多胞材料的动态应力应变状态及其一致近似关系
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摘要
多胞材料在高速冲击下呈现出逐层压溃的变形模式,塑性冲击波模型可以用来表征这种集中变形带的传播行为。本文中采用截面应力计算方法得到了随机蜂窝在恒速冲击下的一维应力分布,进而对冲击波的传播规律进行了分析。比较了高速冲击下由不同方法得到的冲击波速度与冲击速度的关系,结果表明RPP-L(率无关,刚性-理想塑性-锁定)模型高估了冲击波速度,但R-PH(率无关,刚性-塑性硬化)模型以及一维冲击波理论得到的冲击波速度与有限元结果比较接近。冲击波速度与冲击速度在高速情形下趋于线性关系,但随着冲击速度的减小,冲击波速度不断减少并趋于常数。根据这一特征和塑性冲击波模型,发展了可以表征冲击波速度与冲击速度的关系、动态应力应变关系的一致近似模型。
Cellular material under high-speed impact is deformed in a mode of layer-wise propagation of crushing bands,which can be characterized by the plastic shock models. In this paper,we obtained the one-dimensional stress distribution of a random honeycomb under constant-velocity compression using the cross-sectional stress calculation method,analyzed the shockwave propagation,and examined the relation between the shockwave velocity and the impact velocity obtained by different methods under high-velocity impact. The results show that the shockwave speed is overestimated by the R-PP-L( rate-independent,rigid-perfect plastic-locking) model,but the shockwave speeds obtained by the R-PH( rate-independent,rigid-plastic hardening)model and the one-dimensional shock theory are close to that of finite element simulation. The relation between the shockwave velocity and the impact velocity tends to be linear at high impact velocities,and the shockwave speed reduces to a constant with the decrease of the impact velocity. In light of these characteristics and based on the plastic shockwave model,we developed a uniformly approximated model is developed to characterize the relation between the shockwave velocity and the impact velocity and the dynamic stress-strain relation of cellular material.
Cellular material under high-speed impact is deformed in a mode of layer-wise propagation of crushing bands,which can be characterized by the plastic shock models. In this paper,we obtained the one-dimensional stress distribution of a random honeycomb under constant-velocity compression using the cross-sectional stress calculation method,analyzed the shockwave propagation,and examined the relation between the shockwave velocity and the impact velocity obtained by different methods under high-velocity impact. The results show that the shockwave speed is overestimated by the R-PP-L( rate-independent,rigid-perfect plastic-locking) model,but the shockwave speeds obtained by the R-PH( rate-independent,rigid-plastic hardening)model and the one-dimensional shock theory are close to that of finite element simulation. The relation between the shockwave velocity and the impact velocity tends to be linear at high impact velocities,and the shockwave speed reduces to a constant with the decrease of the impact velocity. In light of these characteristics and based on the plastic shockwave model,we developed a uniformly approximated model is developed to characterize the relation between the shockwave velocity and the impact velocity and the dynamic stress-strain relation of cellular material.
引文
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[12]王长峰,郑志军,虞吉林.泡沫杆撞击刚性壁的动态压溃模型[J].爆炸与冲击,2013,33(6):587-593.DOI:10.3969/j.issn.1001-1455.2013.06.005.WANG Changfeng,ZHENG Zhijun,YU Jilin.Dynamic crushing models for a foam rod striking a rigid wall[J].Explosion and Shock Waves,2013,33(6):587-593.DOI:10.3969/j.issn.1001-1455.2013.06.005.
[13]ZHENG Z J,WANG C F,YU J L,et al.Dynamic stress-strain states for metal foams using a 3D cellular model[J].Journal of the Mechanics and Physics of Solids,2014,72:93-114.DOI:10.1016/j.jmps.2014.07.013.
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[15]SUN Y L,LI Q M,MCDONALD S A,et al.Determination of the constitutive relation and critical condition for the shock compression of cellular solids[J].Mechanics of Materials,2016,99:26-36.DOI:10.1016/j.mechmat.2016.04.004.
[16]WANG P,WANG X K,ZHENG Z J,et al.Stress distribution in graded cellular materials under dynamic compression[J].Latin American Journal of Solids and Structures,2017,14(7):1251-1272.DOI:10.1016/j.ijimpeng.2017.10.006.
[17]WANG L L.Foundations of stress waves[M].Amsterdam:Elsevier Science Ltd.,2007.DOI:10.1002/prep.200790014.
[2]REID S R,PENG C.Dynamic uniaxial crushing of wood[J].International Journal of Impact Engineering,1997,19(5/6):531-570.DOI:10.1016/S0734-743X(97)00016-X.
[3]ZHENG Z J,YU J L,LI J R.Dynamic crushing of 2D cellular structures:A finite element study[J].International Journal of Impact Engineering,2005,32(1):650-664.DOI:10.1016/j.ijimpeng.2005.05.007.
[4]LIU Y D,YU J L,ZHENG Z J,et al.A numerical study on the rate sensitivity of cellular metals[J].International Journal of Solids and Structures,2009,46(22):3988-3998.DOI:10.1016/j.ijsolstr.2009.07.024.
[5]张新春,刘颖,章梓茂.组合蜂窝材料面内冲击性能的研究[J].工程力学,2009,26(6):220-225.ZHANG Xinchun,LIU Ying,ZHANG Zimao.Research on dynamic properties of suppercell honeycomb structures under in-plane impact loading[J].Engineering Mechanics,2009,26(6):220-225.
[6]胡玲玲,蒋玲.胞孔构型对金属蜂窝动态力学性能的影响机理[J].爆炸与冲击,2014,34(1):41-46.DOI:10.3969/j.issn.1001-1455.2014.01.008.HU Lingling,JIANG Ling.Mechanism of cell configuration affecting dynamic mechanical properties of metal honeycombs[J].Explosion and Shock Waves,2014,34(1):41-46.DOI:10.3969/j.issn.1001-1455.2014.01.008.
[7]ZOU Z,REID S R,TAN P J,et al.Dynamic crushing of honeycombs and features of shock fronts[J].International Journal of Impact Engineering,2009,36(1):165-176.DOI:10.1016/j.ijimpeng.2007.11.008.
[8]LIAO S F,ZHENG Z J,YU J L.Dynamic crushing of 2D cellular structures:Local strain field and shock wave velocity[J].International Journal of Impact Engineering,2013,57(1):7-16.DOI:10.1016/j.ijimpeng.2013.01.008.
[9]TAN P J,REID S R,HARRIGAN J J,et al.Dynamic compressive strength properties of aluminium foams.PartⅡ:“Shock”theory and comparison with experimental data and numerical models[J].Journal of the Mechanics and Physics of Solids,2005,53(10):2206-2230.DOI:10.1016/j.jmps.2005.05.003.
[10]TAN P J,REID S R,HARRIGAN J J,et al.Dynamic compressive strength properties of aluminium foams.PartⅠ:Experimental data and observations[J].Journal of the Mechanics and Physics of Solids,2005,53(10):2174-2205.DOI:10.1016/j.jmps.2005.05.007.
[11]ZHENG Z J,YU J L,WANG C F,et al.Dynamic crushing of cellular materials:A unified framework of plastic shock wave models[J].International Journal of Impact Engineering,2013,53(1):29-43.DOI:10.1016/j.ijimpeng.2012.06.012.
[12]王长峰,郑志军,虞吉林.泡沫杆撞击刚性壁的动态压溃模型[J].爆炸与冲击,2013,33(6):587-593.DOI:10.3969/j.issn.1001-1455.2013.06.005.WANG Changfeng,ZHENG Zhijun,YU Jilin.Dynamic crushing models for a foam rod striking a rigid wall[J].Explosion and Shock Waves,2013,33(6):587-593.DOI:10.3969/j.issn.1001-1455.2013.06.005.
[13]ZHENG Z J,WANG C F,YU J L,et al.Dynamic stress-strain states for metal foams using a 3D cellular model[J].Journal of the Mechanics and Physics of Solids,2014,72:93-114.DOI:10.1016/j.jmps.2014.07.013.
[14]BARNES A T,RAVI-CHANDA K,KYRIAKIDES S,et al.Dynamic crushing of aluminum foams:PartⅠ:Experiments[J].International Journal of Solids and Structures,2014,51(9):1631-1645.DOI:10.1016/j.ijsolstr.2013.11.019.
[15]SUN Y L,LI Q M,MCDONALD S A,et al.Determination of the constitutive relation and critical condition for the shock compression of cellular solids[J].Mechanics of Materials,2016,99:26-36.DOI:10.1016/j.mechmat.2016.04.004.
[16]WANG P,WANG X K,ZHENG Z J,et al.Stress distribution in graded cellular materials under dynamic compression[J].Latin American Journal of Solids and Structures,2017,14(7):1251-1272.DOI:10.1016/j.ijimpeng.2017.10.006.
[17]WANG L L.Foundations of stress waves[M].Amsterdam:Elsevier Science Ltd.,2007.DOI:10.1002/prep.200790014.