Establishment of a constitutive model of aviation stainless steel 0Cr17Ni4Cu4Nb considering the coupling effects of strain, strain rate and temperature
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摘要: 航空不锈钢0Cr17Ni4Cu4Nb具有优良的特性，广泛应用在各个机械的重要零部件上，零件的加工过程伴随着大应变、高温和高应变率，基于此考虑耦合关系建立能够真实反映切削力学性能的本构模型，为切削仿真提供可靠的数据。以航空不锈钢0Cr17Ni4Cu4Nb为研究对象，利用万能试验机（UTM5305）和高温分离式霍普金森试验装置（Split Hopkinson Pressure Bar，SHPB，ALT1000）分别进行准静态压缩试验（温度为25 ℃，应变率为0.1、0.01、0.001s−1）和动态冲击试验（温度为25、350、500、650 ℃，应变率为750、
1500 、2000、2600 、3500 、4500 s−1），获得该材料的应力应变关系，并分析其力学性能，结果表明该材料具有应变硬化效应、温度软化效应、应变率强化效应和增塑效应。综合应变、应变率和温度三者相互作用，建立耦合作用下的Johnson-Cook（JC）本构方程，统计分析了试验数据与预测数据（原JC本构方程和修正JC本构方程数据），原JC本构方程的相关系数（R）和平均相对误差（AARE）分别为0.96833 和4.77%；修正JC本构方程的相关系数（R）和平均相对误差（AARE）分别为0.987513 和0.51%，表明修正JC本构方程更加准确、可靠预测高应变率下应力应变的关系。Abstract: The aviation stainless steel 0Cr17Ni4Cu4Nb has excellent characteristics and is widely used in important parts of various machines. The machining process of these parts is accompanied by large strain, high temperature and high strain rate. Based on this coupling relationship, a constitutive model that can truly reflect the cutting mechanical properties is established to provide reliable data for cutting simulation. This paper sets the aviation stainless steel 0Cr17Ni4Cu4Nb as the research object, and uses the universal testing machine (UTM5305) and the split Hopkinson Pressure Bar (SHPB, ALT1000) to carry out the quasi-static compression tests (temperature: 25 ℃, strain rate: 0.1, 0.01, 0.001 s−1) and dynamic impact tests (temperature: 25, 350, 500 and 650 ℃, strain rate: 750,1500 ,2000 ,2600 ,3500 and4500 s−1), respectively. The stress-strain relationship of the material is obtained, and its mechanical properties are analyzed. It is shown that the material exhibits strain hardening effect, temperature softening effect, strain rate strengthening effect and plasticizing effect. Combining the interaction of strain, strain rate and temperature, the Johnson-Cook (JC) constitutive equation under the coupling action is established. The test data and prediction data (the original and modified JC constitutive equation) are statistically analyzed. The correlation coefficient (R) and the average phase error (AARE) of the original JC constitutive equation are0.96833 and 4.77%, respectively. The correlation coefficient (R) and average relative error (AARE) of the modified JC constitutive equation are0.987513 and 0.51%, respectively, indicating that the modified JC constitutive equation is more accurate and reliable in predicting the stress-strain relationship at high strain rates. -
图 1 准静态压缩试验的$ \varepsilon - \sigma $曲线
Figure 1. $ \varepsilon - \sigma $ curves by quasi-static compression tests
图 2 不同应变率下SHPB试验$ \varepsilon - \sigma $曲线
Figure 2. $ \varepsilon - \sigma $ curves of SHPB under different strain rates
图 3 不同温度下SHPB试验$ \varepsilon - \sigma $曲线
Figure 3. $ \varepsilon - \sigma $ curves of SHPB under different temperatures
图 4 动态冲击时应变($ \varepsilon $)与应变率敏感指数($ m $)的关系
Figure 4. Relationship between strain ($ \varepsilon $) and strain rate sensitivity index ($ m $)
图 5 动态冲击时应变率的对数(lg$ \dot \varepsilon $)与应变率敏感指数($ m $)的关系
Figure 5. The relationship between the logarithm of the strain rate (lg$ \dot \varepsilon $) and strain rate sensitivity index ($ m $)
图 9 原JC本构模型、修正JC本构模型真应力预测和试验值比较
Figure 9. Comparison of the predicted and tested true stress values between the original and modified JC constitutive models
图 10 原JC本构模型、修正JC本构预测值和试验值之间的关系
Figure 10. Relationship between the original and modified JC constitutive model prediction values and experimental values
图 11 原JC本构模型、修正JC本构模型平均相对误差比
Figure 11. Comparison of the average relative errors of the original and modified JC constitutive models
表 1 0Cr17Ni4Cu4Nb不锈钢化学成分
Table 1. Chemical composition of 0Cr17Ni4Cu4Nb stainless steel
% C Si Cr Ni Mn P S Cu Nb Fe 0.06 0.80 16.25 3.60 0.82 0.030 0.022 3.83 0.28 Bal. 
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表 2 准静态下不同应变率和应变处的强化指数$ n $
Table 2. Strengthening exponent $ n $ at different strain rates and strains under quasi-static state
$ \dot \varepsilon /{{\text{s}}^{ - 1}} $ n $ \varepsilon $=0.20 $ \varepsilon $=0.25 $ \varepsilon $=0.30 $ \varepsilon $=0.35 $ \varepsilon $=0.40 $ \varepsilon $=0.45 0.001 0.1418 0.1250 0.0625 0.0335 0.0210 0.0425 0.01 0.1612 0.0849 0.0611 0.0239 0.0119 0.0390 0.1 0.1187 0.0644 0.0260 0.0004 0.0145 0.0267
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表 3 准静态试样变形量
Table 3. Deformation of quasi-static specimens
应变率/$ {{\text{s}}^{ - 1}} $ 直径/mm 厚度/mm 0.001 7.29 4.31 0.01 7.43 4.11 0.1 7.67 3.78
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表 4 动态试样变形量(T=25 ℃和T=650 ℃)
Table 4. Deformation of quasi-static specimens
T/℃ $ \dot \varepsilon /{{\text{s}}^{ - 1}} $ $ d/{\text{mm}} $ $ h/{\text{mm}} $ 25 750 3.12 2.68 1500 3.18 2.47 2 000 3.64 2.06 2600 3.77 1.86 3500 4.01 1.65 4500 4.42 0.76 650 750 3.36 2.40 1500 3.55 2.22 2 000 3.71 1.97 2600 4.13 1.56 3500 4.37 1.51 4500 4.47 0.77
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表 5 应变项参数值
Table 5. Parameter values of strain item
B0 B1 B2 B3 B4 509.01581 5908.2858 − 21498.54 35937.295 − 23318.67
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表 6 应变率项参数值
Table 6. Parameter values of strain rate item
C0 C1 C2 C3 C4 − 2.42266 0.69941 − 0.06371 0.00192 − 11.18017 C5 C6 C7 C8 C9 3.04559 − 9.69615 1.58625 0.18026 − 0.06239
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表 7 温度项参数值
Table 7. Parameter values of temperature item
a0 a1 a2 a3 a4 a5 − 67.50836 9.61375 − 118.52129 333.90202 15.06135 − 1.08320 a6 a7 a8 a9 a10 0.02552 1.07963 0.00000 − 3.53005 0.39414
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