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摘要: 对第四代粉末高温合金FGH4108晶粒长大行为进行研究。结果表明，γ′相在完全溶解温度以下固溶处理时，晶粒长大幅度较小，与初始组织差别不大（锻态，3～4 μm）；当达到γ′相完全溶解温度时，晶粒发生明显长大；超过γ′相完全溶解温度时，晶粒尺寸大幅增加（30～40 μm），过固溶的几个温度下晶粒尺寸差别不大；保温初期晶粒尺寸显著增加，一定保温时间后晶粒尺寸不再随时间明显变化。温度和时间对晶粒尺寸的影响都与γ′相对晶界迁移的阻碍作用有关，根据温度和时间的影响，对传统晶粒长大模型中界面迁移的表观激活能（Q）、时间指数（n）和广义迁移率常数（A0）进行修正，构建了新的模型，模型预测值与实验值的决定系数（R2）为0.9997，均方误差为0.12 μm，预测精度较高，晶粒长大曲线各项特征能被准确预测出来。Abstract: The grain growth behavior of the fourth generation powder metallurgy (PM) superalloys was studied. The results indicate that the grain growth range is small when the heat treatment temperature is below the γ′ solution temperature, which is similar to the initial microstructure (as-forged, 3~4 μm). However, the grain size greatly increases to 30~40 μm when the heat treatment temperature exceeds the γ′ solution temperature, and there is little difference in grain size at the several temperatures over the γ′ solution temperature. The grain size increases significantly at the initial stage of heat treatment, and no longer changes after a certain holding time. The influence of temperature and time on grain size is related to the pinning effect of γ′ on grain boundary migration. A new model is established by modifying the parameters such as the activation energy for boundary migration (Q), the time exponent (n), and the generalized mobility constant (A0) based on the traditional grain growth model. The determination coefficient (R2) and the mean-square error (MSE) between the predicted and the experimental values are 0.9997 and 0.12 μm, respectively, showing the high prediction accuracy, and the various characteristics of the grain growth curves can also be predicted accurately.
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Key words:
- powder metallurgy superalloys /
- solution heat treatment /
- grain growth /
- prediction model
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图 1 锻态合金显微组织：（a）晶粒组织；（b）γ′相
Figure 1. Microstructure of the forged alloys: (a) particles structure; (b) γ′ phases
图 2 不同温度下平均晶粒尺寸随时间变化曲线和对应显微组织：（a）晶粒尺寸随时间变化曲线；（b）、（c）1190 ℃显微组织；（d）、（e）1160 ℃显微组织；（f），（g）1100 ℃显微组织
Figure 2. Grain growth curves at different temperatures and the corresponding microstructures: (a) grain growth curves at different temperatures; (b), (c) SEM images at 1190 ℃; (d), (e) SEM images at 1160 ℃; (f), (g) SEM images at 1100 ℃
图 3 传统模型拟合：（a）拟合界面迁移表观激活能Q；（b）拟合指数n；（c）计算广义迁移率常数自然对数lnA0
Figure 3. Traditional model fitting: (a) fit Q; (b) fit n; (c) calculate lnA0
图 4 传统模型预测结果（a）和预测结果与实验数据的决定系数和均方误差（b）
Figure 4. Predicted results of the traditional model (a) and R2 and MSE between predicted and experimental results (b)
图 5 传统模型参数修正：（a）温度对Q的影响；（b）n与时间的关系；（c）温度对lnA0的影响
Figure 5. Modified traditional model parameters: (a) effect of T on Q; (b) relationship between n and t; (c) effect of T on lnA0
图 6 改进模型的预测结果（a）和预测结果与实验数据的决定系数R2和均方误差（b）
Figure 6. Predicted results of new model (a) and R2 and MSE between predicted and experimental results (b)
表 1 式（3）参数拟合结果
Table 1. Fitting results of parameters in Eq.(3)
Q1 / (kJ·mol−1) Q2 / (kJ·mol−1) T0 / ℃ ΔT / ℃ 914 293 1170 4.2 
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表 2 各温度下的γ′相体积分数和尺寸数据
Table 2. γ′ phase volume fraction and size at various temperatures
T / ℃ r / μm φ (φ·r−1) / μm−1 1200 0 0 — 1190 0 0 — 1180 0.15142 0.00101 0.00667 1160 0.55211 0.05112 0.09259 1130 1.01630 0.09915 0.09756 1100 1.91278 0.20154 0.10013
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表 3 式(4)参数拟合结果
Table 3. Fitting results of parameters in Eq.(4)
n0 nA t1 / s 7×10−4 0.838 875
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表 4 式（5）参数拟合结果
Table 4. Fitting results of parameters in Eq.(5)
lnA1′ lnA2′ T0 / ℃ ΔT / ℃ 83 31 1170 4.2
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