Research on Johnson-Cook constitutive model of 06Cr19Ni10 austenitic stainless steel at high strain rate
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摘要: 为了探讨06Cr19Ni10奥氏体不锈钢在大应变和高应变率下成形的流动规律，借助高温分离式霍普金森（High Temperature Split Hopkinson Pressure Bar）动态试验装置，进行不同温度和应变率冲击试验。分析试验数据表明，该材料具有增塑、应变率强化和温度软化现象，并建立了Johnson-Cook本构模型。考虑应变率强化效应，依据试验数据进行了JC本构模型的修正，对比修正前后模型预测值和试验值，吻合程度好。运用统计分析，对比修正前后模型的相关系数（R）和平均相对误差（AARE），修正前、后相关系数（R）分别为0.96388、0.97054；修正前、后平均相对误差（AARE）分别为5.63%、4.68%，修正后的模型预测精度优于修正前。结果表明，修正后的模型可以更加精确预测06Cr19Ni10奥氏体不锈钢应力与应变、应变率和温度的关系。Abstract: In order to explore the flow behavior of 06Cr19Ni10 austenitic stainless steel under large strain and high strain rate forming, impact tests had been carried out under different temperature and strain rate with the help of high temperature split hopkinson pressure bar dynamic experimental device. Impact test results show that the material has plasticization, strain rate strengthening and temperature softening phenomena, and the Johnson-Cook (JC) constitutive model has been established. Taking into account the strain rate strengthening effect the JC constitutive model was modified and both the model prediction values before and after the correction showed good agreement with experimental value. The correlation coefficients (R) before and after the model correction were 0.963 88 and 0.970 54, respectively, and the average relative error (AARE) before and after the correction were 5.63 %, 4.68 %, respectively. This indicated that the revised model achieved better prediction accuracy than origin model. The revised model could be used to predict the relationship among stress, strain, strain rate and temperature of 06Cr19Ni10 austenitic stainless steel more accurately.
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图 2 25 ℃时不同应变率下真应变真应力曲线关系
Figure 2. Relationship between true strain and true stress curve at different strain rates (T=25 ℃)
图 3 25 ℃时不同应变率下冲击前后试样的宏观形貌
Figure 3. Macroscopic morphology of the sample before and after impact tests at different strain rates (T=25 ℃)
图 4 3000 s−1时不同温度下真应变真应力曲线关系
Figure 4. True stress-strain curves of the sample at different temperatures (
$ \dot \varepsilon = 3\;000\;{{\text{s}}^{{{ - 1}}}} $ )
图 7
$ \ln (\sigma - A) $ 和$ \ln (\varepsilon /{\varepsilon _0}) $ 的关系Figure 7. Relationship between
$ \ln (\sigma - A) $ and$ \ln (\varepsilon /{\varepsilon _0}) $ 
图 8
$ \sigma /[A + B(\varepsilon /{\varepsilon _0})] - 1 $ 和$ \mathrm{ln}（\dot{\varepsilon }/{\dot{\varepsilon }}_{0}） $ 的关系Figure 8. Relationship between
$ \sigma /[A + B(\varepsilon /{\varepsilon _0})] - 1 $ and ln$ \mathrm{}（\dot{\varepsilon }/{\varepsilon }_{0}） $ 
图 9
$ \ln (1 - \sigma /[A + B(\varepsilon /{\varepsilon _0})][1 + C\ln (\dot \varepsilon /{\dot \varepsilon _0})]) $ 和$ \ln [(T - {T_{\text{r}}})/({T_{\text{m}}} - {T_{\text{n}}})] $ 的关系Figure 9. Relationship between
$ \sigma /[A + B(\varepsilon /{\varepsilon _0})] - 1 $ and ln$ [(T - {T_{\text{r}}})/({T_{\text{m}}} - {T_{\text{n}}})] $ 
图 10
$ (\sigma /[A + B(\varepsilon /{\varepsilon _0})] - 1)/\ln (\dot \varepsilon /{\dot \varepsilon _0}) $ 和应变率的关系Figure 10. Relationship between
$(\sigma /[A + B(\varepsilon /{\varepsilon _0})] - 1)/$ $\ln (\dot \varepsilon /{\dot \varepsilon _0}) $ and strain rate
图 11
$ \mathrm{ln}(1-\sigma /[A+B(\varepsilon /{\varepsilon }_{0})][1+（{C}_{0}+{C}_{1}\dot{\varepsilon }+{C}_{2}{\dot{\varepsilon }}_{2}) $ $\mathrm{ln}(\dot{\varepsilon }/{\dot{\varepsilon }}_{0})]) $ 和$ \ln [(T - {T_{\text{r}}})/({T_{\text{m}}} - {T_{\text{n}}})] $ 的关系Figure 11. Relationship between
$ \mathrm{ln}(1-\sigma /[A+B(\varepsilon /{\varepsilon }_{0})][1+ $ $（{C}_{0}+{C}_{1}\dot{\varepsilon }+{C}_{2}{\dot{\varepsilon }}_{2}）\mathrm{ln}(\dot{\varepsilon }/{\dot{\varepsilon }}_{0})]) $ and$ \ln [(T - {T_{\text{r}}})/$ $({T_{\text{m}}} - {T_{\text{n}}}) $ ]
图 12 Johnson-Cook本构模型修正前后的预测值和试验值对比
Figure 12. Comparison of predicted and experimental values before and after the Johnson-Cook constitutive model modification
图 13 Johnson-Cook本构模型修正前后的预测值和试验值之间的关系
Figure 13. The relationship between the predicted values and the experimental values of Johnson-Cook constitutive model before and after modification
图 14 Johnson-Cook本构模型修正前后平均相对误差对比
Figure 14. Comparison of the average relative error of Johnson-Cook constitutive model before and after modification
表 1 06Cr19Ni10奥氏体不锈钢化学成分
Table 1. Chemical composition of 06Cr19Ni10 stainless steel
% C Si Mn P S Ni Cr Fe 0.08 0.75 2.00 0.045 0.03 8.22 18.89 Bal 
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表 2 Johnson-Cook模型参数
Table 2. Parameters for the Johnson-Cook model
A/MPa B/MPa n C m 511.071 1629.9751 0.88228 0.29719 0.71712
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表 3 修正Johnson-Cook模型参数
Table 3. Modified Johnson-Cook model parameters
A/MPa B/MPa C0 C1 C2 m D 511.071 1629.9751 −5.22651×10−8 2.70165×10−4 −0.07323 0.82144 1.33643
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