J-C Constitutive Relation at Low Strain Rates for DNAN-Based Aluminium Explosives
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摘要: 炸药装药的跌落响应问题是典型的低速撞击点火问题, 表现出应变率低、脉宽长及脉冲小等特点, 与高速冲击点火明显不同。为研究典型水中兵器战斗部装药跌落条件下的动态力学特征, 利用分离式霍普金森压杆对二硝基苯甲醚(DNAN)基含铝炸药进行动态压缩试验, 通过入射波整形技术实现了常应变率加载, 得到了常温常压条件下80、180、280、360和440 s−1等5种低应变率下DNAN基含铝炸药的应力应变曲线, 采用Johnson-Cook(J-C)本构模型对试验数据进行了参数拟合, 并结合数值仿真加以验证。结果表明: DNAN基含铝炸药的弹性模量、屈服强度、屈服应变、失效应力及失效应变均随应变率的提高而增大。利用拟合得到的J-C本构参数可以在数值仿真中很好地还原DNAN基含铝炸药在低应变率下的动态力学行为, 从而为相关跌落安全性数值仿真计算提供数据支撑。Abstract: The drop response problem of the explosive charge is a typical low-velocity impact ignition problem, which exhibits the characteristics of low strain rate, long pulse width, and small pulse, and it is significantly different from the high-velocity impact ignition. In order to study the dynamic mechanical characteristics of a typical underwater weapon warhead charge drop conditions, the dynamic compression test of DNAN-based aluminum explosives was carried out by using the split Hopkinson pressure bar(SHPB), and the normal strain rate loading was achieved by the incident wave shaping technique. The stress-strain curves of DNAN-based aluminum explosives at five low strain rates, 80, 180, 28, 360, and 440 s−1 were obtained under the conditions of normal temperature and normal pressure. The Johnson-Cook(J-C) constitutive model was used to fit the parameters of the test data and verified by numerical simulation. The results show that the elastic modulus, yield strength, yield strain, failure stress, and failure strain of DNAN-based aluminum explosives all increase with the increase in strain rate; using the fitted J-C constitutive parameters can well restore the dynamic mechanical behaviors of DNAN-based aluminum explosives at low strain rate in numerical simulation, and it can provide strong data support for the related numerical simulation calculation of the drop safety.
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图 5 典型试样试验前后形貌对比
Figure 5. Comparison of the shape of a typical specimen before and after testing
图 6 不同应变率下试样的应力应变曲线
Figure 6. Stress-strain curves for specimens at different strain rates
图 7 不同应变率下J-C本构模型与试验结果对比
Figure 7. Comparison of J-C intrinsic model and experimental results for three strain rates
图 9 不同应变率下不同尺寸网格仿真结果对比曲线
Figure 9. Comparison of simulation results with different mesh sizes at different strain rates
表 1 试验前后试样尺寸对比
Table 1. Comparison of specimen dimensions before and after testing
应变率/s−1 试验前 试验后 直径/mm 长度/mm 直径/mm 长度/mm 80 9.9 5.05 10.01 5.04 180 10.01 5.03 10.06 5.02 280 10.10 5.05 10.33 5.04 360 10.04 5.09 10.30 5.01 440 10.10 5.12 10.39 5.07 
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表 2 不同应变率下试样的动态力学参数
Table 2. Dynamic mechanical parameters of specimens at different strain rates
应变率
/s−1弹性模量
/GPa屈服强度
/MPa屈服应变
/%失效应力
/MPa失效应变
/%80 2.42 10.01 0.42 11.61 0.53 180 4.04 14.03 0.44 17.59 0.74 280 5.03 18.02 0.54 21.22 0.98 360 5.54 19.97 0.58 24.87 1.08 440 5.75 20.71 0.59 26.67 1.17
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表 3 DNAN基含铝炸药J-C本构参数
Table 3. J-C constitutive parameters of DNAN-based Aluminium explosives
A/Mbar B/Mbar n C 1.82×10−6 6.5×10−5 0.7 0.45
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表 4 铝杆件线弹性模型参数
Table 4. Model parameters for the linear elasticity of aluminium rod members
$ \rho $/(g·cm−3) 杨氏模量/Mbar 泊松比 2.78 0.71 0.33
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表 5 紫铜整形器J-C模型参数
Table 5. J-C model parameters of the copper shaper
$ \rho $/(g·cm−3) G/Mbar A/Mbar B/Mbar n 8.96 0.46 9×10−4 2.9×10−3 0.31 C m Tm/K Tr/K — 0.025 1.09 1356 210 —
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表 6 不同应变率下不同网格尺寸仿真结果误差
Table 6. Errors of simulation results with different mesh sizes for different strain rates
应变率为80 s−1 网格尺寸/mm 最大相对误差/% 整体相对误差/% 1.00 2.36 1.26 0.75 2.01 0.64 0.50 1.97 0.59 0.25 1.82 0.51 应变率为180 s−1 网格尺寸/mm 最大相对误差/% 整体相对误差/% 1.00 2.57 1.34 0.75 2.45 0.71 0.50 2.39 0.75 0.25 2.29 0.68 应变率为280 s−1 网格尺寸/mm 最大相对误差/% 整体相对误差/% 1.00 3.98 3.05 0.75 2.15 1.46 0.50 1.45 0.79 0.25 1.26 0.77 应变率为360 s−1 网格尺寸/mm 最大相对误差/% 整体相对误差/% 1.00 4.34 3.64 0.75 2.97 1.88 0.50 2.06 1.20 0.25 1.98 1.16 应变率为440 s−1 网格尺寸/mm 最大相对误差/% 整体相对误差/% 1.00 4.83 3.71 0.75 2.60 1.92 0.50 1.95 1.24 0.25 1.82 1.20
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