The Influence of Mg-Based Inclusions on the Grain Boundary Mobility Of

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Article The Inﬂuence of Mg-Based Inclusions on the Grain Boundary Mobility of Austenite in SS400 Steel

Chih-Ting Lai 1, Hsuan-Hao Lai 1, Yen-Hao Frank Su 2 , Fei-Ya Huang 1, Chi-Kang Lin 1, Jui-Chao Kuo 1,* and Hwa-Teng Lee 3

1 Department of Materials Science and Engineering, National Cheng-Kung University, Tainan 701, Taiwan; [email protected] (C.-T.L.); [email protected] (H.-H.L.); [email protected] (F.-Y.H.); [email protected] (C.-K.L.) 2 China Steel Corporation, Kaohsiung 81233, Taiwan; [email protected] 3 Department of Mechanical Engineering, National Cheng-Kung University, Tainan 701, Taiwan; [email protected] * Correspondence: [email protected]; Tel.: +886-6-2754194

Received: 23 January 2019; Accepted: 20 March 2019; Published: 22 March 2019

Abstract: In this study, the effects of the addition of Mg to the grain growth of austenite and the magnesium-based inclusions to mobility were investigated in SS400 steel at high temperatures. A high-temperature confocal scanning laser microscope (HT-CSLM) was employed to directly observe, in situ, the grain structure of austenite under 25 torr Ar at high temperatures. The grain size distribution of austenite showed the log-normal distribution. The results of the grain growth curves using 3D surface ﬁtting showed that the n and Q values of the growth equation parameters ranged from 0.2 to 0.26 and from 405 kJ/mole to 752 kJ/mole, respectively, when adding 5.6–22 ppm of Mg. Increasing the temperature from 1150 to 1250 ◦C for 20 min and increasing the addition of Mg by 5.6, 11, and 22 ppm resulted in increases in the grain boundary velocity. The effects of solute drag and Zener pinning on grain boundary mobility were also calculated in this study.

Keywords: confocal scanning laser microscope; grain growth; magnesium addition; low-carbon steel; mobility; pinning effect

1. Introduction Both medium and thick steel plates are used in the building of high-rise buildings, bridges, and in ships. A high-heat-input welding technique with heat input of over 50 kJ/cm has been employed for high-efficiency, low-cost fabrication of these steel plates. Increasing the heat input energy during welding enhances the coarsening of the austenite grains in the heat-affected zone (HAZ). However, coarse grains have detrimental effects on the impact toughness of weldments [1]. TiN inclusions were first applied to improve the toughness of HAZs, which serve as potential nucleation sites for acicular ferrite (AF) formation [2–4]. The development of TiN inclusions [5–8] can be expressed as the zero generation of inclusions for AF formation, before the use of oxide inclusions. However, Nb, V, and Ti nitrides will dissolve into austenite because of the high heat input from welding temperatures above 1300 ◦C[9]. Thus, Mizoguchi et al. [10] first proposed oxide inclusions to improve the impact toughness of HAZs under high-heat-input welding. Titanium and magnesium oxides can be called the first and second generations of oxide inclusions for AF formation. In this study, Titanium oxides serve as potent nucleation sites for the formation of intragranular AF [11–19]. Magnesium oxide serves as fine dispersed inclusions in steel [20] because Mg has a strong affinity for oxygen and a reasonable amount of Mg is soluble in steel [5]. Kojima et al. [5] first proposed magnesium oxide metallurgy technology, in which MgO, MgS, and Mg(O,S)

Metals 2019, 9, 370; doi:10.3390/met9030370 www.mdpi.com/journal/metals Metals 2019, 9, 370 2 of 14 inclusions were used to pin grain boundaries. According to previous research, Zener pinning was the influence of the dispersion of spherical particles [21], ellipsoidal particles [22] and cylindrical particles [23] on the movement of grain boundaries. The particles acted to prevent the motion of grain boundaries by exerting a pinning force which counteracted the driving force of the grain boundaries. The pinning efficiency against grain growth for grain coarsening was determined by the particle size [21]. This process refined the HAZ microstructure. Suito et al. [24–27] reported that MgO and soluble Mg can hinder excessive growth of austenite grains. In addition, Zhu et al. found that the addition of 0.005 wt% Mg can effectively inhibit austenite grain growth [28,29] and lead to the formation of AF [30]. The chemical composition of steel, the cooling rate at temperatures ranging from 800 to 500 ◦C, the size of austenite grains, and the inclusion parameters affect the formation of intragranular AF in metal [31]. In this study, we investigated the effect of the addition of Mg on austenite grain growth in SS400 low-carbon steel using a high-temperature confocal scanning laser microscope (HT-CSLM) in order to observe the high temperature microstructure in situ. In addition, the pinning effect of the magnesium-based inclusions on the mobility of austenite was studied.

2. Materials and Experiments SS400 low-carbon steels produced by China Steel Corporation were selected as the experimental materials, for which the chemical composition of the steels is listed in Table1, and Fe-5% Mg alloy wire was used for the addition of Mg during the ladle treatment. The experimental materials obtained from the as-cast slab, 8000 mm long, 1800 mm wide, and 270 mm thick, were cut into specimens 50 mm thick and 200 mm wide. After hot rolling at 1200 ◦C, the thickness was reduced from 50 mm to 10 mm, and 6 mm × 5 mm × 2 mm specimens were prepared.

Table 1. Chemical composition of SS400 steel with Mg of 1.5–22 ppm (Unit: wt%).

Mg C Si Mn P S Al N O 1.5 ppm 0.120 0.17 1.18 0.0071 0.0006 0.028 0.0053 0.0041 5.6 ppm 0.118 0.17 0.74 0.0102 0.0035 0.033 0.0054 0.0082 11.0 ppm 0.136 0.28 0.94 0.0075 0.0012 0.020 0.0043 0.0027 22.0 ppm 0.127 0.28 0.87 0.0104 0.0021 0.018 0.0052 0.0016

The specimens were ground using 1500, 2500, and 4000 SiC paper, polished using 3, 1, and 0.1 µm diamond suspensions, respectively, and finally polished with 0.02 µm SiO2 suspensions. After the final polish, the austenite grain structure was observed in situ at high temperature under 25 torr Ar using an HT-CSLM (VL2000DX-SVF17SP, Yonekura, Japan). First, the specimen was placed into an Al2O3 crucible with a diameter of 8 mm and a height of 3.5 mm. Prior to heating, the chamber was evacuated for 5 min using a diffusion pump backfilled with ultrahigh purity Ar gas (>99.999%), with a discharge rate of 300 mL/min passed through a gas cleaning system to reduce the oxygen content. Then, the specimens were heated to 1000, 1100, 1200, and 1250 ◦C for 3, 5, 10, and 20 min, respectively. Afterward, the specimens were cooled at a cooling rate of 100 ◦C/s. After cooling, images of the grain structure were examined with a Leica DM6000 M optical microscope (Leica, Wetzlar, Germany). Microscope Imaging Software (Grain Expert, Leica, Wetzlar, Germany) was used to calculate the average grain size according to the ASTM E112 international standards. Then, the HT-CSLM was employed to investigate the movement of the austenite grains. We used an ASPEX EXplorer system (ASPEX, LLC, Boulder, CO, USA) combining SEM and EDS to automatically classify different types of inclusions and to determine the inclusion size and number within a large measured area. Metals 2019, 9, 370 3 of 14

3. Results and Discussion

3.1. Parameters of Grain Growth Equation Metals 2019, 9, x FOR PEER REVIEW 3 of 14 To determine the number of grains, we adopted the Leica analysis Grain Expert software to detect Metals 2019, 9, x FOR PEER REVIEW 3 of 14 theimage grains, is shown and Figure in Figure1b shows 1a. Then, an image a representative of the detected value grains of the in austenite.minimal number The original of grains image was imageisobtained. shown is shown in Figures Figure in 12aFigurea.– Then,d show 1a. a aThen, representative histogram a representative of grain value size of value the in terms minimal of the of the numberminimal number ofnumber grainsof grains, of was grainswhile obtained. Figurewas obtained.Figure2e shows2a–d Figures the show effect a2a histogram– dof show the number a of histogram grain of size grains of in grain terms on sizethe of the averagein terms number grainof ofthe grains,size number and while standardof grains, Figure 2deviation.whilee shows Figure the The 2eeffectdistributions shows of the the number effect of grain of of the size grains number and on the the of average averagegrains grainon grain the sizes sizeaverage were and standardgrainsimilar. size However, deviation. and standard increasing The distributionsdeviation. the number The of distributionsgrainof grains size and decreased of the grain average sizethe and grainstandard the sizes average deviation. were similar.grain The sizes However, minimal were similar. increasingnumber However, of the grains number increasing was of set grains at the 300 decreased number for the ofthe grains standard decreased deviation. the Thestandard minimal deviation. number The of grains minimal was number set at 300 of forgrains the subsequentwas set at analysis.300 for the

(a) (b)

Figure 1. (a) Initial (imagea) of austenite obtained using optical microscopy and(b) (b) after the detection FigureFigureprocess 1. 1. (using(aa)) Initial Initial analysis image image software of of austenite austenite after obtained obtainedquenching. using using optical optical microscopy microscopy and and ( (bb)) after after the the detection detection processprocess using using analysis analysis software software after after quenching. quenching.

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Average grain size

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Average grain size ( 010 0.6 200 300 400 Standard deviation Average grain size ( 0 Number of grains 0.6 200 300 400 Number(e )of grains (e) FigureFigure 2. 2. HistogramHistogram of austenite graingrain sizesize inin terms terms of of the the measured measured number number of of grains: grains (a:) ( 200,a) 200, (b) ( 250,b) 250,(c) 300,(Figurec) 300, and 2. (and dHistogram) 400. (d) (400e) isof. the(austenitee) is average the grainaverage grain size sizegrainin terms and size standardof theand measured standard deviation number deviation as a of function grains as a: function of(a) the200, measured (b of) the measurednumber250, ( of cnumber) grains.300, and of ( grains.d) 400. (e) is the average grain size and standard deviation as a function of the measured number of grains. AfterAfter measuring measuring the the number number of of grains, grains, a a single single representative representative value value for for the the grain grain sizes sizes should should After measuring the number of grains, a single representative value for the grain sizes should bebe obtained obtained statistically. statistically. Statistical Statistical values, values, including including the the mean, mean, median, median, and and mode, mode, were were considered. considered. be obtained statistically. Statistical values, including the mean, median, and mode, were considered. FigureFigureFigure 3 illustratesillustrates 3 illustrates the the the histogram histogram histogram and and and cu cumulative cumulativemulative frequency distributions distributions of the of thegrain grain size sizeof austenite of of austenite austenite inin SS400 SS400in SS400 with with with 1.5 1.5 1.5ppm ppm ppm Mg. Mg. Mg. Figure Figure Figure 44 4 shows shows thethe evolution of of of the the austenite austenite grain grain size size sizeusing using the three the three statisticalstatisticalstatistical values. values. values. The The The mean mean mean is is isfoundfound found by by adding adding all all givengiven given data data data and and and dividing dividing dividing by bythe by thenumber the number number of data of of data data entries.entries.entries. The The Themedian median median is thetheis the middlemiddle middle number number number of ofof all allall values, values, while while while the the the mode mode mode isis the theis the numbernumber number that thatoccurs occurs most mostoftenmost often in the often in data the in set. thedata data Thus, set. set. Thus, the Thus, mean the the hasmean mean the hashas highest the highest value, value, while value, thewhile while mode the the mode is themode is lowest. the is lowest.the The lowest. medianThe The is medianbetweenmedian is thebetween is mean between andthe the mean mode mean and (Figure and mode mode4). (Figure Therefore,(Figure 4). Theref in thisore,ore, study, in in this wethis study, adapted study, we we adapted the adapted mode the as modethe the mode averageas as thevalue averagethe to average avoid value calculatingvalue to avoidto avoid thecalculating calculating large grains the the becauselargelarge grains large becausebecause grains large leadlarge grains to grains abnormal lead lead to abnormal grainto abnormal growth. grain grain growth. growth.

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Cumulative Frequency Cumulative Frequency 0.00 0.0 0.00 0.0 0.0 0.0 0 500 1000 0 100 (b200) 300 0 200 400(f) 600 800 (j) Grain size(m) Grain size(m) Grain size(m) Figure 3. Cont. (b) (f) (j)

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0.05 (c) (g) (k) Cumulative Frequency

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Cumulative Frequency Cumulative Frequency 0.00 0.0 0.250.00 0.0 1.0 0.0 0.0 0 500 1000 0 100 200 300 0 200 400 600 800 0.25 1.0 1.0 Grain size(m) Grain size(m) 0.20 Grain size(m) 0.3 0.20

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Cumulative Frequency 0.15 Relative Frequency 0.15 Cumulative Frequency 0.00 0.0 0.00 0.50.0 0 500 0.5 1000 0 100 200 300 0.20.0 0.0 0.5 0.10 0.10 0 200 400 600 800 Grain size(m) Grain size(m) 0.05 0.1 Grain size(m) 0.05

Relative Frequency

Cumulative Frequency

Relative Frequency Cumulative Frequency

Relative Frequency Cumulative Frequency 0.00 0.0 0.00 0.0 0 500 1000 0 100(d) 200 300 0.0 (h) 0.0 (l) 0 200 400 600 800 Grain size(m) Grain size(m) Grain size(m) Figure 3. Histogram and cumulative frequency distributions of grain size of austenite in SS400 steel with 1.5 (ppmd) Mg for (a, e, i) 3 min, (b, f, j) 5 min,(h) (c, g, k) 10 min, and (d, h, l) 20 min.(l) Broken lines represent the curves fitted by the log-normal function: (a–d) at 1150 °C, (e–h) at 1200 °C, and (i–l) at FigureFigure 3. Histogram 3. Histogram and and cumulative cumulative frequency distributions distributions of grain of grain size sizeof austenite of austenite in SS400 in SS400steel steel 1250 °C. withwith 1.5 ppm1.5 ppm Mg Mg for for (a, e(a,,i) e, 3 i min,) 3 min, (b, f(,b,j) 5f, min,j) 5 min, (c,g ,(kc,) g, 10 k min,) 10 min, and and (d,h (,d,l) 20h, l min.) 20 min. Broken Broken lines lines represent represent the curves fitted by the log-normal function: (a–d) at 1150 °C, (e–h) at 1200 °C, and (i–l) at the curves ﬁtted by the log-normal function: (a–d) at 1150 ◦C, (e–h) at 1200 ◦C, and (i–l) at 1250 ◦C. 1250 °C.

300

m)  200

 200

100 mean Grain size ( 100 median mean Grain size ( median mode 0 mode 0 0 500 1000 1500 0 500 1000 1500 Time (sec) Time (sec) FigureFigure 4. 4.Grain Grain size size as as a functiona function of of annealing annealing time time for for SS400 SS400 with with 1.5 1.5 ppm ppm Mg Mg at at 1200 1200◦C °C using using the the Figure 4. Grain size as a function of annealing time for SS400 with 1.5 ppm Mg at 1200 °C using the mean, median, and mode. mean,mean, median, median, and and mode. mode.

Next,Next,Next, the the the graingrain grain growthgrowth equation equation was was was derived derived derived after a afterfterthe averagingthe the averaging averaging method method methodwas determined. was was determined. determined. The The Thenumerousnumerous numerous equations equations equations that thathavehave havebeen been proposed been proposed proposed to predictto predict to the predict grainthe grain growth the graingrowth equation growth equation can equationbe candivided be can divided be dividedintointo three three into types. types. three First, types.First, Beck First, et et al. Beckal. [ 3[23]2 et reported] reported al. [32] a reported power a power law a law powerfor normal for lawnormal grain for normalgraingrowth, growth, grainwhile Sellars growth,while et Sellars while et Sellarsal.al. [3 [33 et–33– al.63]6 ]modified [ 33modified–36] modiﬁed Beck’s equation equation Beck’s equationas as follows: follows: as follows:

m m m m m md − d = k · exp (−Q/RT) · t (1) d  do  k0 expo  Q0 / RT t (1) d  do  k0 exp Q / RT t (1) where d is the ﬁnal grain diameter; d0 is the initial grain diameter; t is the annealing time, and m and k0 are constants. Q is the activation energy for grain growth, and T is the temperature in absolute degrees. where d is the final grain diameter; d0 is the initial grain diameter; t is the annealing time, and m and The simpliﬁed Beck’s model was used0 to predict the initial austenitic grain size as follows [37]: wherek0 are d constants. is the final Q grainis the diameter;activation energyd is the for initial grain graingrowth, diameter; and T is tthe is thetemperature annealing in time, absolute and m and k0 are constants. Q is the activation energy for grain growth, and T is the temperature in absolute m d = k0 · exp (−Q/RT) · t (2)

Metals 2019, 9, x FOR PEER REVIEW 6 of 14

2 2 Metals 2019, 9, 370 d − do = k0 ⋅exp(− Q / RT )⋅t (3) 6 of 14

Moreover, Yoshie et al. [38] and Nishizawa [39] reported a model represented as follows: In this study, we applied the grain growth formulation in Equations (1) and (2) to predict the 2 2 grain growth curves for SS400 withd 1.5− d ppmo = k 0Mg· exp at (1200−Q/ °RTC as) · tan example. The parameters of the(3) fitting growth equations are summarized in Table 2. The fitting curves, using Equation (2), agree with the experimentalIn this study, data we appliedwith an R the-value grain of growth0.96, and formulation the results inare Equations remarkably (1) better and (2)than to those predict using the ◦ grainEquation growth (1) with curves an forR-value SS400 of with 0.69 1.5 [Figure ppm Mg5a,b]. at 1200The valuesC as anof example.Q and k0 using The parameters Equation (2) of theare fittingsimilar growth to those equations of Equation are summarized(1). A comparison in Table of2 .the The experimental fitting curves, data using in Figure Equation 5a, (2),b showed agree with that theEquation experimental (2) was data the withbest anfitting R-value equation. of 0.96, Thus, and theEquation results (2) are was remarkably employed better for than the thosesubsequent using Equationinvestigations. (1) with an R-value of 0.69 [Figure5a,b]. The values of Q and k0 using Equation (2) are similar to those of Equation (1). A comparison of the experimental data in Figure5a,b showed that Equation (2) wasTable the best 2. Parameters fitting equation. of the fitting Thus, equations Equation of (2) Equations was employed (1) and (2) for for the SS400 subsequent with 1.5 ppm investigations. Mg.

d0 Q Table 2. ParametersFitting equation of the ﬁtting equations of Equationsm (1) and (2) for SS400k with0 (μm/s) 1.5 ppm Mg. (μm) (kJ/mole) FittingEquation equation (1) d0 (4.3µm) m2 Q (kJ/mole)232 k0 (7.2µm/s)× 109 EqEquationuation (2) (1) 4.30 2.9 2 232622 7.2103.2×9 1025 Equation (2) 0 2.9 622 3.21025

(a) (b)

Figure 5. Mean value of grain size as a function of time using (a)) EquationEquation (1)(1) withwith anan R-valueR-value of 0.96 and ((b)) EquationEquation (2)(2) withwith anan R-valueR-value ofof 0.690.69 forfor SS400SS400 withwith 1.51.5 ppmppm Mg.Mg.

3.2. Effects of TemperatureTemperature andand Mg-ContentMg-Content onon AusteniteAustenite GrainGrain GrowthGrowth Figure3 3 illustrates illustrates thethe histogramhistogram andand cumulativecumulative frequencyfrequency distributionsdistributions ofof thethe graingrain sizesize ofof ◦ austenite with an Mg Mg content content of of 1.5 1.5–22–22 ppm ppm at at 1150 1150–1250–1250 °C.C. The The average average grain grain size size was was plotted plotted in interms terms of the of the annealing annealing time time and and temperature temperature with with different different Mg Mgcontent content,, as shown as shown in Figure in Figure 6, and6, andthe corresponding the corresponding parameters parameters of the of the fitting ﬁtting curves curves are are listed listed in in Table Table 3.3. The The grain sizesize distributionsdistributions followedfollowed thethe log-normallog-normal distribution,distribution, whichwhich ledled toto anan increase inin the average grain size with increases inin annealingannealing temperature.temperature. The Q and n values are listedlisted inin TableTable3 3..

Table 3. Parameters of the ﬁtting equations for steel with Mg content of 1.5-22.0 ppm using Equation (2). Table 3. Parameters of the fitting equations for steel with Mg content of 1.5-22.0 ppm using Equation (2). Mg (ppm) m Q (kJ/mole) k (µm/s) Mg (ppm) m Q (kJ/mole) 0 k0 (μm/s) 1.5 1.52.9 2.9 622622 3.2 × 103.225 × 1025 19 5.6 4.9 405 2.5 × 10 19 5.6 11.04.9 3.8 493405 2.8 × 102.521 × 10 22.0 6 752 1.7 × 1031 21 11.0 3.8 493 2.8 × 10 31 22.0 6 752 1.7 × 10

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(a) (b)

FigureFigure 6. 6.GrainGrain size size as asa function a function of oftime time for for (a) ( a1.5,) 1.5, (b ()b 5.6,) 5.6, (c) ( c11,) 11, and and (d ()d 22) 22 ppm ppm Mg, Mg, where where symbols symbols indicateindicate experimental experimental data data and and the the fitting ﬁtting function function is isindicated indicated by by broken broken lines. lines.

ExceptExcept for for the the case case of of 1.5ppm 1.5ppm Mg, Mg, the the QQ valuevalue increase increasedd from from 81 81 to to 150 150 kJ/mole kJ/mole and and the the n nvalue value waswas in inthe the range range of 0.2 of– 0.2–0.260.26 as Mg as Mgcontent content increased increased from from5.6 to 5.6 22ppm. to 22ppm. It was Itnoted was that noted the that Q value the Q obtainedvalue obtained from the from references the references in Table in 4 Table ranged4 ranged from 64 from to 64437 to kJ/mole 437 kJ/mole with the with exception the exception of 914 of kJ/mole.914 kJ/mole. Thus, our Thus, Q ourand Qn valuesand n values lie in the lie range in the obtained range obtained from the from references. the references.

TableTable 4. 4.ParametersParameters of of n,n Q, Q, and, and k0k for0 for the the growth growth equations. equations.

Steels Steels m mQ (kJ/mol) Q (kJ/mol) kk00 (μm/s)(µm/s) ReferencesReferences Low C-MnLow C-Mn2 267 67 4.34.3 × 101012 [40] [40] Low C-MnLow C-Mn5.6 5.6126 126 9.9.44 × 101038 [37] [37] 12 C-Mn C-Mn2 264 64 1.41.4 × 101012 [41] [41] C-Mn 1 400 (T>1273) 3.9 × 1032 [36] C-Mn 1 400 (T>1273) 3.9 × 1032 [36] C-Mn 1 914 (T<1273) 5.0 × 1053 [36] 53 C-Mn C-Mn-V1 7914 (T<1273) 400 5.01.5 × 101027 [36] [36] C-Mn-V C-Mn-Ti7 10400 437 1.52.6 × 10102728 [33] [36] C-Mn-Ti C-Mn-Nb10 4.5437 435 2.64.1 × 10102823 [33] [33] 25 C-Mn-Nb High C-Mn4.5 5.3435 366 4.19.1 × 101023 [37] [33] High C-Mn 0.12 1170 4.1 x 1063 [31] High C-Mn 5.3 366 9.1 × 1025 [37] High C-Mn 0.12 1170 4.1 x 1063 [31] We differentiated Equation (2) with respect to time (t) to reveal the grain boundary velocity WedD differentiated Equation (2) with respect to time (t) to reveal the grain boundary velocity ( (V = dt ) as follows: dD n−1 V = ) as follows: V = n ∗ ko ∗ exp (−Q/RT) ∗ [t − to] (4) dt The grain boundary velocity was plotted as a function of annealing time in Figure7. When 1.5 ppm µ µ Mg was added, the grain boundary velocity increased fromn−1 0.025 m/s to 0.1 m/s after 20 min as ◦ the annealing temperatureV = n* increasedko ∗exp( from− Q / 1150RT ) to∗[ 1250t − to ]C.The grain boundary velocity(4) after 20 min increased from 0.005 µm/s to 0.01 µm/s, 0.01 µm/s to 0.02 µm/s, and 0.005 µm/s to 0.07 µm/s when 5.6, 11, and 22 ppm of Mg were added, respectively, as the annealing temperature increased ◦ fromThe 1150 grain to boundary 1250 C. Considering velocity was the plotted annealing as a function time of of 20 annealing min, the grain time boundaryin Figure 7. velocity When 1.5 was ◦ ppmplotted Mg was in terms added, of Mg the contentgrain boundary at 1150–1250 velocityC in increased Figure8. However,from 0.025 the μm/s grain to boundary0.1 μm/s after velocity 20 min was as the annealing temperature increased from 1150 to 1250 °C. The grain boundary velocity after 20

Metals 2019, 9, x FOR PEER REVIEW 8 of 14 min increased from 0.005 μm/s to 0.01 μm/s, 0.01 μm/s to 0.02 μm/s, and 0.005 μm/s to 0.07 μm/s when 5.6, 11, and 22 ppm of Mg were added, respectively, as the annealing temperature increased fromMetals 11502019 ,to9, 3701250 °C. Considering the annealing time of 20 min, the grain boundary velocity was8 of 14 plotted in terms of Mg content at 1150–1250 °C in Figure 8. However, the grain boundary velocity was reduced with increases in the Mg content, and steels with the addition of 5.6 ppm and 22 ppm ofreduced Mg exhibited with increases similar intrends. the Mg This content, phenomenon and steels suggests with the that addition the grain of 5.6 boundary ppm and velocity 22 ppm ofwas Mg significantlyexhibited similar decreased trends. by This increasing phenomenon Mg content suggests at that1250 the °C. grain The boundaryresults in velocityTable 3 wasshow signiﬁcantly that the ◦ increasedecreased in Mg by increasingcontent from Mg 1.5 content to 22 at ppm 1250 increasedC. The results the Q inexponent. Table3 show However, that the the increase Q exponent in Mg decreasedcontent from when 1.5 the to 22Mg ppm content increased was 5.6 the andQ exponent. 11 ppm. In However, general, thetheQ activationexponent energy decreased Q for when grain the growthMg content was affected was 5.6 andby the 11 ppm. amount In general, and type the of activation alloying energyelements.Q for For grain materials growth with was affectedinclusion by pinningthe amount and element and types ofof alloyingsolute drag, elements. grain Forgrowth materials was difficult with inclusion and activation pinning andenergy elements increased of solute. In somedrag, mechanisms, grain growth wasthe Q difﬁcult exponent and activationdecreased energy. The m increased. exponent In depended some mechanisms, on the grain the Q exponentgrowth mechanisms.decreased. The When m exponent the m exponent depended was on 2, the the grain materials growth had mechanisms. no defects Whenor inclusions. the m exponent When the was m 2, exponentthe materials was 3, had several no defects phenomena or inclusions., such as When inclusions the m in exponent the grain was, were 3, severalobserved, phenomena, which indicate suchs as theinclusions occurrence in of the the grain, pinning were effect. observed, When which the m exponent indicates was the occurrence4 the alloy element of the pinning exhibited effect. diffusion When inthe the m grain exponent boundaries was 4 and the produce alloy elementd inclusion, exhibited which diffusion indicate ins the the occurrence grain boundaries of pinning and and produced solute draginclusion, effects which[42]. Thus, indicates the effects the occurrence of the pinning of pinning force and and solute solute drag drag on effects austenite [42]. grain Thus, mobility the effects are of consideredthe pinning in force the subsequent and solute dragsection. on austenite grain mobility are considered in the subsequent section.

(a) (b)

FigureFigureMetals 7.7. The2019The, grain9, grainx FOR boundary boundaryPEER REVIEW velocity velocity (V ()V as) as a function a function of of time time for for Mg Mg at at(a ()a 1.5,) 1.5, (b ()b 5.6,) 5.6, (c ()c 11,) 11, and and (9d ()ofd )14 2222 ppm. ppm.

FigureFigure 8. The 8. The grain grain boundary boundary velocityvelocity (V) (V) in interms terms of annealing of annealing temperature temperature after 20 min after of annealing 20 min of annealingtime. time.

3.3. Zener Pinning Effect of Inclusions on the Austenite Grain Mobility According to the model [36], the driving force of grain growth is expressed by: 2σ F = b (5) P R

where R is the radius of the curvature of grains, and σb is the surface energy of the grain boundary. Moreover, inclusions exert the retarding force (FR) on the grain boundaries proposed by Zener [43] as:

3 f σ (6) F = v b R 2r

where fv is the volume fraction of inclusions, σb is the surface energy of the grain boundary, and r is the radius of the inclusions. Here the surface energy of the grain boundary σb is for austenite, the value of which was obtained from Reference [44]. The retarding forces (also called the Zener pinning force) depend on the radius and volume fraction of inclusions, as listed in Table 5. Here the radius (r) is equal to half of the average diameter, and fA is obtained by dividing the number of inclusions (N) by the measured area (A). Next, the equation fA = 2NfV was employed. It has been reported that the addition of 2 ppm Mg led to a change in oxide formation from the Al2O3 to MgO·Al2O3 phase and a change in inclusion formation from Al2O3–MnS to MgO·Al2O3–MnS [45].

Table 5. The retarding force (FR) of inclusions.

Mg A D fA fV FR  FR Inclusion (ppm) (m2) (m) (10−6 × %) (10−4 × %) (kJ/m3) (kJ/m3) 1.5 MgO-MnS 87.6 1.9 2.5 15.9 2.9 MnS 67.9 1.4 2.0 14.0 3.5 11.7

MgAl2O4 693 2.9 19.9 44.6 5.3 5.6 MgO-MnS 26.8 1.9 0.8 8.8 1.6 MnS 26.9 2.1 0.8 8.8 1.5 8.5

MgAl2O4 834 3.1 23.9 48.9 5.4 11 MgO 10.4 1.7 0.2 4.7 1.0 MgO-MnS 46.6 1.9 1.0 10.0 1.8 MnS 861 3.4 18.5 43.0 4.3 20.3

MgAl2O4 2030 3.8 43.7 66.1 6.0 Mg-Al-MnS 2790 3.8 60.0 77.5 7.1

Metals 2019, 9, 370 9 of 14

3.3. Zener Pinning Effect of Inclusions on the Austenite Grain Mobility According to the model [36], the driving force of grain growth is expressed by:

2σ F = b (5) P R where R is the radius of the curvature of grains, and σb is the surface energy of the grain boundary. Moreover, inclusions exert the retarding force (FR) on the grain boundaries proposed by Zener [43] as:

3 f σ F = v b (6) R 2r where f v is the volume fraction of inclusions, σb is the surface energy of the grain boundary, and r is the radius of the inclusions. Here the surface energy of the grain boundary σb is for austenite, the value of which was obtained from Reference [44]. The retarding forces (also called the Zener pinning force) depend on the radius and volume fraction of inclusions, as listed in Table5. Here the radius ( r) is equal to half of the average diameter, and fA is obtained by dividing the number of inclusions (N) by the measured area (A). Next, the equation fA = 2NfV was employed. It has been reported that the addition of 2 ppm Mg led to a change in oxide formation from the Al2O3 to MgO·Al2O3 phase and a change in inclusion formation from Al2O3–MnS to MgO·Al2O3–MnS [45].

Table 5. The retarding force (FR) of inclusions.

Mg A D f f F F Inclusion A V R R (ppm) (m2) (m) (10−6 × %) (10−4 × %) (kJ/m3) (kJ/m3) 1.5 MgO-MnS 87.6 1.9 2.5 15.9 2.9 MnS 67.9 1.4 2.0 14.0 3.5 11.7 MgAl2O4 693 2.9 19.9 44.6 5.3 5.6 MgO-MnS 26.8 1.9 0.8 8.8 1.6 MnS 26.9 2.1 0.8 8.8 1.5 8.5 MgAl2O4 834 3.1 23.9 48.9 5.4 11 MgO 10.4 1.7 0.2 4.7 1.0 MgO-MnS 46.6 1.9 1.0 10.0 1.8 MnS 861 3.4 18.5 43.0 4.3 20.3 MgAl2O4 2030 3.8 43.7 66.1 6.0 Mg-Al-MnS 2790 3.8 60.0 77.5 7.1 22 MgO 108 2.7 3.1 17.6 2.2 MgO-MnS 224 4.4 6.4 25.3 2.0 MnS 310 2.5 8.9 29.8 4.2 17.1 MgAl2O4 235 2.8 6.7 26.0 3.2 Mg-Al-MnS 759 3.0 21.8 46.6 5.5 2 * Note: σb is 1.159 J/m and the measured areas for 1.5, 5.6, 11, 22 ppm Mg are 34.865, 34.865, 46.487 and 2 34.865 mm , respectively. A—area; D—average diameter; fA—area fraction; fV—volume fraction; FR—retarding force, and FR—sum of the retarding forces for inclusions.

In the case of 1.5 and 5.6 ppm Mg, the effective inclusion of MgAl2O4 exerted the greatest retarding force, and, for 11 and 22 ppm Mg, it was Mg-Al-MnS that exerted the greatest retarding force because the volume fraction of MgAl2O4 was the largest phase for 1.5 and 5.6 ppm Mg. The volume fraction of Mg-Al-MnS was the largest phase for 11 and 22 ppm Mg. The average diameter of the inclusions was in the range of 1.4–4.4 µm, and the volume fraction of the inclusions was in the range of 4.7–77.5%. According to Equation (6), the retarding force was mainly determined by the volume fraction because there was no signiﬁcant difference in the average diameter of inclusions seen in Table5. Furthermore, there was no a linear relationship found between the addition of Mg and the retarding force. Metals 2019, 9, x FOR PEER REVIEW 10 of 14

22 MgO 108 2.7 3.1 17.6 2.2 MgO-MnS 224 4.4 6.4 25.3 2.0 MnS 310 2.5 8.9 29.8 4.2 17.1

MgAl2O4 235 2.8 6.7 26.0 3.2 Mg-Al-MnS 759 3.0 21.8 46.6 5.5

*Note: σb is 1.159 J/m2 and the measured areas for 1.5, 5.6, 11, 22 ppm Mg are 34.865, 34.865, 46.487 and 34.865 mm2, respectively. A—area; D—average diameter; fA—area fraction; fV—volume fraction; FR— retarding force, and  FR—sum of the retarding forces for inclusions.

In the case of 1.5 and 5.6 ppm Mg, the effective inclusion of MgAl2O4 exerted the greatest retarding force, and, for 11 and 22 ppm Mg, it was Mg-Al-MnS that exerted the greatest retarding force because the volume fraction of MgAl2O4 was the largest phase for 1.5 and 5.6 ppm Mg. The volume fraction of Mg-Al-MnS was the largest phase for 11 and 22 ppm Mg. The average diameter of the inclusions was in the range of 1.4–4.4 μm, and the volume fraction of the inclusions was in the range of 4.7–77.5%. According to Equation (6), the retarding force was mainly determined by the volume fraction because there was no significant difference in the average diameter of inclusions seen in Table 5. Furthermore, there was no a linear relationship found between the addition of Mg and the retarding force. The mobility of grain growth M is proportional to the net driving force, which is equal to the Metals 2019 9 driving force, , 370of grain growth (FP) subtracted from the Zener pinning force (FR), which was expressed10 of 14 by Reference [43]: The mobility of grain growth M is proportional to the net driving force, which is equal to the

driving force of grain growth (FP)V subtracted= M (FP − fromFR ) the Zener pinning force (FR), which was(7) expressed by Reference [43]: V = M(FP − FR) (7) wherewhere VV isis the the grain grain boundary boundary velocity. velocity. Figure 9 9 shows shows the the grain grain boundary boundary velocity velocity in in terms terms of of the the net netdriving driving force force (F P(F–PF –R ),FR where), where the the grain grain boundary boundary velocity velocity was was proportional proportional to the to netthe drivingnet driving force. force.Here, Here, the ratio the ratio of the of grain the grain boundary boundary velocity velocity to the to net the driving net driving force corresponded force corresponded to the mobilityto the mobilityof grains of M,grains that M, is, thethat slope, is, the and slope, the and corresponding the corresponding values ofvalues mobility of mobility are listed are in listed Table in6. Table It was 6.observed It was observed that increasing that increasing the temperature the temperature resulted resulted in increases in increases in mobility in mobility when when 1.5–22 1.5 ppm–22 ppm of Mg ofwere Mg w addedere added because because the mobilitythe mobility was was dependent dependent on on the the growth growth rate rate V V also also being being proportional proportional to Q toexp( exp(− RT )) inin EquationEquation (4). Here, Here, we we observed observed that that an an increase increase in in Mg Mg content content led led to to a adecrease decrease in in the the 𝑄𝑄 ◦ ◦ mobilitymobility at at 1150 1150 °CC as as well well as as at at 1200 1200 and and 1250 1250 °CC except except for for 5.6 5.6 ppm ppm Mg Mg content, content, as as shown shown in Table 6 . − 𝑅𝑅𝑅𝑅 −4 4 ◦ 6.The The grain grain boundary boundary mobility mobility was was signiﬁcantly significantly reduced reduced from from 19.8 19.8 to to 1.3 1.3× ×10 10−4 × mm4/(kJ/(kJ∙s)·s) at at 1150 1150 °C,C, −4 4 ◦ −4 4 ◦ fromfrom 52.6 52.6 to to 1.7 1.7 × 10× −104 × m4×/(kJm∙s)/(kJ at 1200·s) at °C 1200, andC, from and 105 from to 3.7 105 × to 10 3.7−4 × ×m410/(kJ∙s)× atm 1250/(kJ °C·s), when at 1250 theC, Mgwhen content the Mgwas content increased was from increased 1.5 to from22 ppm. 1.5 to 22 ppm.

Metals 2019, 9, x FOR PEER REVIEW 11 of 14

(a) (b)

FigureFigure 9. 9.TheThe grain grain boundary boundary velocity velocity (V ()V as) asa afunction function of of net net driving driving force force (F (FP P− F−R)F forR) for(a) (1.5a) 1.5 ppm, ppm, (b)( b5.6) 5.6 ppm, ppm, (c) ( c11)11 ppm ppm and and (d ()d 22) 22 ppm ppm Mg, Mg, where where FP F isP theis the driving driving force force of ofgrain grain growth, growth, and and FR F theR the retardingretarding force force on on boundaries. boundaries.

Table 6. The values of mobility [10−4 × m4/(kJ·s)] for 1.5–22 ppm Mg at temperatures of 1150, 1200 and Table 6. The values of mobility [10−4 × m4/(kJ∙s)] for 1.5–22 ppm Mg at temperatures of 1150, 1200 and 1250 ◦C. 1250 °C. Temperature (oC) Mg (ppm) Temperature (oC) Mg (ppm) 1150 1200 1200 1250 1250 1.51.5 19.8 52.6 52.6 105 105 5.65.6 8.0 5.9 7.5 7.5 11.0 7.7 14.2 21.6 11.0 7.7 14.2 21.6 22.0 1.3 1.7 3.7 22.0 1.3 1.7 3.7

In this study, all measurements of grain size were based on a grooved surface. Grooving has a pinning effect on the migration of grain boundaries, which is therefore slow. The grain boundary mobility measured here was the lower limit of the grain boundary mobility.

3.4. Effect of Solute Drag on the Grain Mobility of Austenite A lot of studies have reported that solute elements can segregate from the matrix to the grain boundary, and grain boundary migration may be limited by the diffusivity of the dragged solute atoms. The pressure induced by the solute drag is dependent on the boundary velocity [46–50]. According to Cahn et al., the drag effect of mobility (M) is given by [51]:

M(XMg,T) = ( + · ) (8) 1 −1 𝑀𝑀𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝛼𝛼 𝑋𝑋𝑀𝑀𝑀𝑀 and

( ) α= ( ) 2 (9) 𝑁𝑁𝑣𝑣 𝑘𝑘𝑘𝑘 𝛿𝛿 𝐸𝐸𝑏𝑏 𝐸𝐸𝑏𝑏 𝐼𝐼𝐼𝐼𝐼𝐼 𝐸𝐸𝑏𝑏𝐷𝐷𝑀𝑀𝑀𝑀 𝑠𝑠𝑠𝑠𝑠𝑠ℎ �𝑘𝑘𝑘𝑘� − �𝑘𝑘𝑘𝑘� where Mpure is the mobility of grain boundary in Fe; XMg is the concentration of Mg; δ is the width of a grain boundary; Nv is the number of atoms per unit volume; k is the Boltzmann’s constant, and Eb is the binding energy to the Fe grain boundary. The Mpure is according to Kang et al. [52]:

Metals 2019, 9, 370 11 of 14

1 −1 M(XMg, T) = ( + α·XMg) (8) MPure

and N (kT)2δ E E = v ( ( b ) − ( b )) α Int sinh (9) EbDMg kT kT where Mpure is the mobility of grain boundary in Fe; XMg is the concentration of Mg; δ is the width of a grain boundary; Nv is the number of atoms per unit volume; k is the Boltzmann’s constant, and Eb is the binding energy to the Fe grain boundary. The Mpure is according to Kang et al. [52]:

gb D Vmδ M = β Fe (10) pure b2RT

gb where b is the burger vector; R is the gas constant; T is the temperature; DFe is the diffusivity of Fe atoms in ferrite, and Vm is the molar value of ferrite. The values of all the parameters used are listed ◦ in Table7. The mobility calculation result was 1.8 × 10−3 × m4/(kJ·s) at 1250 C for 22 ppm Mg. According to the pinning force results, the mobility of grain boundary was 3.4 × 10−4 × m4/(kJ·s). Comparing the results, the effect of solute drag on grain boundary mobility is an order higher than the effect of Zener pinning. This implies that the effect of Zener pinning is the dominant mechanism for grain boundary migration.

Table 7. Values of parameters used in the calculation.

Parameter Value Reference δ 1 × 10−9 m [53] b 2.48 × 10−10 m [53] Eb 85 kJ/mol [54] β 0.7 [49] −5 3 Vm 8.26 x10 m - 1.8·10−4 m2/s - g.b · −4 2 [55] DFe 1.5 10 m /s

4. Conclusions In this study, the effect of Mg addition in the range of 1.5–22 ppm on the grain growth behavior of austenite in SS400 steel was investigated at 1150, 1200, and 1250 ◦C. The grain size distribution exhibited a log-normal distribution. The grain boundary velocity and grain mobility were reduced as Mg was increased from 1.5 ppm to 22 ppm. As the temperature increased from 1150 to 1250 ◦C, the grain boundary velocity also increased. The inclusion with the most retarding force was MgAl2O4, and it was Mg-Al-MnS when 11 and 22 ppm of Mg were added. The mobility of the grain boundary affected by Zener pinning was one order smaller than that affected by solute drag. It was therefore concluded that Zener pinning is a dominant factor by which to effectively retard grain boundary migration. Metals 2019, 9, 370 12 of 14

Author Contributions: Conceptualization, J.-C.K. and Y.-H.F.S.; methodology, C.-T.L.; software, H.-H.L.; validation, J.-C.K., Y.H. and H.-T.L.; formal analysis, H.-H.L.; investigation, Y.-H.F.S.; resources, H.-T.L.; data curation, C.-T.L.; writing—original draft preparation, H.-H.L.; writing—review and editing, C.-K.L.; supervision, J.-C.K.; project administration, F.-Y.H.; funding acquisition, Y.-H.F.S. Funding: This research was funded by the Ministry of Science and Technology, grant number MOST 103-2622-E-006-037 and MOST 107-2221-E-006-018” and “The APC was funded by the Ministry of Science and Technology”. Acknowledgments: The authors would like to thank the Ministry of Science and Technology and China Steel Corporation for supporting the funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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