J. Mater. Sci. Technol. ›› 2019, Vol. 35 ›› Issue (4): 687-694.DOI: 10.1016/j.jmst.2018.09.035
• Orginal Article • Previous Articles Next Articles
Chao Fua, Yadong Chena, Xiaofei Yuana, Sammy Tinb, Stoichko Antonova, Koichi Yagic, Qiang Fenga*()
Received:
2018-03-21
Revised:
2018-05-16
Accepted:
2018-09-11
Online:
2019-04-05
Published:
2019-01-28
Contact:
Feng Qiang
Chao Fu, Yadong Chen, Xiaofei Yuan, Sammy Tin, Stoichko Antonov, Koichi Yagi, Qiang Feng. A modified θ projection model for constant load creep curves-II. Application of creep life prediction[J]. J. Mater. Sci. Technol., 2019, 35(4): 687-694.
K465 | DZ125 |
---|---|
900 °C/300 MPa | 900 °C/350 MPa |
900 °C/320 MPa | 900 °C/370 MPa |
950 °C/250 MPa | 950 °C/225 MPa |
950 °C/300 MPa | 980 °C/207 MPa |
975 °C/200 MPa | 980 °C/220 MPa |
1000 °C/137 MPa | 1000 °C/180 MPa |
1100 °C/70 MPa | 1040 °C/137 MPa |
— | 1050 °C/102 MPa |
Table 1 Constant load conditions for the creep tests of K465 superalloy and DZ125 superalloy.
K465 | DZ125 |
---|---|
900 °C/300 MPa | 900 °C/350 MPa |
900 °C/320 MPa | 900 °C/370 MPa |
950 °C/250 MPa | 950 °C/225 MPa |
950 °C/300 MPa | 980 °C/207 MPa |
975 °C/200 MPa | 980 °C/220 MPa |
1000 °C/137 MPa | 1000 °C/180 MPa |
1100 °C/70 MPa | 1040 °C/137 MPa |
— | 1050 °C/102 MPa |
Fig. 1. Creep curves for K465 superalloy obtained under different constant load conditions: (a) creep strain vs time curve, (b-d) strain rate vs time curves.
Alloys | Creep condition | ε˙m(s-1) | Time rage (h) | Strain range (%) |
---|---|---|---|---|
K465 | 900 °C/300 MPa | 1.48 × 10-8 | 3.4?107.1 | 0.04?0.61 |
900 °C/320 MPa | 2.53 × 10-8 | 2.7?67.0 | 0.05?0.66 | |
950 °C/300 MPa | 1.31 × 10-7 | 1.8?17.3 | 0.15?0.96 | |
975 °C/200 MPa | 3.26 × 10-8 | 4.4?70.0 | 0.11?0.92 | |
1000 °C/137 MPa | 1.24 × 10-8 | 12.9?135.5 | 0.30?0.90 | |
DZ125 | 900 °C/350 MPa | 3.85 × 10-8 | 6.6?63.0 | 0.30?1.12 |
900 °C/370 MPa | 5.63 × 10-8 | 4.4?46.1 | 0.38?1.22 | |
980 °C/207 MPa | 5.79 × 10-8 | 7.7?47.0 | 0.28?1.12 | |
980 °C/220 MPa | 8.94 × 10-8 | 3.4?28.9 | 0.23?1.08 | |
1040 °C/137 MPa | 9.64 × 10-8 | 5.2?35.9 | 0.38?1.40 |
Table 2 Minimum creep rate (ε˙m), time range and strain range of the secondary creep stage under different creep conditions of K465 and DZ125 superalloys.
Alloys | Creep condition | ε˙m(s-1) | Time rage (h) | Strain range (%) |
---|---|---|---|---|
K465 | 900 °C/300 MPa | 1.48 × 10-8 | 3.4?107.1 | 0.04?0.61 |
900 °C/320 MPa | 2.53 × 10-8 | 2.7?67.0 | 0.05?0.66 | |
950 °C/300 MPa | 1.31 × 10-7 | 1.8?17.3 | 0.15?0.96 | |
975 °C/200 MPa | 3.26 × 10-8 | 4.4?70.0 | 0.11?0.92 | |
1000 °C/137 MPa | 1.24 × 10-8 | 12.9?135.5 | 0.30?0.90 | |
DZ125 | 900 °C/350 MPa | 3.85 × 10-8 | 6.6?63.0 | 0.30?1.12 |
900 °C/370 MPa | 5.63 × 10-8 | 4.4?46.1 | 0.38?1.22 | |
980 °C/207 MPa | 5.79 × 10-8 | 7.7?47.0 | 0.28?1.12 | |
980 °C/220 MPa | 8.94 × 10-8 | 3.4?28.9 | 0.23?1.08 | |
1040 °C/137 MPa | 9.64 × 10-8 | 5.2?35.9 | 0.38?1.40 |
Fig. 2. Creep curves for DZ125 superalloy obtained under different constant load conditions: (a) creep strain vs time curve, (b-d) strain rate vs time curves.
Creep condition | Model | Strain range (%) | θ1 | θ2 | θ3 | θ4 | θ5 |
---|---|---|---|---|---|---|---|
900 °C/ 370 MPa | Original | 0?4 | 0.388 | 394.31 | 0.375 | 0.0265 | -- |
0?6 | 0.447 | 0.410 | 0.301 | 0.0287 | -- | ||
0?10 | 1.184 | -0.0252 | 1.683 | 0.0252 | -- | ||
Modified | 0?4 | 0.404 | 0.606 | 0.425 | 0.0240 | 0.0131 | |
0?6 | 0.413 | 0.558 | 0.381 | 0.0257 | 0.0066 | ||
0?10 | 0.391 | 0.700 | 0.442 | 0.0239 | 0.0101 | ||
980 °C/ 220 MPa | Original | 0?4 | 0.296 | 0.239 | 0.423 | 0.0361 | -- |
0?6 | 0.416 | 0.126 | 0.300 | 0.0408 | -- | ||
0?10 | 0.369 | 2897.97 | 0.240 | 0.0446 | -- | ||
Modified | 0?4 | 0.227 | 0.390 | 0.703 | 0.0269 | 0.0228 | |
0?6 | 0.238 | 0.355 | 0.635 | 0.0287 | 0.0176 | ||
0?10 | 0.255 | 0.307 | 0.581 | 0.0300 | 0.0153 |
Table 3 θi values obtained in DZ125 superalloy by fitting the creep curves at different strain ranges under different creep conditions, using the original and the modified θ projection model (5-parameter model).
Creep condition | Model | Strain range (%) | θ1 | θ2 | θ3 | θ4 | θ5 |
---|---|---|---|---|---|---|---|
900 °C/ 370 MPa | Original | 0?4 | 0.388 | 394.31 | 0.375 | 0.0265 | -- |
0?6 | 0.447 | 0.410 | 0.301 | 0.0287 | -- | ||
0?10 | 1.184 | -0.0252 | 1.683 | 0.0252 | -- | ||
Modified | 0?4 | 0.404 | 0.606 | 0.425 | 0.0240 | 0.0131 | |
0?6 | 0.413 | 0.558 | 0.381 | 0.0257 | 0.0066 | ||
0?10 | 0.391 | 0.700 | 0.442 | 0.0239 | 0.0101 | ||
980 °C/ 220 MPa | Original | 0?4 | 0.296 | 0.239 | 0.423 | 0.0361 | -- |
0?6 | 0.416 | 0.126 | 0.300 | 0.0408 | -- | ||
0?10 | 0.369 | 2897.97 | 0.240 | 0.0446 | -- | ||
Modified | 0?4 | 0.227 | 0.390 | 0.703 | 0.0269 | 0.0228 | |
0?6 | 0.238 | 0.355 | 0.635 | 0.0287 | 0.0176 | ||
0?10 | 0.255 | 0.307 | 0.581 | 0.0300 | 0.0153 |
Fig. 3. Experimental creep data and the predicted creep curves obtained at 980 °C/220 MPa for DZ125 superalloy using the θi parameters shown in Table 3: (a) predicted by the original model, (b) predicted by the modified model.
900 °C/ 350 MPa | 900 °C/ 370 MPa | 980 °C/ 207 MPa | 980 °C/ 220 MPa | 1000 °C/ 180 MPa | 1040 °C/ 137 MPa | |
---|---|---|---|---|---|---|
θ1 | 0.3032 | 0.3906 | 0.3308 | 0.2552 | 0.5678 | 0.8924 |
θ2 | 0.2970 | 0.6997 | 0.1097 | 0.3069 | 0.0694 | 0.0798 |
θ3 | 0.5515 | 0.4423 | 0.3965 | 0.5814 | 0.2220 | 0.0653 |
θ4 | 0.0144 | 0.0239 | 0.0229 | 0.0300 | 0.0313 | 0.0604 |
θ5 | 0.0136 | 0.0101 | 0.0164 | 0.0153 | 0.0165 | 0.0145 |
Table 4 θi values obtained in DZ125 superalloy by fitting the creep curves corresponding to 0~10% creep strain range under different constant load conditions, using the 5-paramter model.
900 °C/ 350 MPa | 900 °C/ 370 MPa | 980 °C/ 207 MPa | 980 °C/ 220 MPa | 1000 °C/ 180 MPa | 1040 °C/ 137 MPa | |
---|---|---|---|---|---|---|
θ1 | 0.3032 | 0.3906 | 0.3308 | 0.2552 | 0.5678 | 0.8924 |
θ2 | 0.2970 | 0.6997 | 0.1097 | 0.3069 | 0.0694 | 0.0798 |
θ3 | 0.5515 | 0.4423 | 0.3965 | 0.5814 | 0.2220 | 0.0653 |
θ4 | 0.0144 | 0.0239 | 0.0229 | 0.0300 | 0.0313 | 0.0604 |
θ5 | 0.0136 | 0.0101 | 0.0164 | 0.0153 | 0.0165 | 0.0145 |
θ parameter | ai | bi | ci | di | R2 |
---|---|---|---|---|---|
θ1 | -8.669 | 0.0444 | 0.0093 | -4.98E-05 | 0.723 |
θ2 | -28.783 | -0.0472 | 0.0220 | 7.92E-05 | 0.939 |
θ3 | 15.009 | -0.0721 | -0.0171 | 8.03E-05 | 0.957 |
θ4 | -21.375 | 0.0033 | 0.0180 | 6.96E-06 | 0.985 |
θ5 | 5.904 | -0.0030 | -0.0068 | -2.03E-06 | 0.906 |
Table 5 Material constants corresponding to each θi parameter for DZ125 superalloy.
θ parameter | ai | bi | ci | di | R2 |
---|---|---|---|---|---|
θ1 | -8.669 | 0.0444 | 0.0093 | -4.98E-05 | 0.723 |
θ2 | -28.783 | -0.0472 | 0.0220 | 7.92E-05 | 0.939 |
θ3 | 15.009 | -0.0721 | -0.0171 | 8.03E-05 | 0.957 |
θ4 | -21.375 | 0.0033 | 0.0180 | 6.96E-06 | 0.985 |
θ5 | 5.904 | -0.0030 | -0.0068 | -2.03E-06 | 0.906 |
Creep condition | Model | Strain range (%) | θ1 | θ2 | θ3 | θ4 | θ5 |
---|---|---|---|---|---|---|---|
900 °C/ 300 MPa | Original | 0?2.0 | 0.513 | 0.0115 | 0.066 | 0.01478 | -- |
0?2.6 | 0.482 | 0.0122 | 0.072 | 0.01441 | -- | ||
0?3.0 | 0.592 | 0.0099 | 0.056 | 0.01532 | -- | ||
Modified | 0?2.0 | 0.100 | 0.0624 | 0.775 | 0.00438 | 0.1367 | |
0?2.6 | 0.217 | 0.0261 | 0.231 | 0.00923 | 0.0361 | ||
0?3.0 | 0.225 | 0.0253 | 0.220 | 0.00952 | 0.0337 | ||
1000 °C/ 137 MPa | Original | 0?2.0 | 0.416 | 0.0315 | 0.0360 | 0.01809 | -- |
0?2.6 | 0.730 | 0.0138 | 0.0037 | 0.02859 | -- | ||
0?3.0 | 1.548 | 0.0051 | 8.7E-5 | 0.04561 | -- | ||
Modified | 0?.0 | 0.228 | 0.0772 | 0.409 | 0.0057 | 0.1787 | |
0?2.6 | 0.242 | 0.0695 | 0.329 | 0.0065 | 0.1588 | ||
0?3.0 | 0.292 | 0.0501 | 0.190 | 0.0087 | 0.1238 |
Table 6 θi values obtained in K465 superalloy by fitting the creep curves at different strain ranges under different creep conditions using the original and the modified θ projection model (5-parameter model).
Creep condition | Model | Strain range (%) | θ1 | θ2 | θ3 | θ4 | θ5 |
---|---|---|---|---|---|---|---|
900 °C/ 300 MPa | Original | 0?2.0 | 0.513 | 0.0115 | 0.066 | 0.01478 | -- |
0?2.6 | 0.482 | 0.0122 | 0.072 | 0.01441 | -- | ||
0?3.0 | 0.592 | 0.0099 | 0.056 | 0.01532 | -- | ||
Modified | 0?2.0 | 0.100 | 0.0624 | 0.775 | 0.00438 | 0.1367 | |
0?2.6 | 0.217 | 0.0261 | 0.231 | 0.00923 | 0.0361 | ||
0?3.0 | 0.225 | 0.0253 | 0.220 | 0.00952 | 0.0337 | ||
1000 °C/ 137 MPa | Original | 0?2.0 | 0.416 | 0.0315 | 0.0360 | 0.01809 | -- |
0?2.6 | 0.730 | 0.0138 | 0.0037 | 0.02859 | -- | ||
0?3.0 | 1.548 | 0.0051 | 8.7E-5 | 0.04561 | -- | ||
Modified | 0?.0 | 0.228 | 0.0772 | 0.409 | 0.0057 | 0.1787 | |
0?2.6 | 0.242 | 0.0695 | 0.329 | 0.0065 | 0.1588 | ||
0?3.0 | 0.292 | 0.0501 | 0.190 | 0.0087 | 0.1238 |
Fig. 4. Experimental creep data and the predicted creep curves obtained at 1000 °C/137 MPa for K465 superalloy using the θi parameters shown in Table 6: (a) predicted by the original model, (b) predicted by the modified model.
900 °C/300 MPa | 900 °C/320 MPa | 950 °C/300 MPa | 975 °C/200 MPa | 1000 °C/137 MPa | 1100 °C/70 MPa | |
---|---|---|---|---|---|---|
θ1 | 0.0997 | 0.1881 | 0.1043 | 0.1757 | 0.2282 | 22.0849 |
θ2 | 0.0624 | 0.0533 | 1.0186 | 0.1294 | 0.0772 | 0.0003 |
θ3 | 0.7748 | 0.6360 | 2.2032 | 1.3886 | 0.4092 | 0.0007 |
θ4 | 0.00438 | 0.00785 | 0.01614 | 0.00509 | 0.00566 | 0.07074 |
θ5 | 0.1368 | 0.1009 | 0.1736 | 0.2090 | 0.1787 | 0.0203 |
Table 7 θi values obtained in K465 superalloy by fitting the creep curves corresponding to 0~2% creep strain range under different constant load conditions using 5-parameter model.
900 °C/300 MPa | 900 °C/320 MPa | 950 °C/300 MPa | 975 °C/200 MPa | 1000 °C/137 MPa | 1100 °C/70 MPa | |
---|---|---|---|---|---|---|
θ1 | 0.0997 | 0.1881 | 0.1043 | 0.1757 | 0.2282 | 22.0849 |
θ2 | 0.0624 | 0.0533 | 1.0186 | 0.1294 | 0.0772 | 0.0003 |
θ3 | 0.7748 | 0.6360 | 2.2032 | 1.3886 | 0.4092 | 0.0007 |
θ4 | 0.00438 | 0.00785 | 0.01614 | 0.00509 | 0.00566 | 0.07074 |
θ5 | 0.1368 | 0.1009 | 0.1736 | 0.2090 | 0.1787 | 0.0203 |
θ parameter | ai | bi | ci | di | R2 |
---|---|---|---|---|---|
θ1 | -23.12 | 0.0737 | 0.0229 | -7.58E-05 | 0.973 |
θ2 | 19.59 | -0.1361 | -0.0229 | 1.50E-04 | 0.949 |
θ3 | 30.52 | -0.1276 | -0.0319 | 1.35E-04 | 0.999 |
θ4 | -20.59 | 0.0307 | 0.0175 | -2.46E-05 | 0.974 |
θ5 | 11.47 | -0.0480 | -0.0123 | 4.86E-05 | 0.993 |
Table 8 Material constants corresponding to each θi parameter for K465 superalloy.
θ parameter | ai | bi | ci | di | R2 |
---|---|---|---|---|---|
θ1 | -23.12 | 0.0737 | 0.0229 | -7.58E-05 | 0.973 |
θ2 | 19.59 | -0.1361 | -0.0229 | 1.50E-04 | 0.949 |
θ3 | 30.52 | -0.1276 | -0.0319 | 1.35E-04 | 0.999 |
θ4 | -20.59 | 0.0307 | 0.0175 | -2.46E-05 | 0.974 |
θ5 | 11.47 | -0.0480 | -0.0123 | 4.86E-05 | 0.993 |
Alloy | Creep condition | θ1 | θ2 | θ3 | θ4 | θ5 |
---|---|---|---|---|---|---|
K465 | 950 °C /250MPa | 0.1001 | 0.3591 | 2.0563 | 0.0066 | 0.2104 |
DZ125 | 950 °C /225MPa | 0.3172 | 0.0245 | 0.5154 | 0.0090 | 0.0231 |
1050 °C /102 MPa | 1.9335 | 0.0086 | 0.0201 | 0.0404 | 0.0187 |
Table 9 θi values of the predicted creep curves obtained for K465 and DZ125 superalloys under different creep conditions.
Alloy | Creep condition | θ1 | θ2 | θ3 | θ4 | θ5 |
---|---|---|---|---|---|---|
K465 | 950 °C /250MPa | 0.1001 | 0.3591 | 2.0563 | 0.0066 | 0.2104 |
DZ125 | 950 °C /225MPa | 0.3172 | 0.0245 | 0.5154 | 0.0090 | 0.0231 |
1050 °C /102 MPa | 1.9335 | 0.0086 | 0.0201 | 0.0404 | 0.0187 |
Fig. 5. Creep curves for K465 superalloy at 950 °C/250 MPa creep condition predicted by the modified θ projection model and the corresponding experimental data.
Fig. 6. Creep curves for DZ125 superalloy under different creep conditions predicted by the modified θ projection model of and the corresponding experimental data: (a) 950 °C/225 MPa, (b) 1050 °C/102 MPa.
Fig. 7. Dislocation evolution during interrupted creep tests under different creep conditions of K465 superalloy: (a) 900 °C/320 MPa, 0.5% creep strain (B=[1$\bar{1}$$\bar{1}$], g=[02$\bar{2}$]), (b) 900 °C/320 MPa, 1.5% creep strain (B=[01$\bar{1}$], g=[111]), (c) 1000 °C/137 MPa, 0.5% creep strain (B=[10$\bar{1}$], g=[1$\bar{1}$1]), (d) 1000 °C/137 MPa, 1.5% creep strain (B=[01$\bar{1}$], g=[111].
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