J. Cent. South Univ. (2016) 23: 3065-3071

DOI: 10.1007/s11771-016-3370-z

Constitutive modeling of dynamic recrystallization behavior and processing map of Cr5 steel

LIU Xin-bin(刘新彬), WU Guang-liang(吴光亮), ZHOU Chao-yang(周超洋)

School of Minerals Processing and Bioengineering, Central South University, Changsha 410083, China

Central South University Press and Springer-Verlag Berlin Heidelberg 2016

Abstract: The hot deformation behaviors of Cr5 steel were investigated. The hot compression tests were conducted in the temperature range of 900-1150 °C under strain rates of 0.01, 0.1 and 1 s^-1. The constitutive equation and material constants (Q, n, α lnA) are obtained according to the hyperbolic sine function and Zener-Hollomon parameter. Besides, dynamic recrystallization (DRX) grain size model and critical strain model are acquired. The processing maps with the strain of 0.1, 0.3 and 0.5 are obtained on the basis of dynamic materials model. It has been observed that DRX occurs at high temperature and low strain rate. According to the processing map, the safety region exists in the temperature range of 920-1150 °C with strain rate of 0.01-0.20 s^-1.

Key words: flow stress; constitutive equation; material constants; dynamic recrystallization; processing map

1 Introduction

In hot forming processes, the complex microstructural evolutions are often induced by the multiplicate hot deformation mechanisms, such as work hardening (WH), dynamic recovery (DRV) and dynamic recrystallization (DRX) [1-2]. In low stacking fault energy, face-centered cubic alloy and steel, DRX occurs readily during hot working because dynamic recovery is sluggish as climb and cross slip are inhibited so that the driving force for recrystallization is maintained [3]. Dynamic softening behavior during hot processing has generated considerable interest because obtained component properties are influenced significantly by its corresponding microstructural evolution [4]. The microstructural evolutions during dynamic recrystallization are sensitive to the processing parameters, such as strain rate, deformation temperature and strain [5-6]. DRX occurs when a critical strain is reached, and at the same time, the minimum rate of energy dissipating is received [6-7]. The DRX softens metals and reduces the hot working loads during hot deformation. Furthermore, it can lead to a significant grain refinement, which will enhance the mechanical properties and thus the formability of the materials [8-10]. The DRV occurs at high strain rate and low temperature reducing the stored energy greatly and making DRX hard to happen [7].

The processing map on the basis of the dynamic materials model (DMM) and consisting of the efficiency map and the instability map is a valuable approach for coupling the processing conditions such as deformation rate and temperature with desired microstructure to optimize deformation process [11-12]. For optimizing hot workability and controlling the microstructure, DRX is a chosen domain. The damage processes are sometimes very efficient in dissipating power for the generation of new surfaces. On the other hand, the safe processes may become less efficient, because power dissipates through annihilation of dislocations [11]. So, it is important to understand the DRX behavior in hot deformation process. In recent researches, the constitutive equation and processing map have been proposed for steel [13-14], Al-based alloy [15-16], Ni-based alloy [17], Ti-based alloy [18], composite materials [19-20] and other materials [21].

The previous research paid more attention to the DRX behavior of low carbon steels. However, little attention has been paid to the studies of DRX behavior of medium carbon steel by using constitutive equation and processing maps. In the present work, the compressive deformation behavior of Cr5 steel was studied, material constants (Q, n, α lnA) and constitutive equation were obtained, the grain size model and critical strain model were also acquired, and the processing maps at strain of 0.1, 0.3 and 0.5 were obtained and used to determine the instability region.

2 Experimental

The chemical composition of the investigated steel is listed in Table 1.

Table 1 Chemical composition of experiment material (mass fraction, %)

Cylindrical hot compression specimens with height of 12 mm and diameter of 8 mm were machined. In order to minimize the frictions between the specimens and die during hot deformation, the flat ends of the specimen were recessed to a depth of 0.1 mm deep to entrap the lubricant of graphite mixed with machine oil. The thermomechanical processing schedule is schematically shown in Fig. 1.

Fig. 1 Thermal simulation process of test steel

The hot compression tests were performed on Gleeble-3500 thermo-simulation machine in the temperatures range of 900-1150 °C, at an interval of 50 °C, under constant strain rates of 0.01, 0.1 and 1 s^-1, up to the true strain of 0.7. Each specimen was heated to 1200 °C at a rate of 10 °C /s and held for 3 min, and then cooled to the deformed temperature with the rate of 10 °C/s and holding for 30 s. After deformation, the specimens were immediately quenched in tap water. During the whole tests, the high purity argon was used as protective gas.

3 Results and discussion

3.1 Analysis of hot flow curves

The effect of deformation temperature and strain rate on the true stress-true strain curves of the investigated steel is shown in Fig. 2.

According to Fig. 2, at a constant strain rate, the peak stress and peak strain decrease with the increase of temperature. DRX occurs more easily with the increase of deformation temperature and the decrease of strain rate. In the initial stages of deformation, the flow stress increases sharply until a peak stress, which indicates that the work hardening plays a dominant role. After the quickly flow stress increase, the flow stress decreases slowly as the deformation proceeded until a relatively stable stress appears, showing a dynamic flow softening. The DRX begins to play a dominant role when the strain exceeds peak strain. As the strain increases continually, it gets into a steady-state region. Finally, the curves show the equilibrium between work hardening and softening. The typical form of DRX flow curve is observed at high temperatures and low strain rates. At high strain rates, concurrent deformation decelerates the rate of softening [22]. Other researchers [6, 9] also point out that the higher temperatures and lower strain rates can promote the softening process by increasing the mobility of grain boundaries and providing longer time for dislocation annihilation and occurrence of DRX. During the high-temperature deformation process, WH and dynamic softening exist and influence each other at the same time. At the initial stage of straining, WH predominates. As the deformation develops, DRX occurs and the hardening rate decreases. When the hardening rate becomes equal to the softening rate, the peak flow stress is reached. The flow softening exceeds the hardening, the stress drops gradually. Finally, the flow stress becomes steady when a new balance between softening rate and hardening rate is obtained.

Fig. 2 Flow stress curves of Cr5 steel under different deformation conditions

3.2 Determination of material constants and constitutive equations

Hot working can be considered as a thermally activated process, and it can be described as follows, hyperbolic sine law (Eq. (1)), the power law (Eq. (2)) and exponential law (Eq. (3))[6, 9].

                   (1)

                             (2)

                                  (3)

where is the strain rate (s^-1); σ_p is the peak stress (MPa); Q is the activation energy for deformation (J/mol); A, A₁ A₂, β, α, n and n₁ are material constants; R is the mole gas constant (8.314 J/(mol·K).

Taking natural logarithm of both sides of Eqs. (2) and (3) at a constant temperature respectively yields:

                          (4)

                       (5)

Substituting the values of the flow stress and corresponding strain rate into the Eqs. (4) and (5) gives the relationship between the flow stress and strain rate, as shown in Fig. 3. The values of β and n₁ are obtained as 0.081 and 9.173, respectively. The value of the constant α is derived by the division of β and n₁ [6, 9] as 0.0088.

Taking natural logarithm from both sides of Eq. (1) and rearranging them the following equation is derived as

Fig. 3 Relationship between flow stresses and strain rates according to exponential law (a) and power law (b)

               (6)

Partially differentiating Eq. (6) at constant temperature and strain rate yields

                           (7)

                        (8)

The value of n can be derived from the average slopes of the lines in ln[sinh(ασ_p)] versus shown in Fig. 4(a). The value of n is calculated to be 6.90. Similarly, the value of Q is determined from the slop of ln(sinh(ασ_p)) versus 1/T through averaging the slope values at different strain rates shown in Fig. 4(b), the Q value is obtained as 357 580 J/mol. The value of lnA can be derived by substituting the obtained values into Eq. (6). So lnA is calculated to be 29.18.

Substituting all the obtained values into Eq. (1), the constitutive equation can be expressed as

 (9)

In order to evaluate the constitutive equation, the experimental data and predicted data are compared in Fig. 5, it can be seen that the R²=0.992, which indicates that the constitutive equation is quite accurate.

Fig. 4 Relationships between ln[sinh(ασ_p)] and ln (a) and ln[sinh(ασ_p)] and 1/T (b) for Cr5 steel

Fig. 5 Comparison between experimental data and predicted data

3.3 Critical strain model and microstructure

Generally speaking, DRX can be initiated at a critical level of stress accumulation during hot deformation. However DRX actually starts at a critical strain (ε_c) which is lower than the strain at peak stress [6]. Only when the strain exceeds ε_c, DRX occurs in hot deformation process. So, it is important to accurately confirm ε_c in the research of hot deformation parameters.

On the flow curve at which the strain hardening rate equals zero represents the peak stress (σ_p) and the inflection point indicates the critical stress (σ_c) for the initiation of DRX. The critical strains can be determined from the inflection points of the lnθ-ε plots and the critical stresses can be subsequently obtained either from the θ-σ plots or from the initial flow curves [23].

                  (10)

where A₁, A₂, A₃, A₄ are constant parameters for each deformation condition. The second derivative of Eq. (10) with respect to ε can be expressed as

                        (11)

At critical stress for initiation of DRX, the second derivative becomes zero. Therefore,

                             (12)

The results of peak and critical stresses and strains for the temperatures of 950, 1000, 1050, 1100 and 1150 °C under different strain rates of 0.01, 0.1 and 1 s^-1 are summarized in Table 2. The average ε_c/ε_p is 0.47.

The critical strain varies with strain rate and deformation temperature. And the relationship can be described by the Sellars model [24]:

                                   (13)

where A and n are material constants; Z is the Zener- Hollomon parameter. Take the natural logarithm on both sides of Eq. (13):

                           (14)

The relationship between lnε and lnZ can be drawn in Fig. 6.

Figure 6 exhibits the linear regression results of critical and peak strain on the Zener-Hollomon parameter. It can be seen that the critical characteristics of DRX increase with increasing Z parameter. The relationship between these parameters and deformation conditions is expressed by a power law equation. According to the linear regression results, the following equations hold for the investigated steel:

                            (15)

                            (16)

The model of dynamic recrystallization of Cr5 steel can be acquired by using the software MATLAB as shown in Fig. 7.

In Fig. 7, the space is divided to three parts by ε_p surface and ε_c surface. ε_p represents the critical condition of full DRX and ε_c means critical condition of DRX. When the deformation parameters are above ε_p, between ε_p and ε_c, below ε_c, the related recrystallization is full DRX, partial DRX and no DRX, respectively.

Microstructure of Cr5 steel at deformation temperature of 1100 °C under different strains are exhibited in Fig. 8.

Table 2 Critical strain and peak strain of Cr5 steel under different deformation conditions

Fig. 6 Relation ship among ε_c, ε_p and Z

Fig. 7 DRX model of Cr5 steel

The austenite grain sizes in Figs. 8(a), (b) (c) and (d), are 95.6, 80.5, 47.8 and 49.2 μm, respectively. When the strain reach 0.1 the fine recrystallization grain appears in austenite grain boundary, which indicates that the DRX occurs at strain of 0.1. As strain increases from 0.1 to 0.3, the austenite grain becomes fine. When the strain reaches 0.5, the austenite grain size is close to the strain of 0.3, which indicates the DRX ends.

3.4 DRX grain size model

From the above analysis, it is concluded that the recrystallized grain size is affected by the temperature and strain rate during the hot deformation. The Zener- Hollomon parameter reflects the influence of both the temperature and strain rate. Consequently, the parameter Z generally influences the recrystallized grain size. The dependence of dynamically recrystallized grain size on Z can be described by [25]

                                (17)

where C and a are the experimental constants, D_drex is the grain size of DRX.

In all fully recrystallized specimens, DRX grain size under each deformation condition was collected by quantitative metallography method, and the results are shown in Table 3. The DRX grain size reduces with increasing of Z.

The natural logarithm of D_drex versed that of Z for the specimens is plotted in Fig. 9. By linear fitting, the relationship between the two is determined as

                      (18)

Fig. 8 Microstructure of Cr5 steel at deformation temperatures of 1100 °C and strain rate of 0.01 s^-1 under strain of ε=0.1 (a), ε=0.2 (b), ε=0.3 (c) and ε=0.5 (d)

Table 3 Grain size under different deformation conditions

According to Eq. (18), the DRX grain size model at different deformation temperature and strain rate can be acquired by using the software MATLAB as shown in Fig. 10.

Fig. 9 Relationship between lnD_drex and lnZ

Fig. 10 Grain size model of Cr5 steel

3.5 Processing map

The processing maps could not only describe the energy consumption of the microstructure evolution during the hot deformation but also visually show the instability flow regions that should be avoided during forming process.

The power dissipation through microstructural evolution is represented by a dimensionless efficiency index η as a function of strain rate sensitivity m. The efficiency index η can be defined as [1, 12]

                                  (19)

where m is the strain rate sensitivity exponent; when the deformation temperature is fixed, it is a function of the strain rate. The variation of η with deformation temperature and strain rate constitutes a power dissipation map. The power dissipation map represents the power dissipated by the material through microstructural evolution.

The instability criterion parameter is defined as [1, 12]

                        (20)

The variation of the instability parameter with and T at certain strain constitutes an instability map and the flow instability is estimated to occur when becomes negative.

Figure 11 shows the processing maps of Cr5 steel during hot working at strains of 0.1, 0.3 and 0.5. The flow instability region appears at deformation temperature between 900-1150 °C when the strain rate exceeds 0.2 s^-1 under strain of 0.1, 900-1060 °C when the strain rate exceeds 0.25 s^-1 under strain of 0.3, 900- 950 °C when the strain rate exceeds 0.5 s^-1 under strain of 0.5. The optimum condition for hot deformation of Cr5 is the region of 920-1150 °C and 0.01-0.2 s^-1, which indicates that the workability will be modified in this domain.

Fig. 11 Processing map at strain of 0.1 (a), 0.3 (b) and 0.5 (c)

4 Conclusions

1) The DRX is found to be the main flow softening mechanism in almost all deformation conditions, which increase with increasing temperature and decreasing stain rate.

2) The constitutive equations are derived as

.

3) The critical and peak strain can be expressed as ε_c=0.002Z^0.099, ε_p=0.010Z^0.100, the relationship between grain size and Z parameter is D_drex=2.67×10³Z^-0.146.

4) The optimum condition for hot deformation of Cr5 is the region of 920-1150 °C and 0.01-0.2 s^-1.

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(Edited by DENG Lü-xiang)

Foundation item: Project(51322405) supported by the National Natural Science Foundation of China

Received date: 2015-09-14; Accepted date: 2016-01-18

Corresponding author: WU Guang-liang, Professor, PhD; Tel: +86-731-85853069; E-mail: glwu_899@sina.com