Correlation between ferrite grain size, microstructure and tensileproperties of 0.17 wt% carbon steel with traces ofmicroalloying elements

Shankha Nag, Prithak Sardar, Anudeepika Jain, Abhishek Himanshu,Dipak Kumar Mondal n

Department of Metallurgical and Materials Engineering, National Institute of Technology, Durgapur 713209, India

a r t i c l e i n f o

Article history:Received 27 August 2013Received in revised form19 December 2013Accepted 21 December 2013Available online 31 December 2013

Keywords:Grain refinementDegenerated pearliteYield-strengthHall–Petch relationDuctilityLüders elongation

a b s t r a c t

Five different grain sizes are produced in 0.17 wt% carbon steel using varying rates of cooling fromaustenitization temperatures. Controlled furnace cooling from 1100 1C and 950 1C produces coarse ferritegrains of 40 mm and 32 mm diameter, respectively, along with partial degeneration of cementite lamellaewithin pearlite regions. Execution of intermediate (oven at 300 1C) and fast (air) cooling from 950 1Cdevelops finer polygonal ferrite (19 mm and 14 mm) with increased degeneration of pearlite; whilerepeated heating and force air cooling around 950 1C produces a minimum ferrite grain size of 9 mm andcomplete degeneration of the pearlite regions. Influence of micro-alloying is observed by precipitation offine carbides in grain-refined structures. Tensile test results show improvement in strength values andductility parameters with the progress of grain refinement. By comparing the improved yield strengthvalues with the classic Hall–Petch relation: s¼siþKd�1/2, a deviation is observed in the exponent ofgrain size. Lüders strain becomes larger with decrease in ferrite grain size. The flow curves and strainhardening exponents as derived for different grain sizes show increasing plasticity with grain refine-ment. Rate of strain hardening also becomes higher with grain refined structures. Ferrite grainrefinement results in a dominating inter-crystalline mode of tensile fracture.

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1. Introduction

The high strength with superior toughness in low carbon steelsas well as high strength low alloy (HSLA) steels [1–5] have beenobserved to be associated with the influence of cooling rate on thetransformation of austenite to various micro-constituents respon-sible for the final properties. On accelerated cooling, the decreasein austenite to ferrite transformation temperature encouragesferrite nucleation at the austenite grain boundaries and graininterior. The enhanced nucleation rate restricts grain growth dueto early impingement and so causes ferrite grain refinement [6–8].With increasing cooling rate, the nature and morphology of ferritealter from polygonal to plate-like or elongated lath/acicular ferrite[6–11]. Beside this, the use of micro-alloying elements and con-trolled hot rolling may lead to production of fine ferrite grainthrough precipitation of fine carbides or carbonitrides [7,8]. Low-ering of transformation temperature introduced by higher coolingrate additionally causes degeneration of pearlite region eitherpartially or completely. Formation mechanism of degenerated

pearlite has been reported quite judiciously by Mishra et al.[12,13] during studies on niobium- and vanadium-microalloyedsteels processed with varying cooling rates. In this study, theinsufficient carbon diffusion at a lower transformation tempera-ture has been made responsible for pearlite degeneration [12–15].

The microstructural refinement, considered to have an influ-ence on the grain size and distribution of second phase in steels, islikely to modify the strength, toughness, and, in particular, theyield strength. According to the familiar Hall–Petch relation, thequantitative increase in strength varies with the reciprocal root ofthe grain size, in a manner s¼siþKd�1/2, where s is the yieldstrength of the polycrystalline steel, K is the Hall–Petch slope andsi is the yield strength of a single crystal of same composition.Whatever be the mechanism leading to Hall–Petch relation, thereis deviation from Hall–Petch behavior for grain sizes of extremelysmall size [16]. Such deviation from Hall–Petch relation may bedescribed as inverse Hall–Petch behavior as reported duringtensile test of grain refined dual-phase structures in a vanadiummicroalloyed steel bearing grain size less than 10 mm [17]. How-ever, previous research on materials including steels [18,19]suggests inverse Hall–Petch behavior for grain size down to20 nm. The grain size limitation of the Hall–Petch relation hasbeen justified by the hypothesis that when the grain size becomes

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0921-5093/$ - see front matter & 2014 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.msea.2013.12.073

n Corresponding author. Mob.: þ91 9434788003; Fax: þ91 0343 254 7375.E-mail address: dk_mondal2003@yahoo.co.in (D.K. Mondal).

Materials Science & Engineering A 597 (2014) 253–263

sufficiently small, the dominant deformation mechanism in atensile test changes from transgranular slip to grain boundarysliding [18–20].

The objective of this study is to derive the influence of coolingrate on the microstructure and tensile properties of 0.17 wt%carbon steel. Attempt is made to correlate strength and ductilityvalues and strain hardening response during tensile deformationto ferrite grain size and pearlite degeneration. It has also beentried to find out the conformity of the observed strength para-meters to the conventional Hall–Petch relation.

2. Experimental procedure

The chemical composition of the steel is presented in Table 1.Samples for metallography and tensile test were obtained from hotrolled bars of 20 mm�20 mm cross-section. The hot rolled barswere homogenized at 1100 1C for 1 h and then subjected to controlslow (furnace) cooling to produce an initial microstructure withlarge ferrite grain size. With an aim to reduce ferrite grain size, thehomogenized bar was austenitized at 950 1C for 0.5 h and subse-quently cooled in furnace in a controlled manner. In anotherattempt, the homogenized bar was held at 950 1C for 0.5 h andthen quickly transferred in an oven equilibrated at 300 1C in orderto cool it at a rate somewhat faster than controlled furnacecooling. Further to reduce grain size, a fourth set of samples wasaustenitized at 950 1C for 0.5 h and subsequently cooled in still airat room temperature (�25 1C). Finally, a fifth set of samples wassubjected to heating at 950 1C for 0.33 h and subsequent force-aircooling with the help of a blower. The same cycle of heating andforce-air cooling is repeated for five times to achieve reasonablerefinement of the microstructure, particularly with reference toferrite grain size. Accordingly, the steels with five different grainsizes developed were designated as Anneal 1100, Anneal 950,Anneal 950/300, Normalize, and Cyclic 950, respectively. At thetime of heat treatment, suitable packing around samples was usedto avoid de-carburization from the surface.

Microstructural features of the differently heat-treated sampleswere examined under optical (Reichert, Austria) and scanningelectron microscopes (S-3000N, Hitachi, Japan). Energy DispersiveSpectroscopy (EDS) was also carried on precipitate particles toexamine their composition. The grain sizes were measured follow-ing the ASTM method by counting at least 500 grains in each case.The results were reported in ASTM grain size number and averagegrain diameter. The volume fractions of ferrite and pearlite in allheat treated steels were measured with the help of a microscopefitted with an automatic point counter by counting at least 600counts on each sample.

Tensile tests were carried out in duplicate for each heattreatment and an average of readings was recorded. The testswere performed on strips of standard dimensions having gaugelength of 30 mm with the help of an Instron testing machine(Model 8516) using a cross-head speed of 1 mm/min and full scaleload of 100 kN. Values of ultimate tensile strength (UTS), yieldstrength (YS), strain at maximum load (eu) and strain at fracture(ef) were estimated from the load–elongation plots for differentgrain sizes. True stress versus true plastic strain s–εp diagramswere obtained for different grain sizes. The values of strainhardening exponent ‘n’ were obtained by plotting ln s versus

ln εp and measuring the slope of each plot. The strain hardeningrate ds/dεp was also plotted as a function of true plastic strain, εp.All graphs and analyses were made using Origin Pro 8.5 DataAnalysis and Graphing Software [21].

3. Results and discussion

3.1. Grain refinement

The variation of ferrite grain size with different heat treatmentshave been noted in terms of measuring average grain diameterand the corresponding ASTM number as presented in Table 2.In homogeneous anneal condition (Anneal 1100), the ferrite grainsize is quite large (40 mm) due to prolong holding at a highertemperature of 1100 1C and subsequent controlled furnace cooling.On execution of Anneal 950 treatment, the average grain sizereduces nominally to 32 mm. However, the treatment Anneal 950/300 reduces grain size drastically to 19 mm because the coolingrate used here appears somewhat faster than furnace cooling.Though air cooling after austenitization is an effective means offerrite grain refinement, Normalize treatment in the present studyreduces grain size only up to 14 mm. In contrast, on application ofCyclic 950 treatment, significant refinement of microstructureis achieved reducing the average grain diameter to a minimumof 9 mm.

For Normalize treatment, the initially homogenized steel con-taining coarse proeutectoid ferrite and pearlite located at grainboundary triple point corners, are held at 950 °C. At this tempera-ture, both the proeutectoid and eutectoid (pearlitic) ferritechanges rapidly to austenite in a diffusionless massive poly-morphic transformation [22]. Pearlite–ferrite interfaces are con-sidered to act as potential sites for austenitization [23].

In pearlite regions also, austenite nucleates at ferrite–cementiteinterfaces and grows by dissolution of cementite in a diffusion-controlled slow process [22,24], and it leads to incompletedissolution of cementite in austenite due to inadequate holdingperiod of 0.5 h at 950 1C. Beside this, the niobium carbide (NbC)particles, if there be any with the initially homogenized micro-structure, cannot dissolve in the austenite formed at 950 1C. Thepresence of any undissolved cementite or NbC ceases the austenitegrowth. On air cooling, the inadequately grown austenite trans-forms to finer ferrite, thus resulting in an average grain size of14 mm. In case of Cyclic 950 treatment also, small austenite grainsoccur at 950 1C because of reasons described above and transformto finer ferrite following force-air cooling. Repeated heating andforce-air cooling of sample for five times ultimately causessignificant refinement of the ferrite grains, thus producing anaverage grain diameter of 9 mm. The use of niobium as

Table 1Chemical composition of steel.

Element C Mn Si S P Nb V Cu Al

Weight% 0.170 0.512 0.123 0.070 0.091 0.005 o0.002 0.012 o0.001

Table 2Average grain diameter of ferrite after various heat treatments.

Heat treatment designations Average grain diameter, mm ASTM number

Anneal 1100 39.81 (40) 7 (6.70)Anneal 950 32.37 (32) 7 (7.29)Anneal 950/300 18.71 (19) 9 (8.87)Normalize 13.93 (14) 10 (9.73)Cycle 950 9.09 (9) 11 (10.98)

S. Nag et al. / Materials Science & Engineering A 597 (2014) 253–263254

microalloying element and/or faster rate of cooing, in fact, lowersthe austenite to ferrite transformation temperature and so pro-vides less chance of thermally activated growth of the ferritegrains.

3.2. Microstructure

Representative optical micrographs of the steels possessingdifferent grain sizes are presented in Fig. 1(a)–(e). The primarymicro-constituents after controlled furnace cooling from 1100 1Cand 950 1C are polygonal ferrite with well defined pearlite areas.The Anneal 950 sample produces quite a good number of smallferrite grains along with coarse-grained ferrite (Fig. 1(b)), whilethe Anneal 1100 sample produces mainly coarse-grained ferrite(Fig. 1(a)). The Anneal 950/300 sample, though subjected to anintermediate cooling rate, exhibited almost similar pattern ofpolygonal ferrite and pearlite but with reasonable refinement ofboth (Fig. 1(c)). With the increase in cooling rate in case ofNormalize treatment, there is a tendency towards formation offiner ferrite grains with pearlite mostly appearing as thin grainboundary envelops (Fig. 1(d)). On the other hand, Cyclic 950treatment causes further refinement of ferrite grains involvingstrain and widely dispersed pearlite, thus developing an acicularpattern of the resulting microstructure (Fig. 1(e)) in place ofconventional ferrite–pearlite microstructure. Beside the sequential

changes in ferrite grain size and pearlite morphologies, themicrostructures presented in Fig. 1(a)–(e) contain precipitateparticles appearing as fine dots on the ferrite matrix. Previousinvestigators [12,13] have already identified these precipitateparticles as MC type vanadium carbides in vanadium microalloyedsteels and niobium carbides in niobium microalloyed steels.However, to understand the nature and distribution of theprecipitates in the present study, selected specimens are examinedin a Scanning Electron Microscope equipped with Energy Disper-sive Spectroscopy.

Representative scanning electron micrographs (SEMs) showingthe overall pattern of ferrite and pearlite of the differently heattreated steels are given in Fig. 2(a)–(e). As depicted in Fig. 2(a) and(b), large polygonal ferrite contains limited number of coarseprecipitates formed during slow (controlled furnace) cooling fromthe austenitization temperatures. In comparison, Fig. 2(c) and(d) shows small polygonal ferrite with increased precipitationcaused by the state of non-equilibrium maintained with theintermediate as well as fast rate of cooling during Anneal 950/300 and Normalize treatment, respectively. Nearly similar situa-tion arises with Cyclic 950 treatment, when a mixed microstruc-ture of polygonal and acicular ferrite appears along with extensiveprecipitation of carbides on the ferrite matrix (Fig. 2(e)). Thesedifferent ferrite morphologies formed are known to followmechanism involving diffusion or shear [15,25]. Further, to

Fig. 1. Optical micrographs of the samples subjected to treatments: (a) Anneal 1100; (b) Anneal 950; (c) Anneal 950/300; (d) Normalize; and (e) Cyclic 950.

S. Nag et al. / Materials Science & Engineering A 597 (2014) 253–263 255

identify the precipitate particles EDS analyses are carried out onsome coarse precipitates, i.e. points 3 and 4 in Fig. 3 and points 1,2, 5 and 6 in Fig. 4, indicating the presence of iron, manganese andcarbon along with some vanadium in particles formed by Anneal950 treatment and also a combination of iron, manganese andsulfur in particles formed by Cyclic 950 treatment. However, thefine precipitates possibly of niobium or vanadium carbides andoccurring in grain refined structures could not be detectedpresumably because these are too small to be resolved in SEM.

In addition to the modification of ferrite phase, all the heattreated steels have experienced significant degeneration of thepearlite regions with the progress in grain refinement. The extentof degeneration has been made clear by focusing the pearliteregions at higher magnifications. Evidences of partial degenerationand also of nearly complete degeneration of the pearlite regions inAnneal 950/300 sample are quite clear in Fig. 5(a)–(c). It is noticedthat comparatively smaller pearlite regions are more susceptible tothe process of degeneration. In fact, the alignment and distribution

Fig. 2. SEM secondary electron images of the steels subjected to treatments: (a) Anneal 1100; (b) Anneal 950; (c) Anneal 950/300; (d) Normalize; and (e) Cyclic 950.

C-K N-K O-K Al-K Si-K S-K V-K Cr-K Mn-K Fe-K Ni-K Cu-K Nb-L pt1 2.23 6.11 27.01 0.06 0.08 0.11 0.17 0.51 63.32 0.34 0.06 0.00 pt2 0.47 0.64 0.03 0.04 0.00 0.00 1.53 96.80 0.00 0.47 0.03 pt3 1.12 2.55 0.00 0.14 0.06 0.00 5.23 90.01 0.20 0.70 0.00 pt4 0.00 0.00 0.00 0.35 4.80 0.00 0.00 6.21 88.44 0.09 0.00 0.10 pt5 0.00 0.00 0.32 0.54 0.00 0.25 0.47 97.82 0.60 0.00 0.00

Weight %

Fig. 3. EDS analysis of the precipitates particles occuring at different locations in Anneal 950 sample.

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of small and thin cementite segments as illustrated in Fig. 5(c) clearly match with the pattern of degenerated pearlitedescribed in a similar study by Mishra et al. [12]. It is suggestedthat degeneration is initiated by nucleation of cementite at ferrite–austenite interfaces following partitioning process. Insufficientdiffusion of carbon has been made responsible in developingdiscontinuous pattern instead of continuous pattern of lamellarcementite. As a result, the interfacial area between ferrite andcementite in a degenerated pearlite happens to be more than thatin conventional pearlite [12,13,26].

Fast rate of cooling as experienced in Normalize as well asCyclic 950 treatment also results in typical interface precipitationof carbide between the degenerated pearlite and the matrix ferrite.Fig. 6(a)–(d) clearly exhibits this feature as a thick white layer ofcontinuous carbide. Apart from interface precipitation, grainboundary cementite network and cementite cluster within pearliteregion are also evident in the micrographs given in Fig. 6. EDSanalyses in Fig. 4 (points 3 and 4) clearly indicate that both theinterface carbide and grain boundary carbide are mainly of Fe3Ctype and almost free from vanadium or niobium. These grainboundary as well as interface carbides have been identified earlierin low carbon (�0.16 wt%) steel as divorce-eutectoid transforma-tion products occurring due to fast cooling of an austenite poolbelow A1 temperature [27]. In normal eutectoid transformation,

the single phase austenite decomposes into a mixture of lamellarferrite and cementite following cooperative growth mode.Whereas, the divorce-eutectoid transformation occurs when theinitial austenite containing pre-existing nuclei of undissolvedcarbides [28] undergoes transformation below A1 producing amixture of ferrite and spheroidal carbide due to their non-cooperative growth [29–31]. Beside these, before execution ofNormalize and Cyclic 950 treatment, in homogeneous anneal statethe initial microstructure consists of proeutectoid ferrite andcoarse pearlite. The cementite lamellae in pearlite contain lamellarfaults of sharp curvature. During holding at 950 1C, austenite formsat the cost of proeutectoid as well as eutectoid (pearlitic) ferriteand thereafter grows by dissolution of cementite preferably fromthe lamellar fault regions [32–34]. Diffusion of the dissolvedcarbon along the austenite grain boundaries results in carbonenrichment (beyond 0.8%) at the grain boundaries locally. On aircooling in case of normalize treatment or force air cooling in caseof cyclic 950 treatment, the carbon enriched austenite transformsproducing network of proeutectoid cementite at the ferrite–ferritegrain boundaries (Fig. 6(a) and (b)) or ferrite/austenite (pearlite)interfaces (Fig. 6(a) and (d)). While the remaining austenite withundissolved cementite experiences divorce eutectoid transforma-tion [27] producing cluster of cementite enclosed by ferrite matrix.Incidentally, a degenerated pearlite region in Fig. 6(c) clearly

C-K N-K O-K Al-K Si-K S-K V-K Cr-K Mn-K Fe-K Ni-K Cu-K Nb-L pt1 0.00 0.00 0.40 0.04 29.39 0.50 0.06 55.35 11.28 0.90 2.09 0.00 pt2 0.00 0.00 0.12 0.00 32.23 0.30 0.00 62.53 3.67 0.41 0.74 0.00 pt3 1.88 2.83 0.00 0.69 0.19 0.00 0.02 0.00 93.44 0.39 0.27 0.29 pt4 1.34 3.02 0.19 0.09 0.69 0.00 0.40 93.63 0.03 0.59 0.00 pt5 0.00 0.00 3.23 0.00 2.21 18.93 0.00 0.00 40.46 33.52 0.67 0.97 0.00 pt6 0.00 0.00 0.21 0.24 24.86 0.00 0.00 47.66 25.54 0.55 0.94 0.00 pt7 3.39 4.87 0.00 0.30 0.52 0.00 0.25 0.90 89.00 0.00 0.77 0.00 pt8 1.33 3.61 0.47 0.00 0.10 0.00 80.97 13.09 0.43 0.00 0.00

Weight %

Fig. 4. EDS analysis of the precipitates particles occuring at different locations in Cyclic 950 sample.

Degenerated pearlite

Degenerated pearlite

Degenerated pearlite

Divorced cementite

Pearlite D

egeneration

Fig. 5. SEM secondary electron images of steel specimens subjected to (a) Anneal 1100 treatment; (b) Anneal 950 treatment; and (c) Anneal 950/300 treatment.

S. Nag et al. / Materials Science & Engineering A 597 (2014) 253–263 257

shows a long ferrite formed epitaxially at the peripheral edgeof the initial austenite along with clustering of cementite withinthe pearlite region following divorce eutectoid transformation.Divorce eutectoid transformation has been favored by acceleratedcooling introducing defects in the initial austenite before reachingA1 temperature. Defects may be dislocations, slip steps or inho-mogeneity in composition (particularly carbon) within an auste-nite grain. These defects provide high energy sites for preferrednucleation of cementite clusters. Particularly evident from Fig. 6(c), the three well pronounced cementite clusters appearing insequence clearly insinuate the presence of dislocation or progres-sive slip steps when the region was initially austenitic.

3.3. Tensile properties

Tensile test results have been reported in Table 3 which clearlyindicates increase in the yield strength (YS) as well as ultimatetensile strength (UTS) with the progress in ferrite grain refinement.The higher strength values of the steels with smaller grains may beattributed to the enhanced grain boundary areas and the increasedvolume fraction of pearlite regions as given in Table 4. It is likelythat the reported degeneration of pearlite in case of Normalize andCyclic 950 samples also attributes to the improvement in tensilestrength. It is, therefore, evident that the microstructure rather thancomposition is a major factor which ultimately controls the tensileproperties of the heat treated steels. For example, the tensileproperties of annealed and normalized steels are controlled bythe flow and fracture characteristics of the ferrite and also by theamount, shape, and distribution of the cementite [35]. However, anormalized steel in the present study usually assumes higherstrength than the annealed steel (Anneal 1100 and Anneal 950)because the more rapid rate of cooling used in Normalize treatmentproduces finer ferrite and causes the transformation of austenite topearlite at lower temperature producing finer inter-lamellar spacingand simultaneous degeneration of the pearlite regions leading todisintegration of lamellar cementite. Beside this, the strainedacicular ferrite and the associated dislocation density of a Cyclic

Epitaxial ferrite

Cluster of cementite

Divorced

cementite

Divorced cementite

Cluster of cementite

Grain boundary carbide

Fig. 6. SEM secondary electron images of steel specimens subjected to (a) and (b) Normalize treatment; (c) and (d) Cyclic 950 treatment.

Table 3Grain size and the corresponding tensile test results.

Sample Grain size, mm Yield strength, MPa Ultimate tensile strength, MPa Uniform elongation (eu) Total elongation (ef) Lüders elongation (eL)

Anneal 1100 40 27474 48072 0.23170.02 0.34170.003 0.01172E�4Anneal 950 32 30175 49670.25 0.25470.013 0.36370.017 0.014715E�4Anneal 950/300 19 349715 563725 0.27670 0.39570.015 0.01672E�4Normalize 14 387716 588723 0.22170.002 0.34470.022 0.01771E�4Cyclic 950 9 41075.6 64371.1 0.22570.01 0.35070.015 0.01273E�4

Table 4Variation of ferrite and pearlite volume fraction with grain size.

Sample Grain size, mm Percent ferrite Percent pearlite[lamellar plus degenerated]

Anneal 1100 40 82 18Anneal 950 32 85 15Anneal 950/300 19 83 17Normalize 14 77 23Cyclic 950 9 70 30

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950 sample cause hardening by pile-up during tensile deformation.In both Normalize and Cyclic 950 sample, clustering of cementiteoccurring within the pearlite regions is likely to provide furtherenhancement in tensile strength. Thus, whatever be the source ofhigher strength, the present study ultimately suggests a treatmentinvolving repeated (cyclic) heating and force air cooling aroundaustenitizing temperature in order to produce a reasonably goodcombination of strength (UTS¼643 MPa) and uniform elongation(eu¼0.255) in a low carbon steel containing traces of micro-alloyingelements.

3.4. Tensile properties versus grain size

True stress and ductility parameters with respect to varyinggrain sizes are presented in a single plot shown in Fig. 7. The truestress versus grain size plots for both true stress at necking (sU)and true stress at yield point (sYS) show a gradual decrease of truestress values with increasing grain size. These two parameters viz.sYS and sU signify the onset and localization of plastic flow in amaterial, respectively, and so their magnitude depends largely onthe material0s inherent resistance to plastic deformation. Fine-grained microstructures in Normalize and Cyclic 950 samples havegreater grain boundary area compared to coarse grain microstruc-tures available with Anneal 1100 and Anneal 950 samples, thusleading to greater pile-up of dislocations at the grain boundariesduring deformation and, in turn, raising the true stress. Secondly,the volume fraction of pearlite (including lamellar and degener-ated) is more in fine grained microstructure (Table 4), which mayfurther provide impedance to dislocation motion. Beside this, thesmaller inter-lamellar spacing in pearlite coupled with profounddegeneration of cementite lamellae in grain refined Normalizestructure plays an additional role towards enhancing the truestress. Similarly, the mixed microstructure containing polygonal aswell as strained acicular ferrite with intense cementite clusteringin a Cyclic 950 sample also lead to hindrance to grain rotation andreorientation during tensile test and subsequent rise in true stressvalues.

In Fig. 7, it is tried to fit sYS parameter with the well-established Hall–Patch equation: s¼ siþKdn having usual nota-tions and n being an exponent with a value of �0.5 in the idealHall–Petch model. While fitting, s and d values are taken as inputsand si, K and n are made the fitting parameters keeping the valueof n as close as possible to �0.5 to bear conformity to theconventional form of the Hall–Petch equation. The goodness offit is indicated by R2 adjusted by the degree of freedom [21].Further, the fitting equation obtained for the true yield stress (sYS)versus grain size plot is derived taking si as constant viz. 100 MPa.Similar value of si has been considered by Takaki [36] to

characterize yielding in a polycrystalline ferritic steel. Moreover,as the parameter, in principle, relates to yielding in single crystal,attempt has been made to estimate this parameter from the datareported by Stein et al. [37] for iron single crystals. The equation soobtained is

s ðMPaÞ ¼ 100þ760:62½dðμmÞ��0:3862 ð1Þwith adjusted R2¼0.97697.The associated standard error with estimation of si, K and n are

0 (the value 100 being constant), 64.16, and 0.02643, respectively.As depicted by the n value in Eq. (1), the estimated true stress atyielding (Curve 1 in Fig. 7) does not appear in exact conformity tothe conventional Hall–Petch relation. However, if the true yieldstress of Anneal 1100, Anneal 950, Anneal 950/300 and Normalizesamples are fitted, then the equation becomes

sðMPaÞ ¼ 100þ1061:92½dðμmÞ��0:47982 ð2Þwith adjusted R2¼0.96525.The value of n now indicates that the Eq. (2) or the resulting

curve (Curve 2) in Fig. 7 conform to the conventional Hall–Petchrelation. On extrapolation of Curve 2 towards smaller grain size,the true yield stress of the Cyclic 950 sample arrives at �470 MPainstead of observed value of �420 MPa. Such discrepancy may beattributed to the strained acicular ferrite and the associatedpreponderance of defects in the form of high dislocation densityin Cyclic 950 sample. In general, the yield stress can be expressedby the relation [38]: s0¼ssþsi, where ss is the stress to operatethe dislocation sources and si is the friction stress representing thecombining effect of all obstacles to the motion of dislocations.High prior dislocation density of the Cyclic 950 sample eventuallyreduces the si, thus resulting in a yield stress lower than thatpredicted by the conventional Hall–Petch model. The presentstudy thus suggests that Hall–Petch is satisfied primarily whenthere is no influence of metallurgical parameters except grain sizeon the yield strength of a material.

The Lüders elongation values cited in Table 3 also show a trendsimilar to the yield stress except for the Cyclic 950 sample whichshows a sudden drop in Lüders elongation. It was previouslydemonstrated in the work of Tsuchida et al. [39] that Lüderselongation increases with decreasing grain size. It is well estab-lished that Lüders elongation is an inhomogeneous deformationappearing in the form of bands and occurring at stress raisers atthe onset of plastic flow [38]. With decreasing ferrite grain sizes,the ease with which the ferrite grains can reorient themselvestowards the favorable stress direction increases. This, in turn,facilitates the generation of new dislocations and motion of glissiledislocations needed for Lüders elongation. However, for the Cyclic950 sample a different situation arises. Firstly, as mentionedbefore, the reorientation and rotation of ferrite grains is hindered.Moreover, enhanced dislocation pinning further impedes defor-mation. As a result, the individual Lüders band cannot elongatemuch. However, due to the availability of considerable priordislocations in the ferrite matrix, the grains or regions adjacentto a dislocation pile-up readily undergo plastic flow to form a newband of deformation, thus lowering the corresponding yield stressfrom the predicted Hall–Petch value.

The plots of total elongation and uniform elongation versusgrain size show almost a similar trend (Fig. 7). They show gradualincrease with decreasing grain size in the beginning, reach amaximum and then drop and finally level off with further decreasein grain size. This particular behavior of straining during uniaxialtensile loading of the heat treated steels may be matched with thebasic nature of plastic deformation in metals and alloys involvingthe motion of dislocations and subsequent slip. Also, in polycrys-talline materials not all grains are favorably oriented for slip withrespect to the tensile axis during deformation, owing to which

5 10 15 20 25 30 35 40

300

350

400

450

500

550

600

650

700

750

800

Tru

e St

ress

(MPa

)

(True Yield Stress) (True Ultimate Stress)

Total ElongationUniform Elongation

Grain Size (μm)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Elo

ngat

ion

Curve 2: Conforms to the Conventional Hall-Petch

Curve 1: Deviates from Hall-Petch

Fig. 7. Variation of yield strength (sYS), ultimate tensile strength (sU), uniformelongation (UE) and total elongation (TE) as a function of grain size.

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grain reorientation and rotation take place during tensile straining.Large size grains in case of Anneal 1100 and Anneal 950 steels haveless grain boundary area causing less pinning of mobile disloca-tions, thus favoring plastic deformation with less resistance. Yetdue to their size (40 mm and 32 mm, respectively) they are difficultto reorient and rotate during tensile straining; thus the ductilityparameters become comparatively less, producing uniform elon-gation between 0.23 and 0.25. However, the ductility improvesreaching a maximum uniform elongation of 0.276 as the grain sizedrops drastically from 32 mm to 19 mm. While, with furtherdecrease in grain size up to 14 mm using Normalize treatment,the ductility parameters fall (Table 3) owing to increase in grainboundary area, which causes more pinning of mobile dislocations.Finally the ductility parameters stabilize with decreasing grain sizeup to 9 mm in case of Cyclic 950 sample for reasons describedbelow. The mixed pattern of fine polygonal and acicular ferrite andlarge scale disintegration of the pearlite regions developed by theCyclic 950 treatment cause hindrance to grain rotation andreorientation during tensile deformation, thus the possibility ofenhancing ductility in spite of ferrite grain refinement is largelyopposed. In addition to this, the extensive precipitation of car-bides, as illustrated in SEM images in Fig. 6(a)–(d) and being moreeffective in dislocation pinning, is also likely to degrade theductility in Cyclic 950 sample.

3.5. Flow curves and strain hardening exponent

Figs. 8 and 9 show the plots for true stress versus true plasticstrain and natural logarithm of true stress versus natural loga-rithm of true plastic strain, respectively, for different grain sizes.Both the plots are fitted with Holloman relation [38] and itscorollary, namely, s¼ Kεnp; and lnðsÞ ¼ lnðKÞþn lnðεpÞ.

In the said fitting, the true stress s and true plastic strain εp aretaken as inputs and the strength coefficient K and strain hardeningexponent n are made the fitting parameters. Goodness of fit isexpressed by the adjusted R2 value. It is evident from the datatables presented in the two plots (Figs. 8 and 9) that K and n valuesare very much in conformity. The strength coefficient K varies withgrain size as expected showing large value for fine grainedstructure, and decreases with increasing grain size. The n values,on the other hand, decrease from 0.32792 to 0.28708 withdecreasing grain size, except for the extremely fine-grain, i.e.9 mm, where it shows a sudden rise from 0.28708 to 0.30261(Fig. 9). With reference to the fact that n value of ‘1’ implies‘complete elasticity’ and a value of ‘0’ implies ‘complete plasticity’[38], it can be inferred that decreasing n value with grainrefinement signifies a situation tending towards plasticity. Suchan observation based on n values bears conformity to the patternof variation of the ductility parameters in Fig. 7.

The plasticity in a polycrystalline material usually attributes tothe dislocation mobility and ability of the grains to reorient androtate in response to applied tensile stress. With decreasing grainsize the grain boundary area increases, thus increasing the chancesof dislocation pinning at the grain boundaries; and, in turn,decreasing plasticity. On the other hand, grain reorientation androtation is easier with finer grains, thus increasing plasticity. Otherfactors, namely, the size and distribution of the second phase andhardness of the phases appearing in a grain refined structure mayalso be considered to play roles in determining plasticity of steels.Small and dispersed pearlite areas in grain refined steels areknown to reduce the plasticity. However, to understand the roleof individual phase hardness, micro-hardness values are measuredrandomly on ferrite grains and pearlite areas in heat-treated steels.Micro-hardness survey on some 100 numbers of ferrite grains ineach sample shows an increase in ferrite hardness from HV 140–210 range in Anneal 1100 and Anneal 950 steels to HV 200–260range in Normalize and Cyclic 950 steels, possibly due to increasedprecipitation of carbide as well as straining of acicular ferrite.Similarly, the pearlite hardness increases from HV 240–340 rangein Anneal 1100 and Anneal 950 steels to HV 270–450 range inNormalize and Cyclic 950 steels as a result of pearlite degeneration

0.05 0.10 0.15 0.20100

200

300

400

500

600

700

800

Symbol Adj. R2 Grain Size K (MPa) St. Error n St. Error0.99949 39.81 1012.6540 7.0571 0.32788 0.00340.99933 32.37 984.29101 7.54662 0.30918 0.00390.99867 18.71 1156.8097 13.79827 0.31752 0.005040.9989 13.93 1155.7281 11.50933 0.28706 0.00409

0.99808 9.09 1266.4180 15.46327 0.29999 0.00564

Fig. 8. True stress versus true plastic strain plots for different grain sizes.

-1.5 -2.0 -2.5 -3.0 -3.55.2

5.6

6.0

6.4

6.8 Fitting Model: Derived from Holloman EquationFitting Equation: ln(σ) = lnK+ n. ln(εp)

Symbol Adj. R2 Grain Size K (MPa) St. Error n St. Error0.99936 39.81 1012.735 7.03851 0.32792 0.003390.99904 32.37 984.2992 7.56926 0.30917 0.003910.99843 18.71 1156.195 14.04777 0.31765 0.005130.99877 13.93 1155.351 11.57662 0.28708 0.004120.99824 9.09 1273.660 15.28392 0.30261 0.00519

Fig. 9. Natural logarithm of true stress versus natural logarithm of true plasticstrain plots for different grain sizes.

0.05 0.10 0.15 0.20

500

1000

1500

2000

2500

3000

3500

4000

39.81µm 32.37µm 18.71µm 13.93µm 9.09µm

(MPa

)

Fig. 10. Rate of strain hardening versus true plastic strain plots for differentgrain sizes.

S. Nag et al. / Materials Science & Engineering A 597 (2014) 253–263260

and cementite clustering. The cumulative effect of such increase inmicro-hardness values has been clearly reflected by the degrada-tion of plasticity in grain refine structures. Therefore to conclude,there are two sets of opposing factors influencing plasticity; andsince this analysis shows that plasticity effectively increases withdecreasing grain size, it would be wise to conclude that the factorsincreasing plasticity are more influential than the factors decreas-ing the same. Further, the sudden increase in n value in the samplewith lowest grain size (9 mm) may be correlated with the mixedmicrostructure of polygonal and strained acicular ferrite, degen-eration of pearlite along with clustering of cementite along grainboundaries and the large population of carbides precipitated onfiner ferrite, which cause hindrance to dislocation motion andgrain reorientation and a subsequent decrease in plasticity of theCyclic 950 sample.

3.6. Rate of strain hardening versus true plastic strain

Plots of ds/dεp versus εp for different grain sizes, shown inFig. 10, indicate gradual fall in the strain hardening rate withincreasing true plastic strain for the coarse grained steels withgrain sizes 40 mm and 32 mm. In comparison, the fine-grained

steels with ferrite grain sizes 19, 14 and 9 mm show a steeper fall instrain hardening rate till 0.10–0.15 true plastic strain, among whichthe steel with minimum grain size (9 mm) has the steepest fall. It isalready pointed out that the coarse ferrite grains in Anneal 1100and Anneal 950 samples face difficulty in rotation and reorienta-tion during tensile deformation. As a result, the hardening thatoccurs due to straining fails to relax during continued deformationleading to a gradual decrease in the strain hardening rate. On theother hand, fine polygonal and acicular ferrite grains obtained atfaster cooling rate in Normalize and Cyclic 950 samples hardeninitially at a higher strain hardening rate due to high dislocationpile up at grain boundaries, but subsequently tend to soften fromstrain hardened condition by easy rotation and reorientation withrespect to the tensile axis and that makes an initial steep fall of thestrain hardening rate up to 0.10–0.15 true plastic strain. Otherwise,the strain hardening rates for fine-grained samples are higher thanthose obtained at larger grains for the entire range of true plasticstrain. As stated earlier, the fine-grained microstructures offermore hindrance to dislocation motion due to greater grainboundary area. Beside this, finely dispersed carbides in the ferritephase, greater volume fraction of pearlite coupled with disinte-gration of cementite lamellae and presence of strained acicular

Large cavity

Cleavage facet

Large cavity

Void sheet

Void sheet

Irregular void

Fig. 11. SEM fractographs of the tensile tested specimens with different grain sizes: (a) 40 mm; (b) 32 mm; (c) 19 mm; (d) 14 mm; and (e) 9 mm.

S. Nag et al. / Materials Science & Engineering A 597 (2014) 253–263 261

ferrites also contribute to enhanced strain hardening in fine-grained microstructures prepared under non-equilibriumconditions.

3.7. Tensile fracture

To study the influence of grain size on the mode of tensilefracture, SEM fractographs from all heat treated steels are obtainedfor examination. As illustrated in Fig. 11(a) and (b), fracture hasoccurred by both ductile tearing as well as transgranular cleavagedue to some heterogeneity left in the matrix microstructure evenafter Anneal 1100 and Anneal 950 treatments. Both the figuresshow large cavities generated by void coalescence which is acommon mode of tensile fracture in low carbon steels containing alarge volume of ferrite. However, the mixed intergranular andtransgranular cleavage is rather absent in steels subjected toAnneal 950/300 treatment, and the corresponding fractrograph(Fig. 11(c)) contains a large number of dimples of small size. Thereduced dimple size and corresponding increase in number can becorrelated with the increased number of smaller ferrite grains(19 mm) in the sample. Following the same reason, the Normalizesample produces a similar fractograph (Fig. 11(d)) containing largenumber of micro-dimples or voids. At certain locations the micro-voids have coalesced forming typical void-sheets (marked byarrow). This indicates the failure initiation at sites of a cluster offine ferrite grains possibly with grain boundary cementite net-work. On the other hand, Cyclic 950 steel being more refined withrespect to ferrite and pearlite regions, the fracture mode assumes aprominent intergranular pattern. There are also locations indicat-ing transition from intergranular to transgranular fracture (Fig. 11(e)) possibly at regions containing cementite clusters which havetaken place largely in Cyclic 950 steel as a mark of divorcedeutectoid transformation.

4. Conclusions

� Anneal 1100 and Anneal 950 treatments develop coarse ferritegrains of 40 mm and 32 mm size and coarse pearlite with partialdegeneration of cementite lamellae. Major grain refinementoccurs after Anneal 950/300 treatment producing ferrite grainsize of 19 mm and increased degeneration of pearlite. Noappreciable change in grain size occurs on execution of Nor-malize treatment.

� Ferrite grain size reduces to a minimum of 9 mm after Cyclic950 treatment, producing polygonal as well as acicular ferritealong with grain boundary network of cementite and clusteringof cementite in pearlite regions.

� Increase in yield strength (YS) and ultimate tensile strength(UTS) occurs with refinement of grain size. However the valuesof uniform elongation and total elongation initially rise withgrain refinement up to 19 mm and then drop and subsequentlylevel off with further refinement of grain size up to 9 mm.

� Anneal 950/300 treatment produces a good combination ofstrength (UTS¼563 MPa) and ductility (UE¼0.276) in compar-ison to Anneal 1100 and Anneal 950 treatments (UTSE490 MPa and UE¼0.24). Fast cooling during normalizetreatment causes further increase in strength but with reducedductility.

� The mixed microstructure of polygonal and acicular ferriteobtained by Cyclic 950 treatment results in a reasonably goodcombination of UTS (643 MPa) and uniform elongation (0.255).

� The true stress versus grain size plots for both true stress atnecking (su) and true stress at yielding (sYS) show a gradualdecrease of the true stress with increasing grain size. Whilefitting the observed sYS and d values based on the Hall–Petch

relation: s¼siþKdn, n being an exponent having value of�0.5 in the ideal Hall–Petch model, a deviation in the n valuefrom �0.5 to �0.4 is observed. This deviation can be attributedto the Cyclic 950 sample where defects in the form of highdislocation density was introduced due to repeated heating andcooling around the austenitisation temperature.

� While fitting the observed true stress and true plastic strainbased on the Holloman relation, s¼Kεnp, the strength co-efficient ‘K’ assumes large value for grain refined structureand it decreases with increasing grain size. On the other hand,the strain hardening exponent ‘n’ decreases with decreasinggrain size, except for the minimum grain size of 9 mm, wherethe mixed microstructure containing polygonal and acicularferrite and excess degeneration and clustering of cementitewithin pearlite causes a sudden rise in ‘n’ value.

� The strain hardening rates over the entire range of true plasticstrain values increases with decreasing grain size. However, theds/dεp values for grain refined steels fall drastically at initialstrain values; while the Anneal 1100 and Anneal 950 steelsshow a less drastic fall in ds/dεp values during initial straining.

� In coarse-grained microstructures, the tensile fracture showsmixed intergranular and transgranular cleavage. While thegrain-refined microstructures show typical dominance ofinter-crystalline mode of tensile fracture.

Acknowledgment

The authors would like to thank the Director, National Instituteof Technology, Durgapur, India for financial support and facilitiesprovided for this research project.

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