Correlation between ferrite grain size, microstructure and tensile properties of 0.17 wt% carbon steel with traces of microalloying elements

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

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Correlation between ferrite grain size, microstructure and tensile properties of 0.17 wt% carbon steel with traces of microalloying 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

art ic l e i nf o

a b s t r a c t

Article history: Received 27 August 2013 Received in revised form 19 December 2013 Accepted 21 December 2013 Available online 31 December 2013

Five different grain sizes are produced in 0.17 wt% carbon steel using varying rates of cooling from austenitization temperatures. Controlled furnace cooling from 1100 1C and 950 1C produces coarse ferrite grains of 40 mm and 32 mm diameter, respectively, along with partial degeneration of cementite lamellae within pearlite regions. Execution of intermediate (oven at 300 1C) and fast (air) cooling from 950 1C develops finer polygonal ferrite (19 mm and 14 mm) with increased degeneration of pearlite; while repeated heating and force air cooling around 950 1C produces a minimum ferrite grain size of 9 mm and complete degeneration of the pearlite regions. Influence of micro-alloying is observed by precipitation of fine carbides in grain-refined structures. Tensile test results show improvement in strength values and ductility parameters with the progress of grain refinement. By comparing the improved yield strength values with the classic Hall–Petch relation: s ¼ si þ Kd  1/2, a deviation is observed in the exponent of grain size. Lüders strain becomes larger with decrease in ferrite grain size. The flow curves and strain hardening exponents as derived for different grain sizes show increasing plasticity with grain refinement. Rate of strain hardening also becomes higher with grain refined structures. Ferrite grain refinement results in a dominating inter-crystalline mode of tensile fracture. & 2014 Elsevier B.V. All rights reserved.

Keywords: Grain refinement Degenerated pearlite Yield-strength Hall–Petch relation Ductility Lüders elongation

1. Introduction The high strength with superior toughness in low carbon steels as well as high strength low alloy (HSLA) steels [1–5] have been observed to be associated with the influence of cooling rate on the transformation of austenite to various micro-constituents responsible for the final properties. On accelerated cooling, the decrease in austenite to ferrite transformation temperature encourages ferrite nucleation at the austenite grain boundaries and grain interior. The enhanced nucleation rate restricts grain growth due to early impingement and so causes ferrite grain refinement [6–8]. With increasing cooling rate, the nature and morphology of ferrite alter from polygonal to plate-like or elongated lath/acicular ferrite [6–11]. Beside this, the use of micro-alloying elements and controlled hot rolling may lead to production of fine ferrite grain through precipitation of fine carbides or carbonitrides [7,8]. Lowering of transformation temperature introduced by higher cooling rate additionally causes degeneration of pearlite region either partially or completely. Formation mechanism of degenerated

n

Corresponding author. Mob.: þ 91 9434788003; Fax: þ 91 0343 254 7375. E-mail address: [email protected] (D.K. Mondal).

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

pearlite has been reported quite judiciously by Mishra et al. [12,13] during studies on niobium- and vanadium-microalloyed steels processed with varying cooling rates. In this study, the insufficient carbon diffusion at a lower transformation temperature has been made responsible for pearlite degeneration [12–15]. The microstructural refinement, considered to have an influence on the grain size and distribution of second phase in steels, is likely to modify the strength, toughness, and, in particular, the yield strength. According to the familiar Hall–Petch relation, the quantitative increase in strength varies with the reciprocal root of the grain size, in a manner s ¼ si þKd  1/2, where s is the yield strength of the polycrystalline steel, K is the Hall–Petch slope and si is the yield strength of a single crystal of same composition. Whatever be the mechanism leading to Hall–Petch relation, there is deviation from Hall–Petch behavior for grain sizes of extremely small size [16]. Such deviation from Hall–Petch relation may be described as inverse Hall–Petch behavior as reported during tensile test of grain refined dual-phase structures in a vanadium microalloyed steel bearing grain size less than 10 mm [17]. However, previous research on materials including steels [18,19] suggests inverse Hall–Petch behavior for grain size down to 20 nm. The grain size limitation of the Hall–Petch relation has been justified by the hypothesis that when the grain size becomes

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Table 1 Chemical 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

o 0.002

0.012

o 0.001

sufficiently small, the dominant deformation mechanism in a tensile test changes from transgranular slip to grain boundary sliding [18–20]. The objective of this study is to derive the influence of cooling rate on the microstructure and tensile properties of 0.17 wt% carbon steel. Attempt is made to correlate strength and ductility values and strain hardening response during tensile deformation to ferrite grain size and pearlite degeneration. It has also been tried to find out the conformity of the observed strength parameters 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 hot rolled bars of 20 mm  20 mm cross-section. The hot rolled bars were homogenized at 1100 1C for 1 h and then subjected to control slow (furnace) cooling to produce an initial microstructure with large ferrite grain size. With an aim to reduce ferrite grain size, the homogenized bar was austenitized at 950 1C for 0.5 h and subsequently cooled in furnace in a controlled manner. In another attempt, the homogenized bar was held at 950 1C for 0.5 h and then quickly transferred in an oven equilibrated at 300 1C in order to cool it at a rate somewhat faster than controlled furnace cooling. Further to reduce grain size, a fourth set of samples was austenitized at 950 1C for 0.5 h and subsequently cooled in still air at room temperature (  25 1C). Finally, a fifth set of samples was subjected to heating at 950 1C for 0.33 h and subsequent force-air cooling with the help of a blower. The same cycle of heating and force-air cooling is repeated for five times to achieve reasonable refinement of the microstructure, particularly with reference to ferrite grain size. Accordingly, the steels with five different grain sizes developed were designated as Anneal 1100, Anneal 950, Anneal 950/300, Normalize, and Cyclic 950, respectively. At the time of heat treatment, suitable packing around samples was used to avoid de-carburization from the surface. Microstructural features of the differently heat-treated samples were examined under optical (Reichert, Austria) and scanning electron microscopes (S-3000N, Hitachi, Japan). Energy Dispersive Spectroscopy (EDS) was also carried on precipitate particles to examine their composition. The grain sizes were measured following the ASTM method by counting at least 500 grains in each case. The results were reported in ASTM grain size number and average grain diameter. The volume fractions of ferrite and pearlite in all heat treated steels were measured with the help of a microscope fitted with an automatic point counter by counting at least 600 counts on each sample. Tensile tests were carried out in duplicate for each heat treatment and an average of readings was recorded. The tests were performed on strips of standard dimensions having gauge length of 30 mm with the help of an Instron testing machine (Model 8516) using a cross-head speed of 1 mm/min and full scale load of 100 kN. Values of ultimate tensile strength (UTS), yield strength (YS), strain at maximum load (eu) and strain at fracture (ef) were estimated from the load–elongation plots for different grain sizes. True stress versus true plastic strain s–εp diagrams were obtained for different grain sizes. The values of strain hardening exponent ‘n’ were obtained by plotting ln s versus

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

Average grain diameter, mm

ASTM number

Anneal 1100 Anneal 950 Anneal 950/300 Normalize Cycle 950

39.81 32.37 18.71 13.93 9.09

7 7 9 10 11

(40) (32) (19) (14) (9)

(6.70) (7.29) (8.87) (9.73) (10.98)

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

3. Results and discussion 3.1. Grain refinement The variation of ferrite grain size with different heat treatments have been noted in terms of measuring average grain diameter and the corresponding ASTM number as presented in Table 2. In homogeneous anneal condition (Anneal 1100), the ferrite grain size is quite large (40 mm) due to prolong holding at a higher temperature of 1100 1C and subsequent controlled furnace cooling. On execution of Anneal 950 treatment, the average grain size reduces nominally to 32 mm. However, the treatment Anneal 950/ 300 reduces grain size drastically to 19 mm because the cooling rate used here appears somewhat faster than furnace cooling. Though air cooling after austenitization is an effective means of ferrite grain refinement, Normalize treatment in the present study reduces grain size only up to 14 mm. In contrast, on application of Cyclic 950 treatment, significant refinement of microstructure is achieved reducing the average grain diameter to a minimum of 9 mm. For Normalize treatment, the initially homogenized steel containing coarse proeutectoid ferrite and pearlite located at grain boundary triple point corners, are held at 950 °C. At this temperature, both the proeutectoid and eutectoid (pearlitic) ferrite changes rapidly to austenite in a diffusionless massive polymorphic transformation [22]. Pearlite–ferrite interfaces are considered to act as potential sites for austenitization [23]. In pearlite regions also, austenite nucleates at ferrite–cementite interfaces and grows by dissolution of cementite in a diffusioncontrolled slow process [22,24], and it leads to incomplete dissolution of cementite in austenite due to inadequate holding period of 0.5 h at 950 1C. Beside this, the niobium carbide (NbC) particles, if there be any with the initially homogenized microstructure, cannot dissolve in the austenite formed at 950 1C. The presence of any undissolved cementite or NbC ceases the austenite growth. On air cooling, the inadequately grown austenite transforms to finer ferrite, thus resulting in an average grain size of 14 mm. In case of Cyclic 950 treatment also, small austenite grains occur at 950 1C because of reasons described above and transform to finer ferrite following force-air cooling. Repeated heating and force-air cooling of sample for five times ultimately causes significant refinement of the ferrite grains, thus producing an average grain diameter of 9 mm. The use of niobium as

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255

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.

microalloying element and/or faster rate of cooing, in fact, lowers the austenite to ferrite transformation temperature and so provides less chance of thermally activated growth of the ferrite grains. 3.2. Microstructure Representative optical micrographs of the steels possessing different grain sizes are presented in Fig. 1(a)–(e). The primary micro-constituents after controlled furnace cooling from 1100 1C and 950 1C are polygonal ferrite with well defined pearlite areas. The Anneal 950 sample produces quite a good number of small ferrite grains along with coarse-grained ferrite (Fig. 1(b)), while the Anneal 1100 sample produces mainly coarse-grained ferrite (Fig. 1(a)). The Anneal 950/300 sample, though subjected to an intermediate cooling rate, exhibited almost similar pattern of polygonal ferrite and pearlite but with reasonable refinement of both (Fig. 1(c)). With the increase in cooling rate in case of Normalize treatment, there is a tendency towards formation of finer ferrite grains with pearlite mostly appearing as thin grain boundary envelops (Fig. 1(d)). On the other hand, Cyclic 950 treatment causes further refinement of ferrite grains involving strain and widely dispersed pearlite, thus developing an acicular pattern of the resulting microstructure (Fig. 1(e)) in place of conventional ferrite–pearlite microstructure. Beside the sequential

changes in ferrite grain size and pearlite morphologies, the microstructures presented in Fig. 1(a)–(e) contain precipitate particles appearing as fine dots on the ferrite matrix. Previous investigators [12,13] have already identified these precipitate particles as MC type vanadium carbides in vanadium microalloyed steels and niobium carbides in niobium microalloyed steels. However, to understand the nature and distribution of the precipitates in the present study, selected specimens are examined in a Scanning Electron Microscope equipped with Energy Dispersive Spectroscopy. Representative scanning electron micrographs (SEMs) showing the overall pattern of ferrite and pearlite of the differently heat treated steels are given in Fig. 2(a)–(e). As depicted in Fig. 2(a) and (b), large polygonal ferrite contains limited number of coarse precipitates formed during slow (controlled furnace) cooling from the austenitization temperatures. In comparison, Fig. 2(c) and (d) shows small polygonal ferrite with increased precipitation caused by the state of non-equilibrium maintained with the intermediate as well as fast rate of cooling during Anneal 950/ 300 and Normalize treatment, respectively. Nearly similar situation arises with Cyclic 950 treatment, when a mixed microstructure of polygonal and acicular ferrite appears along with extensive precipitation of carbides on the ferrite matrix (Fig. 2(e)). These different ferrite morphologies formed are known to follow mechanism involving diffusion or shear [15,25]. Further, to

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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.

Weight % pt1 pt2 pt3 pt4 pt5

C-K 2.23 0.47 1.12 0.00 0.00

N-K O-K 6.11 27.01 0.64 2.55 0.00 0.00

Al-K 0.06 0.03 0.00 0.00 0.32

Si-K 0.08 0.04 0.14 0.35 0.54

S-K V-K 0.11 0.00 0.06 4.80 0.00 0.00

Cr-K 0.17 0.00 0.00 0.00 0.25

Mn-K 0.51 1.53 5.23 6.21 0.47

Fe-K 63.32 96.80 90.01 88.44 97.82

Ni-K 0.34 0.00 0.20 0.09 0.60

Cu-K 0.06 0.47 0.70 0.00 0.00

Nb-L 0.00 0.03 0.00 0.10 0.00

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

identify the precipitate particles EDS analyses are carried out on some 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 and carbon along with some vanadium in particles formed by Anneal 950 treatment and also a combination of iron, manganese and sulfur in particles formed by Cyclic 950 treatment. However, the fine precipitates possibly of niobium or vanadium carbides and occurring in grain refined structures could not be detected presumably because these are too small to be resolved in SEM.

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

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

257

Weight % pt1 pt2 pt3 pt4 pt5 pt6 pt7 pt8

C-K 0.00 0.00 1.88 1.34 0.00 0.00 3.39 1.33

N-K 0.00 0.00 2.83 3.02 0.00 0.00 4.87 3.61

O-K

0.00 3.23 0.00

Al-K 0.40 0.12 0.69 0.19 0.00 0.21 0.30 0.47

Si-K 0.04 0.00 0.19 0.09 2.21 0.24 0.52 0.00

S-K V-K 29.39 0.50 32.23 0.30 0.00 0.69 18.93 0.00 24.86 0.00 0.00 0.10

Cr-K 0.06 0.00 0.02 0.00 0.00 0.00 0.25 0.00

Mn-K 55.35 62.53 0.00 0.40 40.46 47.66 0.90 80.97

Fe-K 11.28 3.67 93.44 93.63 33.52 25.54 89.00 13.09

Ni-K 0.90 0.41 0.39 0.03 0.67 0.55 0.00 0.43

Cu-K 2.09 0.74 0.27 0.59 0.97 0.94 0.77 0.00

Nb-L 0.00 0.00 0.29 0.00 0.00 0.00 0.00 0.00

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

Degenerated pearlite Divorced cementite Pearlite Degeneration Degenerated pearlite

Degenerated pearlite

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.

of small and thin cementite segments as illustrated in Fig. 5 (c) clearly match with the pattern of degenerated pearlite described in a similar study by Mishra et al. [12]. It is suggested that degeneration is initiated by nucleation of cementite at ferrite– austenite interfaces following partitioning process. Insufficient diffusion of carbon has been made responsible in developing discontinuous pattern instead of continuous pattern of lamellar cementite. As a result, the interfacial area between ferrite and cementite in a degenerated pearlite happens to be more than that in conventional pearlite [12,13,26]. Fast rate of cooling as experienced in Normalize as well as Cyclic 950 treatment also results in typical interface precipitation of carbide between the degenerated pearlite and the matrix ferrite. Fig. 6(a)–(d) clearly exhibits this feature as a thick white layer of continuous carbide. Apart from interface precipitation, grain boundary cementite network and cementite cluster within pearlite region are also evident in the micrographs given in Fig. 6. EDS analyses in Fig. 4 (points 3 and 4) clearly indicate that both the interface carbide and grain boundary carbide are mainly of Fe3C type and almost free from vanadium or niobium. These grain boundary as well as interface carbides have been identified earlier in low carbon (  0.16 wt%) steel as divorce-eutectoid transformation products occurring due to fast cooling of an austenite pool below A1 temperature [27]. In normal eutectoid transformation,

the single phase austenite decomposes into a mixture of lamellar ferrite and cementite following cooperative growth mode. Whereas, the divorce-eutectoid transformation occurs when the initial austenite containing pre-existing nuclei of undissolved carbides [28] undergoes transformation below A1 producing a mixture of ferrite and spheroidal carbide due to their noncooperative growth [29–31]. Beside these, before execution of Normalize and Cyclic 950 treatment, in homogeneous anneal state the initial microstructure consists of proeutectoid ferrite and coarse pearlite. The cementite lamellae in pearlite contain lamellar faults of sharp curvature. During holding at 950 1C, austenite forms at the cost of proeutectoid as well as eutectoid (pearlitic) ferrite and thereafter grows by dissolution of cementite preferably from the lamellar fault regions [32–34]. Diffusion of the dissolved carbon along the austenite grain boundaries results in carbon enrichment (beyond 0.8%) at the grain boundaries locally. On air cooling in case of normalize treatment or force air cooling in case of cyclic 950 treatment, the carbon enriched austenite transforms producing network of proeutectoid cementite at the ferrite–ferrite grain boundaries (Fig. 6(a) and (b)) or ferrite/austenite (pearlite) interfaces (Fig. 6(a) and (d)). While the remaining austenite with undissolved cementite experiences divorce eutectoid transformation [27] producing cluster of cementite enclosed by ferrite matrix. Incidentally, a degenerated pearlite region in Fig. 6(c) clearly

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Grain boundary carbide

Cluster of cementite Divorced cementite

Cluster of cementite

Divorced cementite

Epitaxial ferrite

Fig. 6. SEM secondary electron images of steel specimens subjected to (a) and (b) Normalize treatment; (c) and (d) Cyclic 950 treatment. Table 3 Grain 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 Anneal 950 Anneal 950/300 Normalize Cyclic 950

40 32 19 14 9

274 74 301 75 349 715 387 716 410 75.6

480 72 496 70.25 563 725 588 723 643 71.1

0.2317 0.02 0.254 7 0.013 0.2767 0 0.2217 0.002 0.225 7 0.01

0.341 7 0.003 0.363 7 0.017 0.395 7 0.015 0.344 7 0.022 0.3507 0.015

0.0117 2E  4 0.0147 15E  4 0.0167 2E  4 0.0177 1E  4 0.0127 3E  4

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

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

Anneal 1100 40 Anneal 950 32 Anneal 950/300 19 Normalize 14 Cyclic 950 9

82 85 83 77 70

18 15 17 23 30

shows a long ferrite formed epitaxially at the peripheral edge of the initial austenite along with clustering of cementite within the pearlite region following divorce eutectoid transformation. Divorce eutectoid transformation has been favored by accelerated cooling introducing defects in the initial austenite before reaching A1 temperature. Defects may be dislocations, slip steps or inhomogeneity in composition (particularly carbon) within an austenite grain. These defects provide high energy sites for preferred nucleation of cementite clusters. Particularly evident from Fig. 6 (c), the three well pronounced cementite clusters appearing in sequence clearly insinuate the presence of dislocation or progressive slip steps when the region was initially austenitic.

3.3. Tensile properties Tensile test results have been reported in Table 3 which clearly indicates increase in the yield strength (YS) as well as ultimate tensile strength (UTS) with the progress in ferrite grain refinement. The higher strength values of the steels with smaller grains may be attributed to the enhanced grain boundary areas and the increased volume fraction of pearlite regions as given in Table 4. It is likely that the reported degeneration of pearlite in case of Normalize and Cyclic 950 samples also attributes to the improvement in tensile strength. It is, therefore, evident that the microstructure rather than composition is a major factor which ultimately controls the tensile properties of the heat treated steels. For example, the tensile properties of annealed and normalized steels are controlled by the flow and fracture characteristics of the ferrite and also by the amount, shape, and distribution of the cementite [35]. However, a normalized steel in the present study usually assumes higher strength than the annealed steel (Anneal 1100 and Anneal 950) because the more rapid rate of cooling used in Normalize treatment produces finer ferrite and causes the transformation of austenite to pearlite at lower temperature producing finer inter-lamellar spacing and simultaneous degeneration of the pearlite regions leading to disintegration of lamellar cementite. Beside this, the strained acicular ferrite and the associated dislocation density of a Cyclic

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

(True Yield Stress)

800

(True Ultimate Stress)

750

Total Elongation Uniform Elongation

0.5

650 0.4

600 550

0.3

500 450

0.2

Curve 2: Conforms to the Conventional Hall-Petch

400 350

0.1

Curve 1: Deviates from Hall-Petch

300

Elongation

True Stress (MPa)

700

0.6

0.0 5

10

15

20

25

30

35

40

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

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 data reported by Stein et al. [37] for iron single crystals. The equation so obtained is

s ðMPaÞ ¼ 100 þ760:62½dðμmÞ  0:3862

3.4. Tensile properties versus grain size True stress and ductility parameters with respect to varying grain sizes are presented in a single plot shown in Fig. 7. The true stress versus grain size plots for both true stress at necking (sU) and true stress at yield point (sYS) show a gradual decrease of true stress values with increasing grain size. These two parameters viz. sYS and sU signify the onset and localization of plastic flow in a material, respectively, and so their magnitude depends largely on the material0 s inherent resistance to plastic deformation. Finegrained microstructures in Normalize and Cyclic 950 samples have greater grain boundary area compared to coarse grain microstructures available with Anneal 1100 and Anneal 950 samples, thus leading to greater pile-up of dislocations at the grain boundaries during deformation and, in turn, raising the true stress. Secondly, the volume fraction of pearlite (including lamellar and degenerated) is more in fine grained microstructure (Table 4), which may further provide impedance to dislocation motion. Beside this, the smaller inter-lamellar spacing in pearlite coupled with profound degeneration of cementite lamellae in grain refined Normalize structure plays an additional role towards enhancing the true stress. Similarly, the mixed microstructure containing polygonal as well as strained acicular ferrite with intense cementite clustering in a Cyclic 950 sample also lead to hindrance to grain rotation and reorientation during tensile test and subsequent rise in true stress values. In Fig. 7, it is tried to fit sYS parameter with the welln established Hall–Patch equation: s ¼ si þKd having usual notations and n being an exponent with a value of  0.5 in the ideal Hall–Petch model. While fitting, s and d values are taken as inputs and si , K and n are made the fitting parameters keeping the value of n as close as possible to  0.5 to bear conformity to the conventional form of the Hall–Petch equation. The goodness of fit 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

ð1Þ

2

with adjusted R ¼ 0.97697. 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 at yielding (Curve 1 in Fig. 7) does not appear in exact conformity to the conventional Hall–Petch relation. However, if the true yield stress of Anneal 1100, Anneal 950, Anneal 950/300 and Normalize samples are fitted, then the equation becomes

sðMPaÞ ¼ 100 þ 1061:92½dðμmÞ  0:47982 2

950 sample cause hardening by pile-up during tensile deformation. In both Normalize and Cyclic 950 sample, clustering of cementite occurring within the pearlite regions is likely to provide further enhancement in tensile strength. Thus, whatever be the source of higher strength, the present study ultimately suggests a treatment involving repeated (cyclic) heating and force air cooling around austenitizing temperature in order to produce a reasonably good combination of strength (UTS¼643 MPa) and uniform elongation (eu ¼0.255) in a low carbon steel containing traces of micro-alloying elements.

259

ð2Þ

with adjusted R ¼ 0.96525. The value of n now indicates that the Eq. (2) or the resulting curve (Curve 2) in Fig. 7 conform to the conventional Hall–Petch relation. On extrapolation of Curve 2 towards smaller grain size, the true yield stress of the Cyclic 950 sample arrives at  470 MPa instead of observed value of  420 MPa. Such discrepancy may be attributed to the strained acicular ferrite and the associated preponderance of defects in the form of high dislocation density in Cyclic 950 sample. In general, the yield stress can be expressed by the relation [38]: s0 ¼ ss þ si, where ss is the stress to operate the dislocation sources and si is the friction stress representing the combining effect of all obstacles to the motion of dislocations. High prior dislocation density of the Cyclic 950 sample eventually reduces the si, thus resulting in a yield stress lower than that predicted by the conventional Hall–Petch model. The present study thus suggests that Hall–Petch is satisfied primarily when there is no influence of metallurgical parameters except grain size on the yield strength of a material. The Lüders elongation values cited in Table 3 also show a trend similar to the yield stress except for the Cyclic 950 sample which shows a sudden drop in Lüders elongation. It was previously demonstrated in the work of Tsuchida et al. [39] that Lüders elongation increases with decreasing grain size. It is well established that Lüders elongation is an inhomogeneous deformation appearing in the form of bands and occurring at stress raisers at the onset of plastic flow [38]. With decreasing ferrite grain sizes, the ease with which the ferrite grains can reorient themselves towards the favorable stress direction increases. This, in turn, facilitates the generation of new dislocations and motion of glissile dislocations needed for Lüders elongation. However, for the Cyclic 950 sample a different situation arises. Firstly, as mentioned before, the reorientation and rotation of ferrite grains is hindered. Moreover, enhanced dislocation pinning further impedes deformation. As a result, the individual Lüders band cannot elongate much. However, due to the availability of considerable prior dislocations in the ferrite matrix, the grains or regions adjacent to a dislocation pile-up readily undergo plastic flow to form a new band of deformation, thus lowering the corresponding yield stress from the predicted Hall–Petch value. The plots of total elongation and uniform elongation versus grain size show almost a similar trend (Fig. 7). They show gradual increase with decreasing grain size in the beginning, reach a maximum and then drop and finally level off with further decrease in grain size. This particular behavior of straining during uniaxial tensile loading of the heat treated steels may be matched with the basic nature of plastic deformation in metals and alloys involving the motion of dislocations and subsequent slip. Also, in polycrystalline materials not all grains are favorably oriented for slip with respect to the tensile axis during deformation, owing to which

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800

4000

700

3500

600

3000

39.81µm 32.37µm 18.71µm 13.93µm 9.09µm

2500

(MPa)

500

400

2000 1500

300

Symbol

200

Adj. R2 Grain Size 0.99949 39.81 0.99933 32.37 0.99867 18.71 0.9989 13.93 0.99808 9.09

K (MPa) 1012.6540 984.29101 1156.8097 1155.7281 1266.4180

St. Error 7.0571 7.54662 13.79827 11.50933 15.46327

n 0.32788 0.30918 0.31752 0.28706 0.29999

St. Error 0.0034 0.0039 0.00504 0.00409 0.00564

1000 500

100 0.05

0.10

0.15

0.20

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

0.05

0.10

0.15

0.20

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

3.5. Flow curves and strain hardening exponent Fitting Model: Derived from Holloman Equation Fitting Equation: ln( σ) = lnK+ n. ln(εp)

6.8

6.4

6.0

Symbol

5.6

Adj. R2 Grain Size 0.99936 39.81 0.99904 32.37 0.99843 18.71 0.99877 13.93 0.99824 9.09

K (MPa) 1012.735 984.2992 1156.195 1155.351 1273.660

St. Error 7.03851 7.56926 14.04777 11.57662 15.28392

n 0.32792 0.30917 0.31765 0.28708 0.30261

St. Error 0.00339 0.00391 0.00513 0.00412 0.00519

5.2 -1.5

-2.0

-2.5

-3.0

-3.5

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

grain reorientation and rotation take place during tensile straining. Large size grains in case of Anneal 1100 and Anneal 950 steels have less grain boundary area causing less pinning of mobile dislocations, thus favoring plastic deformation with less resistance. Yet due to their size (40 mm and 32 mm, respectively) they are difficult to reorient and rotate during tensile straining; thus the ductility parameters become comparatively less, producing uniform elongation between 0.23 and 0.25. However, the ductility improves reaching a maximum uniform elongation of 0.276 as the grain size drops drastically from 32 mm to 19 mm. While, with further decrease in grain size up to 14 mm using Normalize treatment, the ductility parameters fall (Table 3) owing to increase in grain boundary area, which causes more pinning of mobile dislocations. Finally the ductility parameters stabilize with decreasing grain size up to 9 mm in case of Cyclic 950 sample for reasons described below. The mixed pattern of fine polygonal and acicular ferrite and large scale disintegration of the pearlite regions developed by the Cyclic 950 treatment cause hindrance to grain rotation and reorientation during tensile deformation, thus the possibility of enhancing ductility in spite of ferrite grain refinement is largely opposed. In addition to this, the extensive precipitation of carbides, as illustrated in SEM images in Fig. 6(a)–(d) and being more effective in dislocation pinning, is also likely to degrade the ductility in Cyclic 950 sample.

Figs. 8 and 9 show the plots for true stress versus true plastic strain and natural logarithm of true stress versus natural logarithm of true plastic strain, respectively, for different grain sizes. Both the plots are fitted with Holloman relation [38] and its corollary, namely, s ¼ K εnp ; and lnðsÞ ¼ lnðKÞ þ n lnðεp Þ. In the said fitting, the true stress s and true plastic strain εp are taken as inputs and the strength coefficient K and strain hardening exponent n are made the fitting parameters. Goodness of fit is expressed by the adjusted R2 value. It is evident from the data tables presented in the two plots (Figs. 8 and 9) that K and n values are very much in conformity. The strength coefficient K varies with grain size as expected showing large value for fine grained structure, and decreases with increasing grain size. The n values, on the other hand, decrease from 0.32792 to 0.28708 with decreasing 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 grain refinement signifies a situation tending towards plasticity. Such an observation based on n values bears conformity to the pattern of variation of the ductility parameters in Fig. 7. The plasticity in a polycrystalline material usually attributes to the dislocation mobility and ability of the grains to reorient and rotate in response to applied tensile stress. With decreasing grain size the grain boundary area increases, thus increasing the chances of dislocation pinning at the grain boundaries; and, in turn, decreasing plasticity. On the other hand, grain reorientation and rotation is easier with finer grains, thus increasing plasticity. Other factors, namely, the size and distribution of the second phase and hardness of the phases appearing in a grain refined structure may also be considered to play roles in determining plasticity of steels. Small and dispersed pearlite areas in grain refined steels are known to reduce the plasticity. However, to understand the role of individual phase hardness, micro-hardness values are measured randomly on ferrite grains and pearlite areas in heat-treated steels. Micro-hardness survey on some 100 numbers of ferrite grains in each sample shows an increase in ferrite hardness from HV 140– 210 range in Anneal 1100 and Anneal 950 steels to HV 200–260 range in Normalize and Cyclic 950 steels, possibly due to increased precipitation of carbide as well as straining of acicular ferrite. Similarly, the pearlite hardness increases from HV 240–340 range in Anneal 1100 and Anneal 950 steels to HV 270–450 range in Normalize and Cyclic 950 steels as a result of pearlite degeneration

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261

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.

and cementite clustering. The cumulative effect of such increase in micro-hardness values has been clearly reflected by the degradation of plasticity in grain refine structures. Therefore to conclude, there are two sets of opposing factors influencing plasticity; and since this analysis shows that plasticity effectively increases with decreasing grain size, it would be wise to conclude that the factors increasing plasticity are more influential than the factors decreasing the same. Further, the sudden increase in n value in the sample with lowest grain size (9 mm) may be correlated with the mixed microstructure of polygonal and strained acicular ferrite, degeneration of pearlite along with clustering of cementite along grain boundaries and the large population of carbides precipitated on finer ferrite, which cause hindrance to dislocation motion and grain reorientation and a subsequent decrease in plasticity of the Cyclic 950 sample. 3.6. Rate of strain hardening versus true plastic strain Plots of ds/dεp versus εp for different grain sizes, shown in Fig. 10, indicate gradual fall in the strain hardening rate with increasing true plastic strain for the coarse grained steels with grain 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 in strain hardening rate till 0.10–0.15 true plastic strain, among which the steel with minimum grain size (9 mm) has the steepest fall. It is already pointed out that the coarse ferrite grains in Anneal 1100 and Anneal 950 samples face difficulty in rotation and reorientation during tensile deformation. As a result, the hardening that occurs due to straining fails to relax during continued deformation leading to a gradual decrease in the strain hardening rate. On the other hand, fine polygonal and acicular ferrite grains obtained at faster cooling rate in Normalize and Cyclic 950 samples harden initially at a higher strain hardening rate due to high dislocation pile up at grain boundaries, but subsequently tend to soften from strain hardened condition by easy rotation and reorientation with respect to the tensile axis and that makes an initial steep fall of the strain hardening rate up to 0.10–0.15 true plastic strain. Otherwise, the strain hardening rates for fine-grained samples are higher than those obtained at larger grains for the entire range of true plastic strain. As stated earlier, the fine-grained microstructures offer more hindrance to dislocation motion due to greater grain boundary area. Beside this, finely dispersed carbides in the ferrite phase, greater volume fraction of pearlite coupled with disintegration of cementite lamellae and presence of strained acicular

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3.7. Tensile fracture To study the influence of grain size on the mode of tensile fracture, SEM fractographs from all heat treated steels are obtained for examination. As illustrated in Fig. 11(a) and (b), fracture has occurred by both ductile tearing as well as transgranular cleavage due to some heterogeneity left in the matrix microstructure even after Anneal 1100 and Anneal 950 treatments. Both the figures show large cavities generated by void coalescence which is a common mode of tensile fracture in low carbon steels containing a large volume of ferrite. However, the mixed intergranular and transgranular cleavage is rather absent in steels subjected to Anneal 950/300 treatment, and the corresponding fractrograph (Fig. 11(c)) contains a large number of dimples of small size. The reduced dimple size and corresponding increase in number can be correlated with the increased number of smaller ferrite grains (19 mm) in the sample. Following the same reason, the Normalize sample produces a similar fractograph (Fig. 11(d)) containing large number of micro-dimples or voids. At certain locations the microvoids have coalesced forming typical void-sheets (marked by arrow). This indicates the failure initiation at sites of a cluster of fine ferrite grains possibly with grain boundary cementite network. On the other hand, Cyclic 950 steel being more refined with respect to ferrite and pearlite regions, the fracture mode assumes a prominent intergranular pattern. There are also locations indicating transition from intergranular to transgranular fracture (Fig. 11 (e)) possibly at regions containing cementite clusters which have taken place largely in Cyclic 950 steel as a mark of divorced eutectoid transformation.

relation: s ¼ si þ Kd , n being an exponent having value of  0.5 in the ideal Hall–Petch model, a deviation in the n value from  0.5 to 0.4 is observed. This deviation can be attributed to the Cyclic 950 sample where defects in the form of high dislocation density was introduced due to repeated heating and cooling around the austenitisation temperature. While fitting the observed true stress and true plastic strain based on the Holloman relation, s ¼Kεnp , the strength coefficient ‘K’ assumes large value for grain refined structure and it decreases with increasing grain size. On the other hand, the strain hardening exponent ‘n’ decreases with decreasing grain size, except for the minimum grain size of 9 mm, where the mixed microstructure containing polygonal and acicular ferrite and excess degeneration and clustering of cementite within pearlite causes a sudden rise in ‘n’ value. The strain hardening rates over the entire range of true plastic strain values increases with decreasing grain size. However, the ds/dεp values for grain refined steels fall drastically at initial strain values; while the Anneal 1100 and Anneal 950 steels show a less drastic fall in ds/dεp values during initial straining. In coarse-grained microstructures, the tensile fracture shows mixed intergranular and transgranular cleavage. While the grain-refined microstructures show typical dominance of inter-crystalline mode of tensile fracture. n

ferrites also contribute to enhanced strain hardening in finegrained microstructures prepared under non-equilibrium conditions.







Acknowledgment The authors would like to thank the Director, National Institute of Technology, Durgapur, India for financial support and facilities provided for this research project. References

4. Conclusions

 Anneal 1100 and Anneal 950 treatments develop coarse ferrite







 

grains of 40 mm and 32 mm size and coarse pearlite with partial degeneration of cementite lamellae. Major grain refinement occurs after Anneal 950/300 treatment producing ferrite grain size of 19 mm and increased degeneration of pearlite. No appreciable change in grain size occurs on execution of Normalize treatment. Ferrite grain size reduces to a minimum of 9 mm after Cyclic 950 treatment, producing polygonal as well as acicular ferrite along with grain boundary network of cementite and clustering of cementite in pearlite regions. Increase in yield strength (YS) and ultimate tensile strength (UTS) occurs with refinement of grain size. However the values of uniform elongation and total elongation initially rise with grain refinement up to 19 mm and then drop and subsequently level off with further refinement of grain size up to 9 mm. Anneal 950/300 treatment produces a good combination of strength (UTS ¼563 MPa) and ductility (UE ¼ 0.276) in comparison to Anneal 1100 and Anneal 950 treatments (UTS E490 MPa and UE ¼0.24). Fast cooling during normalize treatment causes further increase in strength but with reduced ductility. The mixed microstructure of polygonal and acicular ferrite obtained by Cyclic 950 treatment results in a reasonably good combination of UTS (643 MPa) and uniform elongation (0.255). The true stress versus grain size plots for both true stress at necking (su) and true stress at yielding (sYS) show a gradual decrease of the true stress with increasing grain size. While fitting the observed sYS and d values based on the Hall–Petch

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