On the hot deformation behavior of AISI 420 stainless steel based onconstitutive analysis and CSL model

Yu Cao a,n, Hongshuang Di a, R.D.K. Misra b, Xiao Yi c, Jiecen Zhang a, Tianjun Ma d

a State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819, Chinab Laboratory for Excellence in Advanced Steel Research, Center for Structural and Functional Materials, University of Louisiana at Lafayette,P.O. Box 44130, LA 70503, USAc Dongfang Heavy machinery Co. Ltd., Guangzhou 511455, Chinad Baoshan Iron & Steel Co., Ltd., Shanghai 200940, China

a r t i c l e i n f o

Article history:Received 19 October 2013Received in revised form4 November 2013Accepted 10 November 2013Available online 19 November 2013

Keywords:Hot compressionConstitutive equationDynamic recrystallizationZ-parameterCSL model

a b s t r a c t

We describe here the hot deformation behavior of AISI 420 stainless steel using hot compression tests inthe temperature range of 950–1150 1C and strain rate of 0.01–10 s�1. By considering the relative materialconstants as a function of strain with sixth polynomial fitting, the effect of strain was studied using anArrhenius type constitutive equation. The deformation activation energy was estimated to be in therange of 362–435 kJ/mol. The constitutive equations developed were consistent with the experimentaldata using standard statistical parameters. The Z-parameter map at the strain of 0.6 was plotted andit can be concluded that the occurrence of DRX is associated with the condition that ln Z is less than32 s�1. The lower Z-parameter indicates the larger extent of dynamic softening, especially the process ofDRX. It is worth noting that the most dominant CSL boundary is the Σ3 twin boundary, the fraction ofwhich remains constant after the process of DRX. However, the fraction of Σ11 boundary, Σ33c boundary,and Σ41c boundary is almost at the same level, which is approximate a quarter of the Σ3 fraction anddecreases slightly after DRX.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Generally speaking, the hot deformation behavior of metals andalloys has been investigated through numerical simulation topropose a set of proper parameters (i.e., temperature and strainrate) for hot processing. The modeling of hot deformation behavioris generally performed using constitutive equations, which relatethe flow stress to relevant processing conditions [1–3]. Thus, anumber of researchers proposed constitutive equations of materi-als based on experimental data to describe the hot deformationbehavior. Jonas et al. [4] developed a phenomenological approachwhich consists of a model expressed by the hyperbolic laws in anArrhenius type of equation. In recent years, a modified hyperbolicsine constitutive equation, which takes into consideration theinfluence of strain has been proposed to predict the flow behaviorunder hot deformation of 42CrMo steel [5], Incoloy 800H super-alloy [6], 9Cr–1Mo steel [7], AZ81 magnesium alloy [8] and A356Al alloy [9].

Dynamic recrystallization (DRX) is an effective metallurgicalprocess for grain refinement during hot deformation. It is accepted

that DRX is a softening mechanism during hot processing and hassignificant effect on the microstructure, grain size, and flow stress.Zener–Hollomon parameter (Z-parameter) is an important hotprocessing index, proposed by Zener and Hollomon in 1944 [10],and has been extensively applied to characterize the combinedeffects of strain rate and deformation temperature on the hotdeformation process, particularly on the flow stress. The physicalmeaning of Z-parameter is the temperature-compensated strainrate and the Z-parameter map at a given strain can be simply usedto evaluate the hot workability of materials [11–14].

Martensitic stainless steels are commonly used for manufacturingcomponents with excellent mechanical properties and moderatecorrosion resistance. AISI 420 stainless steel, which is widely usedin the polymer industry as a tool material and in mechanicalconstruction as a structural material, has a martensitic microstruc-ture containing spherodized carbides [15]. There is, however, almostno information on the hot deformation behavior of this importantengineering steel. Thus, the main objective of the present work is tostudy the effect of deformation temperature and strain rate on thecompressive deformation characteristics of AISI 420 stainless steel byhot compression tests. First, the constitutive equations describing thedependence of the flow stress on strain, strain rate, and temperatureare proposed and confirmed. Second, the Z-parameter map wasdeveloped to describe the relationship between microstructure and

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0921-5093/$ - see front matter & 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.msea.2013.11.030

n Corresponding author. Tel.: þ86 24 83681190.E-mail address: vieri32825@126.com (Y. Cao).

Materials Science & Engineering A 593 (2014) 111–119

hot deformation conditions. Lastly, the grain boundary distributioncharacterization after hot deformation was studied based on thecoincidence site lattice (CSL) model.

2. Materials and experimental procedure

The material used for the study was commercial AISI 420stainless steel supplied by Baoshan Iron & Steel Co., Ltd., Chinaof normal chemical composition in weight (%) of Fe–0.19C–12.16Cr–0.68Si–0.69Mn–0.1Ni–0.041P–0.0018S. Cylindrical speci-mens with diameter of 10 mm and height of 15 mm weremachined according to the ASTM E209 standard [16]. The phasecontent of AISI 420 stainless steel as calculated by JMatPro ispresented as a function of temperature in Fig. 1. Thermodynamiccalculations using JMatPro 6.0 software suggest that the fraction ofM23C6 and austenite are �0.28% and �99.71% respectively at thedeformation temperature of 950 1C. From this, it can infer thatonly austenite is formed in the temperature range of 950–1200 1C.

The hot compression tests were performed using MMS-300thermo-mechanical simulator at five different temperatures(950 1C, 1000 1C, 1050 1C, 1100 1C and 1150 1C) and six differentstrain rates (0.01 s�1, 0.1 s�1, 0.5 s�1, 1 s�1, 5 s�1 and 10 s�1).As schematically illustrated in Fig. 2, specimens were heated to1200 1C at a heating rate of 20 1C/s by thermo-coupled feedback-controlled AC current, homogenized at the experimental tempera-ture for 180 s, cooled at the rate of 10 1C/s to the deformationtemperature, and held for 60 s to eliminate thermal gradient priorto the compression tests. The reduction in the height of cylinderwas 60% after compression and the specimens were immediately

water quenched to preserve the high temperature microstructure.In order to minimize the friction between the specimen and the dieduring hot compression, the flat ends of the specimens were coveredby a lubricant consisting of graphite powder and machine oil.

Deformed specimens were cut parallel to the compression axisat the geometric center for examination by optical microscope.Metallographic specimens were prepared using standard mechan-ical grinding and polishing techniques. The polished specimenswere etched with hot supersaturated picric acid to reveal the prioraustenite grain boundaries. Specimens for electron backscatterdiffraction (EBSD) were prepared by standard mechanical polish-ing, followed by electrochemical polishing in a solution of 4%HClO4 in alcoholic at 27V DC for 20–30 s. EBSD measurements andanalysis were performed using a Zeiss UltraPlus analytical fieldemission gun scanning electron microscope (FEG-SEM) equippedwith an EBSD detector (HKL Technology). Step size of 0.2 μm wasselected to scan the deformed portion available at the cut surface.The Channel 5 software was used to analyze and display the data.The substructure and morphology of deformed specimen werealso investigated by FEI Tecnai G2 F20 transmission electronmicroscopy (TEM). TEM specimens were prepared by electroche-mical polishing at �30 1C in a solution containing 10% perchloricacid and 90% methanol.

3. Results and discussion

3.1. Flow stress behavior

Examples of the representative flow stress plots obtained atdifferent deformation conditions are presented in Fig. 3a and b,correspondingly. It may be noted that the effect of temperature andstrain rate on the flow stress is pronounced. Higher temperatureand lower strain rate provide higher mobility for nucleation andgrowth of DRX grains and dislocation annihilation, longer time forenergy accumulation, and therefore lower the flow stress level [17].

Majority of the flow stress plots at lower strain rate indicate thefollowing characteristics: there exists a peak stress at small straindue to initial work hardening, after which the flow stressdecreases continuously with strain, which is a typical character-istic of DRX. The microstructure (Fig. 4a) also confirms theoccurrence of DRX, which shows the nucleation and growth ofsome new DRX grains. However, at strain rates greater than 1 s�1,the plots are characterized by a steady state without any peak,which is widely recognized to have resulted from the dynamicrecovery (DRV) process. The corresponding microstructure of thespecimen deformed at 1100 1C and 10 s�1 shows that the initialgrains are elongated along the deformation direction and there isno sign of DRX as shown in Fig. 4b.

3.2. Deformation constitutive equation

The constitutive relation of material refers to the relationshipbetween flow stress and deformation conditions during hotdeformation. The Arrhenius equation is widely used to describethe relationship between strain rate, flow stress, and temperature,especially at the elevated temperature. Additionally, the effect oftemperature and strain rate on the flow behavior can be formu-lated in terms of Zener–Hollomon parameter (Z-parameter) usingthe following exponent-type equation [4,18,19]:

Z ¼ _ε exp½Q=ðRTÞ� ¼ f ðsÞ ð1Þ

_ε¼Asn1 exp½�Q=ðRTÞ� αso0:8A expðβsÞ exp½�Q=ðRTÞ� αs41:2A½ sinhðαsÞ�n exp½�Q=ðRTÞ� for all s

8><>: ð2Þ

Fig. 1. Phase fraction as a function of test temperature calculated by JMatPro 6.0 forthe experimental AISI 420 stainless steel.

Fig. 2. Experimental procedure for hot compression tests.

Y. Cao et al. / Materials Science & Engineering A 593 (2014) 111–119112

where Z is the Zener–Hollomon parameter, which can be used todemonstrate the combined effect of strain rate and temperatureon the hot deformation behavior of materials; _ε is the strain rate(s�1); R is the universal gas constant (8.31 J mol�1 K�1); T is theabsolute temperature (K); Q is the deformation activation energyfor hot deformation (kJ mol�1); s is the flow stress (MPa) for agiven strain; A, n1, n, α and β are the material constants, α¼β/n1.The power law description of flow stress in Eq. (2) is convention-ally employed for creep deformation. Conversely, the exponentiallaw in Eq. (2) is appropriate for higher strain rates, whereas thehyperbolic sine law in Eq. (2) can be used for a wide range ofdeformation conditions [20].

3.2.1. Determination of material constantTo further investigate the flow behavior of AISI 420 stainless

steel, it is inevitable to study the constitutive characteristics. Thetrue stress–strain data obtained through hot compression tests canbe used to determine the material constant in the constitutiveequation. It is widely acknowledged that the effect of deformationstrain on flow stress is not embodied. There exists a functionalrelationship between strain and the material constant in theconstitutive equation. Therefore, the influence of strain on thematerial constant was determined. Considering deformation strainof 0.1, as an example, the material constant was estimated.

At low-stress level (αso0.8) and high-stress level (αs41.2),the relationship between flow stress and strain rate is formulatedas follows:

_ε¼ Asn1 exp½�Q=ðRTÞ� ¼ Bsn1 ð3Þ

_ε¼ A expðβsÞexp½�Q=ðRTÞ� ¼ B′ expðβsÞ ð4Þ

where B and B′ are material constants, which are dependent ondeformation temperature.

Taking natural logarithm on both sides of Eqs. (3) and (4), gives,

lnðsÞ ¼ 1n1

lnð_εÞ� 1n1

lnðBÞ ð5Þ

s¼ 1βlnð_εÞ�1

βlnðB′Þ ð6Þ

For all the flow stress values (including low and high stresslevels), Eq. (7) is derived as

ln ½ sinhðαsÞ� ¼ ln _ε=nþQ=ðnRTÞ� ln A=n ð7Þ

Fig. 3. Flow stress plots for specimens deformed at (a) constant strain rate of0.01 s�1 and different deformation temperatures and (b) at different strain ratesand constant temperature of 1150 1C.

Fig. 4. The microstructure of specimens deformed at a temperature of 1100 1C andstrain rate of (a) 0.01 s�1 and (b) 10 s�1.

Y. Cao et al. / Materials Science & Engineering A 593 (2014) 111–119 113

and at a given strain rate, Q is calculated by differentiating Eq. (7)as follows:

Q ¼ 10;000 nR∂ ln ½ sinhðαsÞ�� �∂ð10;000=TÞ ð8Þ

Substituting the value of the flow stress and correspondingstrain rate at a strain of 0.1 in Eqs. (5) and (6) gives relationshipbetween flow stress and strain rate. The values of n1 and β arecalculated from the slope of lines in ln _ε vs. ln s and ln _ε vs. s plots(Fig. 5a and b), respectively. Given that the slope of lines atdifferent temperatures is approximately same, the mean value ofn1 and β is computed to be 9.249 and 0.077 by the linear fittingmethod, and α¼β/n1¼0.008287. The slope of ln[sinh(αs)] vs. ln _εyields to 1/n (Fig. 5c) and n is calculated to be 6.945. The Q value isdetermined from the slope of ln[sinh(αs)] vs. 1000/T (Fig. 5d). Thevalue of ln A is estimated from the interception of the same linesas Q. The value of Q varies in the range of 362–435 kJ/mol, with amean value of 399 kJ/mol for different deformation strains in thetemperature range of 950–1150 1C. These values are in agreementwith the Q values reported for 17-4 PH stainless steel [20] and 13%Cr martensitic stainless steel [21]. It may be noted that somedeviation in the deformation energy is because of the nature of thelinear regression method applied to solve the Q-value [22].

3.2.2. Compensation of deformation strainIt is known that the activation energy and material constants

are strongly affected by deformation strain. Thus, compensation of

strain may lead to a more accurate prediction of flow stressand should be considered for deriving constitutive equations.The values of Q and other three material constants were calculatedat various deformation strains to be within the range of 0.05–0.6and are listed in Table 1, and the corresponding plots areillustrated in Fig. 6.

The above values were subsequently employed to fit thepolynomial functions. Generally, a fourth or fifth order polynomialfit can be applied [1,2,6]. In this study, a sixth order polynomialrepresented a good fit for the effect of strain on the materialconstants, and is presented in Fig. 6. However, with increase in the

Fig. 5. Evaluation of the value (a) n1 by plotting ln s vs. ln _ε, (b) β by plotting s vs. ln _ε, (c) n by plotting ln[sinh(αs)] vs. ln _εand (d) Q by plotting ln[sinh(αs)] vs. T�1/10�4.

Table 1Values of the material constants of AISI 420 stainless steel at different deformationstrains.

Strain α n Q (kJ/mol) ln A

0.05 0.010055 8.003 434.680 36.8690.1 0.008287 6.945 402.536 34.2630.15 0.007726 6.652 409.078 34.9050.2 0.007443 6.337 399.754 34.0480.25 0.007357 6.030 393.600 33.4950.3 0.007407 5.725 384.939 32.7420.35 0.007531 5.414 379.190 32.2120.4 0.007635 5.173 374.398 31.7730.45 0.007730 4.918 370.841 31.4570.5 0.007802 4.721 368.594 31.2530.55 0.007883 4.514 366.122 31.0550.6 0.007911 4.300 361.563 30.666

Y. Cao et al. / Materials Science & Engineering A 593 (2014) 111–119114

order of polynomial fitting, Runge's phenomenon may appearto increase the computational error and affect instabilities ofcomputation [23]. The polynomial fitting results of α, n, Q andln A are given as follows:

α¼ 0:0139�0:109εþ0:777ε2�2:99ε3þ6:46ε4�7:30ε5þ3:34ε6

n¼ 10:7�80:8εþ677:5ε2�3015:3ε3þ7012:5ε4�8155:3ε5þ3747:1ε6

Q ¼ 541:5�3519:5εþ34;766:1ε2�167;489:6ε3þ410;970:6ε4

�496;711:6ε5þ234;838:5ε6

ln A¼ 45:6�289:1εþ2885:4ε2�14;003:7ε3þ34;499:1ε4

�41;786:0ε5þ19;779:1ε6

8>>>>>>>>><>>>>>>>>>:

ð9ÞAccording to Eq. (9), the material constants can be evaluated to

predict the flow stress at a given strain. Considering Eqs. (1) and(2), the constitutive equation that relates the flow stress to theZ-parameter is expressed as follows:

s¼ 1α

sinh�1 ZA

� �1=n" #

ð10Þ

3.2.3. Verification of the developed constitutive equationIn order to verify the constitutive equation developed for AISI

420 stainless steel at elevated temperature, the calculated flowstress data was compared with the experimental data. The flow

stress values can be calculated for strain rates between 0.01 s�1

and 10 s�1 and for all analysis temperatures between 950 1C and1150 1C from the above- mentioned computation. It can be seenfrom Fig. 7 that the proposed deformation constitutive equationprovides an accurate estimate of the flow stress, which can beemployed to solve the problems associated with the metal formingprocess. The predictive ability of constitutive equation is quanti-fied based on standard statistical parameters such as correlationcoefficient (R) and average absolute relative error (AARE), which iscomputed as follows:

R¼ ∑Ni ¼ 1ðEi�EÞðCi�CÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

∑Ni ¼ 1ðEi�EÞ2ðCi�CÞ2

q ð11Þ

and

AARE¼ 1N

∑N

i ¼ 1

Ei�Ci

Ei

�������� ð12Þ

where E is the experimental value and C is the calculated value inthe developed constitutive equations. E and C are the mean valuesof E and C, respectively. N is the number of data applied in thecalculation. A good correlation exists between the experimentaland calculated data, which can be observed in Fig. 7.

Generally, the value of R is used to analyze the linear relation-ship between the experimental and calculated data. The predictive

Fig. 6. Relationship between (a) α, (b) n, (c) Q, (d) ln A and true strain.

Y. Cao et al. / Materials Science & Engineering A 593 (2014) 111–119 115

accuracy of a model may not be proportional to the value of R [24].The AARE is also calculated through a term by comparison of therelative error and is therefore more reliable to determine theaccuracy of the developed model [25]. The values of R and AAREwere found to be in the range of 0.979–0.999 and 2.04–14.53%,respectively. Poor agreements were observed at 950 1C and0.01 s�1 with R and AARE being 0.986% and 14.53%, respectively.The error can be ascribed to the fact such as the cumulative errorsfrom the successive steps to determine the material constants orthe error in the experimental measurement of flow stress [6].Moreover, the validity of the developed model should be exam-ined by the data which has not been used to determine thematerial constants. To be specific, a comparison has been per-formed between the experimental and the calculated flow stressvalues at 1100 1C with different strain rates in Fig. 8. The corre-sponding results confirm the accuracy and reliability of thedeveloped constitutive equation.

3.3. The evolution of microstructure during hot deformation

3.3.1. Dynamic recrystallization and Z-parameter mapIt is widely acknowledged that the deformation temperature

and strain rate are two main factors in hot deformation. As shownin Eq. (1), the combined effects of deformation temperatureand strain rate are represented by the Z-parameter. Apparently,

the Z-parameter increases with decrease in temperature orincrease in strain rate. Fig. 9 shows that deformation temperatureand strain rate have significant effect on Z-parameter at

Fig. 8. Comparison between the experimental and calculated flow stress from theconstitutive equation at 1100 1C with strain rates of 0.5 s�1 and 5 s�1.

Fig. 9. Z-parameter map at the strain of 0.6. Contour numbers illustrate the valuesof ln Z.

Fig. 7. Correlation between the experimental and calculated flow stress data by thedeveloped constitutive equations.

dDRX= 16μm

dDRX = 21μm

Fig. 10. Typical microstructures of AISI 420 stainless steel deformed with lower ln Zat 1100 1C and strain rates: (a) 0.2 s�1; (b) 0.3 s�1.

Y. Cao et al. / Materials Science & Engineering A 593 (2014) 111–119116

temperatures in the range of 950–1150 1C and strain rate of 0.01–10 s�1. Contour numbers represent the value of ln Z and shadedregion corresponds to the domain where no DRX occurred at astrain of 0.6. It is noted from the map that Z-parameter reachespeak at 950 1C and 10 s�1. According to the microstructuralanalysis of the deformed specimens, the DRX is more likely tooccur when ln Z is less than 32 s�1. Moreover, the lower the Z-parameter, the larger the extent of dynamic softening and moreeasily DRX may occur. As shown in Fig. 10, fully equiaxed DRXoccurred and grain size (dDRX) increases with decreasing ln Z.

The higher strain rate can result in the formation of adiabaticshear band or flow localization at lower temperature, whereas itcan also lead to intergranular cracking at higher temperatures.Microstructural examination of the specimen deformed at 950 1Cand 10 s�1 (Fig. 11a) revealed that the grains are elongated likepancakes and intense flow localization occurs obviously in thevicinity of grain boundaries because of possible inhomogeneousdeformation. In the high temperature domain (1150 1C and10 s�1), it is evident that the DRX grains are significantly finerthan those obtained with lower value of ln Z (Fig. 11b). However,the microstructure exhibits intergranular cracking because of thepresence of iron as well as coarse carbides at the grain boundaries

Flow localization

Intergranular cracking

dDRX = 12μm

Fig. 11. Typical microstructures of AISI 420 stainless steel deformed with higherln Z under different conditions: (a) 950 1C, 10 s�1; (b) 1150 1C, 10 s�1.

Lath type martensite

Dislocation-cell type martensite

Cr23C6

Fig. 12. TEM micrographs illustrating distinct features of specimen subjected to hotdeformation condition of 1150 1C and 10 s�1.

Fig. 13. The linear relationship between Z-parameter and flow stress s at the truestrain of 0.6 within the DRX domain.

Y. Cao et al. / Materials Science & Engineering A 593 (2014) 111–119 117

(Fig. 12a), which causes fracture at high strain rates due toembrittlement of grain boundaries at higher temperatures [26].Fig. 12b presents a combination of two different types of marten-site: lath type and dislocation-cell type. The latter one containshigh dislocation density compared to lath-type martensite. It hasbeen demonstrated earlier that the crystallographic distortion ofthe martensite within the matrix leads to change in morphology

20μm

20μm

Fig. 14. The OIM band contrast microstructures for deformed specimen: (a)1000 1C, 0.1 s�1 and (b) 1150 1C, 0.1 s�1. Σ3 twin, Σ11, Σ33c and Σ41c boundariesare respectively shown as red, yellow, blue and green lines. (For interpretation ofthe references to color in this figure legend, the reader is referred to the webversion of this article.)

Table 2Allowed maximum deviation from exact orientation relationship according toBrandon.

Σ Deviation Δω¼ 151=ffiffiffiffiffi∑

p(deg)

3 8.6611 4.52

33c 2.6141c 2.34

Fig. 15. Length fractions of dominant CSL boundaries at different deformationtemperatures and constant strain rate of 0.1 s�1.

Twins

Prior austenite GBs

Twins

Fig. 16. TEM micrographs illustrating twins and prior austenite GBs at 1150 1C and0.1 s�1.

Y. Cao et al. / Materials Science & Engineering A 593 (2014) 111–119118

from lath to dislocation cell-type martensite in the severelydeformed martensite [27].

According to Eq. (1), the linear relationship between Z-para-meter and flow stress at a strain of 0.6 within the DRX domain isillustrated in Fig. 13, from which the regression equation isderived:

ln Z ¼ 10:058þ4:373 ln s ð13ÞIt can be concluded that lower the Z-parameter, the smaller is

the flow stress. A lower Z-parameter also favors flow softening andDRX, as described above.

3.3.2. CSL grain boundariesAccording to the coincidence site lattice (CSL) model, the grain

boundaries (GBs) can be classified into three types: low-angleboundary, CSL and random high-angle boundary [28]. The repre-sentative CSL boundary distribution for deformed specimen afterquenching is presented in Fig. 14. It is observed that some CSLboundaries except for Σ3 boundaries are the prior austenite GBs.It has been proposed previously that Σ3 boundaries are predomi-nantly observed at the packet/block boundaries whose misorien-tations are greater than 10.531 [29]. Fig. 14 shows a comparisonbetween the DRX microstructure (1150 1C and 0.1 s�1) and a non-DRX microstucture (1000 1C and 0.1 s�1). Σ3 twin boundaries(misorientation of 601 about a ⟨111⟩ axis), Σ11 boundaries (mis-orientation of 50.481 about a ⟨110⟩ axis), Σ33c boundaries (mis-orientation of 58.981 about a ⟨110⟩ axis) and Σ41c boundaries(misorientation of 55.881 about a ⟨110⟩ axis) are highlighted inFig. 14. Under these two deformation conditions, CSL boundary ofΣ3 was observed to be the most dominant with other threeboundaries frequency nearly the same. The length faction of CSLboundaries was calculated by applying the Brandon criterion [30]to determine the allowable deviation from the exact orientationrelationship (Table 2) and the results are shown in Fig. 15. It can beseen that the Σ3 fraction undergoes very little change through theprocess of DRX. However, the fraction of other three CSL bound-aries decreases only slightly. It is worth noting that all of the threeCSL boundaries share the same rotational axis: ⟨110⟩ axis and thedeviation angles are between 2.341 and 4.521. Within the region oftwin, some blocky martensite and dense dislocation structure canbe observed (Fig. 16).

4. Conclusion

We have studied the hot deformation behavior of AISI 420stainless steel over a wide range of strain rate and temperature byuniaxial hot compression tests using thermo-mechanical simula-tor. The following conclusions can be obtained:

(1) The flow stress plot suggests that the flow stress level of AISI420 stainless steel decreases with increase in deformationtemperature and decrease in strain rate during hot deforma-tion. The microstructure of AISI 420 stainless steel after hotdeformation revealed that the occurrence of DRX is moreobvious at lower strain rates at the investigated experimentaltemperatures, while the softening mechanism of DRV isdominant at strain rates greater than 1 s�1.

(2) The activation energy for hot deformation of AISI 420 stainlesssteel at different strains is within the range of 362–435 kJ/mol.

A sixth order polynomial was applied to represent the influ-ence of strain on material constants (α, n, Q and ln A) with verygood correlation and generalization. The constitutive equationwith the compensation of deformation strain during hotdeformation can be used to accurately predict the flow stress.

(3) Based on the Z-parameter map and microstructural analysis,we can conclude that the DRX is more likely to occur with ln Zless than 32 s�1. The lower the Z-parameter, the lower flowstress is and the more easily DRX may occur. The hotdeformation with higher strain rate will lead to adiabaticshear band or flow localization at lower temperature andintergranular cracking at higher temperature.

(4) The Σ3 twin boundary, Σ11 boundary, Σ33c boundary, andΣ41c boundary are the four dominant CSL boundaries withinthe deformed microsturcture. The fraction of Σ3 twin bound-ary is larger than that of any other three boundaries. It can beobserved that the Σ3 fraction undergoes very little changethrough the process of DRX, while the fraction of other threeCSL boundaries decreases only slightly.

Acknowledgments

This work was supported by the 973 Program (No. 2011CB606306-2). The authors would like to gratefully acknowledge thesupport from them.

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