Constitutive Relationship Modeling and Characterization of Flow Behavior under Hot Working for Fe–Cr–Ni–W–Cu–Co Super-Austenitic Stainless Steel
Abstract
:1. Introduction
2. Experimental Material and Methods
3. Results and Discussion
3.1. Flow Behavior
3.2. Constitutive Flow Curves Equations
α (MPa−1) | β (MPa−1) | n1 | n | Q (kJ·mol−1) | |
---|---|---|---|---|---|
0.005 | 0.074 | 13.692 | 10.066 | 652.73 | 2.124 × 1026 |
3.3. Verification of the Developed Constitutive Model with Strain Compensation
α | Value | β | Value | n | Value | Q | Value | lnA | Value |
---|---|---|---|---|---|---|---|---|---|
B0 | 0.011 | C0 | 0.201 | D0 | 20.820 | E0 | 366.971 | F0 | 31.416 |
B1 | −0.056 | C1 | −1.573 | D1 | −122.340 | E1 | 1727.233 | F1 | 183.033 |
B2 | 0.205 | C2 | 6.529 | D2 | 520.308 | E2 | −5021.468 | F2 | −538.010 |
B3 | −0.379 | C3 | −13.180 | D3 | −1063.531 | E3 | 8758.577 | F3 | 917.189 |
B4 | 0.346 | C4 | 12.967 | D4 | 1062.198 | E4 | −6905.828 | F4 | −710.467 |
B5 | −0.124 | C5 | −4.975 | D5 | −415.579 | E5 | 1661.322 | F5 | 170.838 |
Strain Rate (s−1) | Temperature (K) | AARE (%) | R |
---|---|---|---|
0.1 | 1173 | 0.865 | 0.999 |
1273 | 0.699 | 0.998 | |
1373 | 3.236 | 0.999 | |
1 | 1173 | 2.638 | 0.999 |
1273 | 1.911 | 0.992 | |
1373 | 1.077 | 0.994 | |
10 | 1173 | 6.758 | 0.962 |
1273 | 1.669 | 0.912 | |
1373 | 3.475 | 0.994 |
3.4. Relationship between the Dynamic Restoration Condition and the Zener-Hollomon Parameter
4. Conclusions
- All flow stress curves gradually returned to a balanced stress state without notable peak stress characteristics and flow softening. Most of the flow curves presented a slight increase in stress with the increasing of the strain, which was a result of the unfinished dynamic balance of the work hardening and restoration processes.
- The constitutive model of the studied steel was developed on an Arrhenius-type equation to predict the flow behavior under specific deformation conditions. The material constants and deformation activation energy (including α, β, n, Q, and A) were incorporated with strain compensation with fifth order polynomial fitting, and the results indicated good correlation and generalization.
- The comparison between the experimental and predicted values exhibited a high precision and good reliability with regard to the constitutive equations according to the mean error. The absolute average relative error (AARE) values for all of the deformation conditions were below 6.8% and all the correlation coefficient (R) values were found to be above 0.9.
- From the exponent-type Zener-Hollomon parameter map and corresponding observation of the microstructure, the critical values for the occurrence of the dynamic restoration processes at large strains were determined. A lower value could give rise to higher levels of recrystallization and increment of grain size.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Yang, L.-C.; Pan, Y.-T.; Chen, I.-G.; Lin, D.-Y. Constitutive Relationship Modeling and Characterization of Flow Behavior under Hot Working for Fe–Cr–Ni–W–Cu–Co Super-Austenitic Stainless Steel. Metals 2015, 5, 1717-1731. https://doi.org/10.3390/met5031717
Yang L-C, Pan Y-T, Chen I-G, Lin D-Y. Constitutive Relationship Modeling and Characterization of Flow Behavior under Hot Working for Fe–Cr–Ni–W–Cu–Co Super-Austenitic Stainless Steel. Metals. 2015; 5(3):1717-1731. https://doi.org/10.3390/met5031717
Chicago/Turabian StyleYang, Li-Chih, Yeong-Tsuen Pan, In-Gann Chen, and Dong-Yih Lin. 2015. "Constitutive Relationship Modeling and Characterization of Flow Behavior under Hot Working for Fe–Cr–Ni–W–Cu–Co Super-Austenitic Stainless Steel" Metals 5, no. 3: 1717-1731. https://doi.org/10.3390/met5031717