steel wires to study the dissolution ofcementite. But during tension, necking is easy to happen and thefracture strain is very small. Zhang et al. [12] reported that the frac-ture strain of the patented pearlitic steel wires is only about 0.09. Itis not large enough to exhibit the whole mechanical behavior of

steel wires. In order to study the mechanical behavior over a largestrain range, Langford [2,4] implemented a number of tensile teststo measure the strength of pearlitic steel wires after every pass ofdrawing. It becomes a well accepted method to exhibit the rela-tionship between strain and strength during drawing [12–14].However, the wire experiences a very complicated strain path dur-ing drawing and the following tensile tests, which has an impor-tant influence on the working hardening due to the remarkableanisotropy [15]. So a kind of monotonic loading over a large strainis required to investigate the mechanical behaviors of pearliticsteel wires.

Because a larger strain can be applied before plastic instabilityin torsion, it is employed here to study the mechanical behaviorsof steel wires over a large strain range. Moreover, the torsion prop-erties of the pearlitic steel wires are very important for the subse-quent manufacturing processes. In Ref. [16], the torsion was alsoused to investigate the influence of temperature raise during draw-ing. But only the number of circles was used. Here, the equivalentstrain equivalent stress curves during torsion are used.

It has been widely accepted that the hardening of pearlitic steelwires mainly results from the refinement of the lamellar structure.The cementite is unable to plastically deform and reckoned as onlythe barriers of dislocation movements [1,4,5]. With the develop-ment of microscopy techniques, now it is allowed to study the

Fig. 1. Illustration of sample processing and circular line method.

398 T.-Z. Zhao et al. / Materials and Design 59 (2014) 397–405

deformation mechanisms more precisely and at smaller scales[12,13,17–23]. For example, Zelin [13] reported that heavily drawnpearlite represented a nanocomposite. The stretching and rotationof pearlite colonies resulted in their alignment with the wire axis.And many localized SBs appeared at high strain. Zhang et al. [12]proposed three strengthening mechanisms: boundary strengthen-ing, dislocation strengthening and solid solution strengthening.The newest results showed that the cementite could deform plas-tically to some extent [24] and de-composite during wire drawing[25]. Furthermore, the dislocation arrangement and movement inthis nanolamellar structure are different from piling up in thecoarse grains. The deformation is attributed to the glides of dislo-cations in the individual ferrite [26], and the dislocations act likebowing in the lamellar structure with spacing smaller than100 nm [27].

Many studies have shown that a large number of SBs will formduring the wire drawing [13,21,24]. Bae et al. [7] found many frag-mentations of cementite in steel wire during torsion. But fewresearchers have taken the influence of SBs and fragmentationsof cementite into consideration when establishing the hardeninglaw of the steel wire. Since the SBs and fragmentations play animportant role in the deformation of the pearlitic steel wire, anew model which can consider the influence of ILS, SBs and frag-mentations is needed.

In this article, the torsion is used to exhibit the mechanicalbehaviors of pearlitic steel wires in a large strain range (up to0.59). The lamellar morphology and the dislocation arrangementwere observed using SEM and TEM. The discussion and analysisare focused on the ILS, formation of SBs, cementite fragmentations,as well as their contribution to the mechanical behaviors, includingboth hardening and softening aspects. And a microstructure basedanalytical flow stress model is established.

2. Experimental procedure

A pearlitic steel wire with carbon content 0.8 wt.% was investi-gated. The samples were supplied by NV Bekaert SA. The as-received samples (diameter 1.26 mm) were processed to obtain afine pearlitic microstructure, which undergoes patenting andbrass-plating.

The torsion tests were performed on Zwick/Roell TL200 tester atroom temperature with a rotating speed of 60 rounds per minute.The distance between specimen-holders was 126 mm, 100 timeslonger than diameter. Tensile tests were carried out Zwick B2010tester at room temperature. The gauge was 50 mm and the speedwas set as 30 mm/min. Both the tension and torsion were repeatedthree times. And they were conducted to fracture. The fracturepositions were located randomly between the two ends of thespecimen. No delamination was found and the fracture surface isflat. The traces at the surface of steel wire due to the torsion werevery homogenous which indicates that the deformation along thelongitudinal direction is uniform.

SEM was used to examine the evolution the lamellar structurewith strain increasing. It was carried on a FEI Nova Nano micro-scope. The selected positions for observation were on the longitu-dinal section near the surface of the wire, far from the fracturesurface and the ends of the specimen, as illustrated in Fig. 1. Stan-dard grinding, polishing and electro-polishing were applied to pre-pare samples. The electro-polishing condition was 15 V, �20 �Cand 8% (volume) perchloric acid in ethanol. The circular line meth-od (CLM) was used to measure the average ILS [28], shown in Fig. 1.The ILS was calculated using the following formula:

�s ¼ 0:5LN

ð1Þ

where L is the length of the circle and N is the number of intersec-tions between the circular line and the lamella. Each data was anaverage of 50 measurements on randomly chosen areas.

TEM was used to capture lamellar configurations and disloca-tion arrangements in ferrite. The positions for observation wereon the longitudinal section and located within the 10% range ofthe whole section from the surface of wires.

3. Experimental results

3.1. Equivalent strain–stress curve in torsion

The initial data from torsion tests are a relationship betweenthe twist (degree) and applied torque (Nm) as depicted in Fig. 2a.Unlike the tensile test, the strain distribution over the cross sectionin torsion is not uniform. The outer layer of wires has yielded,while the core part of wire still stays in the elastic stage. The rela-tionship between shear strain and stress is not linear any more.Special method is needed to convert the twist-torque curve toshear strain (c)–stress (s) curve. The method employed here wasproposed by Bailery [29], which is on an assumption that the strainis a linear function of radius. It is necessary to emphasize that thecalculated strain–stress is for the surface part of the sample. Theformula is as follows:

c ¼ RhL

ð2Þ

and

s ¼ 12pR3 3T þ h � dT

dh

� �ð3Þ

where R is the radius, L is the length of specimen. h (rad) representsthe twist and T (N�mm) the torque. The calculated result is given inFig. 2b. The equivalent stress in torsion is easy to get via:

req ¼ffiffiffi3p

s ð4Þ

Fig. 2. Mechanical behavior of pearlitic steel wires in torsion. (a) Initial twist-torque curve, (b) shear stress–strain curve, (c) equivalent stress–strain curve and(d) strain hardening rate-equivalent strain curve.

Fig. 3. Distribution of lamellar directions distribution in the as-received pearliticsteel wire. (a) Each colony is looped with red thread and the blue arrows arelamellar directions. The inserted picture illustrates the relative position anddirection of observed area in the wire. (b) Frequency of colonies with differentlamellar directions. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

T.-Z. Zhao et al. / Materials and Design 59 (2014) 397–405 399

It is a commonly used relationship between req (equivalentstress) and s. Several methods were discussed to compute accumu-lated equivalent strain during torsion tests [30–32]. The appliedmethod here is:

eeq ¼2ffiffiffi3p ln 0:5cþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 0:25c2

q� �ð5Þ

where eeq is the accumulated equivalent strain. It has been provedcorrect to calculate accumulated equivalent strain for small strains.

The equivalent strain–stress curve is shown in Fig. 2c (the blackcurve). The fracture strain in torsion reaches 0.59. The evolution ofthe strain hardening rate with strain is revealed in Fig. 2d. Thehardening rate gets to be zero when strain equals to 0.154, whichis much smaller than the fracture strain. In other words, the stresssaturates quickly.

For comparison, the red one in Fig. 2c is the true strain–stresscurve in tensile test. It is similar to the torsion curve in the begin-ning hardening stage. But the fracture strain in tension is just0.073, which is much smaller than the stress–saturation strain intorsion (0.154).

3.2. Lamellar structure evolution

The lamellar directions in the as-received steel wire are investi-gated on the cross section of wires using SEM. As shown in Fig. 3a,the chosen areas for observation are all located at the radial direc-tion line. The angle between the radial direction and the lamellardirection of 120 colonies were measured and analyzed. The resultsare given in Fig. 3b. The frequency in the range of each 10� isabout 10%. It can be concluded that the lamellar directions in theas-received steel wire are random.

Fig. 5. Evolution of inter-lamellar spacing with equivalent strain.

400 T.-Z. Zhao et al. / Materials and Design 59 (2014) 397–405

SEM was employed to observe the lamellar configuration atdifferent strains during torsion. The observations were carriedout at the surface of six different wires which were deformed todifferent rotations. The corresponding equivalent strains were cal-culated to be 0, 0.12, 0.24, 0.36, 0.48 and 0.59. The results areshown in Fig. 4.

In Fig. 4a–d and f, the white part is cementite and the black partis ferrite, while the white part is ferrite and the black part iscementite in Fig. 4e. Using the CLM mentioned previously, ILS ismeasured. The results are depicted in Fig. 5. The average ILSof the as-received steel wires is 75 nm. It can be seen thatILS decreases with the increasing of equivalent strain. And theaverage ILS of pearlite reaches 60 nm after torsion. A linear fittingis used to express the relationship between the ILS and the equiv-alent strain:

S ¼ 75� 30 � ep ð6Þ

where S is the ILS and ep the plastic strain. The calculated result isshown in Fig. 5. It can be seen that this linear relationship agreeswell with the experimental results.In Fig. 4a, there are few SBs inthe as-received wire. A lot of SBs appear under the large strainshown in Fig. 4f, marked by the yellow arrows. Additionally, thelamellar structure is broken into pieces (labeled using red arrowsin Fig. 4e and f). More examples are given in Fig. 6 under large strain(0.59). It is obvious that the initial perfect lamellar structure turnsinto lots of periodic SBs and fragmentations.

3.3. Dislocation arrangement

The maximum equivalent strain after torsion was 0.59 and lo-cated at the surface of wires. The observation positions for TEMwere located within the 10% range of the whole section from the

Fig. 4. SEM micrographs of lamellar structures at different equivalent str

surface of wires. So the equivalent strain for observation after tor-sion is larger than 0.48.

Fig. 7a and b present TEM micrographs of pearlite morphologyand dislocation arrangement in the as-received steel wire. Thecementite (dark) and the ferrite (light) stay parallel to each other.And only a few dislocations are found, marked by the arrows.Based on these observations, we consider that dislocations startfrom one interface, thread through the ferrite layer in randomdirection and end in the neighboring interface. Many dislocationstangle in ferrite. Additionally, the interfaces of these two phasesare flat and smooth.

A TEM micrograph of dislocation arrangements after torsion isshown in Fig. 7c. A selected area is enlarged in Fig. 7d. It can beseen that the ferrite/cementite interfaces are very rough, indicating

ains of torsion. (a) 0, (b) 0.12, (c) 0.24, (d) 0.36, (e) 0.48 and (f) 0.59.

Fig. 6. The shear bands and cementite fragmentations after torsion (strain = 0.59).

T.-Z. Zhao et al. / Materials and Design 59 (2014) 397–405 401

that many dislocations get stored there. In ferrite layers, disloca-tions gradually tangle and form a network. The dislocations accu-mulation will result in hardening.

The dislocation arrangement near the colony boundary isshown in Fig. 7e. Fig. 7f is the corresponding dark filed micrograph.Many parallel dislocations can be seen piling up against the colonyboundary, indicated by blue arrows. It indicates that gliding of

Fig. 7. TEM micrographs of dislocation arrangements in pearlite. (a) and (b) The as-receivwith yellow frame. (f) The dark field of (e).

dislocations along the lamellar direction results in piling up of dis-location at the colony boundary.

As mentioned previously, a large number of SBs and fragmenta-tions are generated under large strain. The investigation is focusedon their formation as well as their influence on the dislocationarrangement. TEM micrographs of pearlitic morphology after tor-sion (smallest strain = 0.48) are shown in Fig. 8. Lots of periodicSBs and fragmentations can be seen clearly in Fig. 8a and b. The ini-tially perfect lamellae are separated into several parts which arestill parallel but no longer in line due to the transverse localizeddisplacement, i.e. SBs. They lead to the discontinuity of thelamellae.

In fact, the formation of fragmentations just follows the initia-tion of SBs when the strain is large enough. Transverse displace-ment takes place under the applied shear stress (the red arrows)as depicted in Fig. 8c. At first, it is the gliding of dislocations to sup-port the main deformation. When deformation continues, the SBswill appear. Many dislocations get stored at two ends of the shearzone as marked with blue arrows. And the cementite is still contin-uous because of its plasticity. But in the area where the deforma-tion is much severe (labeled using yellow triangle frame inFig. 8c), the lamellar structure starts to be broken. A similar processcan be seen in Fig. 8d. AB and CD initially align in line and thenstagger due to the shear bands. In the shear zone from 1 to 4, thedeformation magnitude increases gradually and the fracture ofthe cementite takes place at point 4.

Fig. 8e and f show the dislocation arrangement after lamellarfragmentations. As shown in Fig. 8e, part A and B root from a singlecolony and share the same lamellar direction initially. After defor-mation dislocations accumulate. In the area marked with a bluesquare, the fracture of lamellar structure takes place and the dislo-cations annihilate. The same phenomenon can be observed inframes 1 and 2 in Fig. 8f. We consider that this dislocation annihi-lation will lead to softening.

4. Discussion

The mechanical behavior in torsion shown in Section 3.1 revealsthat the stress saturates soon after yielding in the monotonic shear

ed wires and (c)–(f) after torsion (smallest strain = 0.48). (d) The selected area in (c)

Fig. 8. TEM micrographs of pearlitic morphology after torsion (smallest strain = 0.48). (a) and (b) The shear bands and fragmentations of cementite. (c) and (d) Illustrations ofthe formation process. (e) and (f) The influence of fragmentations on dislocation arrangement.

402 T.-Z. Zhao et al. / Materials and Design 59 (2014) 397–405

deformation. This interesting phenomenon drives us to rethink thefundamental deformation mechanisms of pearlitic steel wire undermonotonic loading. In this section, it is focused to analyze themechanisms in torsion based on the microstructures observation.Finally, a new microstructure based analytical flow stress modelis established.

4.1. Hardening mechanism

The hardening mainly results from two aspects: the accumula-tion of dislocations and the decrease of ILS.

The plastic deformation is mainly attributed to the movementof dislocations in pearlitic steel wires. As analyzed above in Section3.3, dislocations thread through the ferrite layer. Under the shearstress, dislocations glide along the ferrite layer as bowing [5,14]and get stored at the interface. When the mobile dislocations ex-haust, dislocations will propagate in the ferrite layer with Orowanloops [33], Frank-Read or Bulging mechanisms [25]. The interac-tion between the dislocations will act as obstacles for their furthermovement, thus deformation becomes more difficult. This is thetypical latent hardening [34,35]. So the dislocations accumulationresults in the hardening.

As the most significant structure parameter in pearlite, ILS is al-ways regarded to determine the strength. Zhang et al. [12] consid-ered that the cementite lamellae act as obstacles to dislocationsglide and the ILS was estimated to be half of the mean free pathof dislocations. Also it is considered that the thickness of ferrite la-mella is proportional to the mean free path of dislocations and theaverage dislocation spacing [5]. When the ILS is smaller, it is moredifficult for dislocations to be activated and to move, which leadsto hardening.

As shown in Section 3.2, the ILS decreases gradually with strainincreasing during torsion. In Fig. 9, schematic pictures for thelamellar evolution during shear deformation are given. As shownin Fig. 9a, there is a lamella in the material (the blue rectangle).Two parallel dark lines represent cementite and the volume be-tween them is ferrite phase. The angle between the lamellar direc-tion and the shear direction is a. Then a shear deformation is

applied. The configuration of the material becomes a parallelo-gram, shown in Fig. 9b. The change of ILS during the shear isdependent on a. When a is equal or larger than 90�, the ILS (h inthe diagram) will decrease to h1. The lamella deforms like tensionwith the length of the lamella (L) increasing. But for the lamellawith a smaller than 90�, it deforms like compression firstly. TheILS (shown in Fig. 9c) increases first from h to h2, shown inFig. 9d. Only if the shear strain is large enough (a2 is larger than(180 � a)) the lamellar spacing would be smaller than the initiallamellar spacing (h). But the cementite is easy to bend during com-pression, shown in Fig. 9e. So a shear band is generated. The similarlamellar configuration is observed in Fig. 8c. If the shear deforma-tion is too large and cementite cannot correspond with its ownplasticity, fragmentations would take place as shown in Fig. 9f.The ILS will have a little change under this situation. To sum up,in the colonies with random directions, the ILS will decrease withthe increasing of shear deformation.

4.2. Softening mechanism

The decrease of ILS results in hardening, but the stress saturatesquickly. So a softening mechanism must exist. This softening phe-nomenon also was found by Aernoudt and Sevillano [3], which canbe dated back to 1973. He attributed the softening to the constantslipping distance of the dislocation. However, during the deforma-tion the lamellar structure will be refined, i.e. the mean free path ofdislocations will get smaller with strain.

The first thing to be considered is the dynamic recovery. Theway it influences the mechanical behavior is to reduce the disloca-tion density. As illuminated previously, a lot of SBs are generatedunder large strain. The localization of deformation in the SBs willabsorb most of energy induced by the imposed strain, which canrelax the applied stress to some extent [36]. Also the adiabaticheating can contribute the softening because it can make the dy-namic recovery of deformed structure more intense [37]. In pearl-itic lamella, Ref. [38] reported the localized phase transformationwhich can prove that the SBs lead to temperature rising.

Fig. 9. Schematic diagram of the lamellar structure evolution during shear deformation.

T.-Z. Zhao et al. / Materials and Design 59 (2014) 397–405 403

So the SBs will bring two types of contributions to the softeninghere: local temperature rising and stress relaxing. The temperaturerise at SBs must exist, although this is not measured. It may havenot been high enough to cause phase transformation, because notransformation product was observed in the microstructure usingSEM. However, its effect on dynamic recovery cannot be ignored.On the other hand, the SBs resulting from the macro strain concen-tration can relax the applied stress. Consequently, the overall stresswill decrease.

The last point is the change in dislocation arrangement afterlamellar fragmentations. Smith [39] studied the formation of acleavage crack in a crystalline solid and his conclusion can helpunderstand the fragmentations of cementite. It was supposed thatthe dislocations that get stored at two sides of the cementite havedifferent signs. The stress concentration leads to the fracture ofcementite. The fragmentations of the lamellae mean that theobstacles for dislocation movement disappear. The dislocations,which could not meet each other at the two sides of the cementitebefore fragmentation, can now react and annihilate. So the disloca-tion density decreases and the moving distance of dislocations nearthe fragmentation increases. These would finally lead to temporarysoftening.

4.3. A microstructure based flow stress analytical model

In Refs. [12,14], the mechanical behaviors of pearlitic steel wireswith different deformation histories have been investigated. Sev-eral hardening models were proposed, but no one has taken thesoftening mechanisms into accounts. Our micro-mechanism analy-sis above gives a deeper understanding for the monotonic defor-mation of fully pearlitic steel wire and guides for developing amodel considering both the hardening and softening mechanisms.To establish a new microstructure based analytical flow stressmodel, the following items must be considered:

� Accumulation of dislocations.� Evolution of the ILS.� Dynamic recovery.� Shear bands and fragmentations of cementite lamellae.

There is no doubt that the evolution of dislocation density is akey factor determining the strength of materials. The well-known

model proposed by Kocks and Mecking [34,35,40] is chosen as abase for our model. Rauch [41,42] also used this model as a funda-ment to establish a model considering strain path effects on themechanical behavior of low carbon steel. A new microstructurebased analytical model named ‘‘Modified KM model’’ is:

req ¼ffiffiffi3p

s� q � fs ð7Þ

where s is shear stress, fs is the fraction of SBs and fragmentationsand q is a coefficient. The shear stress (s) is a function of dislocationdensity (q) and given by:

s ¼ s0 þ albffiffiffiffiqp ð8Þ

where l is the shear modulus of ferrite, b is the Burgers vector offerrite and a is a factor related to dislocations interactions, theyare all constants. s0 is the stress related to the lattice friction. Theyielding stress is determined by this lattice-friction-stress and theinitial dislocation density together. In the equivalent strain-stresscurve, the yielding stress is about 980 MPa. And the measured ini-tial dislocation density from Ref. [12] is used here (q0 = 7.5 � 107

mm�2), because the as-received pearlitic wires is the same. Thus,the lattice friction stress is calculated to be 460 MPa.

It can be seen that the shear stress is determined by the dislo-cation density during deformation. And the evolution of the dislo-cation density with shear strain follows the formula:

dqdc¼ 1

bx� fq ð9Þ

where c is the resolved shear strain, x is the mean free path and f isthe factor expressing activity of thermally dynamic recovery. So thechange in dislocation density is because of two reasons. The firstone is contributed by the mean free path for hardening. And the sec-ond one is from the dynamic recovery resulting in softening, whichis dependent on the temperature and strain rate. 1

x is related to thefeature of dislocation arrangement and the geometry of theobstacles:

1x¼

ffiffiffiffiqpKþ 1

Dð10Þ

In this simple model, K is the number of forest dislocations for a dis-location to cross. And D is a characteristic size of material, such asgrain size or distance between large precipitates. In pearlitic steelwire, it is related to ILS, which decreases with increasing strain

Fig. 10. Influence of dynamic recovery (f) on mechanical behavior. Fig. 11. Comparison of the calculated and experimentally measured stress–straincurves in torsion.

404 T.-Z. Zhao et al. / Materials and Design 59 (2014) 397–405

as Eq. (6). So we define D as a function of ILS. The evolutionallaw is:

D ¼ g � S ¼ g � ð75� 30 � epÞ ð11Þ

where g is a proportionality coefficient. Dislocations glide in ferritelayer in the pearlitic steel wire. It is considered that the mean freepath is proportional to the ILS [5,25]. So the parameter g is used.And the mean free path is larger than the ILS. The value of g is largerthan 1.

K equals 180 in [41] at room temperature for the low carbonsteel. The number of dislocations for one dislocation to cross getssmaller in the pearlitic lamella with the average ILS 65 nm, whichis much smaller than the studied low carbon steel. So we considerthat K is smaller than 180.

The dynamic recovery is a very important contribution for thesoftening during torsion. It influences the appearance of the stresssaturation directly. In a Rauch’s work [41], the value of f in Eq. (9) is2.8 in low carbon steel and 6 in aluminum alloy. The dynamicrecovery is strongly dependent on the temperature. During torsion,the heat generated by the localized SBs will make the dynamicrecovery more intense. So the f value increases. In Fig. 10, theequivalent strain-stress curves are given with different values off. When the f is small (2.8), the stress is much higher than theexperimental curve. The stress is impossible to get saturationwithin current strain (0.59). And 18 is too high for f because thehardening is lower than the experimental curve from thebeginning. It is about 11.5. It also indicates that the dynamicrecovery is a very significant factor determining the mechanicalbehavior.

If D is a constant, the shear stress will saturate eventually due tothe balance between the dislocation density increase and the dy-namic recovery. But the D decreases with increasing strain. Thestress will never saturate no matter what the value of D is.

As discussed in Section 4.2, the generation of SBs and the frag-mentation of cementite lamellae lead to softening. In order to con-sider this softening effect in this new model, we use the secondterm in Eq. (7). fs is a quantity lying in the range [0,1). q is the stressreduction when fs equals 1. We consider that the fs changes withstrain in an exponential formula:

fs ¼ 1� expð�AeeqÞ ð12Þ

Table 1The parameters used in the model.

g s0 (MPa) q0 (mm�2) A b (mm)

3.3 460 7.5e+7 0.21 2.46E�7

where A is a coefficient. It is very difficult to quantify the fraction ofSBs and fragmentations via experimental measurements. The abovemethod is just a way to describe the fraction of SBs and fragmenta-tions in a mathematic view. The values of q and A can be obtainedby fitting.

After necessary fitting and optimization, all the needed param-eters are obtained, as listed in Table 1. The contributions of the twoterms in Eq. (7) are shown in Fig. 11. The largest stress softeningcaused by the SBs and fragmentations of cementite (at strain0.59) is just 128 MPa. Compared to the contribution of dynamicrecovery, it is very small. So the main softening results from thedynamic recovery. The mechanical curve in torsion predicted byEq. (7) is given in Fig. 11. It has a good capability to describe themechanical behavior of pearlitic steel wire under torsion.

This Modified KM model for the pearlitic steel wire can only beused in the monotonic loading. It is not valid in wire drawing, be-cause the wire experiences very complicated strain paths duringdrawing. A weak point is that the parameters are from other refer-ences, fitting or speculating. More experimental measurements areexpected to carry out to justify them. We hope this new modelcould help to understand the mechanisms of pearlitic steel wiremore deeply.

5. Conclusions

With the intention of investigating the mechanical behaviors ofpearlitic steel wires in a large strain range, the torsion behaviors ofhigh carbon steel wires with a carbon content 0.8 wt.% is investi-gated. Evolution of dislocation arrangement and lamellar configu-ration are examined by SEM and TEM. The conclusions aresummarized as follows:

1. During torsion of the pearlitic steel wire, the strain hardeningrate drops to zero quickly after yielding.

2. Dislocations spread through the ferrite with two ends at the fer-rite/cementite interfaces. They glide in the ferrite layers, result-ing in dislocation network and piling up against colonyboundaries. The dislocations get stored at the interfaces after

f K a q (MPa) l (MPa)

11.5 150 0.5 1100 85,000

T.-Z. Zhao et al. / Materials and Design 59 (2014) 397–405 405

torsion. The dislocation accumulation makes a main contribu-tion to hardening. Additionally, the inter-lamellar spacingdecreases with equivalent strain during torsion.

3. The softening mechanisms are attributed to three mechanisms:dynamic recovery, shear bands and the fragmentations ofcementite. Dynamic recovery is a main factor. A lot of shearbands and the fragmentations occur with increasing strain.They lead to a reduction of the strength because of stress relax-ing and reduction of the overall dislocation density.

4. A new microstructure based analytical flow stress model forpearlitic steel wires under monotonic strain path is proposed.

Acknowledgements

The financial support of NV BEKAERT SA (Belgium), Natural Sci-ence Foundation of China (51034009) and Strategic Cooperationwith Guangdong Province (2012B091100251) is gratefullyacknowledged.

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