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Dynamic recrystallization kinetics of 42CrMo steel during compression at different temperatures and strain rates
Materials Science and Engineering A 528 (2011) 4643–4651
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Dynamic recrystallization kinetics of 42CrMo steel during compression at different temperatures and strain rates Guo-Zheng Quan ∗ , Gui-Sheng Li, Tao Chen, Yi-Xin Wang, Yan-Wei Zhang, Jie Zhou School of Material Science and Engineering, Chongqing University, Chongqing 400044, China
a r t i c l e
i n f o
Article history: Received 9 December 2010 Received in revised form 16 February 2011 Accepted 26 February 2011 Available online 6 March 2011 Keywords: Dynamic recrystallization Critical strain Flow stress High-strength steel
a b s t r a c t In order to improve the understanding of the coupling effect in dynamic recrystallization (DRX) behavior and flow behavior for extruded 42CrMo high-strength steel, a series of isothermal upsetting experiments with height reduction of 60% were performed at the temperatures of 1123 K, 1198 K, 1273 K and 1348 K, and the strain rates of 0.01 s−1 , 0.1 s−1 , 1 s−1 and 10 s−1 on a Gleeble1500 thermo-mechanical simulator. The initiation and evolution of DRX were investigated by using the process variables derived form flow curves. By the regression analysis for conventional hyperbolic sine equation, the activation energy of DRX was determined as Q = 599.7321 kJ mol−1 , and a dimensionless parameter controlling the ˙ stored energy were determined as Z/A = ε exp (599.73210 × 103 )/8.31T /2.44154 × 1025 . Based on the conventional strain hardening rate curves (d/dε versus ), the characteristic parameters including the critical strain for DRX initiation (εc ), the strain for peak stress (εp ), and the strain for maximum softening rate (ε*) were identified. Basedon the regression analysis results for a modified Avrami type equation XDRX = 1 − exp
− (ε − εc ) /ε∗
m
0.06704
in which εc , ε* and m were described as |εc | = 0.16707(Z/A)
,
0.08207
|ε∗ | = 0.61822(Z/A) and m = 3.85582 respectively, the evolutions of DRX volume were described as following: for a fixed strain rate, the strain required for the same amount of DRX volume fraction increases with decreasing deformation temperature, in contrast, for a fixed temperature, it increases with increasing strain rate. Finally, the theoretical predictions were validated by the microstructure graphs. © 2011 Elsevier B.V. All rights reserved.
1. Introduction 42CrMo is one of the representative medium carbon and low alloy steels. Due to its good balance of strength, toughness and wear resistance, 42CrMo high-strength steel is widely used for many general purpose parts including automotive crankshaft, rams, spindles, etc. [1]. During hot forming process steel is liable to undergo work hardening (WH), dynamic recovery (DRV) and dynamic recrystallization (DRX), three metallurgical phenomena for controlling microstructure and mechanical properties [2–4]. In light alloys such as magnesium alloy and aluminum alloy, dynamic recovery (DRV) can balance work hardening, and a plateau is achieved [5,6]. However, in austenitic steels with higher deformation resistance, the kinetics of DRV is lower, and DRX can be initiated at a critical condition of stress accumulation [7]. The occurrence of DRX brings about grain refinement and deformation resistance reduction, due to which the evaluation of the rate and progress of DRX in terms of deformation conditions is important [8]. The general descriptive model for DRX is that the nucleation of DRX
∗ Corresponding author. Tel.: +86 023 6510 3065; fax: +86 023 6511 1493. E-mail address: quangz [email protected] (G.-Z. Quan). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.02.090
grains can start at a critical strain which is a function of initial microstructure and deformation conditions. Then, the evolution of DRX microstructure can proceed further by increasing deformation and through the formation of a necklace structure [9]. Considerable research on DRX kinetics have focused on measuring by metallographic images or EBSD maps of the frozen microstructures at different deformation conditions such as temperature, strain rate and plastic deformation amount, meanwhile analyzing the relationships between microstructure variations and deformation parameter levels. However, few attention has been paid to model microstructure evolution by analyzing flow curves collected by hot compression tests [1–9]. For austenitic steels such as 42CrMo, during a plastic forming process a pronounced interaction between DRX evolution and mechanical property is implicit in flow behavior. Thus, it is realizable to model DRX evolution by analyzing the true stress–strain curves. In the present work, three characteristic points including the critical strain for DRX initiation (εc ), the strain for peak stress (εp ), and the strain for maximum softening rate (ε*) have been identified from the true stress–strain curves of extruded 42CrMo high-strength steel, and their existence means that the evolution of DRX can be characterized by the process variables. The object of this study is to uncover and describe the general nature of the influence
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of strain, strain rate and temperature on DRX behavior of 42CrMo high-strength steel using a series of true stress–strain curves collected from compression tests at the temperature of 1123–1348 K and the strain rate of 0.01–10 s−1 . The effects of strain, temperature and strain rate on flow stress and DRX behavior are represented by Zener–Hollomon parameter, Z, in an exponent-type function of temperature and strain rate. In addition, Zener–Hollomon parameter and another essential material constant, DRX activation energy, implicit in the Arrhenius type equation of flow stress, have been achieved by fitting this equation. Then the relationships between process variables and DRX volume fraction were coupled by the modified Avrami type equation including εc and ε* as a function of Z. Finally, the theoretical predictions by the derived equations were validated by the microstructure graphs.
2. Experimental procedure The chemical compositions of extruded 42CrMo high-strength steel used in this study were (wt.%) C 0.450, Si 0.280, Cr 0.960, Mn 0.630, Mo 0.190, P 0.016, Cu 0.014, S 0.012, Fe (balance). The extruded rod with diameter 10 mm was homogenized under temperature 1123 K for twelve hours. Then the rod was scalped to height 12 mm with grooves on both sides filled with machine oil mingled with graphite powder as lubricant to reduce friction between the anvils and specimen. A computer-controlled, servo-hydraulic Gleeble 1500 testing machine was used for the compression experiments. This machine can be programmed to simulate both the thermal and the mechanical industrial process variables for a wide range of hot deformation conditions. The specimens were resistance heated at a heating rate of 1 K/s and held at a certain temperature for 180 s by thermo-coupledfeedback-controlled AC current, which decreased the anisotropy in
flow deformation behavior effectively. Three thermocouples were welded at the mid-span of billet to provide accurate temperature control and measurement during testing. The compression tests corresponding to a height reduction of 60% were carried out at four different temperatures of 1123 K, 1198 K, 1273 K and 1348 K and four different strain rates of 0.01 s−1 , 0.1 s−1 , 1 s−1 , 10 s−1 . Then, such sixteen specimens deformed were rapidly quenched with water to retain the recrystallized microstructures. All the specimens were sectioned perpendicular to the longitudinal compression axis for metallographic examination. The sections were polished and etched in an abluent solution of saturated picric acid. The optical microstructures in the center region of the section plane were examined. In addition, the variations of stress and strain were monitored continuously by a personal computer equipped with an automatic data acquisition system. The true stress and true strain were derived from the measurement of the nominal stress–strain relationship according to the following formula [1]: T = N (1 + εN ), εT = ln(1+εN ), where T is the true stress, N is the nominal strain, εT is the true strain and εN is the nominal strain.
3. Results and discussion 3.1. Flow stress behavior The true stress–true strain curves of 42CrMo high-strength steel compressed at different deformation conditions are shown in Fig. 1a–d. It is shown that flow stress is in direct correlation with strain, temperature and strain rate. Comparing these curves with one another, it is found that, for a specific strain rate, the flow stress decreases markedly with increasing temperature. In contrast, for a fixed temperature, the flow stress generally increases
Fig. 1. True stress–strain curves of 42CrMo high-strength steel obtained by Gleeble 1500 under the different deformation temperatures with strain rates. (a) 0.01 s−1 , (b) 0.1 s−1 , (c) 1 s−1 and (d) 10 s−1 .
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Fig. 2. d/dε versus plots up to the peak points of the true stress–strain curves under different deformation temperatures with strain rates (a) 0.01 s−1 , (b) 0.1 s−1 , (c) 1 s−1 and (d) 10 s−1 .
as the strain rate increases. The cause lies in the fact that lower strain rate and higher temperature provide longer time for the energy accumulation and higher mobilities at boundaries which result in the nucleation and growth of dynamically recrystallized grains and dislocation annihilation. From the true stress–strain curves in Fig. 1a–d, it can be seen that the stress evolution with strain exhibits three distinct stages [10]. At the first stage where work hardening (WH) predominates, flow stress exhibits a rapid increase to a critical value. At the second stage, flow stress exhibits a smaller and smaller increase until a peak value or an inflection of work-hardening rate, which shows that the thermal softening due to DRX and dynamic recovery (DRV) becomes more and more predominant, then it exceeds WH. At the third stage, three types of curve variation tendency can be generalized as following: decreasing gradually to a steady state with DRX softening (1123–1348 K and 0.01 s−1 , 1198–1348 K and 0.1 s−1 , 1273–1348 K and 1 s−1 ), maintaining higher stress level without significant softening and work-hardening (1123–1198 K and 1 s−1 , 1123–1348 K and 10 s−1 ), and increasing continuously with significant workhardening (1123 K and 0.1 s−1 ). Thus, it can be concluded that the typical form of flow curve with DRX softening, including a single peak followed by a steady state flow as a plateau, is more recognizable at high temperatures and low strain rates. That is because at higher strain rates and lower temperatures, the higher workhardening rate slows down the rate of DRX softening, and both the peak stress and the onset of steady state flow are therefore shifted to higher strain levels. 3.2. The initiation of DRX From the true compressive stress–strain data shown in Fig. 1a–d, the values of the strain hardening rate ( = d/dε) were calculated. The critical conditions for the onset of DRX can be attained when the value of −d/d , where strain hardening rate = d/dε, reaches
the minimum which corresponds to an inflection of d/dε versus curve [11]. In this study, analysis of inflections in the plot of d/dε versus up to the peak point of the true stress–strain curve has been performed to reveal whether DRX occurs. Results confirm that the d/dε versus curves have characteristic inflections as shown in Fig. 2a–d, which indicates that DRX is initiated at corresponding deformation conditions. The critical stress to initiation can be identified, and hence the corresponding critical strain to initiation can be obtained from true stress–strain curve. As a result, the values of critical strain and peak stress at different deformation conditions were shown in Table 1, from which it can be seen that the critical strain and critical stress depend on temperature and strain rate nonlinearly, and it is summarized that εc /εp = 0.165–0.572, c / p = 0.645–0.956. 3.3. Arrhenius equation for flow behavior with DRX It is known that the thermally activated stored energy developed during deformation controls softening mechanisms which induce different DRX softening and work-hardening. The activation energy of DRX, an important material parameter, determines the critical conditions for DRX initiation. So far, several empirical equations have been proposed to determine the deformation activation energy and hot deformation behavior of metals. The most frequently used one is Arrhenius equation which designs a famous Zener–Hollomon parameter, Z, to represent the effects of the temperatures and strain rate on the deformation behaviors, and then uncovers the approximative hyperbolic law between Z parameter and flow stress [10,11]. Z = ε˙ exp
Q RT
ε˙ = AF() exp
−Q RT
(1) (2)
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Table 1 Values of εc , c , εp and p at different deformation conditions. Strain rate (s−1 )
Temperature (K) 1123
True strain 0.01 εc 0.1 1 10 0.01 εp 0.1 1 10 True stress (MPa) 0.01 c 0.1 1 10 0.01 p 0.1 1 10 0.01 εc /εp 0.1 1 10 0.01 c / p 0.1 1 10
1198
1273
1348
−0.177 −0.336 −0.146 −0.259 −0.400 −0.818 −0.545 −0.564
−0.160 −0.172 −0.135 −0.359 −0.309 −0.436 −0.591 −0.627
−0.113 −0.140 −0.077 −0.247 −0.236 −0.318 −0.455 −0.600
−0.083 −0.142 −0.059 −0.218 −0.355 −0.264 −0.355 −0.573
−100.875 −137.038 −153.988 −215.180 −119.111 −155.026 −187.522 −235.405 0.441 0.411 0.268 0.459 0.847 0.884 0.821 0.914
−70.523 −89.748 −122.629 −203.734 −83.558 −110.287 −151.374 −213.198 0.519 0.394 0.229 0.572 0.844 0.814 0.810 0.956
−45.244 −63.469 −76.918 −131.429 −57.221 −77.083 −114.790 −149.191 0.476 0.439 0.170 0.412 0.791 0.823 0.670 0.881
−35.122 −42.362 −55.127 −105.296 −40.714 −53.280 −85.495 −122.623 0.234 0.540 0.165 0.381 0.863 0.795 0.645 0.859
||n ˛ || < 0.8 where, F() = exp(ˇ ||)˛ || > 1.2 where ε˙ is the strain rate [sinh(˛ ||)]n for all −1 (s ), R is the universal gas constant (8.31 J mol−1 K−1 ), T is the absolute temperature (K), Q is the activation energy of DRX (kJ mol−1 ), is the flow stress (MPa) for a given stain, A, ˛ and n are the material constants (˛ = ˇ/n).
For the low stress level (˛ < 0.8), substituting the power law of F() into Eq. (2) and taking natural logarithms on both sides of Eq. (2) give: Q RT
(2) Calculation of material constant ˇ For the high stress level (˛ || > 1.2), substituting the exponential law of F() into Eq. (2) and taking natural logarithms on both sides of Eq. (2) give: ln ε˙ = ln A + ˇ || −
Q RT
(4)
˙ ||. The peak stresses at different temperaThen, ˇ = d ln ε/ tures and strain rates can be identified for the target stresses with high level. The linear relationships between || and ln ε˙ at different temperatures were fitted out as Fig. 4. The mean value of all the slope rates is accepted as the inverse of material constant ˇ, thus ˇ value is obtained as 0.07558 MPa−1 . Thus, another material constant ˛ = ˇ/n = 0.00913 MPa−1 . (3) Calculation of DRX activation energy Q For all the stress level (including low and high stress levels), Eq. (2) can be represented as the following:
(1) Calculation of material constant n
ln ε˙ = ln A + n ln || −
˙ Fig. 3. The relationships between ln and ln ε.
(3)
˙ Then, n = d ln ε/d ln ||. In 2010, Quan et al. [1] plotted the relationships between the true stress and true strain of 42CrMo high-strength steel in ln–ln scale under different temperatures and strain rates, and hence found a true strain range of −0.08 to −0.18 including part of the first stage and the second stage described in the previous, in which all the stresses increase gradually with almost the same ratios. Therefore, this true strain range was accepted as a steady WH stage corresponding to low stress level. In further, Quan et al. [1] fitted the relationships between the stress and the strain rate as the true strain was −0.14, and then found almost equally linear relationships which revealed that the influence of temperature was very small. Thus, it can be deduced that to evaluate the material constant n of Arrhenius equation, the stress–strain data in the true strain range of −0.08 to −0.18 contribute to the minimum calculation tolerance. Here true strain ε = − 0.1 was chose. Fig. 3 shows the relationships between ln || and ln ε˙ for ε = − 0.1 under different temperatures. The linear relationship is observed for each temperature and the slope rates are almost similar with each other. The mean value of all the slope rates is accepted as the inverse of material constant n, thus n value is obtained as 8.27780.
ln ε˙ = ln A + n [ln sinh(˛ ||)] −
Q RT
(5)
If ε˙ is constant, there is a linear relationship between ln sinh(˛ ||) and 1/T, and Eq. (5) can be rewritten as: Q = Rn
d
[ln sinh(˛ ||)] d(1/T )
(6)
The peak stresses at different temperatures and strain rates can be identified for the present target stresses. The linear relationships between ln sinh(˛) and 1/T at different strain rates were fitted out as Fig. 5. The mean value of all the slope rates is accepted
˙ Fig. 4. The relationships between || and ln ε.
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2.4
lnsinh ασ
1.6 0.8 0.0 -1
0.01 s
-0.8
-1
0.1 s
little higher than that of as-cast 42CrMo steel adopted by Lin et al. The difference of two average Q values results from the different as-received statuses. In common, the higher deformation activation energy will be found in hot deformation of as-received steels with higher yield strength. It is obvious that the true stress data of extruded rods in this work are higher than that of as-cast billets in the work of Lin et al. In addition, the difference of experiment projects involving strain rate between this work and the work of Lin et al. is another important reason for the difference of calculation results.
-1
1s
-1.6
-1
10 s -2.4 0.00072
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0.00076
0.00080
0.00084
0.00088
0.00092
-1
1/T K Fig. 5. The relationships between ln sinh(˛ ||) and 1/T.
as Q/Rn value, then Q is calculated as 599.73210 kJ mol−1 . The activation energy of DRX is a term defined as the energy that must be overcome in order for the nucleation and growth of new surface or grain boundary to occur. In 2008, Lin et al. found that the activation energy of as-cast 42CrMo steel is not a constant but a variable 392–460 kJ mol−1 as a function of strain, and the peak value of DRX energy corresponds to the peak stress [2,3,8]. In this investigate, the influence of strain on the variable activation energy was ignored to simplify the following calculations, and only the peak value of DRX energy was accepted as the activation energy of DRX. This simplification ensures the predicted occurrence of DRX by the derived equations. Lin et al. also pointed that the average value of the activation energy of as-cast 42CrMo steel is 438.865 kJ mol−1 [2,3,8]. The average Q value of extruded 42CrMo steel, 599.73210 kJ mol−1 , is a
(4) Construction of constitutive equation ˙ T and into Eq. (5), the Substituting ˛, n, Q and four sets of ε, mean value of material constant A is obtained as 2.44154 × 1025 s−1 . ˙ T and can be expressed as: Thus, the relationships between ε,
ε˙ = 2.44154 × 1025 sinh(0.00913 ||)8.27780
× exp
−599.73210 × 103 8.31T
Substituting Z = ε˙ exp
(7)
599.73210×103 8.31T
into Eq. (7), thus, the flow
stress can be expressed as:
|| = 109.52903 ln
+
⎧ ⎨
1/8.27780
Z
⎩ 2.44154 × 1025
Z 2.44154 × 1025
2/8.27780
1/2 ⎫ ⎬
+1
⎭
(8)
Fig. 6. d/dε versus plots after the peak points of the true stress–strain curves under different deformation temperatures with strain rates (a) 0.01 s−1 , (b) 0.1 s−1 , (c) 1 s−1 and (d) 10 s−1 .
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G.-Z. Quan et al. / Materials Science and Engineering A 528 (2011) 4643–4651 Table 3 The kinetic model of DRX calculated from true compressive stress–strain curves.
Table 2 The deformation strain corresponding to XDRX = 1. True strain −0.5 to −0.9 −0.4 to −0.9 −0.3 to −0.9 −0.6 to −0.9 −0.4 to −0.9
Temperature (K)
Strain rate (s−1 )
1198 1273 1348 1273 1348
0.01 0.01 0.01 0.1 0.1
Volume fractions of dynamic recrystallization
Exponents
XDRX = 1 − exp
|ε∗ | = 0.61822(Z/A)
m ε−εc −
ε∗
|εc | = 0.16707(Z/A) Z = ε˙ exp
0.08207
0.06704
599.73210×103 8.31T
A = 2.44154 × 1025 s−1 m = 3.85582
3.4. DRX kinetic model During thermoplastic deformation process, dislocations continually increase and accumulate to such an extent that at a critical strain, DRX nucleus would form and grow up near grain boundaries, twin boundaries and deformation bands. It is well known that the conflicting effects coexist between the multiplication of dislocation due to continual hot deformation and the annihilation
a
2
of dislocation due to DRX. When work-hardening corresponding to the former and DRX softening corresponding to the later are in dynamic balance, flow stress will keep constant with increasing strain, meanwhile deformation comes to a steady stage in which complete DRX grains have equiaxed shape and keep constant size [9–14]. In common, the kinetics of DRX can be described in terms of
b
1
0
ln|εc|
0
ln|ε*|
2
-1
-2
-4
-2
ε * = 0.61822( Z/A)
-3 -12
-8
-4
0
4
ε c = 0.16707( Z/A) 0.06704
0.08207
8
-6 -12
12
-8
ln ( Z/A)
-4
0
4
8
1348 K 1273 K 1198 K
1123 K
12
ln ( Z/A)
Fig. 7. Relationships between the dimensionless parameter, Z/A, and (a) ε*, (b) εc .
1.0
b
ε& = 0.01s -1
1.0
0.8
0.8
0.6
0.6
1348 K 1273 K 1198 K
0.4
1123 K
XDRX
XDRX
a
ε& = 0.1s -1
0.4
0.2
0.2
0.0 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9
0.0 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9
ε
ε
d
ε& = 1s -1
1.0
0.8
0.8
0.6
0.6
XDRX
XDRX
c
1.0
0.4 0.2
1348 K 1273 K 1198 K
1123 K
0.0 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9
ε
ε& = 10s -1
0.4 0.2
1348 K 1273 K 1198 K
1123 K
0.0 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9
ε
Fig. 8. Predicted volume fractions of dynamic recrystallization obtained under different deformation temperatures with strain rates (a) 0.01 s−1 , (b) 0.1 s−1 , (c) 1 s−1 and (d) 10 s−1 .
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Fig. 9. Microstructures at the strain rate of 0.1 s−1 and temperatures of (a) as-received, (b) 1123 K, (c) 1198 K, (d) 1273 K and (e) 1348 K.
normal S-curves of the recrystallized volume expressed as a function of time. In a constant strain rate, time can be replaced by strain and recrystallized volume fraction can be expressed by modified Avrami equation [13,14]. Thus, the kinetics of DRX evolution can be predicted by the following equation [9]. XDRX = 1 − exp
ε − εc m −
ε∗
(9)
where XDRX is the volume fraction of dynamic recrystallized grain and m is Avrami’s constant. This expression, which is modified from the Avrami’s equation, means that XDRX depends on strain, strain rate and temperature. The true stress–strain curve data after the peak stress point were adopted to calculate DRX softening rate ( = d/dε versus ) plots, and the results were shown as Fig. 6a–d. The maximum softening rate corresponds to the negative peak of such plot. The strain for maximum softening rate, ε*, identified from Fig. 6a–d, and the crit-
ical strain, εc , identified from Fig. 2a–d can be considered with a power function of dimensionless parameter, Z/A (Fig. 7a–b). The function expressions linearly fitted by the method of least squares 0.08207 0.06704 are |ε∗ | = 0.61822(Z/A) and |εc | = 0.16707(Z/A) . In order to solve the Avrami’s constant, m, it is essential to identify the deformation conditions corresponding to XDRX = 1 meaning that the flow stress reaches a steady state in which complete DRX grains have equiaxed shape and keep constant size. From the true compressive stress–strain curves in Fig. 1a–d, and d/dε versus plots in Fig. 6a–d, such the deformation conditions can be identified as shown in Table 2. Substituting these deformation conditions corresponding to XDRX = 1 into Eq. (9), the mean value of the Avrami’s constant m can be obtained as 3.85582. Thus, the kinetic model of DRX calculated from true compressive stress–strain curves can be expressed as Table 3. Based on the calculation results of this model, the effect of deformation temperature, strain and strain rate on the recrystallized volume fraction is shown in Fig. 8a–d. These figures show that
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Fig. 10. Microstructures at the temperature of 1348 K and strain rate of (a) 0.01 s−1 , (b) 0.1 s−1 , (c) 1 s−1 and (d) 10 s−1 .
as the strain’ absolute value increases, the DRX volume fraction increases and reaches a constant value of 1 meaning the completion of DRX process. Comparing these curves with one another, it is found that, for a specific strain rate, the deformation strain required for the same amount of DRX volume fraction increases with decreasing deformation temperature, which means that DRX is delayed to a longer time. In contrast, for a fixed temperature, the deformation strain required for the same amount of DRX volume fraction increases with increasing strain rate, which also means that DRX is delayed to a longer time. This effect can be attributed to decreased mobility of grain boundaries (growth kinetics) with increasing strain rate and decreasing temperature. Thus, under higher strain rates and lower temperatures, the deformed metal tends to incomplete DRX, that is to say, the DRX volume fraction tends to be less than 1. 3.5. Microstructure observations The DRX microstructures on the section plane of specimen deformed to the true strain of −0.9 were examined and analyzed under the optical microscope. The initial microstructure of asreceived 42CrMo high-strength steel consists of rough equiaxed grains with a large quantity of twin boundaries (as shown in Fig. 9a). Fig. 9b–e shows the typical microstructures of the specimens deformed to a strain of −0.9 at the strain rate of 0.1 s−1 and at the temperatures of 1123 K, 1198 K, 1273 K and 1348 K, respectively. The recrystallized grains with wavy or corrugated grain boundaries can be easily identified at these deformation conditions. The deformed metal completely or partially transforms to a microstructure of approximately equiaxed defect-free grains which are predominantly bounded by high angle boundaries (i.e. a recrystallized microstructure) by relatively localized boundary migration. Fig. 9b shows that at the lower temperature of 1123 K,
only a small fraction of the deformed metal transforms to recrystallized microstructure due to lower mobility of grain boundaries (growth kinetics), and the grain boundaries of the left untransformed metal reveal an uniform vector in radial direction due to weaker recovery for grain boundary torsion. As deformation temperature increases, more and more deformed metal transforms to recrystallized microstructure due to higher mobility of grain boundaries, and all the grains tend to be more and more homogeneous due to stronger adaptivity for grain boundary migration (as shown in Fig. 9c–e). It is worth emphasizing that as deformation temperature increases, the grain growth is apparently promoted. As depicted, for a specific strain rate 0.1 s−1 , the microstructure of the as-received billet with average grain size of 85 m becomes refined up to about 28 m after upsetting under temperature 1123 K, to about 35 m under temperature 1198 K, to about 43 m under temperature 1273 K, to about 50 m under temperature 1348 K. In contrast, for a fixed temperature of 1348 K, the typical microstructures of the specimens deformed to a strain of −0.9 at the strain rates of 0.01 s−1 , 0.1 s−1 , 1 s−1 and 10 s−1 are shown as Fig. 10a–d, respectively. It can be seen that at all the four strain rates, all the initial equiaxed grains with a large quantity of twin boundaries transform to recrystallized grains with wavy or corrugated grain boundaries. In addition, as deformation strain rate increases, the microstructure of the as-received billet with average grain size of 85 m becomes more and more refined due to increasing migration energy stored in grain boundaries and decreasing grain growth time. 4. Conclusions The stress–strain curves of extruded 42CrMo high-strength steel compressed in the temperature range of 1123–1348 K and the strain rate range of 0.01–10 s−1 exhibits three distinct stages. At the
G.-Z. Quan et al. / Materials Science and Engineering A 528 (2011) 4643–4651
first stage, flow stress exhibits a rapid increase to a critical value. At the second stage, flow stress exhibits a smaller and smaller increase until a peak value or an inflection of work-hardening rate. At the third stage, three types of curve variation tendency can be generalized as following: decreasing gradually to a steady state with DRX softening, maintaining higher stress level without significant softening and work-hardening, and increasing continuously with significant work-hardening. It can be summarized that the typical form of DRX flow curve, including a single peak followed by a steady state flow as a plateau, is more recognizable at high temperatures and low strain rates. The inflections in the plot of d/dε versus up to the stress peak point reveal that the occurrence and evolution of DRX for extruded 42CrMo high-strength steel can be expressed by the process variables identified from the flow stress curves. By the regression analysis for conventional hyperbolic sine equation, the dependence of flow stress on temperature and strain rate was described, and what’s more, the activation energy of DRX (Q) and a dimensionless parameter controlling the stored energy (Z/A) were determined. In further, the strain for maximum softening rate, ε*, and the critical strain, εc were described by the functions of dimensionless parameter, Z/A. Thus, the evolution of DRX volume fraction was characterized by the modified Avrami type equation including the above parameters, and the effect of deformation conditions was described in detail. The microstructure observation of the specimens deformed to a strain of −0.9 at the strain rate of 0.1 s−1 and at the temperatures of 1123 K, 1198 K, 1273 K and 1348 K, and the
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specimens deformed to a strain of −0.9 at the temperature of 1348 K and at the strain rates of 0.01 s−1 , 0.1 s−1 , 1 s−1 and 10 s−1 , verify the influence of deformation conditions on the evolution of DRX volume fraction. Acknowledgement This work was supported by the Fundamental Research Funds for the Central Universities (Project No. CDJZR11130009). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
G.Z. Quan, Y. Tong, G. Luo, J. Zhou, Comput. Mater. Sci. 50 (2010) 167–171. Y.C. Lin, X.M. Chen, Mater. Des. 32 (2011) 1733–1759. Y.C. Lin, M.S. Chen, J. Zhong, Comput. Mater. Sci. 43 (2008) 1117–1122. S.I. Kim, Y. Lee, S.M. Byon, J. Mater. Process. Technol. 140 (2003) 84–89. Q.G. Zheng, T. Ying, Z. Jie, Proc. Inst. Mech. Eng. Part B–J. Eng. Manuf. 224 (2010) 1707–1716. G.Z. Quan, K.W. Liu, J. Zhou, Trans. Nonferrous Met. Soc. China 19 (2009) S537–S541. A. Momeni, K. Dehghani, H. Keshmiri, G.R. Ebrahimi, Mater. Sci. Eng. A 527 (2010) 1605–1611. Y.C. Lin, M.S. Chen, J. Zhong, Comput. Mater. Sci. 42 (2008) 470–477. S.I. Kim, Y.C. Yoo, Mater. Sci. Eng. A 311 (2010) 108–113. D. Ponge, G. Gottstein, Acta Mater. 46 (1998) 69–80. C.X. Yue, L.W. Zhang, S.L. Liao, J.B. Pei, H.J. Gao, Y.W. Jia, X.J. Lian, Mater. Sci. Eng. A 499 (2009) 177–181. G.L. Ji, F.G. Li, Q.H. Li, H.Q. Li, Z. Li, Mater. Sci. Eng. A 527 (2010) 2350–2355. S.F. Medina, C.A. Hernandez, Acta Mater. 44 (1996) 149–154. S.F. Medina, C.A. Hernandez, Acta Mater. 44 (1996) 165–171.
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Dynamic recrystallization kinetics of 42CrMo steel during compression at different temperatures and strain rates Guo-Zheng Quan ∗ , Gui-Sheng Li, Tao Chen, Yi-Xin Wang, Yan-Wei Zhang, Jie Zhou School of Material Science and Engineering, Chongqing University, Chongqing 400044, China
a r t i c l e
i n f o
Article history: Received 9 December 2010 Received in revised form 16 February 2011 Accepted 26 February 2011 Available online 6 March 2011 Keywords: Dynamic recrystallization Critical strain Flow stress High-strength steel
a b s t r a c t In order to improve the understanding of the coupling effect in dynamic recrystallization (DRX) behavior and flow behavior for extruded 42CrMo high-strength steel, a series of isothermal upsetting experiments with height reduction of 60% were performed at the temperatures of 1123 K, 1198 K, 1273 K and 1348 K, and the strain rates of 0.01 s−1 , 0.1 s−1 , 1 s−1 and 10 s−1 on a Gleeble1500 thermo-mechanical simulator. The initiation and evolution of DRX were investigated by using the process variables derived form flow curves. By the regression analysis for conventional hyperbolic sine equation, the activation energy of DRX was determined as Q = 599.7321 kJ mol−1 , and a dimensionless parameter controlling the ˙ stored energy were determined as Z/A = ε exp (599.73210 × 103 )/8.31T /2.44154 × 1025 . Based on the conventional strain hardening rate curves (d/dε versus ), the characteristic parameters including the critical strain for DRX initiation (εc ), the strain for peak stress (εp ), and the strain for maximum softening rate (ε*) were identified. Basedon the regression analysis results for a modified Avrami type equation XDRX = 1 − exp
− (ε − εc ) /ε∗
m
0.06704
in which εc , ε* and m were described as |εc | = 0.16707(Z/A)
,
0.08207
|ε∗ | = 0.61822(Z/A) and m = 3.85582 respectively, the evolutions of DRX volume were described as following: for a fixed strain rate, the strain required for the same amount of DRX volume fraction increases with decreasing deformation temperature, in contrast, for a fixed temperature, it increases with increasing strain rate. Finally, the theoretical predictions were validated by the microstructure graphs. © 2011 Elsevier B.V. All rights reserved.
1. Introduction 42CrMo is one of the representative medium carbon and low alloy steels. Due to its good balance of strength, toughness and wear resistance, 42CrMo high-strength steel is widely used for many general purpose parts including automotive crankshaft, rams, spindles, etc. [1]. During hot forming process steel is liable to undergo work hardening (WH), dynamic recovery (DRV) and dynamic recrystallization (DRX), three metallurgical phenomena for controlling microstructure and mechanical properties [2–4]. In light alloys such as magnesium alloy and aluminum alloy, dynamic recovery (DRV) can balance work hardening, and a plateau is achieved [5,6]. However, in austenitic steels with higher deformation resistance, the kinetics of DRV is lower, and DRX can be initiated at a critical condition of stress accumulation [7]. The occurrence of DRX brings about grain refinement and deformation resistance reduction, due to which the evaluation of the rate and progress of DRX in terms of deformation conditions is important [8]. The general descriptive model for DRX is that the nucleation of DRX
∗ Corresponding author. Tel.: +86 023 6510 3065; fax: +86 023 6511 1493. E-mail address: quangz [email protected] (G.-Z. Quan). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.02.090
grains can start at a critical strain which is a function of initial microstructure and deformation conditions. Then, the evolution of DRX microstructure can proceed further by increasing deformation and through the formation of a necklace structure [9]. Considerable research on DRX kinetics have focused on measuring by metallographic images or EBSD maps of the frozen microstructures at different deformation conditions such as temperature, strain rate and plastic deformation amount, meanwhile analyzing the relationships between microstructure variations and deformation parameter levels. However, few attention has been paid to model microstructure evolution by analyzing flow curves collected by hot compression tests [1–9]. For austenitic steels such as 42CrMo, during a plastic forming process a pronounced interaction between DRX evolution and mechanical property is implicit in flow behavior. Thus, it is realizable to model DRX evolution by analyzing the true stress–strain curves. In the present work, three characteristic points including the critical strain for DRX initiation (εc ), the strain for peak stress (εp ), and the strain for maximum softening rate (ε*) have been identified from the true stress–strain curves of extruded 42CrMo high-strength steel, and their existence means that the evolution of DRX can be characterized by the process variables. The object of this study is to uncover and describe the general nature of the influence
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of strain, strain rate and temperature on DRX behavior of 42CrMo high-strength steel using a series of true stress–strain curves collected from compression tests at the temperature of 1123–1348 K and the strain rate of 0.01–10 s−1 . The effects of strain, temperature and strain rate on flow stress and DRX behavior are represented by Zener–Hollomon parameter, Z, in an exponent-type function of temperature and strain rate. In addition, Zener–Hollomon parameter and another essential material constant, DRX activation energy, implicit in the Arrhenius type equation of flow stress, have been achieved by fitting this equation. Then the relationships between process variables and DRX volume fraction were coupled by the modified Avrami type equation including εc and ε* as a function of Z. Finally, the theoretical predictions by the derived equations were validated by the microstructure graphs.
2. Experimental procedure The chemical compositions of extruded 42CrMo high-strength steel used in this study were (wt.%) C 0.450, Si 0.280, Cr 0.960, Mn 0.630, Mo 0.190, P 0.016, Cu 0.014, S 0.012, Fe (balance). The extruded rod with diameter 10 mm was homogenized under temperature 1123 K for twelve hours. Then the rod was scalped to height 12 mm with grooves on both sides filled with machine oil mingled with graphite powder as lubricant to reduce friction between the anvils and specimen. A computer-controlled, servo-hydraulic Gleeble 1500 testing machine was used for the compression experiments. This machine can be programmed to simulate both the thermal and the mechanical industrial process variables for a wide range of hot deformation conditions. The specimens were resistance heated at a heating rate of 1 K/s and held at a certain temperature for 180 s by thermo-coupledfeedback-controlled AC current, which decreased the anisotropy in
flow deformation behavior effectively. Three thermocouples were welded at the mid-span of billet to provide accurate temperature control and measurement during testing. The compression tests corresponding to a height reduction of 60% were carried out at four different temperatures of 1123 K, 1198 K, 1273 K and 1348 K and four different strain rates of 0.01 s−1 , 0.1 s−1 , 1 s−1 , 10 s−1 . Then, such sixteen specimens deformed were rapidly quenched with water to retain the recrystallized microstructures. All the specimens were sectioned perpendicular to the longitudinal compression axis for metallographic examination. The sections were polished and etched in an abluent solution of saturated picric acid. The optical microstructures in the center region of the section plane were examined. In addition, the variations of stress and strain were monitored continuously by a personal computer equipped with an automatic data acquisition system. The true stress and true strain were derived from the measurement of the nominal stress–strain relationship according to the following formula [1]: T = N (1 + εN ), εT = ln(1+εN ), where T is the true stress, N is the nominal strain, εT is the true strain and εN is the nominal strain.
3. Results and discussion 3.1. Flow stress behavior The true stress–true strain curves of 42CrMo high-strength steel compressed at different deformation conditions are shown in Fig. 1a–d. It is shown that flow stress is in direct correlation with strain, temperature and strain rate. Comparing these curves with one another, it is found that, for a specific strain rate, the flow stress decreases markedly with increasing temperature. In contrast, for a fixed temperature, the flow stress generally increases
Fig. 1. True stress–strain curves of 42CrMo high-strength steel obtained by Gleeble 1500 under the different deformation temperatures with strain rates. (a) 0.01 s−1 , (b) 0.1 s−1 , (c) 1 s−1 and (d) 10 s−1 .
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Fig. 2. d/dε versus plots up to the peak points of the true stress–strain curves under different deformation temperatures with strain rates (a) 0.01 s−1 , (b) 0.1 s−1 , (c) 1 s−1 and (d) 10 s−1 .
as the strain rate increases. The cause lies in the fact that lower strain rate and higher temperature provide longer time for the energy accumulation and higher mobilities at boundaries which result in the nucleation and growth of dynamically recrystallized grains and dislocation annihilation. From the true stress–strain curves in Fig. 1a–d, it can be seen that the stress evolution with strain exhibits three distinct stages [10]. At the first stage where work hardening (WH) predominates, flow stress exhibits a rapid increase to a critical value. At the second stage, flow stress exhibits a smaller and smaller increase until a peak value or an inflection of work-hardening rate, which shows that the thermal softening due to DRX and dynamic recovery (DRV) becomes more and more predominant, then it exceeds WH. At the third stage, three types of curve variation tendency can be generalized as following: decreasing gradually to a steady state with DRX softening (1123–1348 K and 0.01 s−1 , 1198–1348 K and 0.1 s−1 , 1273–1348 K and 1 s−1 ), maintaining higher stress level without significant softening and work-hardening (1123–1198 K and 1 s−1 , 1123–1348 K and 10 s−1 ), and increasing continuously with significant workhardening (1123 K and 0.1 s−1 ). Thus, it can be concluded that the typical form of flow curve with DRX softening, including a single peak followed by a steady state flow as a plateau, is more recognizable at high temperatures and low strain rates. That is because at higher strain rates and lower temperatures, the higher workhardening rate slows down the rate of DRX softening, and both the peak stress and the onset of steady state flow are therefore shifted to higher strain levels. 3.2. The initiation of DRX From the true compressive stress–strain data shown in Fig. 1a–d, the values of the strain hardening rate ( = d/dε) were calculated. The critical conditions for the onset of DRX can be attained when the value of −d/d , where strain hardening rate = d/dε, reaches
the minimum which corresponds to an inflection of d/dε versus curve [11]. In this study, analysis of inflections in the plot of d/dε versus up to the peak point of the true stress–strain curve has been performed to reveal whether DRX occurs. Results confirm that the d/dε versus curves have characteristic inflections as shown in Fig. 2a–d, which indicates that DRX is initiated at corresponding deformation conditions. The critical stress to initiation can be identified, and hence the corresponding critical strain to initiation can be obtained from true stress–strain curve. As a result, the values of critical strain and peak stress at different deformation conditions were shown in Table 1, from which it can be seen that the critical strain and critical stress depend on temperature and strain rate nonlinearly, and it is summarized that εc /εp = 0.165–0.572, c / p = 0.645–0.956. 3.3. Arrhenius equation for flow behavior with DRX It is known that the thermally activated stored energy developed during deformation controls softening mechanisms which induce different DRX softening and work-hardening. The activation energy of DRX, an important material parameter, determines the critical conditions for DRX initiation. So far, several empirical equations have been proposed to determine the deformation activation energy and hot deformation behavior of metals. The most frequently used one is Arrhenius equation which designs a famous Zener–Hollomon parameter, Z, to represent the effects of the temperatures and strain rate on the deformation behaviors, and then uncovers the approximative hyperbolic law between Z parameter and flow stress [10,11]. Z = ε˙ exp
Q RT
ε˙ = AF() exp
−Q RT
(1) (2)
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Table 1 Values of εc , c , εp and p at different deformation conditions. Strain rate (s−1 )
Temperature (K) 1123
True strain 0.01 εc 0.1 1 10 0.01 εp 0.1 1 10 True stress (MPa) 0.01 c 0.1 1 10 0.01 p 0.1 1 10 0.01 εc /εp 0.1 1 10 0.01 c / p 0.1 1 10
1198
1273
1348
−0.177 −0.336 −0.146 −0.259 −0.400 −0.818 −0.545 −0.564
−0.160 −0.172 −0.135 −0.359 −0.309 −0.436 −0.591 −0.627
−0.113 −0.140 −0.077 −0.247 −0.236 −0.318 −0.455 −0.600
−0.083 −0.142 −0.059 −0.218 −0.355 −0.264 −0.355 −0.573
−100.875 −137.038 −153.988 −215.180 −119.111 −155.026 −187.522 −235.405 0.441 0.411 0.268 0.459 0.847 0.884 0.821 0.914
−70.523 −89.748 −122.629 −203.734 −83.558 −110.287 −151.374 −213.198 0.519 0.394 0.229 0.572 0.844 0.814 0.810 0.956
−45.244 −63.469 −76.918 −131.429 −57.221 −77.083 −114.790 −149.191 0.476 0.439 0.170 0.412 0.791 0.823 0.670 0.881
−35.122 −42.362 −55.127 −105.296 −40.714 −53.280 −85.495 −122.623 0.234 0.540 0.165 0.381 0.863 0.795 0.645 0.859
||n ˛ || < 0.8 where, F() = exp(ˇ ||)˛ || > 1.2 where ε˙ is the strain rate [sinh(˛ ||)]n for all −1 (s ), R is the universal gas constant (8.31 J mol−1 K−1 ), T is the absolute temperature (K), Q is the activation energy of DRX (kJ mol−1 ), is the flow stress (MPa) for a given stain, A, ˛ and n are the material constants (˛ = ˇ/n).
For the low stress level (˛ < 0.8), substituting the power law of F() into Eq. (2) and taking natural logarithms on both sides of Eq. (2) give: Q RT
(2) Calculation of material constant ˇ For the high stress level (˛ || > 1.2), substituting the exponential law of F() into Eq. (2) and taking natural logarithms on both sides of Eq. (2) give: ln ε˙ = ln A + ˇ || −
Q RT
(4)
˙ ||. The peak stresses at different temperaThen, ˇ = d ln ε/ tures and strain rates can be identified for the target stresses with high level. The linear relationships between || and ln ε˙ at different temperatures were fitted out as Fig. 4. The mean value of all the slope rates is accepted as the inverse of material constant ˇ, thus ˇ value is obtained as 0.07558 MPa−1 . Thus, another material constant ˛ = ˇ/n = 0.00913 MPa−1 . (3) Calculation of DRX activation energy Q For all the stress level (including low and high stress levels), Eq. (2) can be represented as the following:
(1) Calculation of material constant n
ln ε˙ = ln A + n ln || −
˙ Fig. 3. The relationships between ln and ln ε.
(3)
˙ Then, n = d ln ε/d ln ||. In 2010, Quan et al. [1] plotted the relationships between the true stress and true strain of 42CrMo high-strength steel in ln–ln scale under different temperatures and strain rates, and hence found a true strain range of −0.08 to −0.18 including part of the first stage and the second stage described in the previous, in which all the stresses increase gradually with almost the same ratios. Therefore, this true strain range was accepted as a steady WH stage corresponding to low stress level. In further, Quan et al. [1] fitted the relationships between the stress and the strain rate as the true strain was −0.14, and then found almost equally linear relationships which revealed that the influence of temperature was very small. Thus, it can be deduced that to evaluate the material constant n of Arrhenius equation, the stress–strain data in the true strain range of −0.08 to −0.18 contribute to the minimum calculation tolerance. Here true strain ε = − 0.1 was chose. Fig. 3 shows the relationships between ln || and ln ε˙ for ε = − 0.1 under different temperatures. The linear relationship is observed for each temperature and the slope rates are almost similar with each other. The mean value of all the slope rates is accepted as the inverse of material constant n, thus n value is obtained as 8.27780.
ln ε˙ = ln A + n [ln sinh(˛ ||)] −
Q RT
(5)
If ε˙ is constant, there is a linear relationship between ln sinh(˛ ||) and 1/T, and Eq. (5) can be rewritten as: Q = Rn
d
[ln sinh(˛ ||)] d(1/T )
(6)
The peak stresses at different temperatures and strain rates can be identified for the present target stresses. The linear relationships between ln sinh(˛) and 1/T at different strain rates were fitted out as Fig. 5. The mean value of all the slope rates is accepted
˙ Fig. 4. The relationships between || and ln ε.
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2.4
lnsinh ασ
1.6 0.8 0.0 -1
0.01 s
-0.8
-1
0.1 s
little higher than that of as-cast 42CrMo steel adopted by Lin et al. The difference of two average Q values results from the different as-received statuses. In common, the higher deformation activation energy will be found in hot deformation of as-received steels with higher yield strength. It is obvious that the true stress data of extruded rods in this work are higher than that of as-cast billets in the work of Lin et al. In addition, the difference of experiment projects involving strain rate between this work and the work of Lin et al. is another important reason for the difference of calculation results.
-1
1s
-1.6
-1
10 s -2.4 0.00072
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0.00076
0.00080
0.00084
0.00088
0.00092
-1
1/T K Fig. 5. The relationships between ln sinh(˛ ||) and 1/T.
as Q/Rn value, then Q is calculated as 599.73210 kJ mol−1 . The activation energy of DRX is a term defined as the energy that must be overcome in order for the nucleation and growth of new surface or grain boundary to occur. In 2008, Lin et al. found that the activation energy of as-cast 42CrMo steel is not a constant but a variable 392–460 kJ mol−1 as a function of strain, and the peak value of DRX energy corresponds to the peak stress [2,3,8]. In this investigate, the influence of strain on the variable activation energy was ignored to simplify the following calculations, and only the peak value of DRX energy was accepted as the activation energy of DRX. This simplification ensures the predicted occurrence of DRX by the derived equations. Lin et al. also pointed that the average value of the activation energy of as-cast 42CrMo steel is 438.865 kJ mol−1 [2,3,8]. The average Q value of extruded 42CrMo steel, 599.73210 kJ mol−1 , is a
(4) Construction of constitutive equation ˙ T and into Eq. (5), the Substituting ˛, n, Q and four sets of ε, mean value of material constant A is obtained as 2.44154 × 1025 s−1 . ˙ T and can be expressed as: Thus, the relationships between ε,
ε˙ = 2.44154 × 1025 sinh(0.00913 ||)8.27780
× exp
−599.73210 × 103 8.31T
Substituting Z = ε˙ exp
(7)
599.73210×103 8.31T
into Eq. (7), thus, the flow
stress can be expressed as:
|| = 109.52903 ln
+
⎧ ⎨
1/8.27780
Z
⎩ 2.44154 × 1025
Z 2.44154 × 1025
2/8.27780
1/2 ⎫ ⎬
+1
⎭
(8)
Fig. 6. d/dε versus plots after the peak points of the true stress–strain curves under different deformation temperatures with strain rates (a) 0.01 s−1 , (b) 0.1 s−1 , (c) 1 s−1 and (d) 10 s−1 .
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G.-Z. Quan et al. / Materials Science and Engineering A 528 (2011) 4643–4651 Table 3 The kinetic model of DRX calculated from true compressive stress–strain curves.
Table 2 The deformation strain corresponding to XDRX = 1. True strain −0.5 to −0.9 −0.4 to −0.9 −0.3 to −0.9 −0.6 to −0.9 −0.4 to −0.9
Temperature (K)
Strain rate (s−1 )
1198 1273 1348 1273 1348
0.01 0.01 0.01 0.1 0.1
Volume fractions of dynamic recrystallization
Exponents
XDRX = 1 − exp
|ε∗ | = 0.61822(Z/A)
m ε−εc −
ε∗
|εc | = 0.16707(Z/A) Z = ε˙ exp
0.08207
0.06704
599.73210×103 8.31T
A = 2.44154 × 1025 s−1 m = 3.85582
3.4. DRX kinetic model During thermoplastic deformation process, dislocations continually increase and accumulate to such an extent that at a critical strain, DRX nucleus would form and grow up near grain boundaries, twin boundaries and deformation bands. It is well known that the conflicting effects coexist between the multiplication of dislocation due to continual hot deformation and the annihilation
a
2
of dislocation due to DRX. When work-hardening corresponding to the former and DRX softening corresponding to the later are in dynamic balance, flow stress will keep constant with increasing strain, meanwhile deformation comes to a steady stage in which complete DRX grains have equiaxed shape and keep constant size [9–14]. In common, the kinetics of DRX can be described in terms of
b
1
0
ln|εc|
0
ln|ε*|
2
-1
-2
-4
-2
ε * = 0.61822( Z/A)
-3 -12
-8
-4
0
4
ε c = 0.16707( Z/A) 0.06704
0.08207
8
-6 -12
12
-8
ln ( Z/A)
-4
0
4
8
1348 K 1273 K 1198 K
1123 K
12
ln ( Z/A)
Fig. 7. Relationships between the dimensionless parameter, Z/A, and (a) ε*, (b) εc .
1.0
b
ε& = 0.01s -1
1.0
0.8
0.8
0.6
0.6
1348 K 1273 K 1198 K
0.4
1123 K
XDRX
XDRX
a
ε& = 0.1s -1
0.4
0.2
0.2
0.0 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9
0.0 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9
ε
ε
d
ε& = 1s -1
1.0
0.8
0.8
0.6
0.6
XDRX
XDRX
c
1.0
0.4 0.2
1348 K 1273 K 1198 K
1123 K
0.0 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9
ε
ε& = 10s -1
0.4 0.2
1348 K 1273 K 1198 K
1123 K
0.0 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9
ε
Fig. 8. Predicted volume fractions of dynamic recrystallization obtained under different deformation temperatures with strain rates (a) 0.01 s−1 , (b) 0.1 s−1 , (c) 1 s−1 and (d) 10 s−1 .
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Fig. 9. Microstructures at the strain rate of 0.1 s−1 and temperatures of (a) as-received, (b) 1123 K, (c) 1198 K, (d) 1273 K and (e) 1348 K.
normal S-curves of the recrystallized volume expressed as a function of time. In a constant strain rate, time can be replaced by strain and recrystallized volume fraction can be expressed by modified Avrami equation [13,14]. Thus, the kinetics of DRX evolution can be predicted by the following equation [9]. XDRX = 1 − exp
ε − εc m −
ε∗
(9)
where XDRX is the volume fraction of dynamic recrystallized grain and m is Avrami’s constant. This expression, which is modified from the Avrami’s equation, means that XDRX depends on strain, strain rate and temperature. The true stress–strain curve data after the peak stress point were adopted to calculate DRX softening rate ( = d/dε versus ) plots, and the results were shown as Fig. 6a–d. The maximum softening rate corresponds to the negative peak of such plot. The strain for maximum softening rate, ε*, identified from Fig. 6a–d, and the crit-
ical strain, εc , identified from Fig. 2a–d can be considered with a power function of dimensionless parameter, Z/A (Fig. 7a–b). The function expressions linearly fitted by the method of least squares 0.08207 0.06704 are |ε∗ | = 0.61822(Z/A) and |εc | = 0.16707(Z/A) . In order to solve the Avrami’s constant, m, it is essential to identify the deformation conditions corresponding to XDRX = 1 meaning that the flow stress reaches a steady state in which complete DRX grains have equiaxed shape and keep constant size. From the true compressive stress–strain curves in Fig. 1a–d, and d/dε versus plots in Fig. 6a–d, such the deformation conditions can be identified as shown in Table 2. Substituting these deformation conditions corresponding to XDRX = 1 into Eq. (9), the mean value of the Avrami’s constant m can be obtained as 3.85582. Thus, the kinetic model of DRX calculated from true compressive stress–strain curves can be expressed as Table 3. Based on the calculation results of this model, the effect of deformation temperature, strain and strain rate on the recrystallized volume fraction is shown in Fig. 8a–d. These figures show that
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Fig. 10. Microstructures at the temperature of 1348 K and strain rate of (a) 0.01 s−1 , (b) 0.1 s−1 , (c) 1 s−1 and (d) 10 s−1 .
as the strain’ absolute value increases, the DRX volume fraction increases and reaches a constant value of 1 meaning the completion of DRX process. Comparing these curves with one another, it is found that, for a specific strain rate, the deformation strain required for the same amount of DRX volume fraction increases with decreasing deformation temperature, which means that DRX is delayed to a longer time. In contrast, for a fixed temperature, the deformation strain required for the same amount of DRX volume fraction increases with increasing strain rate, which also means that DRX is delayed to a longer time. This effect can be attributed to decreased mobility of grain boundaries (growth kinetics) with increasing strain rate and decreasing temperature. Thus, under higher strain rates and lower temperatures, the deformed metal tends to incomplete DRX, that is to say, the DRX volume fraction tends to be less than 1. 3.5. Microstructure observations The DRX microstructures on the section plane of specimen deformed to the true strain of −0.9 were examined and analyzed under the optical microscope. The initial microstructure of asreceived 42CrMo high-strength steel consists of rough equiaxed grains with a large quantity of twin boundaries (as shown in Fig. 9a). Fig. 9b–e shows the typical microstructures of the specimens deformed to a strain of −0.9 at the strain rate of 0.1 s−1 and at the temperatures of 1123 K, 1198 K, 1273 K and 1348 K, respectively. The recrystallized grains with wavy or corrugated grain boundaries can be easily identified at these deformation conditions. The deformed metal completely or partially transforms to a microstructure of approximately equiaxed defect-free grains which are predominantly bounded by high angle boundaries (i.e. a recrystallized microstructure) by relatively localized boundary migration. Fig. 9b shows that at the lower temperature of 1123 K,
only a small fraction of the deformed metal transforms to recrystallized microstructure due to lower mobility of grain boundaries (growth kinetics), and the grain boundaries of the left untransformed metal reveal an uniform vector in radial direction due to weaker recovery for grain boundary torsion. As deformation temperature increases, more and more deformed metal transforms to recrystallized microstructure due to higher mobility of grain boundaries, and all the grains tend to be more and more homogeneous due to stronger adaptivity for grain boundary migration (as shown in Fig. 9c–e). It is worth emphasizing that as deformation temperature increases, the grain growth is apparently promoted. As depicted, for a specific strain rate 0.1 s−1 , the microstructure of the as-received billet with average grain size of 85 m becomes refined up to about 28 m after upsetting under temperature 1123 K, to about 35 m under temperature 1198 K, to about 43 m under temperature 1273 K, to about 50 m under temperature 1348 K. In contrast, for a fixed temperature of 1348 K, the typical microstructures of the specimens deformed to a strain of −0.9 at the strain rates of 0.01 s−1 , 0.1 s−1 , 1 s−1 and 10 s−1 are shown as Fig. 10a–d, respectively. It can be seen that at all the four strain rates, all the initial equiaxed grains with a large quantity of twin boundaries transform to recrystallized grains with wavy or corrugated grain boundaries. In addition, as deformation strain rate increases, the microstructure of the as-received billet with average grain size of 85 m becomes more and more refined due to increasing migration energy stored in grain boundaries and decreasing grain growth time. 4. Conclusions The stress–strain curves of extruded 42CrMo high-strength steel compressed in the temperature range of 1123–1348 K and the strain rate range of 0.01–10 s−1 exhibits three distinct stages. At the
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first stage, flow stress exhibits a rapid increase to a critical value. At the second stage, flow stress exhibits a smaller and smaller increase until a peak value or an inflection of work-hardening rate. At the third stage, three types of curve variation tendency can be generalized as following: decreasing gradually to a steady state with DRX softening, maintaining higher stress level without significant softening and work-hardening, and increasing continuously with significant work-hardening. It can be summarized that the typical form of DRX flow curve, including a single peak followed by a steady state flow as a plateau, is more recognizable at high temperatures and low strain rates. The inflections in the plot of d/dε versus up to the stress peak point reveal that the occurrence and evolution of DRX for extruded 42CrMo high-strength steel can be expressed by the process variables identified from the flow stress curves. By the regression analysis for conventional hyperbolic sine equation, the dependence of flow stress on temperature and strain rate was described, and what’s more, the activation energy of DRX (Q) and a dimensionless parameter controlling the stored energy (Z/A) were determined. In further, the strain for maximum softening rate, ε*, and the critical strain, εc were described by the functions of dimensionless parameter, Z/A. Thus, the evolution of DRX volume fraction was characterized by the modified Avrami type equation including the above parameters, and the effect of deformation conditions was described in detail. The microstructure observation of the specimens deformed to a strain of −0.9 at the strain rate of 0.1 s−1 and at the temperatures of 1123 K, 1198 K, 1273 K and 1348 K, and the
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specimens deformed to a strain of −0.9 at the temperature of 1348 K and at the strain rates of 0.01 s−1 , 0.1 s−1 , 1 s−1 and 10 s−1 , verify the influence of deformation conditions on the evolution of DRX volume fraction. Acknowledgement This work was supported by the Fundamental Research Funds for the Central Universities (Project No. CDJZR11130009). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
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