具有恒定冲击载荷的梯度泡沫金属材料设计
|
摘要
多胞材料可通过大变形大量地吸收冲击能量,引入密度梯度可进一步提高其耐撞性。梯度多胞材料的宏观力学响应对材料密度分布极为敏感,不同类型的细观构型的影响也极为不同。已有的研究工作主要局限在对给定的密度梯度分析其动态响应,较少对耐撞性设计方法进行研究。本文针对梯度闭孔泡沫金属材料,基于非线性塑性冲击波模型发展了耐撞性反向设计方法,以维持冲击物受载恒定为目标,运用级数法获得了简化模型和渐近解。利用变胞元尺寸法构建了连续梯度变化的三维Voronoi细观有限元模型,并利用ABAQUS/Explicit有限元软件对理论设计进行数值验证。结果表明,反向设计理论简化模型的渐近解对于梯度闭孔泡沫金属材料的耐撞性设计是有效的,所提出的耐撞性设计方法在控制冲击吸能过程和冲击物受载方面具有指导意义。
Cellular materials can absorb a large amount of impact energy with large deformation, and their crashworthiness may be improved by introducing density gradients. The macroscopic mechanical responses of graded cellular materials are very sensitive to their relative density distributions and the effects of mesostructures can be very different. Some of existing studies is mainly limited to the analysis on the dynamic mechanical response of graded cellular material with a given density gradient, and less on the crashworthiness design method is considered. Based on the nonlinear plastic shock wave model, a backward crashworthiness design method is developed for graded foams. A simplified model and an asymptotic solution are derived by applying the series method with the aim of maintaining a constant load on the impact object. The cell-based finite element models based on three-dimensional Voronoi structures with density continuously changing are constructed by applying the variable cell size method. The theoretical design is verified by using finite element software ABAQUS/Explicit. The numerical simulation results show that the asymptotic solution of the simplified model is effective for the crashworthiness design of graded foams, and the proposed crashworthiness design method is of instructive significance in controlling the energy absorption and impact process.
Cellular materials can absorb a large amount of impact energy with large deformation, and their crashworthiness may be improved by introducing density gradients. The macroscopic mechanical responses of graded cellular materials are very sensitive to their relative density distributions and the effects of mesostructures can be very different. Some of existing studies is mainly limited to the analysis on the dynamic mechanical response of graded cellular material with a given density gradient, and less on the crashworthiness design method is considered. Based on the nonlinear plastic shock wave model, a backward crashworthiness design method is developed for graded foams. A simplified model and an asymptotic solution are derived by applying the series method with the aim of maintaining a constant load on the impact object. The cell-based finite element models based on three-dimensional Voronoi structures with density continuously changing are constructed by applying the variable cell size method. The theoretical design is verified by using finite element software ABAQUS/Explicit. The numerical simulation results show that the asymptotic solution of the simplified model is effective for the crashworthiness design of graded foams, and the proposed crashworthiness design method is of instructive significance in controlling the energy absorption and impact process.
引文
[1]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.
[2]华云龙,余同希.多胞材料的力学行为[J].力学进展,1990,21(4):457-469.DOI:10.6052/1000-0992-1991-4-J1991-052.HUA Yunlong,YU Tongxi.Mechanical behavior of cellular solids[J].Advances in Mechanics,1990,21(4):457-469.DOI:10.6052/1000-0992-1991-4-J1991-052.
[3]ELNASRI I,PATTOFATTO S,ZHAO H,et al.Shock enhancement of cellular structures under impact loading:partⅠexperiments[J].Journal of the Mechanics and Physics of Solids,2007,55(12):2652-2671.DOI:10.1016/j.jmps.2007.04.005.
[4]GIBSON L J,ASHBY M F.Cellular solids:structure and properties[M].Cambridge:Cambridge University Press,1999.
[5]CUI L,KIERNAN S,GILCHRIST M D.Designing the energy absorption capacity of functionally graded foam materials[J].Materials Science and Engineering:A,2009,507(1):215-225.DOI:10.1016/j.msea.2008.12.011.
[6]WANG X K,ZHENG Z J,YU J L,et al.Impact resistance and energy absorption of functionally graded cellular structures[J].Applied Mechanics and Materials,2011,69:73-78.DOI:10.4028/www.scientific.net/AMM.69.73.
[7]WANG X K,ZHENG Z J,YU J L.Crashworthiness design of density-graded cellular metals[J].Theoretical and Applied Mechanics Letters,2013,3(3):031001.DOI:10.1063/2.1303101.
[8]SHEN C J,YU T X,LU G X.Double shock mode in graded cellular rod under impact[J].International Journal of Solids and Structures,2013,50(1):217-233.DOI:10.1016/j.ijsolstr.2012.09.021.
[9]ZHENG J,QIN Q,WANG T J.Impact plastic crushing and design of density-graded cellular materials[J].Mechanics of Materials,2016,94:66-78.DOI:10.1016/j.mechmat.2015.11.014.
[10]SHEN C J,LU G X,YU T X.Investigation into the behavior of a graded cellular rod under impact[J].International Journal of Impact Engineering,2014,74:92-106.DOI:10.1016/j.ijimpeng.2014.02.015.
[11]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.
[12]蔡正宇,丁圆圆,王士龙,等.梯度多胞牺牲层的抗爆炸分析[J].爆炸与冲击,2017,37(3):396-404.DOI:10.11883/1001-1455(2017)03-0396-09.CAI Zhengyu,DING Yuanyuan,WANG Shilong,et al.Anti-blast analysis of graded cellular sacrificial cladding[J].Explosion and Shock Waves,2017,37(3):396-404.DOI:10.11883/1001-1455(2017)03-0396-09.
[13]YANG J,WANG S L,DING Y Y,et al.Crashworthiness of graded cellular materials:a design strategy based on a nonlinear plastic shock model[J].Materials Science and Engineering:A,2017,680:411-420.DOI:10.1016/j.msea.2016.11.010.
[14]DING Y Y,WANG S L,ZHAO K,et al.Blast alleviation of cellular sacrificial cladding:a nonlinear plastic shock model[J].International Journal of Applied Mechanics,2016,8(4):1650057.DOI:10.1142/S1758825116500575.
[15]LI K,GAO X L,WANG J.Dynamic crushing behavior of honeycomb structures with irregular cell shapes and non-uniform cell wall thickness[J].International Journal of Solids and Structures,2007,44(14-15):5003-5026.DOI:10.1016/j.ijsolstr.2006.12.017.
[16]AJDARI A,NAYEB-HASHEMI H,VAZIRI A.Dynamic crushing and energy absorption of regular,irregular and functionally graded cellular structures[J].International Journal of Solids and Structures,2011,48(3-4):506-516.DOI:10.1016/j.ijsolstr.2010.10.018.
[17]张新春,刘颖.密度梯度蜂窝材料动力学性能研究[J].工程力学,2012,29(8):372-377.DOI:10.6052/j.issn.1000-4750.2010.12.0872.ZHANG Xinchun,LIU Ying.Research on the dynamic crushing of honeycombs with density gradient[J].Engineering Mechanics,2012,29(8):372-377.DOI:10.6052/j.issn.1000-4750.2010.12.0872.
[18]吴鹤翔,刘颖.梯度变化对密度梯度蜂窝材料力学性能的影响[J].爆炸与冲击,2013,33(2):163-168.DOI:10.3969/j.issn.1001-1455.2013.02.008.WU Hexiang,LIU Ying.Influences of density gradient variation on mechanical performances of density-graded honeycomb materials[J].Explosion and Shock Waves,2013,33(2):163-168.DOI:10.3969/j.issn.1001-1455.2013.02.008.
[19]FAN J H,ZHANG J J,WANG Z H,et al.Dynamic crushing behavior of random and functionally graded metal hollow sphere foams[J].Materials Science and Engineering:A,2013,561:352-361.DOI:10.1016/j.msea.2012.10.026.
[20]ZHANG J J,WANG Z H,ZHAO L M.Dynamic response of functionally graded cellular materials based on the Voronoi model[J].Composites Part B:Engineering,2016,85:176-187.DOI:10.1016/j.compositesb.2015.09.045.
[21]CHEN D,KITIPORNCHAI S,YANG J.Dynamic response and energy absorption of functionally graded porous structures[J].Materials&Design,2018,140:473-487.DOI:10.1016/j.matdes.2017.12.019.
[22]常白雪,郑志军,赵凯,等.梯度多胞材料耐撞性设计的简化模型和渐近解[J].中国科学:物理学力学天文学,2018,48(9):094615.DOI:10.1360/SSPMA2018-00162.CHANG Baixue,ZHENG Zhijun,ZHAO Kai,et al.A simplified model and its asymptotic solution for the crashworthiness design of graded cellular material[J].Scientia Sinica:Physica,Mechanica&Astronomica,2018,48(9):094615.DOI:10.1360/SSPMA2018-00162.
[23]DING Y Y,WANG S L,ZHENG Z J,et al.Dynamic crushing of cellular materials:a unique dynamic stress-strain state curve[J].Mechanics of Materials,2016,100:219-31.DOI:10.1016/j.mechmat.2016.07.001.
[24]WANG P,ZHENG Z J,LIAO S F,et al.Strain-rate effect on initial crush stress of irregular honeycomb under dynamic loading and its deformation mechanism[J].Acta Mechanica Sinica,2018,34(1):117-129.DOI:10.1007/s10409-017-0716-1.
[25]HE S Y,ZHANG Y,DAI G,et al.Preparation of density-graded aluminum foam[J].Materials Science and Engineering A,2014,618:496-499.DOI:10.1016/j.msea.2014.08.087.
[2]华云龙,余同希.多胞材料的力学行为[J].力学进展,1990,21(4):457-469.DOI:10.6052/1000-0992-1991-4-J1991-052.HUA Yunlong,YU Tongxi.Mechanical behavior of cellular solids[J].Advances in Mechanics,1990,21(4):457-469.DOI:10.6052/1000-0992-1991-4-J1991-052.
[3]ELNASRI I,PATTOFATTO S,ZHAO H,et al.Shock enhancement of cellular structures under impact loading:partⅠexperiments[J].Journal of the Mechanics and Physics of Solids,2007,55(12):2652-2671.DOI:10.1016/j.jmps.2007.04.005.
[4]GIBSON L J,ASHBY M F.Cellular solids:structure and properties[M].Cambridge:Cambridge University Press,1999.
[5]CUI L,KIERNAN S,GILCHRIST M D.Designing the energy absorption capacity of functionally graded foam materials[J].Materials Science and Engineering:A,2009,507(1):215-225.DOI:10.1016/j.msea.2008.12.011.
[6]WANG X K,ZHENG Z J,YU J L,et al.Impact resistance and energy absorption of functionally graded cellular structures[J].Applied Mechanics and Materials,2011,69:73-78.DOI:10.4028/www.scientific.net/AMM.69.73.
[7]WANG X K,ZHENG Z J,YU J L.Crashworthiness design of density-graded cellular metals[J].Theoretical and Applied Mechanics Letters,2013,3(3):031001.DOI:10.1063/2.1303101.
[8]SHEN C J,YU T X,LU G X.Double shock mode in graded cellular rod under impact[J].International Journal of Solids and Structures,2013,50(1):217-233.DOI:10.1016/j.ijsolstr.2012.09.021.
[9]ZHENG J,QIN Q,WANG T J.Impact plastic crushing and design of density-graded cellular materials[J].Mechanics of Materials,2016,94:66-78.DOI:10.1016/j.mechmat.2015.11.014.
[10]SHEN C J,LU G X,YU T X.Investigation into the behavior of a graded cellular rod under impact[J].International Journal of Impact Engineering,2014,74:92-106.DOI:10.1016/j.ijimpeng.2014.02.015.
[11]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.
[12]蔡正宇,丁圆圆,王士龙,等.梯度多胞牺牲层的抗爆炸分析[J].爆炸与冲击,2017,37(3):396-404.DOI:10.11883/1001-1455(2017)03-0396-09.CAI Zhengyu,DING Yuanyuan,WANG Shilong,et al.Anti-blast analysis of graded cellular sacrificial cladding[J].Explosion and Shock Waves,2017,37(3):396-404.DOI:10.11883/1001-1455(2017)03-0396-09.
[13]YANG J,WANG S L,DING Y Y,et al.Crashworthiness of graded cellular materials:a design strategy based on a nonlinear plastic shock model[J].Materials Science and Engineering:A,2017,680:411-420.DOI:10.1016/j.msea.2016.11.010.
[14]DING Y Y,WANG S L,ZHAO K,et al.Blast alleviation of cellular sacrificial cladding:a nonlinear plastic shock model[J].International Journal of Applied Mechanics,2016,8(4):1650057.DOI:10.1142/S1758825116500575.
[15]LI K,GAO X L,WANG J.Dynamic crushing behavior of honeycomb structures with irregular cell shapes and non-uniform cell wall thickness[J].International Journal of Solids and Structures,2007,44(14-15):5003-5026.DOI:10.1016/j.ijsolstr.2006.12.017.
[16]AJDARI A,NAYEB-HASHEMI H,VAZIRI A.Dynamic crushing and energy absorption of regular,irregular and functionally graded cellular structures[J].International Journal of Solids and Structures,2011,48(3-4):506-516.DOI:10.1016/j.ijsolstr.2010.10.018.
[17]张新春,刘颖.密度梯度蜂窝材料动力学性能研究[J].工程力学,2012,29(8):372-377.DOI:10.6052/j.issn.1000-4750.2010.12.0872.ZHANG Xinchun,LIU Ying.Research on the dynamic crushing of honeycombs with density gradient[J].Engineering Mechanics,2012,29(8):372-377.DOI:10.6052/j.issn.1000-4750.2010.12.0872.
[18]吴鹤翔,刘颖.梯度变化对密度梯度蜂窝材料力学性能的影响[J].爆炸与冲击,2013,33(2):163-168.DOI:10.3969/j.issn.1001-1455.2013.02.008.WU Hexiang,LIU Ying.Influences of density gradient variation on mechanical performances of density-graded honeycomb materials[J].Explosion and Shock Waves,2013,33(2):163-168.DOI:10.3969/j.issn.1001-1455.2013.02.008.
[19]FAN J H,ZHANG J J,WANG Z H,et al.Dynamic crushing behavior of random and functionally graded metal hollow sphere foams[J].Materials Science and Engineering:A,2013,561:352-361.DOI:10.1016/j.msea.2012.10.026.
[20]ZHANG J J,WANG Z H,ZHAO L M.Dynamic response of functionally graded cellular materials based on the Voronoi model[J].Composites Part B:Engineering,2016,85:176-187.DOI:10.1016/j.compositesb.2015.09.045.
[21]CHEN D,KITIPORNCHAI S,YANG J.Dynamic response and energy absorption of functionally graded porous structures[J].Materials&Design,2018,140:473-487.DOI:10.1016/j.matdes.2017.12.019.
[22]常白雪,郑志军,赵凯,等.梯度多胞材料耐撞性设计的简化模型和渐近解[J].中国科学:物理学力学天文学,2018,48(9):094615.DOI:10.1360/SSPMA2018-00162.CHANG Baixue,ZHENG Zhijun,ZHAO Kai,et al.A simplified model and its asymptotic solution for the crashworthiness design of graded cellular material[J].Scientia Sinica:Physica,Mechanica&Astronomica,2018,48(9):094615.DOI:10.1360/SSPMA2018-00162.
[23]DING Y Y,WANG S L,ZHENG Z J,et al.Dynamic crushing of cellular materials:a unique dynamic stress-strain state curve[J].Mechanics of Materials,2016,100:219-31.DOI:10.1016/j.mechmat.2016.07.001.
[24]WANG P,ZHENG Z J,LIAO S F,et al.Strain-rate effect on initial crush stress of irregular honeycomb under dynamic loading and its deformation mechanism[J].Acta Mechanica Sinica,2018,34(1):117-129.DOI:10.1007/s10409-017-0716-1.
[25]HE S Y,ZHANG Y,DAI G,et al.Preparation of density-graded aluminum foam[J].Materials Science and Engineering A,2014,618:496-499.DOI:10.1016/j.msea.2014.08.087.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |