J. Mater. Sci. Technol. ›› 2021, Vol. 71: 129-137.DOI: 10.1016/j.jmst.2020.07.036
• Research Article • Previous Articles Next Articles
Min Yanga, Jun Zhanga,*(
), Weimin Guib, Songsong Hua, Zhuoran Lia, Min Guoa, Haijun Sua, Lin Liua
Received:2020-06-01
Revised:2020-07-22
Accepted:2020-07-31
Published:2021-04-30
Online:2021-04-30
Contact:
Jun Zhang
About author:* E-mail address: zhjscott@nwpu.edu.cn (J. Zhang).Min Yang, Jun Zhang, Weimin Gui, Songsong Hu, Zhuoran Li, Min Guo, Haijun Su, Lin Liu. Coupling phase field with creep damage to study γʹ evolution and creep deformation of single crystal superalloys[J]. J. Mater. Sci. Technol., 2021, 71: 129-137.
Fig. 1. Microstructure in Ni-18.5 at.% Al single crystal alloy after heat treatment.
| Parameter | Value | Unit | |
|---|---|---|---|
| Equilibrium concentration in γʹ cp [ | 0.23 | ||
| Equilibrium concentration in γ cm [ | 0.15 | ||
| Gradient coefficients α | 1.7 × 10-8 | J/m | |
| Gradient coefficients β | 1.06 × 10-10 | J/m | |
| Material parameter n | 3.5 | ||
| Material parameter K | 1550 | MPa s1/n | |
| Material parameter bs | 800 | ||
| Material parameter Qs | 20 | MPa | |
| Material parameter m | 2 | ||
| Material parameter Da | 1.3 × 10-20 | MPa1/m | |
| Initial threshold for γ ${{r}_{0m}}$ | 10 | MPa | |
| Initial threshold for γʹ ${{r}_{0p}}$ | 125 | MPa | |
| γʹ/γ lattice misfit δ [ | 0.0056 | ||
| Elastic moduli for γ [ | $C_{11}^{\text{m}}$ | 112 | GPa |
| $C_{12}^{\text{m}}$ | 63 | GPa | |
| $C_{44}^{\text{m}}$ | 57 | GPa | |
| Elastic moduli for γʹ [ | $C_{11}^{\text{p}}$ | 167 | GPa |
| $C_{12}^{\text{p}}$ | 107 | GPa | |
| $C_{44}^{\text{p}}$ | 99 | GPa | |
Table 1 The values of parameters used in creep PF model.
| Parameter | Value | Unit | |
|---|---|---|---|
| Equilibrium concentration in γʹ cp [ | 0.23 | ||
| Equilibrium concentration in γ cm [ | 0.15 | ||
| Gradient coefficients α | 1.7 × 10-8 | J/m | |
| Gradient coefficients β | 1.06 × 10-10 | J/m | |
| Material parameter n | 3.5 | ||
| Material parameter K | 1550 | MPa s1/n | |
| Material parameter bs | 800 | ||
| Material parameter Qs | 20 | MPa | |
| Material parameter m | 2 | ||
| Material parameter Da | 1.3 × 10-20 | MPa1/m | |
| Initial threshold for γ ${{r}_{0m}}$ | 10 | MPa | |
| Initial threshold for γʹ ${{r}_{0p}}$ | 125 | MPa | |
| γʹ/γ lattice misfit δ [ | 0.0056 | ||
| Elastic moduli for γ [ | $C_{11}^{\text{m}}$ | 112 | GPa |
| $C_{12}^{\text{m}}$ | 63 | GPa | |
| $C_{44}^{\text{m}}$ | 57 | GPa | |
| Elastic moduli for γʹ [ | $C_{11}^{\text{p}}$ | 167 | GPa |
| $C_{12}^{\text{p}}$ | 107 | GPa | |
| $C_{44}^{\text{p}}$ | 99 | GPa | |
| Slip system | Normal vector of slip surface n | Slip direction l |
|---|---|---|
| 1 | $\frac{1}{\sqrt{3}}(111)$ | $\frac{1}{\sqrt{2}}(10 \bar{1})$ |
| 2 | $\frac{1}{\sqrt{3}}(111)$ | $\frac{1}{\sqrt{2}}(0 \bar{1} 1)$ |
| 3 | $\frac{1}{\sqrt{3}}(111)$ | $\frac{1}{\sqrt{2}}( \bar{1} 10)$ |
| 4 | $\frac{1}{\sqrt{3}}(\bar{1}11)$ | $\frac{1}{\sqrt{2}}(0 \bar{1} 1)$ |
| 5 | $\frac{1}{\sqrt{3}}(\bar{1}11)$ | $\frac{1}{\sqrt{2}}(101)$ |
| 6 | $\frac{1}{\sqrt{3}}(\bar{1}11)$ | $\frac{1}{\sqrt{2}}(\bar{1}\bar{1}0)$ |
| 7 | $\frac{1}{\sqrt{3}}(\bar{1}\bar{1}1)$ | $\frac{1}{\sqrt{2}}( \bar{1} 0 \bar{1})$ |
| 8 | $\frac{1}{\sqrt{3}}(\bar{1}\bar{1}1)$ | $\frac{1}{\sqrt{2}}(011)$ |
| 9 | $\frac{1}{\sqrt{3}}(\bar{1}\bar{1}1)$ | $\frac{1}{\sqrt{2}}( 1 \bar{1} 0)$ |
| 10 | $\frac{1}{\sqrt{3}}(1\bar{1}1)$ | $\frac{1}{\sqrt{2}}( 0 \bar{1} \bar{1})$ |
| 11 | $\frac{1}{\sqrt{3}}(1\bar{1}1)$ | $\frac{1}{\sqrt{2}}( \bar{1} 1 0)$ |
| 12 | $\frac{1}{\sqrt{3}}(1\bar{1}1)$ | $\frac{1}{\sqrt{2}}( 1 1 0)$ |
Table 2 Slip planes and slip directions for octahedral slip systems.
| Slip system | Normal vector of slip surface n | Slip direction l |
|---|---|---|
| 1 | $\frac{1}{\sqrt{3}}(111)$ | $\frac{1}{\sqrt{2}}(10 \bar{1})$ |
| 2 | $\frac{1}{\sqrt{3}}(111)$ | $\frac{1}{\sqrt{2}}(0 \bar{1} 1)$ |
| 3 | $\frac{1}{\sqrt{3}}(111)$ | $\frac{1}{\sqrt{2}}( \bar{1} 10)$ |
| 4 | $\frac{1}{\sqrt{3}}(\bar{1}11)$ | $\frac{1}{\sqrt{2}}(0 \bar{1} 1)$ |
| 5 | $\frac{1}{\sqrt{3}}(\bar{1}11)$ | $\frac{1}{\sqrt{2}}(101)$ |
| 6 | $\frac{1}{\sqrt{3}}(\bar{1}11)$ | $\frac{1}{\sqrt{2}}(\bar{1}\bar{1}0)$ |
| 7 | $\frac{1}{\sqrt{3}}(\bar{1}\bar{1}1)$ | $\frac{1}{\sqrt{2}}( \bar{1} 0 \bar{1})$ |
| 8 | $\frac{1}{\sqrt{3}}(\bar{1}\bar{1}1)$ | $\frac{1}{\sqrt{2}}(011)$ |
| 9 | $\frac{1}{\sqrt{3}}(\bar{1}\bar{1}1)$ | $\frac{1}{\sqrt{2}}( 1 \bar{1} 0)$ |
| 10 | $\frac{1}{\sqrt{3}}(1\bar{1}1)$ | $\frac{1}{\sqrt{2}}( 0 \bar{1} \bar{1})$ |
| 11 | $\frac{1}{\sqrt{3}}(1\bar{1}1)$ | $\frac{1}{\sqrt{2}}( \bar{1} 1 0)$ |
| 12 | $\frac{1}{\sqrt{3}}(1\bar{1}1)$ | $\frac{1}{\sqrt{2}}( 1 1 0)$ |
 |
Table 3 Expression of the interaction matrix for octahedral slip systems.
| |
Fig. 2. (a) Creep strain and (b) creep rate curves of Ni-18.5 at.% Al single crystal alloy crept at 1223 K/100 MPa. The illustrations are the partial enlargements.
Fig. 3. Microstructural evolution of Ni-18.5 at.% Al single crystal alloy during creep at 1223 K/100 MPa: (a) 7.5 h interrupted, (b) 45 h interrupted, and (c) creep failure.
Fig. 4. Initial microstructure used for PF simulations: (a) microstructure of Ni-18.5 at.% Al single crystal alloy within yellow square in Fig. 1, (b) transformed initial concentration field, and (c) transformed initial LRO parameter field. In (c), the yellow area is γ matrix and the other four color areas are the γ? phases with four different LRO structures.
Fig. 5. Simulation of microstructural evolution in Ni-18.5 at.% Al single crystal alloy during creep at 1223 K/100 MPa: (a) t = 7.5 h, (b) t = 45.6 h, (c) t = 98.8 h, and (d) t = 145.8 h. t is creep time.
Fig. 6. Comparison of final microstructures of Ni-18.5 at.% Al single crystal alloy after creep rupture at 1223 K/100 MPa: (a) experimental result (b) simulation result considering creep damage, and (c) simulation reslut without considering creep damage.
Fig. 7. “Island-like” γ phases in Ni-18.5 at.% Al single crystal alloy after creep rupture at 1223 K/100 MPa.
Fig. 8. Comparison of simulation and experimental creep strain curves under 1223 K/100 MPa condition.
Fig. 9. (a) Creep strain and (b) creep rate curves of Ni-18.5 at.% Al single crystal alloy under creep at 1223 K/80, 100, 120 MPa.
| Creep stress (MPa) | Creep life (h) | Steady-state creep rate (s-1) | ||
|---|---|---|---|---|
| Experiment | Simulation | Experiment | Simulation | |
| 80 | 373.00 | 263.89 | 6.29 × 10-9 | 4.14 × 10-9 |
| 100 | 143.16 | 152.78 | 2.62 × 10-8 | 2.00 × 10-8 |
| 120 | 56.52 | 86.80 | 1.47 × 10-7 | 1.31 × 10-7 |
Table 4 Creep life and steady-state creep rate of Ni-18.5 at.% Al single crystal alloy.
| Creep stress (MPa) | Creep life (h) | Steady-state creep rate (s-1) | ||
|---|---|---|---|---|
| Experiment | Simulation | Experiment | Simulation | |
| 80 | 373.00 | 263.89 | 6.29 × 10-9 | 4.14 × 10-9 |
| 100 | 143.16 | 152.78 | 2.62 × 10-8 | 2.00 × 10-8 |
| 120 | 56.52 | 86.80 | 1.47 × 10-7 | 1.31 × 10-7 |
Fig. 10. Evolutions of (a1-d1) stress field (unit, Pa) and (a2-d2) plastic strain field among γ?/γ phases during creep at 1223 K/100 MPa. (a1,a2) t = 7.5 h, (b1,b2) t = 45.6 h, (c1,c2) t = 98.8 h, and (d1,d2) t = 136.8 h.
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