J-C Constitutive Relation at Low Strain Rates for DNAN-based Aluminium Explosives
-
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、脉冲小等特点, 与高速冲击点火显著不同。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(SHPB)对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 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 is significantly different from the high-velocity impact ignition. In order to study the dynamic mechanical characteristics of a typical underwater weapon combatant charge drop conditions, the dynamic compression test of DNAN-based aluminium explosives was carried out by using the separated Hopkinson press bar(SHPB), and the normal strain rate loading was achieved by the incident wave shaping technique, and the stress-strain curves of DNAN-based aluminium explosives at three low strain rates, 180/s, 280/s and 360/s, were obtained under the conditions of normal temperature and normal pressure, and the Johnson -Chester strain curve was used. The Johnson-Cook intrinsic 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 aluminium explosives all increase with the increase of strain rate; using the fitted JC principal parameters, the dynamic mechanical behaviour of DNAN-based aluminium explosives under low strain rate can be well restored in numerical simulation, and it can provide a strong data support for the related numerical simulation calculation of the safety of fall.
-
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 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 表 3 DNAN基含铝炸药的J-C本构参数
Table 3. JC intrinsic parameters of DNAN-based underwater explosives
A/Mbar B/Mbar n C 1.82×10−6 6.5×10−5 0.7 0.45 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 表 5 紫铜整形器J-C模型参数
Table 5. Copper shaper JC model parameters
$ \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 — 表 6 不同应变率下不同网格尺寸仿真结果误差
Table 6. Fig6 Error of simulation results with different mesh sizes for 80/s strain rate
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 2.36 1.26 0.75 2.01 0.64 0.5 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 2.57 1.34 0.75 2.45 0.71 0.5 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 3.98 3.05 0.75 2.15 1.46 0.5 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 4.34 3.64 0.75 2.97 1.88 0.5 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 4.83 3.71 0.75 2.60 1.92 0.5 1.95 1.24 0.25 1.82 1.20 -
[1] 王新颖, 王树山, 王绍慧, 等. 典型水中战斗部炸药装药跌落撞击响应特性[J]. 兵工学报, 2021, 42(S1): 33-39.WANG X Y, WANG S S, WANG S H, et al. Drop impact response characteristics of typical explosive charge in underwater warhead[J]. Acta Armamentarii, 2021, 42(S1): 33-39. [2] HORIE Y. Shock wave science and technology reference library, Vol. 2: Solids I[M]. Berlin Heidelberg: Springer, 2007. [3] 李尚昆, 黄西成, 王鹏飞. 高聚物黏结炸药的力学性能研究进展[J]. 火炸药学报, 2016, 39(4): 1-11.LI S K, HUANG X C, WANG P F. Recent advances in the investigation on mechanical properties of PBX[J]. Chinese Journal of Explosives & Propellants, 2016, 39(4): 1-11. [4] CAMPBELL A W, DAVIS W C, TRAVIS J R. Shock initiation of detonation in liquid explosives[J]. The Physics of Fluids, 1961, 4(4): 498-510. doi: 10.1063/1.1706353 [5] XIAO Y C, WANG Z Y, WANG R S, et al. A viscoelastic–viscoplastic constitutive model for polymer bonded explosives under low impact loading[J]. Scientific Reports, 2022, 12(1): 21845. doi: 10.1038/s41598-022-26525-z [6] PUSHKOV V A, MIKHAILOV A L, TSIBIKOV A N, et al. Studying the characteristics of explosives under dynamic load using the split hopkinson pressure bar technique[J]. Combustion, Explosion, and Shock Waves, 2021, 57(1): 112-121. doi: 10.1134/S0010508221010135 [7] FENG X J, FENG B, XUE L X, et al. Mechanical properties and constitutive equation of pressed CL−20 based aluminized explosives[J]. Fire P hys Chem, 2021, 1(3): 185-189. doi: 10.1016/j.fpc.2021.08.001 [8] 胡海波, 傅华, 李涛, 等. 压装密实炸药装药非冲击点火反应传播与烈度演化实验研究进展[J]. 爆炸与冲击, 2020, 40(1): 4-17.HU H B, FU H, LI T, et al. Progress in experimental studies on the evolution behaviors of non-shock initiation reaction in low porosity pressed explosive with confinement[J]. Explosion and Shock Waves, 2020, 40(1): 4-17. [9] 李东伟, 苗飞超, 张向荣, 等. 2, 4-二硝基苯甲醚基不敏感熔注炸药动态力学性能[J]. 兵工学报, 2021, 42(11): 2344-2349.LI D W, MIAO F C, ZHANG X R, et al. Dynamic mechanical properties of an insensitive DNAN-based melt-cast explosive[J]. Acta Armamentarii, 2021, 42(11): 2344-2349. [10] LESEUR D. Experimental investigations of material models for Ti-6A1-4V and 2024-T3: UCRL-ID-134691 [R]. California USA: Lawrence Livermore National Laboratory(LLNL), 1999: 1-28. [11] 孙文旭, 罗智恒, 唐明峰, 等. PBX-1炸药的力学性能和本构关系[J]. 爆炸与冲击, 2019, 39(7): 39-45.SUN W X, LUO Z H, TANG M F, et al. Compressive mechanical properties and constitutive relations of PBX-1[J]. Explosion and Shock WAVES, 2019, 39(7): 39-45. [12] 李俊玲, 王硕, 傅华, 等. SHPB实验加载方式对PBX炸药力学响应的影响研究[J]. 含能材料, 2019, 27(10): 824-829.LI J L, WANG S, FU H, et al. Investigation into the influences of SHPB loading ways on the mechanical response of PBX[J]. Chinese Journal of Energetic Materials, 2019, 27(10): 824-829. [13] 徐先勇, 李志华. 水雷炸药现状分析及发展方向的思考[J]. 舰船电子工程, 2015, 35(10): 14-16,155.XU X Y, LI Z H. Present and prospect of mine charging[J]. Ship Electronic Engineering, 2015, 35(10): 14-16,155. [14] 焦纲领, 朱曦全, 陈津虎. 海军战术导弹贮存试验方法与寿命评估研究[J]. 强度与环境, 2020, 47(5): 42-47.JIAO G L, ZHU X Q, CHEN J H. Research on storage test method and life evaluation of naval tactical missile[J]. Structure & Environment Engineering, 2020, 47(5): 42-47. [15] Johnson G R, Cook W H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[J]. Engineering Fracture Mechanics, 1983, 21: 541-548.