J. TIAN et al.: MODIFIED PHYSICALLY-BASED CONSTITUTIVE MODEL FOR As-CAST Mn18Cr18N ... 243–251 MODIFIED PHYSICALLY-BASED CONSTITUTIVE MODEL FOR As-CAST Mn18Cr18N AUSTENITIC STAINLESS STEEL AT ELEV ATED TEMPERATURES MODIFICIRAN FIZIKALNI KONSTITUTIVNI MODEL VRO^E DEFORMACIJE LITEGA A VSTENITNEGA NERJA VNEGA JEKLA VRSTE Mn18Cr18N Jihong Tian, Fei Chen, Fengming Qin, Jiansheng Liu, Huiqin Chen * School of Materials Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, P. R. China Prejem rokopisa – received: 2020-08-23; sprejem za objavo – accepted for publication: 2020-11-12 doi:10.17222/mit.2020.168 The hot-deformation behavior of the as-cast Mn18Cr18N high-nitrogen austenitic stainless steel, produced with the electroslag-remelting metallurgical technology, was studied using isothermal-compression tests in a temperature range of 1223–1473 K) and a strain-rate range of 0.001–1 s –1 ). The flow-stress curves of the Mn18Cr18N steel were obtained under dif- ferent hot-deformation conditions. By establishing the hyperbolic sine-law Zener-Hollomon equation, the hot-deformation acti- vation energy of the Mn18Cr18N steel was obtained. Based on the mechanism of dislocation evolution, a physically-based con- stitutive model was established. In addition, the expression of the dynamic-recovery coefficient of the model was modified. Compared with the model before the modification, the modified constitutive model could effectively improve the prediction ac- curacy of the flow stress for the as-cast Mn18Cr18N austenitic stainless steel. Keywords: as-cast Mn18Cr18N, work hardening, dynamic recovery, dynamic recrystallization, constitutive model Avtorji v ~lanku opisujejo {tudijo vro~e deformacije litega Mn18Cr18N nerjavnega jekla z visoko vsebnostjo du{ika. Jeklo je bilo izdelano s postopkom elektro-pretaljevanja pod `lindro. Preizkuse so izvajali s tla~no deformacijo v temperaturnem obmo~ju med 1223 K in 1473 K ter pri hitrostih deformacije med 0,001 s –1 i n1s –1 . Izdelali so krivulje te~enja izbranega jekla pri razli~nih pogojih vro~e deformacije. Po potrditvi sinus-hiperboli~nega zakona Zener–Hollomon ena~be, so dolo~ili {e aktivacijsko energijo za vro~o deformacijo jekla Mn18Cr18N. Na osnovi mehanizma razvoja dislokacij so izdelali fizikalni konstitucijski model. Dodatno so modificirali izraz za koeficient poprave v modelu. Primerjava modelov, brez in z modifikacijo, je pokazala, da modificirani konstitutivni model lahko u~inkoviteje izbolj{a natan~nost napovedi poteka krivulj te~enja izbranega litega avstenitnega jekla vrste Mn18Cr18N. Klju~ne besede: lito avstenitno jeklo Mn18Cr18N, deformacijsko utrjevanje, dinami~na poprava, dinami~na rekristalizacija, konstitutivni model 1 INTRODUCTION The development of the ultra-supercritical-unit manu- facturing technology is an important way of realizing en- ergy conservation and emission reduction while develop- ing the basic industry. The Mn18Cr18N stainless steel is used in the generator ring, which is one of the important basic parts of an ultra-supercritical unit due to its excel- lent corrosion resistance, ductility and toughness. 1–3 The forming of a generator ring usually includes ingot cogging, punching and bulging. In the forging process, the processing is various and the process is complex. However, there are a few researches on the plastic-defor- mation behavior of the as-cast Mn18Cr18N austenitic stainless steel using the electroslag-remelting (ESR) pro- cess at an elevated temperature. The rheological behavior of a metal at an elevated temperature is closely related to the strain, strain rate and deformation temperature. 4 Based on the coupling of work hardening and dynamic softening during deformation, flow-stress curves tend to exhibit a highly nonlinear law. 5 Therefore, a study of the thermal-deformation behavior of the as-cast ESR Mn18Cr18N at an elevated temperature and establish- ment of a high-precision nonlinear constitutive model are important for the optimization of the production pro- cesses and quality improvement of the generator ring. A lot of research on the hot-deformation behavior of metals has done by many scholars. J. H. Hollomon 6 pro- posed a flow-stress model, which took into account that the flow stress was an exponential function of strain. C. M. Sellars et al. 7,8 proposed a hyperbolic-sine mathemati- cal model to characterize the flow stress of a metal. B. S. Yu et al. 9 systematically studied the stress-strain curves of a shape-memory alloy (SMA), using a neural-network algorithm with back-propagation training to establish a nonlinear model based on the experimental results for the SMA. L. Li et al. 10 analyzed the hot-deformation dy- namics and flow stability of a TC17 alloy, and a strain- compensated constitutive model of the TC17 alloy was established. 10 A modified steel J-C model for 10%Cr was Materiali in tehnologije / Materials and technology 55 (2021) 2, 243–251 243 UDK 66.040:691.714.018.8:621.785.6 ISSN 1580-2949 Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 55(2)243(2021) *Corresponding author's e-mail: chen_huiqin@126.com (Huiqin Chen) developed by J. L. He et al. 11 on the basis of the tradi- tional J-C constitutive model. This modified model not only considered the coupling effects of the strain, strain rate and temperature, but also introduced work hardening and dynamic softening into the entire deformation to im- prove the accuracy of the traditional J-C constitutive model. Based on the stress-dislocation relationship and dynamic recrystallization dynamics, a two-stage consti- tutive model was established to predict the flow stress of nickel-based superalloys by Y .C. Lin et al. 12 G. Z. V oyiadjis et al. 13 developed a physically-based constitu- tive model to describe the high-temperature deformation behavior of face-centered cubic metals. The expression of the flow stress was used to simulate the experimental results of oxygen-free high-conductivity copper at differ- ent temperatures and strain rates. F. Chen et al. 14 using isothermal-compression tests obtained the flow-stress curves of the as-cast CL70 steel. To forecast the flow stress for forging, a constitutive model based on the dis- location-density evolution was established. Constitutive models have been studied for over a hundred years and researchers have constructed various constitutive models using different methods. Among these models, the physically-based constitutive model based on the dislocation-evolution mechanism is one of the most accurate constitutive models. In view of the fact that the studies on the constitutive model of the as-cast Mn18Cr18N steel produced with electroslag remelting are relatively rare at present, this paper obtained the flow-stress curves of the as-cast Mn18Cr18N steel based on isothermal-compression test, established a physi- cally-based constitutive model and modified the model to improve its accuracy. This provides a reference for the optimization of the cogging process for the as-cast Mn18Cr18N. 2 EXPERIMENTAL PART The experimental material used in this paper is the as-cast Mn18Cr18N austenitic stainless steel received as an ingot cast with electroslag remelting. Its specific chemical composition is shown in Table 1. An isother- mal-compression test was used to investigate the ele- vated-temperature deformation behavior of the steel. The experiment was carried out on a Thermecmastor-Z ther- mal mechanical simulator. A standard sample for a compression test is a ( 8×12) mm cylinder. And the specimen should be heated to 1473 K and kept warm for 120 s. Then, it should be cooled to the deformation temperature and kept warm for 60 s. The deformation was 50 %. The de- formation temperature was 1223–1473 K and the strain rate was 0.001–1 s –1 . Finally, the hot-deformation sample was cooled to room temperature with liquid nitrogen at a cooling rate of 50 K/s. 3 RESULTS AND DISCUSSION 3.1 Characteristics of the flow stress Figure 1 shows the flow-stress curves of the as-cast Mn18Cr18N steel. As shown, the Mn18Cr18N steel has two types of stress-strain curves, representing work hard- ening/dynamic recovery and dynamic recrystallization. A work hardening/dynamic recovery curve is ex- pressed in two different stages with an increase in the strain at a high temperature. In the first stage, the flow stress increases with the increase in the strain, while the growth rate decreases gradually. This is because the in- crease of dislocations caused by work hardening (WH) is greater than the loss of dislocations caused by dynamic recovery (DRV), resulting in an increased stress. In the second stage, the flow stress is in a relatively stable state. J. TIAN et al.: MODIFIED PHYSICALLY-BASED CONSTITUTIVE MODEL FOR As-CAST Mn18Cr18N ... 244 Materiali in tehnologije / Materials and technology 55 (2021) 2, 243–251 Table 1: Chemical composition of the as-cast Mn18Cr18N austenitic stainless steel (w/%) Cr Mn N Ni Mo Cu Si Al C Ti P S 20 19.21 0.61 0.14 0.022 0.035 0.59 0.023 0.074 0.016 0.014 0.001 Figure 1: Flow-stress curves of the as-cast Mn18Cr18N steel: a) the strain rate of 1 s –1 , b) the strain rate of 0.1 s –1 At this point, the dislocation increment caused by WH is equivalent to the dislocation disappearance caused by DRV , and the stress does not increase any more. The dynamic-recrystallization (DRX) curve is di- vided into three stages. At the beginning, WH is domi- nant and the flow stress increases to the critical stress of DRX. Then, the flow stress reaches the peak and begins to fall until the curve stabilizes, as DRV and DRX play a significant softening role in this phase. However, the hardening effect is still greater than the softening effect. In the third stage, as the DRX softening increases, the flow stress decreases. Finally, due to the same degree of hardening and softening, the dislocation annihilation rate is equal to the dislocation proliferation rate, and the flow-stress curve tends to be stable. 3.2 Arrhenius model Based on the thermal-mechanical coupling, C. M. Sellars and W. J. Tegart proposed the following mod - els: 7,8 [] sinh( exp '( . ) '' exp( )( ' = − ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ < A Q RT A A n n 08 > ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ 12 .) (1) Then, Equation (2) can be obtained with a logarith- mic transformation of Equation (1): [] ln ln sinh( ln 'ln ln ' = +− nA Q RT nA ln ' A ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ (2) According to the isothermal-compression experi- ment, the peak stresses of the Mn18Cr18N austenitic stainless steel can be obtained from the stress-strain curves under different deformation conditions. The rela- tional graphs for ln and ln p , p are established, as shown in Figures 2a and 2b. The slopes can be deter- mined with linear fitting. So, n’ = 9.136, = 0.0845 and coefficient = /n’ = 0.00925. Based on Equation (2), the relational graphs between ln[sinh( p )] and ln , 1000/T, are established, as shown in Figures 2c and 2d. Using the same method, it can be found that n = 6.768, Q/1000nR = 12.637 and A = 7.067 × 10 25 . Finally, the activation energy of hot deformation of the as-cast Mn18Cr18N steel was obtained, Q = 711073.274 J/mol. To make it easier to characterize the effects of the strain, strain rate and deformation temperature on the flow stress, Zener and Hollomon introduced the Zener-Hollomon parameter, represented by letter Z. 15 The expression of parameter Z is shown in Equation (3): Z Q RT = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ exp (3) J. TIAN et al.: MODIFIED PHYSICALLY-BASED CONSTITUTIVE MODEL FOR As-CAST Mn18Cr18N ... Materiali in tehnologije / Materials and technology 55 (2021) 2, 243–251 245 Figure 2: Relationship between p and , T:a )l n p –l n ,b ) p –l n ,c )l n [sinh( p )] –l n ,d )l n [sinh( p )] – 1000/T According to the above calculation results, parameter Z can be expressed as follows: Z RT = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = =× exp . . sinh( . 711073 274 7 067 10 00925 25 [] p 6 768 . (4) Equation (4) can be rewritten to calculate the peak stress: p = − 410811 000152 1 0 1478 .s i n h( ) . Z (5) 3.3 Work hardening/dynamic recovery modelling According to WH and DRV , the evolution of the dis- location density with strain can be expressed as: 16 d d =− kk 12 (6) where d /d is the increasing rate of the dislocation den- sity with strain, is the dislocation density, k 1 is the work-hardening coefficient and k 2 is the dynamic-recov- ery coefficient. During the hot-deformation process, the evolution law for the flow stress of the material with the dislocation density is expressed as: 17,18 rec = b (7) where is the material constant, μ is the shear modu- lus and b is the Burgers vector. By taking a derivative of Equation (7) with respect to , Equation (8) can be obtained: d d rec = b 2 (8) Synthesizing Equations (6) and (8), the work-harden- ing rate can be expressed with the following formula: d d d d d d rec rec rec =⋅ = = − = − bk bk bk k 12 12 2 2 (9) When =0 , sat is shown as: sat = bk k 1 2 (10) where sat is the saturated stress. Based on Equation (9), d is readily expressed with the equivalent transfor- mation as: d d2 d rec rec rec = − bk k 12 (11) Integrating Equation (11), Equation (12) is obtained: k bk k C 2 12 1 ln( ) −+ rec (12) Then, Equation (12) can be written as: bk k C k 12 2 2 2 −=− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ rec exp (13) For = 0 and = 0 , Equation (13) is written as: Cb kk 120 − (14) where 0 is the yield stress. Synthesizing Equations (13) and (14), the flow stress is written as Equation (15): rec sat sa = −−− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = =− bk bk k k k 11 2 0 2 2 2 () e x p ( t 0 −− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ )exp k 2 2 (15) And yield stress 0 can be written as a function of peak stress. Using linear fitting, the yield stress can be expressed as Equation (16): 0 0681 14636 =+ .. p (16) In addition, dynamic-recovery coefficient k 2 can be obtained with Equation (15). According to Figure 3,c o - efficient k 2 can be expressed as: kZ 2 0 04496 228 0238 = − . . (17) Besides, the saturated stress can be expressed as a function of peak stress. Using linear fitting, the saturated stress can be expressed with Equation (18): sat p =+ 0 998 2823 .. (18) In short, the constitutive model for the as-cast Mn18Cr18N during the work hardening/dynamic recov- ery stage can be written as: J. TIAN et al.: MODIFIED PHYSICALLY-BASED CONSTITUTIVE MODEL FOR As-CAST Mn18Cr18N ... 246 Materiali in tehnologije / Materials and technology 55 (2021) 2, 243–251 Figure 3: Relationship between k 2 and ln Z ! rec sat sat 0 sat p 0 + 2.823 =−− − = ( ) exp( . k 2 0 998 = = − 0681 228 0238 2 0 04496 . . . p +14.636 = exp(711073 kZ Z .274 ) p /RT Z = ⎧ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ − 10811 0 000152 1 0 1478 .s i n h(. ) . ⎪ (19) 3.4 Dynamic-recrystallization modelling When plastic deformation occurs at a higher tempera- ture or lower strain rate, DRX starts when the strain reaches a certain threshold. The volume-fraction model of DRX can be described with the following formula: 19,20 Xk n d dd c p =− − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 1e x p (20) where k d , n d are the material constants. And the volume fraction of DRX can also be calculated as Equation (21): X d rec sat ss = − − (21) Combining Equations (20) and (21), the flow stress can be written as: =−−−− − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎧ ⎨ WH sat ss d c p () e x p 1 k n d ⎪ ⎩ ⎪ ⎫ ⎬ ⎪ ⎭ ⎪ ≥ () c (22) The steady-state stress can also be expressed as a function of peak stress. Using linear fitting, the steady-state stress can be expressed with Equation (23): ss p =− 1006 14 720 .. (23) The peak stress is an important characteristic point of the flow-stress curve, which indicates that the increment and decrease of dislocations in the metal are equal for the first time, after which the stress begins to decrease. The strain corresponding to the peak stress is the peak strain, which can be expressed with the following for- mula: p =CZ k 3 3 (24) After the transformation, Equation (24) is expressed as: ln ln ln p =+ CkZ 33 (25) Figure 4 shows the relationship between ln p and ln Z. Using linear fitting, it can be found that k 3 = 0.10705 and C 3 = 1.11×10 –4 . Then, Equation (24) is rewritten as: p =× − 111 10 4 0 10705 . . Z (26) One of the important parameters of a metal constitu- tive model is the critical strain, which represents the starting point of dynamic recrystallization. It is generally assumed that the critical strain c = 0.6–0.85. Since this parameter is difficult to obtain accurately, based on the previous research results, it is determined that c = 0.8. 20 Then it can be written as Equation (27): cp =108 . (27) After the transformation, Equation (20) is expressed as: [] ln ln( ) ln ln −−=+ − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ 1Xkn ddd c p (28) Figure 5 shows the relationship between ln[-ln(1-X d )] and ln[( - c )/ p ]. Using linear fitting, coefficients k d and n d are 0.02324 and 2.343, respectively. According to the above calculation results, the vol- ume-fraction model of DRX can be expressed as: X d p p =− − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 1 08 2 343 exp . . (29) In conclusion, the dynamic-recrystallization constitu- tive model for the as-cast Mn18Cr18N steel can be writ- ten as: J. TIAN et al.: MODIFIED PHYSICALLY-BASED CONSTITUTIVE MODEL FOR As-CAST Mn18Cr18N ... Materiali in tehnologije / Materials and technology 55 (2021) 2, 243–251 247 Figure 4: Relationship between ln p and ln Z Figure 5: Relationship between ln [–ln(1–X d )] and ln[( - c )/ p ] rec rec sat 0 c p =−−−− − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ()e x p . . 1 0 02324 2 343 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎧ ⎨ ⎪ ⎩ ⎪ ⎫ ⎬ ⎪ ⎭ ⎪ ≥ =−− − () ( )exp( c rec rec sat ss k 2 0 998 2 823 1006 14 7 ! sat p ss p =+ =− .. .. 2 0 0 681 14 636 10811 0 000152 1 0 1478 0p p =+ = − .. .s i n h(. . Z ) . . . kZ /RT 2 0 04496 228 0238 11 = = − Z = exp(711073.274 ) p 11 0 088 10 4 0 10705 5 0 10705 × =× ⎧ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪ − − Z Z . . . c ⎪ ⎪ ⎪ ⎪ ⎪ (30) 3.5 Model validation According to the calculation above, the constitutive model of the as-cast Mn18Cr18N steel was obtained. In this paper, the mean absolute relative error (AARE) and root mean square error (RMSE) of the constitutive model were calculated based on Equations (31) and (32) to ob- tain the reliability and accuracy of the model: AARE n i n = − × = ∑ 1 100 1 ep e % (31) RMSE n i n =− = ∑ 1 2 1 " ep ) (32) where e is the measured flow stress, p is the flow stress predicted by the constitutive model and n is the total number of data sets, used to verify the model. Figure 6 shows graphs of comparisons of the consti- tutive model and experiments. The results show that the AARE is 14.9 % and the RMSE is 21.1 MPa. 3.6 Model modification This physically-based constitutive model includes the values of flow stress for a higher accuracy of prediction. However, in the process of establishing the model, dy- namic-recovery coefficient k 2 depends on the Z parame- ter, which is related to the deformation temperature and strain rate. When ignoring the effect of strain on dy- namic-response coefficient k 2 , it is easy to create a model at the starting point of the deformation-rheological stress, which increases the error of the predicted value. In order to improve the accuracy of the model, the effect J. TIAN et al.: MODIFIED PHYSICALLY-BASED CONSTITUTIVE MODEL FOR As-CAST Mn18Cr18N ... 248 Materiali in tehnologije / Materials and technology 55 (2021) 2, 243–251 Figure 6: Comparison between the experimental and predicted flow stress at different strains for strain rates of a) 1 s –1 , b) 0.1 s –1 , c) 0.01 s –1 , d) 0.001 s –1 of strain on dynamic-recovery coefficient k 2 is added to the model to modify it. Figure 7 shows the relationship between dynamic-re- covery coefficient k 2 and strain when the strain rate is 1s –1 . In accordance with the curve morphology in the figure, k 2 can be modified as follows: ka c b 2 10 =× + (33) where a, b and c are the model coefficients. The relationship between dynamic-recovery coeffi- cient k 2 and strain can be fitted using the custom nonlin- ear function in the Origin software to obtain the model coefficients under different conditions. In accordance with the characteristics of the function from Equation (33) and through nonlinear fitting, coefficient b can be –6 and the value of coefficient c can be taken as the dy- namic-recovery coefficient before the modification, namely c = 228.0238 Z –0.04496 . Besides, the relationship J. TIAN et al.: MODIFIED PHYSICALLY-BASED CONSTITUTIVE MODEL FOR As-CAST Mn18Cr18N ... Materiali in tehnologije / Materials and technology 55 (2021) 2, 243–251 249 Figure 8: Relationship between a and lnZ Figure 7: Relationship between k 2 and strain Figure 9: Comparison between the experimental and predicted flow stress at different strains for strain rates of: a) 1 s –1 ,b )0 . 1s –1 , c) 0.01 s –1 , d) 0.001 s –1 between coefficient a and ln Z is shown in Figure 8. Using linear fitting, it can be obtained that: aZ =− + 8 90 61582 .l n . (34) In conclusion, the modified constitutive model for the as-cast Mn18Cr18N is: =< =≥ =−−−− rec c drx c drx rec sat ss () () () e x p 1 0 02324 2 343 . . − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎧ ⎨ ⎪ ⎩ ⎪ ⎫ ⎬ ⎪ ⎭ ⎪ = c p rec sat sat o sat p −− − =+ ( )exp( .. ! k 2 0 998 2 823 1 006 14 720 0 681 14 636 10811 ss p 0p p =− =+ = .. .. .s i n h − − =− + × + 1 0 1478 2 6 0 000152 8 90 61582 10 228 (. ) (.l n .) . . Z kZ 0238 111 10 0 04496 40 Z /RT Z − − =× . . Z = exp(711073.274 ) p . . . 10705 5 0 10705 088 10 c =× ⎧ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ − Z (35) Figure 9 shows graphs of comparisons between the modified constitutive model and experiments. The results show that the AARE is 10.2 % and the RMSE is 10.8 MPa. They show that the modified constitutive model can further reduce the error and improve the accuracy. 4 CONCLUSIONS In this study, the thermal deformation behavior of the as-cast Mn18Cr18N steel was studied based on an iso- thermal-compression test involving deformation temper- atures in a range of 1223–1473 K and strain rates in a range of 0.001–0.1 s –1 . Besides, a constitutive model for the steel at elevated temperatures was established. Based on these studies, the following conclusions were ob- tained: 1) The flow-stress curves of the as-cast Mn18Cr18N steel are of two types. One is the work hardening/dy- namic recovery type and the other is the dy- namic-recrystallization type. The dominant softening mechanisms of these two types of curves are dynamic re- covery and dynamic recrystallization, respectively. 2) In accordance with the Arrhenius equation, the ac- tivation energy of the as-cast Mn18Cr18N steel is ob- tained and its value is 711073.274 J/mol. 3) Based on the traditional physically-based constitu- tive model, the dynamic-recovery coefficient of the model is revised and the influence of strain on the coeffi- cient is considered in the modified model. Compared with the model before the modification, the prediction accuracy of the modified model is greatly improved. The AARE and RMSE are 10.2 % and 10.8 MPa, respec- tively. Acknowledgments The work was supported by the National Natural Sci- ence Foundation of China (No.51575372) and the Start-Up Fund for Scientific Research of the Taiyuan University of Science and Technology (No.20172011). 5 REFERENCES 1 F. M.Qin, H. Zhu, Z. X. Wang, X. D. Zhao, W. W. He, H. Q. Chen, Dislocation and twinning mechanisms for dynamic recrystallization of as-cast Mn18Cr18N steel, Materials Science and Engineering: A, 684 (2017) 27, 634–644, doi:10.1016/j.msea.2016.12.095 2 F. M. Qin, Y . J. Li, W. W. He, X. D. Zhao,H. Q. Chen, Effects of de- formation microbands and twins on microstructure evolution of as-cast Mn18Cr18N austenitic stainless steel, Journal of Materials Research, 32 (2017) 20, 3864–3874, doi:10.1557/jmr.2017.389 3 Z. H. Wang, H. P. Xue, W. T. Fu, Fracture Behavior of High-Nitro- gen Austenitic Stainless Steel Under Continuous Cooling: Physical Simulation of Free-Surface Cracking of Heavy Forgings, Metallurgi- cal & Materials Transactions A, 49 (2018) 5, 1470–1474, doi:10.1007/s11661-018-4561-z 4 Y . C. Lin, J. Zhang, J. Zhong, Application of neural networks to pre- dict the elevated temperature flow behavior of a low alloy steel, Computational Materials Science, 43 (2008) 4, 752–758, doi:10.1016/j.commatsci.2008.01.039 5 Q. Yang, X. Wang, X. Li, Z. Deng, Z. Jia, Z. Zhang, G. Huang, Q. Liu, Hot deformation behavior and microstructure of AA2195 alloy under plane strain compression, Materials Characterization, 131 (2017) 500–507, doi:10.1016/j.matchar.2017.06.001 6 J. H. Hollomon, Tensile Deformation, Transactions of the Metallur- gical Society of AIME, 162 (1945), 268–290 (without doi) 7 C. M. Sellars, W. J. McTegart, On the mechanism of hot deforma- tion,ActaMetallurgica, 14 (1966) 9, 1136–1138, doi:10.1016/0001- 6160(66)90207-0 8 C. M. Sellars, Computer modeling of hot-working processes, Mate- rials Science and Technology, 1 (1985) 4, 325–332, doi:10.1179/ mst.1985.1.4.325 9 B. S. Yu, S. L. Wang, T. Yang, Y . J. Fan, BP Neural Netwok Consti- tutive Model Based on Optimization with Genetic Algorithm for SMA,ActaMetallurgicaSinica, 53 (2017) 2, doi:10.11900/0412.1961. 2016.00218 10 L. Li, M. Q. Li, Constitutive model and optimal processing parame- ters of TC17 alloy with a transformed microstructure via kinetic analysis and processing maps, Materials Science & Engineering A, 698 (2017) 20, 302–312, doi:10.1016/j.msea.2017.05.034 11 J. L. He, F. Chen, B. Wang, L. B. Zhu, A modified Johnson-Cook model for 10%Cr steel at elevated temperatures and a wide range of strain rates, Materials Science & Engineering, A, 715 (2018) 7, 1–9, doi:10.1016/j.msea.2017.10.037 12 Y . C. Lin, X. M. Chen, D. X. Wen, M. S. Chen, A physically-based constitutive model for a typical nickel-based superalloy, Computa- tional Materials Science, 83 (2014) 15, 282–289, doi:10.1016/ j.commatsci.2013.11.003 13 G. Z. Voyiadjis, A. H. Almasri, A physically based constitutive model for fcc metals with applications to dynamic hardness, Me- chanics of Materials, 40 (2008) 6, 549–563, doi:10.1016/j.mechmat. 2007.11.008 14 F. Chen, X. D. Zhao, J. Y. Ren, H. Q. Chen, X. F. Zhang, Physically-Based Constitutive Modelling of As-Cast CL70 Steel for Hot Deformation, Metals and Materials International, (2019), doi:10.1007/s12540-019-00541-7 15 C. Zener, J. H. Hollomon, Effect of Strain Rate Upon Plastic Flow of Steel, Journal of Applied Physics, 15 (1944) 1, 22–32, doi:10.1063/ 1.1707363 J. TIAN et al.: MODIFIED PHYSICALLY-BASED CONSTITUTIVE MODEL FOR As-CAST Mn18Cr18N ... 250 Materiali in tehnologije / Materials and technology 55 (2021) 2, 243–251 16 Y . Estrin, H. Mecking, A unified phenomenological description of work hardening and creep based on one-parameter models, ActaMetallurgica, 32 (1984) 1, 57–70, doi:10.1016/0001-6160(84) 90202-5 17 H. Mecking, U. F. Kocks, Kinetics of flow and strain-hardening, ActaMetallurgica, 29 (1981) 11, 1865–1875, doi:10.1016/0001- 6160(81)90112-7 18 N. Hansen, D. Kuhlmann-Wilsdorf, Low energy dislocation struc- tures due to unidirectional deformation at low temperatures, Mate- rials Science and Engineering, 81 (1986) 141–161, doi:10.1016/ 0025-5416(86)90258-2 19 Y . Estrin, Dislocation theory based constitutive modelling: founda- tions and applications, Journal of Materials Processing Technology, 80–81 (1998) 33–39, doi:10.1016/S0924-0136(98)00208-8 20 H. M. Zhang, G. Chen, Q. Chen, F. Han, Z. D. Zhao, A physi- cally-based constitutive modelling of a high strength aluminum alloy at hot working conditions, Journal of Alloys and Compounds, 743 (2018) 283–293, doi:10.1016/j.jallcom.2018.02.039 J. TIAN et al.: MODIFIED PHYSICALLY-BASED CONSTITUTIVE MODEL FOR As-CAST Mn18Cr18N ... Materiali in tehnologije / Materials and technology 55 (2021) 2, 243–251 251