J-C model of high-entropy alloy Ta-Hf-Nb-Zr system and its application test
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摘要: 针对包含高密度、高热值元素的高熵合金材料在聚能战斗部药型罩上的应用问题，选取Ta-Hf-Nb-Zr体系高熵合金为研究对象，采用INSTRON材料试验机、分离式霍普金森压杆试验平台，探寻该高熵合金在应变率为10−3～103 s−1、温度为25～900 ℃以及应力三轴度为0.33～0.89条件下的力学响应规律，基于静动态力学性能试验结果，获取该合金的Johnson-Cook（J-C）本构方程参数及损伤失效模型参数，并建立爆炸加载下高熵合金爆炸成型弹丸（explosively formed projectile，EFP）数值模型。开展EFP成型脉冲X射线验证试验，结果显示：117 μs时，高熵合金EFP成型较为完整，EFP长度为51.1 mm，直径为12.27 mm；187 μs时，EFP尾部产生3处断裂，头部长度为24.3 mm，直径为12.27 mm，EFP速度为
2496.3 m/s。模拟与试验的EFP长度、直径以及速度的误差均小于8.2%，模拟的断裂形态与试验结果基本一致，J-C模型有效预测了爆炸加载条件下高熵合金EFP的成型状态。-
关键词:
- 高熵合金 /
- Johnson-Cook模型 /
- 爆炸成型弹丸 /
- 脉冲X射线
Abstract: In relation to the application of high-entropy alloy systems containing high-density and high-calorific value elements in the liner of shaped charge warheads, the Ta-Hf-Nb-Zr high-entropy alloy system is investigated. The study employed an INSTRON material testing machine and a split Hopkinson pressure bar testing platform to explore the mechanical response of this high-entropy alloy across a wide range of strain rates from 10−3 to 103 s−1, temperatures ranging from 25 to 900 °C, and stress triaxiality values ranging from 0.33 to 0.89. Yield strength and failure strain data were obtained from static round bar tensile tests and dynamic compression tests conducted under these varying conditions. By using least squares fitting, the parameters of the Johnson-Cook (J-C) constitutive equation as well as the damage failure model parameters, are derived. Subsequently, a simulation model for explosively formed projectile (EFP) made from high-entropy alloys under explosive loading conditions was developed. Pulse X-ray tests of the EFP formation were performed, and numerical simulations of the EFP formation process are conducted using LS-DYNA software. The results show that at 117 μs, the high-entropy alloy EFP remains largely intact, with a length of 51.1 mm and a diameter of 12.27 mm. At 187 μs, three fractures are observed at the tail of the EFP, with the head length measuring 24.3 mm, the diameter at 12.27 mm, and the EFP speed recorded at2496.3 m/s. The numerical simulations demonstrate that the EFP length, diameter, and velocity at these time instants match the test data with errors of less than 8.2%. Moreover, the fracture patterns observed experimentally align closely with those predicted by the simulations. This consistency indicates that the J-C model effectively predicts the formation characteristics of high-entropy alloy EFPs under explosive loading conditions, confirming its utility in accurately simulating the EFP formation process.-
Key words:
- high-entropy alloy /
- Johnson-Cook model /
- explosively formed projectile /
- pulsed X-ray
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图 2 不同应变率下光滑圆棒的静态应力-应变曲线及拉断试件
Figure 2. Static stress-strain curves of smooth round bars under different strain rates and specimens with tensile fracture
图 3 不同缺口半径下带缺口圆棒试件的静态力-位移曲线及拉断试件
Figure 3. Static force-displacement curves of notched round bar specimens with different notch radii and specimens with tensile fracture
图 4 不同温度下带光滑圆棒试件的静态应力-应变曲线及拉断试件
Figure 4. Static stress-strain curves of smooth round bars at different temperatures and specimens with tensile fracture
图 7 不同应变率下高熵合金的动态应力-应变曲线
Figure 7. Dynamic stress-strain curves of HEA at different strain rates
图 8 高温高应变率下合金的应力-应变曲线
Figure 8. Stress-strain curves of alloy under high temperature and high strain rate
图 9 失效应变与应力三轴度的关系
Figure 9. Relationship between fracture strain and stress triaxiality
图 10 失效应变与无量纲应变率的关系
Figure 10. Relationship between fracture strain and the logarithmic non-dimensional strain rate
图 17 数值模拟与脉冲X射线试验的EFP成型形态对比
Figure 17. Comparison of EFP forming morphology between numerical simulation and pulsed X-ray testing
表 1 不同应变率下光滑圆棒试件的失效应变
Table 1. Failure strain of smooth round bar specimens at different strain rates
试件编号 应变率/s−1 εf 1-1 0.001 0.67 1-2 0.010 0.73 1-3 0.050 0.86 1-4 0.100 0.87 
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表 2 不同缺口半径下缺口试件的失效应变
Table 2. Failure strain of notch specimens under different notch radii
试件编号 σ* εf 2-1 0.89 0.35 2-2 0.74 0.46 2-3 0.56 0.53 2-4 0.47 0.50 2-5 0.43 0.55 2-6 0.33 0.67
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表 3 高温拉伸试验中光滑圆棒试件的失效应变
Table 3. Failure strain of smooth round bar specimens in high temperature tensile test
试件编号 温度/℃ εf 3-1 100 0.60 3-2 300 0.34 3-3 500 0.17 3-4 700 0.08
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表 4 不同应变率下高熵合金的屈服强度
Table 4. HEA yield stress under different strain rates
应变率/s−1 屈服强度/MPa 2160 639.1 3000 648.4 3600 650.8 4200 679.0
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表 5 不同温度条件下高熵合金的屈服强度
Table 5. Variation of yield strength of HEA under different temperatures
温度/℃ 屈服强度/MPa 300 353.7 700 295.3 800 248.9 900 233.7
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表 7 药型罩材料的J-C本构方程参数
Table 7. J-C constitutive equation parameters for liner materials
A/MPa B/MPa n C m 270.2 571.3 0.79 0.062 0.638
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表 6 药型罩材料的Grüneisen状态方程参数[5]
Table 6. Grüneisen state equation parameters for liner materials
ρ/(g·cm−3) γ C0/(m·s−1) S 11.7 1.1147 3213.0 1.1218
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表 8 药型罩材料的J-C失效方程参数
Table 8. J-C failure equation parameters for liner materials
D1 D2 D3 D4 D5 0.24 0.78 −1.98 0.076 −3.269
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