Constitutive Modeling of Dynamic Recrystallization

Constitutive Modeling of Dynamic Recrystallization Behavior and Processing Map of 38MnVS6 Non-Quenched Steel Sen-dong Gu, Li-wen Zhang, Jin-hua Ruan, Ping-zhen Zhou & Yu Zhen

Journal of Materials Engineering and Performance ISSN 1059-9495 J. of Materi Eng and Perform DOI 10.1007/s11665-013-0808-4

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JMEPEG DOI: 10.1007/s11665-013-0808-4

Constitutive Modeling of Dynamic Recrystallization Behavior and Processing Map of 38MnVS6 Non-Quenched Steel Sen-dong Gu, Li-wen Zhang, Jin-hua Ruan, Ping-zhen Zhou, and Yu Zhen (Submitted July 4, 2013; in revised form November 11, 2013) The dynamic recrystallization behavior of 38MnVS6 non-quenched steel was investigated by hot compression tests on a Gleeble1500 thermomechanical simulator. True stress-strain curves and deformed specimens were obtained in the temperature range of 850-1200 °C and the strain rate range of 0.01-10 s21. By regression analysis of the experimental results, the critical strain model and austenite grain size model for dynamic recrystallization were established as a function of Zener-Hollomon parameter. The dynamic recrystallization kinetic model for 38MnVS6 non-quenched steel was established on the basis of the modified Avrami equation. In addition, based on the dynamic material model, the processing map of the steel was established at the strain of 0.5. It was found that the unstable phenomena of the steel did not appear at the deformation conditions. The processing map exhibited a domain of complete dynamic recrystallization occurring in the temperature range of 950-1200 °C and the strain rate range of 0.01-5 s21, which were the optimum parameters for the hot working of the steel.

Keywords

38MnVS6 non-quenched steel, dynamic recrystallization behavior, flow stress, processing map

1. Introduction 38MnVS6 is one of the representative medium carbon nonquenched steels, which is widely used in hot forging automotive components. The main benefit of these kinds of steels is the cost saving because one of their important strength increases is achieved by microalloy additions (e.g., Al, Nb, Ti, and V) without quenching and tempering (Ref 1). Therefore, the dynamic recrystallization (DRX) behavior of workpiece during hot deformation affects the macroscopic characteristics, which directly determines the final mechanical properties of products. Early in the 1970s, Sellars (Ref 2) suggested the DRX models of C-Mn steels initially on the basis of researching the microstructural evolution of low carbon steels during hot working. After the innovatory work, DRX behaviors of low carbon steels with different chemical compositions and the thermomechanical treatments have been studied (Ref 3-6). Recently, based on the dynamic material model (DMM) proposed by Prasad (Ref 7), processing map has been utilized to investigate the hot deformation behavior of alloys successfully (Ref 8, 9). The previous researches paid more attention to the DRX behavior of low carbon steels. However, little attention has been paid to the studies of DRX behavior of Sen-dong Gu, Li-wen Zhang, Jin-hua Ruan, and Ping-zhen Zhou, School of Materials Science and Engineering, Dalian University of Technology, Dalian 116023, China; and Yu Zhen, Suzhou Suxin Special Steel Group Co., Ltd., Suzhou 215151 Jiangsu, China. Contact e-mail: [email protected].

Journal of Materials Engineering and Performance

medium carbon microalloy non-quenched steel using processing maps, and the related data are still scarce. Further studies on the DRX behavior and processing map of 38MnVS6 nonquenched steel are still essential. In this article, based on the hot compression experimental data obtained in the temperature range of 850-1200 °C and the strain rate range of 0.01-10 s1, the DRX model and processing map of 38MnVS6 non-quenched steel were established, and the effects of different deformation conditions on these were analyzed. They are helpful to provide useful models and optimize parameters for hot working of the steel.

2. Experimental Procedure The material used in this study was provided by Suzhou Suxin Special Steel Group. Table 1 shows the chemical composition of 38MnVS6 non-quenched steel. Cylindrical compression specimens were machined with a diameter of 8 mm and a height of 12 mm. The flat and smooth ends enabled the specimen to maintain a single stress state during the hot compression. The isothermal hot compression tests were performed on a Gleeble1500 thermomechanical simulator. Figure 1 shows the heating and compression conditions schematically. The specimens were heated to 1250 °C at the heating rate of 10 °C/s and held at this temperature for 300 s to make sure that the initial grain sizes of all the specimens were in conformance with each other. Then, the specimens were cooled at a rate of 10 °C/s to the desired deformation temperature and held for 30 s to eliminate temperature gradient (Ref 10). Subsequently, the specimens were deformed to strain about 0.8 at the temperatures of 850-1200 °C at intervals of 50 °C and the strain rates of 0.001, 0.1, 1, and 10 s1. The specimens were quenched with water after each test immediately to retain the crystal boundary of high-temperature

Author's personal copy Table 1 Chemical composition of 38MnVS6

38MnVS6

C

Mn

Si

Cr

Cu

V

Ti

Al

S

P

0.430

1.451

0.623

0.198

0.139

0.113

0.017

0.017

0.033

0.015

Equation 3 is the Arrhenius equation which is used to indicate the relationship between the strain rate, the flow stress, and the temperature at elevated temperature.

3.2 DRX Model The DRX is characterized by some of the parameters, such as critical strain (ec), peak strain (ep), DRX volume fraction (Xdyn), and DRX grain size (Ddyn). Many researchers (Ref 10, 12-15) estimated the critical strain for the onset of DRX using the following equation: ec ¼ c ep ðc ¼ 0:67 0:86Þ

Fig. 1

Experimental procedure for hot compression tests

austenite microstructures. Finally, the specimens were sectioned along the longitudinal axis, and the microstructures were obtained from the quenched specimens after longitudinal sections were polished and then etched in aqueous solution of saturated picric acid. The grain size was examined by optical microscopy. In order to obtain the initial microstructures without deformation, a specimen was heated to 1250 °C and held for 300 s, immediately quenched in water, and finally examined by optical microscopy.

ðEq 4Þ

where c is the constant; as per the report (Ref 2), the constant evaluated is equal to 0.83 in this article. When the effect of the initial grain size is neglected, the peak strain is represented as the function of Zener-Hollomon parameter (Ref 15, 16). Hence, the model for peak strain can be modified as ep ¼ A1 Z k

ðEq 5Þ

3. Modeling Approaches

where A1 and k are the constants. The recrystallization volume fraction Xdyn is based on the modified Avrami equation (Ref 14, 17) which incorporates an empirical time constant for 50% recrystallization t0.5/dyn. The recrystallization volume fraction is expressed as nd t ðEq 6Þ Xdyn ¼ 1 exp 0:693 t0:5=dyn

3.1 Zener-Hollomon Parameter

t0:5=dyn ¼ A2 e_ A3 exp

The Zener-Hollomon parameter (Ref 11, 12) is widely introduced to present the effect of strain rate and temperature on the deformation behavior in an exponential equation. Z parameter can be expressed as follows: Q ðEq 1Þ Z ¼ e_ exp RT where Q is the activation energy of DRX (KJ/mol), e_ is the strain rate, T is the absolute temperature, and R is the universal gas constant. The hyperbolic sine function, proposed by Sellars (Ref 13), has been employed to describe the relationship of Z parameter and the peak stress according to n ðEq 2Þ Z ¼ A sinh arp where n is the stress exponent, A and a are the material constants, and rp is the peak stress. Deducing from Eq 1 and 2, we obtain n Q ðEq 3Þ e_ ¼ A sinh arp exp RT

Q RT

ðEq 7Þ

where t is the deformation time after the critical strain; and are constants. A2, A3, and Q The DRX volume fraction can be determined by strainstress curves, which is defined as the following (Ref 14, 18): rWH r ðEq 8Þ Xdyn ¼ rs rss where rWH indicates the flow stress if dynamic recovery (DRV) is the only softening mechanism. It can be described as the following (Ref 19): 0:5 ðEq 9Þ rWH ¼ r2s þ r20 r2s ee where r0 is the initial stress; X is the coefficient of DRV and can be calculated through converting Eq 9.

ln r2WH r2s r20 r2s X= ; ðEq 10Þ e because rs is difficult to be determined from stress-strain curves and its value is equal to the one of rp approximately, rp is used in the place of rs in this article.


Author's personal copy

Fig. 2

Stress-strain curves at various temperatures with strain rates of (a) 0.01 s1; (b) 0.1 s1; (c) 1 s1; and (d) 10 s1

3.3 Processing Map Based on the theory of DMM, processing map consists of a power dissipation map and an instability map (Ref 7, 20). The variation of the efficiency of power dissipation g with temperature and strain rate constitutes a contour map called power dissipation map, which is used to describe microstructural changes during deformation. g is defined as g¼

2m mþ1

ðEq 11Þ

where m is the strain rate sensitivity parameter of material. It can be calculated as the following equation, when temperature and strain are constants: m¼

@ ðln rÞ @ ðln e_ Þ

ðEq 12Þ

In the power dissipation map, the different contour values of g describe various deformation mechanisms. In general, the domain of better workability is correlated with the higher g value (Ref 21). The instability map is developed by an instability parameter n with temperature and strain rate on the basis of the extremum principles of irreversible thermodynamics (Ref 22, 23). n is given as n¼

@ ln½m=ð1 þ mÞ þm0 @ ðln e_ Þ

ðEq 13Þ

According to Eq (13), when the value of n is less than or equal to zero, the deformation conditions of material correspond to instability flow, at which the materials present the characteristics of shear deformation bands and free surface cracking.


Fig. 3 Schematic diagram of stress-strain curves of the three types

4. Result and Discussion 4.1 Analysis of Flow Stress and Microstructures Figure 2 shows the stress-strain curves under different temperatures and strain rates. It is clear that the curves can be ranged into three principal types depending on the relationship between stress and strain. Figure 3 shows a schematic diagram of stress-strain curves of the three types. In the first type, the stress enhances correspondingly with the increasing strain till the maximum, which represents working hardening (WH) phenomena (Ref 24, 25), as shown by the curves at the temperatures of 850 and 900 °C in Fig. 2(a) and at the temperature of 850 °C in Fig. 2(b, c, and d). In the second type, the relationship between stress and strain is dominated mainly by WH and DRV during the hot deformation process (Ref 24-


Fig. 4 Microstructures of 38MnVS6 non-quenched steel under different deformation conditions: (a) no deformation; and (b) deformation (T = 850 °C, e_ = 0.01 s1); (c) deformation (T = 850 °C, e_ = 10 s1); (d) deformation (T = 1050 °C, e_ = 1 s1); and (e) deformation (T = 1200 °C, e_ = 1 s1)

Fig. 5

Relationships between lnsinh(arp) and ln e_

26). The stress remains constant or changes slightly when strain is large enough as shown by the curves above the temperature of 950 °C in Fig. 2(d). In the third type are seen the typical stress-strain curves when the DRX occurs (Ref 15, 27). The

Fig. 6 Relationships between lnsinh(arp) and ln1/T

curves can be divided into two regions. In region I, the stress increases to a peak because of the dominance of WH, and the strain for the peak stress is the peak strain ep. The critical strain for the onset of DRX, called critical strain ec, is lower than the



Fig. 7

Relationship between lnep and lnZ

predominant as a result of the decreasing DRX (Ref 28). The phenomenon is distinguished from the similar phenomena reported (Ref 29, 30). The curves show that as the temperature increases or the strain rate decreases, the peak stress and steady stress decrease, and the stress increases to a peak at smaller strain. Compared with other C-Mn steels (15, 24-27), the carbon and microalloy addition can increase the peak stress and peak strain, and DRX is more difficult to occur. Figure 4 shows the microstructures at the center of specimens under different deformation conditions. Compared with the microstructures without deformation as shown in Fig. 4(a), the ones in Fig. 4(b and c) are composed of elongated grains, and there are numerous deformation bands that increase the recrystallization nucleation sites in the elongated coarse austenite grain, indicating that incomplete DRX occurs at low temperatures during deformation. From Fig. 4(d and e), when DRX takes place at high temperatures, it is obvious that the microstructures are composed of refined equiaxed grains, and the average grain sizes are 22.9 and 32 lm, respectively. The DRX grain size increases with the increasing temperature and the decreasing strain rate.

4.2 Determination of Zener-Hollomon Parameter Taking natural logarithm of both sides of Eq 3, we obtained the following equation: Q ln e_ ¼ ln A þ n ln sinh arp RT

Fig. 8

Relationship between ln[ln(1Xdyn)] and ln(t/t0.5/dyn)

ðEq 14Þ

If the T is constant and assuming that the activation energy is constant, the following equation can be deduced from Eq 14: 1 @ ln sinh arp ¼ ðEq 15Þ n @ ðln e_ Þ Based on the analysis of stress-strain curves from the compression tests, values of rp for the stress-strain curves at different deformation conditions were obtained. Hence, a linear relationship is found between lnsinh(arp) and ln e_ . As shown in Fig. 5, the value of n is determined by the reciprocal of linear slope, and the average value of n is 4.767. According to Eq 14, when e_ is constant, the value of Q can be derived as the following linear relationship: @ ln sinh arp ðEq 16Þ Q ¼ Rn @ ð1=T Þ

Fig. 9

Relationship between lnDdyn and lnZ

peak strain. In region II, the stress decreases gradually to a steady stress rss with the increasing strain as a result of DRX overtaking WH. As shown in Fig. 2, the stress-strain curves of the steel, deformed above the temperature of 1000 °C and at the strain rates of 0.01, 0.1, and 1 s1 characterize the typical DRX behavior. Furthermore, when deformed at 950-1050 °C under the strain rate 0.01 s1 and at 950 °C under the strain rate 0.1 s1, the flow stress at the end of curves has ascended obviously. The reason is that the WH becomes more and more


According to the linear relationship of lnsinh(arp) and ln1/T at different strain rates as shown in Fig. 6, if the average value of the slope is 8779.00, then the average value of Q is determined as 347.9 KJ/mol. Substituting Q into Eq 1, Z parameter can be obtained as 347:9 103 ðEq 17Þ Z ¼ e_ exp RT

4.3 Constitutive Equation of DRX Following Eq 5, through regression analysis, the dependence of the peak strain on Z parameter is fitted from the relationship between lnep and lnZ in Fig. 7 and A1 and k are determined. Hence, the model for peak strain of 38MnVS6 non-quenched steel can be expressed as

Author's personal copy ep ¼ 0:0058Z 0:123

ðEq 18Þ

Combining Eq 6 and 8, the value of nd is determined by the linear slope from linear relationship of ln[ln(1Xdyn)] and ln(t/t0.5/dyn) as shown in Fig. 8. The expression of t0.5/dyn is also obtained through multiple linear regressions. Then, the DRX volume fraction of 38MnVS6 non-quenched steel can be described by the following equations: " 3:048 # t ðEq 19Þ Xdyn ¼ 1 exp 0:693 t0:5=dyn 27385:80 t0:5=dyn ¼ 0:0167_e0:84 exp RT

ðEq 20Þ

To reflect the dependence of the austenite grain size on deformation temperature and strain rate, Z parameter is introduced to describe the relationship (Ref 15). By fitting a linear regression to the DRX grain size in Fig. 9, the DRX grain size of 38MnVS6 non-quenched steel can be described by the following equation: Ddyn ¼ 4989:046 Z 0:169

ðEq 21Þ

parameter n is greater than zero, which means that instable domain does not appear under the experimental conditions.

5. Conclusions The DRX behavior of 38MnVS6 non-quenched steel was investigated by hot compression tests using a Gleeble1500 thermomechanical simulator in the temperature range of 8501200 °C and the strain rate range of 0.01-10 s1. The following conclusions can be drawn from the tests: (1)

(2)

(3)

By the regression analysis of the experimental data from the true stress-strain curves, the stress exponent and activation energy for 38MnVS6 non-quenched steel were determined to be 4.767 and 347.9 KJ/mol, respectively. The DRX model for 38MnVS6 non-quenched steel was established in this article. The peak strain and DRX grain size were the functions of Zener-Hollomon parameter. The DRX kinetic model was described by the modified Avrami equation. The processing map of 38MnVS6 non-quenched steel at the strain of 0.5 was obtained. The domain of complete DRX occurs in the temperature range of 950-1200 °C and strain rate range of 0.01-5 s1, which are the optimum parameters for hot working of the steel.

4.4 Establishment of Processing Map The processing map of 38MnVS6 non-quenched steel at the strain of 0.5 was established as shown in Fig. 10. The efficiency of power dissipation revealed an increasing tendency with the increasing deformation temperature and the decreasing strain rate. The processing map is divided into two domains on the basis of the value of g, including domain I with a peak efficiency of around 30% which is separated by shaded areas, and domain II is the rest. The deformation mechanism of domain I is incomplete DRX, as shown by the micrographs in Fig. 4(b and c). The deformation mechanism of domain II is complete DRX, as shown by the micrographs of Fig. 4(d and e). The analysis leads to the conclusion that the optimum processing conditions of 38MnVS6 non-quenched steel are the domain with the temperature range of 950-1200 °C and strain rates of 0.01-5 s1. In this article, the value of instability

Fig. 10

Processing map of the steel at strain of 0.5

Acknowledgment The authors appreciate the financial support received from the Suzhou Suxin Special Steel Group Co., Ltd.

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