Rheological behaviours and constitutive models of 9Cr18Mo stainless steel at high temperature and high strain rate
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摘要: 在UTM5305万能试验机和剖分式 Hopkinson 压杆试验装置上，对9Cr18Mo不锈钢进行了压缩试验研究，获得准静态（应变率为0.001～0.1 s−1）及动态下（温度范围为25～650 ℃，应变率范围为800～4000 s−1）的应力—应变曲线关系。由获取的应力—应变曲线，探讨了其高温度、高应变率下的流变行为。依据所得到的试验数据，对其进行了J-C、P-L两种本构模型参数的识别，并对比分析了两种本构模型的相关系数（R）和平均相对误差（AARE）。结果表明，9Cr18Mo不锈钢具有应变率敏感性和显著的温度软化效应，即其流动应力随着应变率的增加而增加，随着温度的升高而显著下降。两种本构模型的相关系数（R）分别为0.9697、0.9896，平均相对误差（AARE）分别为2.77%、1.85%，即P-L本构模预测精度要高于J-C本构模型，更能精确地描述其高温、高应变率下的流变行为。
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关键词:
- 9Cr18Mo不锈钢 /
- 流变行为 /
- 本构模型 /
- 相关性系数 /
- 平均相对误差
Abstract: The compression tests of 9Cr18Mo stainless steel were conducted by using the UTM5305 universal testing machine and the split Hopkinson pressure bar (SHPB) test device. In this way, the stress–strain curves pertaining to quasi-static (strain rate: 0.001-0.1 s−1) and dynamic (temperature: 25-650 ℃ and strain rate: 800-4000 s−1) states were attained. According to the stress-strain curves, the rheological behaviours of 9Cr18Mo stainless steel at high temperature and high strain rate were discussed. Based on the testing data, the parameters of two constitutive models (Johnson-Cook (J-C) and Power-Law (P-L)) of 9Cr18Mo stainless steel were identified, and the correlation coefficients (R) and average absolute relative errors (AAREs) of the two constitutive models were compared. The results showed that 9Cr18Mo stainless steel presents strain rate sensitivity and significant thermal softening. That is the flow stress of 9Cr18Mo stainless steel increases with strain rate while significantly decreases with increasing temperature. The R values are 0.9697 and 0.9896, while the AAREs of two constitutive models are 2.77% and 1.85%, respectively. Hence, the P-L constitutive model shows a higher prediction accuracy which can describe the rheological behaviours of 9Cr18Mo stainless steel at high temperature and high strain rate more precisely compared with the J-C constitutive model. -
图 2 温度在25 ℃时不同应变率下的应力—应变曲线
Figure 2. Stress-strain curves at different strain rates (T=25 ℃)
图 3 25 ℃时不同应变率范围内，应变率敏感性参数β随真应变的变化关系
Figure 3. Relationship between strain rate sensitivity parameter (β) and strain within different strain rate ranges
图 4 温度为650 ℃时绝热温升随应变率的变化关系
Figure 4. Relationship between adiabatic temperature rise and strain rate(T=650 ℃)
图 5 应变率为4000 s−1时不同温度下的绝热温升
Figure 5. Adiabatic temperature rise at different temperatures (
$ \dot \varepsilon $ = 4000 s−1)
图 6 应变率为4000 s−1时不同温度下的应力—应变曲线
Figure 6. The stress-strain curves at different temperatures (
$ \dot \varepsilon $ = 4000 s−1)
图 7 不同温度变化范围内，温度灵敏度随应变变化曲线（应变率为4000 s−1）
Figure 7. Relationship between temperature sensitivity and strain within different temperature ranges(
$ \dot \varepsilon $ = 4000 s−1)
图 11
$ \ln (\sigma ({\varepsilon _s})/{\sigma _0}) $ 和$ \ln (1 + {\varepsilon _s}/{\varepsilon _0}) $ 的关系Figure 11. Relationship between
$ \ln (\sigma ({\varepsilon _s})/{\sigma _0}) $ and$ \ln (1 + {\varepsilon _s}/{\varepsilon _0}) $ 
图 12
$ \ln (\sigma ({\varepsilon _s},{\dot \varepsilon _s})/g({\varepsilon _s})) $ 和$ \ln (1 + {\dot \varepsilon _s}/{\dot \varepsilon _0}) $ 的关系Figure 12. Relationship between
$ \ln (\sigma ({\varepsilon _s},{\dot \varepsilon _s})/g({\varepsilon _s})) $ and$ \ln (1 + {\dot \varepsilon _s}/{\dot \varepsilon _0}) $ 
图 13
$ \sigma ({\varepsilon _s},{\dot \varepsilon _s},T)/g({\varepsilon _s})\Gamma ({\dot \varepsilon _s}) $ 和温度的关系Figure 13. Relationship between
$ \sigma ({\varepsilon _s},{\dot \varepsilon _s},T)/g({\varepsilon _s})\Gamma ({\dot \varepsilon _s}) $ and temperatures
图 14 不同应变率下应力—应变曲线的实验值与模型预测值的对比
Figure 14. Comparisons of the experimental values of stress-strain curves and the model predictions at different strain rates
图 15 两种本构模型下的试验值与预测值间的相关性
Figure 15. The correlation between experimental and predicted values of two constitutive models
表 1 试样化学成分
Table 1. Chemical composition of the sample
% C Si Cr Ni Mn P S Mo Fe 0.99 0.70 18.0 0.40 0.68 0.03 0.02 0.59 Bal. 
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表 2 不同试验条件下两种本构模型绝对误差的平均值
Table 2. Average absolute error of two constitutive models under different experimental conditions
T/℃ $ \dot \varepsilon $/s−1 $ \Delta {\sigma _{{\text{JC}}}} $/MPa $ \Delta {\sigma _{{\text{PL}}}} $/MPa T/℃ $ \dot \varepsilon $/s−1 $ \Delta {\sigma _{{\text{JC}}}} $/MPa $ \Delta {\sigma _{{\text{PL}}}} $/MPa 25 800 6.424471638 6.109457399 500 800 32.79624831 17.3101421 1500 38.98703638 15.33518007 1500 28.39327725 23.19058462 2000 37.04814443 9.391618684 2000 45.03536918 39.11484364 2500 29.46215782 5.722001128 2500 49.39455932 46.36667909 3000 22.34984852 5.923465121 3000 41.94325487 45.30685472 4000 5.982440216 3.902910575 4000 9.845891459 10.62832331 350 800 27.04190337 10.60611432 650 800 31.25790377 30.58632256 1500 20.1336439 18.2893326 1500 49.19664884 27.14529 2000 40.92181462 37.65429567 2000 51.54404536 26.74278264 2500 42.34938154 41.79854765 2500 33.93195871 11.88201571 3000 29.80158046 36.78908546 3000 26.76224827 9.985216708 4000 12.46319636 11.87826906 4000 20.68909126 15.5467803
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