The effect of interstitial carbon on the initiation of plastic deformation of steels

Materials Science and Engineering A 530 (2011) 396–401

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The effect of interstitial carbon on the initiation of plastic deformation of steels Kaoru Sekido a,b , Takahito Ohmura b,∗ , Ling Zhang b , Toru Hara b , Kaneaki Tsuzaki a,b a b

Doctoral Program in Materials Science and Engineering, University of Tsukuba, 1-2-1 Sengen, Tsukuba, Ibaraki, 305-0047, Japan National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki, 305-0047, Japan

a r t i c l e

i n f o

Article history: Received 28 April 2011 Received in revised form 8 August 2011 Accepted 27 September 2011 Available online 4 October 2011 Keywords: Nanoindentation Steel Dislocations Plasticity

a b s t r a c t Pop-in behavior in nanoindentation was studied as a mechanism for the initiation of plastic deformation in two kinds of steels with different interstitial carbon contents; interstitial free (IF) and ultra low carbon (ULC) steels. The critical load Pc at which the pop-in occurs is higher in ULC than in IF, and the Pc decreases with decreasing loading rate, indicating that the pop-in mechanism is based on a thermal activation process. The interstitial carbon is thought to yield higher friction stress against dislocation movement and have an influence on the critical stress for the activation of the dislocation source formed underneath the indenter. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Nanoindentation is widely used as a method for evaluating the mechanical properties of materials. It is particularly useful for investigating the microstructure-related strengthening factors separately, since the mechanical properties can be evaluated from a small volume in traditional bulk solids. The nanoindentation technique has the advantage of being able to evaluate not only the hardness but also to obtain the load–displacement behavior on a loading-unloading process. One of the characteristic events in nanoindentation is the pop-in phenomenon that appears as a sudden increase in the displacement on a load–displacement curve under a load control condition. Pop-in phenomena have been observed in many bulk and thin film materials, such as tungsten [1], silicon–iron [1–3], and nickel [2,3]. Arguments have been made that the pop-in is caused by the initiation of dislocation motion [4,5] and the destruction of surface film [2,3,6]. Minor [7] used in situ nanoindentation in TEM and showed that dislocation nucleation occurs in a defect free area before a large pop-in, and the pop-in phenomenon corresponds to a sudden multiplication of mobile dislocations in Al. Ohmura and Tsuzaki [8] showed that the pop-in behavior represents the initiation of plastic deformation which proceeds from a sudden nucleation of dislocation and multiplication in interstitial free (IF) steel.

∗ Corresponding author. Tel.: +81 29 859 2164; fax: +81 29 859 2101. E-mail addresses: [email protected] (K. Sekido), [email protected] (T. Ohmura), [email protected] (L. Zhang), [email protected] (T. Hara), [email protected] (K. Tsuzaki). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.09.102

We focus on the effect of carbon in steel in this study, since carbon is, needless to say, the most important element for steels. The effect of interstitial carbon on plastic deformation was studied in the early 19th century, and Cottrell and Bilby [9] presented a wellknown phenomenon in bcc metals of a yield drop in a stress–strain curve of the tensile test. This phenomenon is believed to be related to the solid-solution strengthening by interstitial carbon; however, the details of the yield drop and solid-solution strengthening mechanisms are still unclear. Therefore, nanoindentation becomes a useful tool for understanding the carbon effect on the plastic deformation directly, since the other factors such as grain boundary and second phase can be separated by choosing the appropriate size and position in a complex microstructure. Moreover, an analysis for the pop-in behavior of the Fe–C alloy can provide a further understanding of the elementary step of plasticity initiation that may be associated with the particular yielding phenomena in the alloy. In this study, we investigate the effect of interstitial carbon on the dislocation movement through an analysis of the pop-in behavior in an early stage of plastic deformation, and propose a model of plasticity initiation that includes the pop-in behavior.

2. Experimental procedure A ultra low carbon (ULC) steel and a Ti added interstitial-free steel were used in this study. The chemical composition of these steels is shown in Table 1. The samples were heat treated under the condition shown in Table 2 before mechanical testing. Interstitial carbon in IF was collected from the TiC precipitates that were formed during holding at 700 ◦ C after the hot rolling [10].

K. Sekido et al. / Materials Science and Engineering A 530 (2011) 396–401

800 ◦ C, 90 s ↓ Air cooling Thickness Coiling temp. (◦ C) Cooling rate (◦ C/s) Finishing temp. (◦ C)

Sample name

Fig. 1 shows the typical stress–strain curves of the IF and ULC from the tensile tests at room temperature. The yield drop phenomenon, which is known to be caused by the presence of interstitial C in the ferrite matrix [9], appears in ULC; however, it does not occur in IF. Although the nominal carbon contents in both steels are comparable as shown in Table 1, the stress–strain curve for ULC shows that it has a higher content of interstitial carbon in the ferrite matrix than IF. Fig. 2 shows the orientation maps of IF and ULC obtained by EBSD. The grain sizes of IF and ULC are estimated to be around 12 ␮m and 11 ␮m, respectively. These grain sizes are much larger than the size of the indentation-induced plastic zone, which is less than 1 ␮m, and the indentation probe was positioned within a grain. Therefore, the deformation behavior upon indentation is dominated by the grain interior without any contribution from the grain boundary. In this study, we chose grains with a 1 1 1 surface normal for nanoindentation, since a texture of {1 1 1}//rolling plane developed in both steels. Fig. 3(a) shows the STEM image of the IF.

Table 2 Heat treated condition for IF and ULC.

3. Results

1 mm 1

Thickness

The content of C in IF is 0.0158 at% and Ti is 0.0734 at%, and the Ti content is large enough to consume C by forming TiC. The samples for nanoindentation were mechanically polished, and subsequently electropolished in a solution of 8% perchloric acid, 10% butylcellosolve, 60% ethanol, and 22% water at 273 K under a potential of 40 V to remove the damaged layer. Electron backscatter diffraction (EBSD) analysis was carried out to characterize the crystallographic orientation using a Carl-Zeiss LEO1550 Schottky Field Emission SEM, equipped with a TSL orientation-imaging microscope (OIM) system. Nanoindentation experiments were performed using a Hysitron Triboindenter. Grains with surface normal of the 1 1 1 direction were chosen for the indentation tests to minimize the effect from crystallographic orientations. The indentation tests were conducted under a load-controlled condition with a maximum load of 1 mN. A Berkovich indenter was employed, and the tip truncation was calibrated using a reference specimen of fused silica. Analyses for the tip calibration and the calculation of hardness were conducted using the Oliver and Pharr method [11]. Probed sites and indent configurations on the specimen surfaces were observed before and after the indentation measurements with a scanning probe microscope (SPM) with capabilities of a Triboindenter. The dimensions of the tensile test specimens met the requirements of the JIS-5 standard (i.e. 50 mm in gauge length and 1 mm in thickness). The loading axis for the tensile tests was set parallel to the rolling direction. Tensile tests were carried out with an AG-50kNG (Shimadzu Corporation) under an initial strain rate of 2.8 × 10−4 s−1 at room temperature. The microstructures of the steels were characterized by a Scanning Transmission Electron Microscopy (STEM). The foils for STEM observations were mechanically thinned to 100 ␮m, and perforated by a twin-jet electropolisher, and the observation was conducted on a JEOL-2010F operated at 200 kV. The dislocation density was determined by measuring the total length of the dislocations on STEM images under the assumption that the foil thickness is 100 nm. In addition, TEM–EDS analysis was performed on the IF steel for identifying the TiC particles, and the conventional micro-Vickers hardness tests were performed with a load of 1 kgf.

72% 72%

Bal. Bal.

3.55 3.55

Fe

0.0015 0.0016

700 Ambient temp.

N

0.002 0.063

50 50

Ti

0.032 0.034

970 960

Al

0.0031 0.0031

1150 1150

S

0.003 0.002

IF ULC

P

0.1 0.1

Cold rolling reduction

Mn

0.009 0.009

Cold rolling condition

Si

0.0038 0.0034

Hot rolling condition

C

ULC IF

Heating temp. (◦ C)

wt%

Salt-bath annealing condition

Table 1 Chemical compositions of IF and ULC.

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300

1000

250

800

200

Load, P / μN

Engineering stress, σ / MPa

398

150

600

Hertzian Fit

Pc

pop-in

Δh 400

ULC

100

IF

200 50 ULC IF

0

0 0

10

20

30

40

50

0

60

40

80

120

Penetration depth, h / nm

Engineering strain, ε / %

Fig. 4. The typical load–displacement curves for IF and ULC.

Fig. 1. Typical stress–strain curves for IF and ULC steels.

contact theory [12], the load P and penetration depth h below the critical load Pc are given by the following equations: The size of the TiC particle is estimated to be around 200 nm in diameter. Fig. 3(b) shows the SPM image of the IF after nanoindentation with an indent size of around 1 ␮m. A few precipitations are observed in this image and appear to be TiC particles. The indent positions were selected within a TiC free zone. Fig. 4 shows a typical load–displacement curve (P–h curve) obtained by nanoindentation. The pop-in behavior on the loading curve is observed in both IF and ULC. Hereafter, the critical load at which the pop-in occurs is defined as Pc , and the corresponding penetration depth is represented as h. According to the Hertz

P=

4 1/2 3/2 ER h 3 i

1 (1 − vs 2 ) (1 − vi 2 ) = + ∗ E Es Ei

(1) (2)

where Ri is the curvature of the indenter tip, E* is the reduced modulus given by Eq. (2), vs and vi are the Poisson’s ratios of the specimen and the indenter, and Es and Ei are the Young’s moduli of the specimen and the indenter. The broken line in Fig. 4 represents the calculated P–h curve that was obtained by substituting the values of 230 GPa and 230 nm into E* and Ri, respectively, in Eq. (1).

Fig. 2. Orientation maps of (a) IF and (b) ULC steels of obtained by EBSD analysis. The average grain size is 12 ␮m for IF, and 11 ␮m for ULC.

Fig. 3. a STEM image for IF. The size of TiC is around 200 nm. (b) SPM image for IF after nanoindentation.

K. Sekido et al. / Materials Science and Engineering A 530 (2011) 396–401

Excursion depth, Δh / nm

100

IF ULC

80

60

40

20

Ave. IF : 190μN Ave. ULC : 490μN 0 0

200

400

600

800

1000

Pop-in load, Pc / μN Fig. 5. The relationship between h and Pc for IF and ULC.

E* is estimated from the unloading curve in Fig. 4, and Ri is given by measuring a standard sample [13]. The calculated curve shows a good agreement with the data that were obtained experimentally in IF and ULC indicating a purely elastic deformation before the pop-in. In addition, IF and ULC have similar curves before the pop-in event meaning that the Young’s moduli of the two steels are also almost the same. Based on the above calculations, the plastic deformation is presumed to start at the pop-in load of Pc = 112 ␮N for IF, and Pc = 590 ␮N for ULC. The maximum shear stress,  max underneath the indenter is given as follows using the Hertz contact theory [12]:

 E∗ 2/3

max = 0.18

Ri

P 1/3

(3)

By substituting E* = 203 ± 24 GPa for IF and E* = 230 ± 30 GPa for ULC and Ri = 230 nm into Eq. (3), the values of  max immediately before the pop-in event are calculated to be about 10 GPa for IF and 14 GPa for ULC. These values are in the order of the ideal strength of G/10, where the shear modulus of ferrite G is 83 GPa. Fig. 5 shows the relationship between Pc and h in both steels, including the results from more than 30 points of indentation for each specimen. The average Pc value of 490 GPa in ULC is significantly higher than that of 190 GPa in IF. Table 3 summarizes the results of the mechanical tests for ULC and IF and includes the values for the tensile yield (or 0.2% proof) stress ( y ), micro-Vickers hardness (Hv ), nano-hardness (Hn ), and

399

Pc from nanoindentation. The standard deviations are also shown in Table 3. The standard deviation of Pc is significantly higher than that of the other data, suggesting that the scattering of data is a characteristic of Pc upon nanoindentation. Fig. 5 shows that ULC exhibits a larger dispersion than IF; however, the standard deviations of Pc for ULC and IF are the same which implies that there is no difference in the degree of distribution in Pc for ULC and IF. Therefore, the data for IF and ULC do not show any significant dependence on the probing position in the samples with the exception of Pc . On the other hand, the Pc reflects the difference in the microstructure at the probed positions, hence the large distributions originate from the inhomogeneous microstructures consisting of dislocations, vacancies, and substitution atoms. Fig. 6 shows the STEM images for IF and ULC. The dislocation densities of IF and ULC are estimated to be approximately 1013 m−2 and 1012 m−2 , respectively. The average spacing of dislocations is calculated to be 0.8–1 ␮m from these values. The depth underneath the indenter at the  max is estimated to be 20–30 nm. The indentation areas are selected at random for dislocations. Accordingly, nanoindentation is unlikely to appear on areas containing dislocations, and the pop-in behavior corresponds to the dislocation nucleation and multiplication underneath the indenter. Cottrell and Bilby [9] reported the effect of carbon on the stress–strain curve with different dislocation density. According to them, the yield drop appears on the stress–strain curve in steel which includes carbon more than 10−6 wt% when the dislocation density is around 1012 m−2 . This result agrees with our stress–strain curve of ULC in Fig. 1, which shows clear yield drop. We have focused on the thermal activation process of the dislocation motion to ascertain the effect of interstitial carbon on the pop-in event. Interstitial carbon is a short-range obstacle, and the passing mechanism of dislocation on the interstitial carbon should be a thermal activation process. Therefore, if the pop-in behavior is affected by interstitial carbon in ULC, the indentation rate could have an effect on Pc . Fig. 7 shows the average Pc with the maximum and minimum Pc as error bars for IF and ULC plotted as a function of loading rate. ULC shows a lower Pc at a low indentation rate (10 ␮N/s); however, IF does not show any difference with indentation rate. 4. Discussion Ahn et al. [14] reported that a pop-in corresponds to a burst of dislocations that are pinned by interstitial carbon in ferrite steel based on the yield drop phenomenon in the tensile tests. However, Figs. 1 and 4 show pop-ins in IF even when yield drops do not appear on the stress–strain curve of a tensile test. These facts suggest that

Fig. 6. STEM images for (a) IF and (b) ULC. The dislocation density is 1013 m−2 for IF, and 1012 m−2 for ULC.

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Table 3 The results of mechanical tests for IF and ULC: tensile yield (or 0.2% proof) stress ( y ), micro-Vickers hardness (Hv ), nano-hardness (Hn ), and Pc from nanoindentation. The standard deviation values are also shown. y

IF ULC

Hn (1 mN)

Pc

Std. (%)

GPa

Std. (%)

GPa

Std. (%)

␮N

Std. (%)

104 ± 16 269 ± 13

16 5

0.708 ± 0.014 0.830 ± 0.017

2 2

1.72 ± 0.12 2.00 ± 0.34

7 17

190 ± 97 490 ± 250

51 51

1000

Pop-in load, Pc / μN

Hv (1 kgf)

MPa

10μN/s

50μN/s

1000μN/s

800

600

ULC 400

IF

200

0 10

100

1000

Indentation rate (μN/s) Fig. 7. Average values of Pc with maximum and minimum data as an error bar while indentation rate is 10, 50, and 1000 ␮N for IF and ULC.

pinning of pre-existing dislocations by interstitial carbon is not the major factor for the pop-in behavior of nanoindentation. Thus, in this study, the mechanism of the yield drop cannot be revealed. But we expect that understanding the effect of carbon on the popin behavior is helpful to investigate the elementary step of increase the yield point in ULC. We discuss the effect of interstitial carbon for the pop-in phenomenon by considering the difference in the pop-in behavior in IF and ULC. In Fig. 7, we found that Pc in ULC is lower at a slower indentation rate, suggesting that the value of Pc depends on a thermal activation process. Since the process for a dislocation to pass through some short-range obstacles such as interstitial carbon is a

thermal activation process, the higher Pc for ULC originates from the higher friction stress on the slip plane that was caused by the interstitial carbon. Hereafter, we propose a model for the effect of interstitial carbon on the pop-in behavior by considering following points. (1) When the indenter contacts the sample surface, the indenter does not provide a maximum shear stress on the sample surface but on the sub-surface of the sample based on the Hertz contact theory [12], suggesting that the dislocation nucleation occurs in the sub-surface region. (2) Minor [7] showed by using in situ nanoindentation in TEM that the dislocation nucleation in a defect free area occurs before a large pop-in, and the pop-in behavior corresponds to a sudden multiplication of mobile dislocations. (3) The crystallographic structures of IF and ULC are bcc with high stacking fault energy, hence the dislocations cannot be extended and allows the cross slip to occur easily. Three load levels of P1 , P2 , and Pc are considered as shown in Fig. 8(a). Three load revels of P1 , P2 , and Pc are assumed as shown in Fig. 8(a). We assume that a shear loop nucleates at a defect free area when the load is P1 , and the first cross slip and a subsequent double cross slip occur at P2 to form a Frank–Read source with the Frank–Read length lc . When the applied shear stress is higher than the critical shear stress  c given as: c =

Gb lc

(4)

The Frank–Read source is activated at Pc . Hereafter, the effect of interstitial carbon will be discussed using this model. The critical loop size is estimated to be around 2 nm from Eqs. (3) and (4). The distance of carbon is estimated to be around 4 nm from the 0.0177 at% C contents when the segregation of carbon is not considered. Since the order of the distance of carbon is comparable with the critical dislocation loop size, we believe that

Fig. 8. A schematic P–h curve, and (b) the model for the relationship between dislocation movement and pop-in.

K. Sekido et al. / Materials Science and Engineering A 530 (2011) 396–401

b 1 / lc∝ Pc1/3

IF ULC t1

Time / s

Frank-Read length, lc / nm

Frank-Read length, lc / nm

a

Pc

Pc

(IF)

(ULC)

Pop-in load, Pc / μN

Fig. 9. (a) The relationship between loading period and Frank–Read length. (b) The relationship between pop-in load and Frank–Read length.

the carbon interacts with the nucleated dislocation loop with high probability. The effect of carbon on edge dislocations is higher than that on screw dislocations since the binding energy between carbon and edge dislocation is higher [15]. Thus, the mobility of the edge component should be lower in ULC than in IF, resulting in different dislocation loop sizes as shown in Fig. 8(b) with thicker and thinner dislocation lines, respectively. Therefore lc in ULC becomes shorter than that in IF, even though the load has been maintained for a certain period of time in both steels. In addition, the relationship between lc and Pc is defined as: 1 1/3 ∝ Pc lc

(5)

From Eqs. (3) and (4). Accordingly, ULC with a shorter lc needs a higher Pc than that of IF for the initiation of plastic deformation. This mechanism is explained through an alternative way with some schematic graphs in Fig. 9. Fig. 9(a) shows the relationship between the loading period t and the corresponding Frank–Read length lc with a direct proportion based on constant dislocation mobility. Fig. 9(b) shows a schematic drawing of the relationship between the lc and Pc as given in Eq. (5). When we assume that a double cross slip occurs and a Frank–Read source is formed at t1 , a shorter Frank–Read length lc for ULC is produced due to the lower mobility of edge dislocations caused by the interstitial carbon. Accordingly, the shorter lc in ULC needs a higher shear stress to activate the Frank–Read source, resulting in a higher Pc in the pop-in phenomenon. 5. Summary The pop-in behavior in IF and ULC obtained by nanoindentation was analyzed to study the effect of interstitial carbon on the initiation of plastic deformation.

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The deformation before the pop-in is purely elastic, and the critical load Pc at which the pop-in occurs corresponds to a shear stress in the order of an ideal strength in both steels. Since the dislocation densities are remarkably low in both steels, the spacing of dislocations is significantly large. Therefore, the indentation is rarely made on the pre-existing dislocation and the pop-in phenomenon is dominated by the dislocation nucleation and multiplication underneath the indenter. The average Pc is higher in ULC than in IF. When the indentation rate is low, the average Pc decreases in only ULC meaning that the interstitial carbon in ULC causes a higher friction stress for the slip deformation, since the process of dislocation passing the interstitial carbon is a thermal activation process. A model is proposed for studying the effect of carbon on the popin behavior and is based on the theory of the Frank–Read source that was formed by a double cross slip. Since interstitial carbon causes a higher friction stress against the edge dislocation motion, the lower mobility of edge dislocation produces a shorter Frank–Read length lc in ULC than in IF. Since Pc 1/3 is directly proportional to 1/lc , ULC needs a higher Pc than that of IF to initiate the plastic deformation. Acknowledgements The steel sheets in this study were supplied by Steel Research Laboratories, Nippon Steel Corporation. This study was supported by JST, CREST. K.S. acknowledges the National Institute for Materials Science for the provision of a NIMS Graduate Research Assistantship. References [1] D.F. Bahr, D.E. Kramer, W.W. Gerberich, Acta Materialia 46 (1998) 3605–3617. [2] W.W. Gerberich, S.K. Venkataraman, H. Huang, S.E. Harvey, D.L. Kohlstedt, Acta Metallurgica et Materialia 43 (1995) 1569–1576. [3] W.W. Gerberich, J.C. Nelson, E.T. Lilleodden, P. Anderson, J.T. Wyrobek, Acta Materialia 44 (1996) 3585–3598. [4] H.J.K.A. Gouldstone, K.Y. Zeng, A.E. Giannakopoulos, S. Suresh, Acta Materials 48 (2000). [5] U.R.P. Murali, Acta Materials 53 (2005). [6] R.J.P.B.J. Kooi, N.J.M. Carvalho, J.Th.M. DeHosson, M.W. Barsoum, Acta Materials 51 (2003). [7] A.M. Minor, Nature Materials 5 (2006). [8] T. Ohmura, K. Tsuzaki, Journal of Materials Science 42 (2007) 1728–1732. [9] A.H. Cottrell, B.A. Bilby, Proceedings of the Physical Society, Section A 62 (1949) 49–62. [10] N. Sugiura, N. Yoshinaga, K. Kawasaki, Y. Yamaguchi, T. Yamada, TetsuTo-Hagane/Journal of the Iron and Steel Institute of Japan 94 (2008) 179–187. [11] W.C. Oliver, G.M. Pharr, Journal of Materials Research 7 (1992) 1564–1580. [12] K.L. Jonson, Contact Mechanics, Cambridge University Press, Cambridge, UK, 1985, pp. 84–106. [13] T. Ohmura, K. Tsuzaki, F. Yin, Materials Transactions 46 (2005) 2026–2029. [14] T.-H. Ahn, C.-S. Oh, D.H. Kim, K.H. Oh, M. Kim, H. Bei, E.P. George, H.N. Han, International Conference on Advanced Steel (2010). [15] E. Clouet, S. Garruchet, H. Nguyen, M. Perez, C.S. Becquart, Acta Materialia 56 (2008) 3450–3460.