薄板在冲击载荷下线弹性理想塑性响应的相似性研究

李肖成 徐绯 杨磊峰 王帅 刘小川 惠旭龙 刘继军

李肖成, 徐绯, 杨磊峰, 王帅, 刘小川, 惠旭龙, 刘继军. 薄板在冲击载荷下线弹性理想塑性响应的相似性研究[J]. 爆炸与冲击, 2021, 41(11): 113103. doi: 10.11883/bzycj-2020-0374
引用本文: 李肖成, 徐绯, 杨磊峰, 王帅, 刘小川, 惠旭龙, 刘继军. 薄板在冲击载荷下线弹性理想塑性响应的相似性研究[J]. 爆炸与冲击, 2021, 41(11): 113103. doi: 10.11883/bzycj-2020-0374
LI Xiaocheng, XU Fei, YANG Leifeng, WANG Shuai, LIU Xiaochuan, XI Xulong, LIU Jijun. Study on the similarity of elasticity and ideal plasticity response of thin plate under impact loading[J]. Explosion And Shock Waves, 2021, 41(11): 113103. doi: 10.11883/bzycj-2020-0374
Citation: LI Xiaocheng, XU Fei, YANG Leifeng, WANG Shuai, LIU Xiaochuan, XI Xulong, LIU Jijun. Study on the similarity of elasticity and ideal plasticity response of thin plate under impact loading[J]. Explosion And Shock Waves, 2021, 41(11): 113103. doi: 10.11883/bzycj-2020-0374

薄板在冲击载荷下线弹性理想塑性响应的相似性研究

doi: 10.11883/bzycj-2020-0374
基金项目: 国家自然科学基金 (11972309);陕西省自然科学基础研究计划(2019JQ-625);高等学校学科创新引智计划 (111计划) (BP0719007);
详细信息
    作者简介:

    李肖成(1995- ),男,硕士研究生,lixiaocheng@mail.nwpu.edu.cn

    通讯作者:

    徐 绯(1970- ),女,博士,教授,xufei@nwpu.edu.cn

  • 中图分类号: O344; V214.4

Study on the similarity of elasticity and ideal plasticity response of thin plate under impact loading

  • 摘要: 对于比例模型和原型使用不同弹塑性材料的冲击相似性问题,由于弹性和塑性阶段材料特性的差别及其在不同变形阶段的弹性塑性共存现象,将导致原有的结构冲击相似性理论失效。基于薄板冲击问题的理论模型,采用方程分析方法重新推导了材料线弹性以及理想刚塑性共存时的冲击响应的相似律。提出了一种能够同时考虑弹性变形和塑性变形的结构缩放响应相似性分析的厚度补偿方法,并利用数值分析验证了提出方法的适用性。分析结果表明,使用厚度补偿方法得到的比例模型结构响应能够准确地预测原型结构的冲击响应。
  • 图  1  不同材料应力应变缩放结果

    Figure  1.  Stress-strain scaling results for different materials

    图  2  圆板冲击示意图

    Figure  2.  Schematic diagram of the circular plate under impact loading

    图  3  不同材料应力应变曲线

    Figure  3.  Stress-strain curves of different materials

    图  4  速度冲击比例模型与原型圆板中点处位移响应曲线对比

    Figure  4.  Comparison of displacement response between the velocity impact scale model and the prototype at the midpoint of the circular plate

    图  5  速度冲击比例模型与原型圆板中点处动能响应曲线对比

    Figure  5.  Comparison of kinetic energy response between the velocity impact scale model and the prototype at the midpoint of the circular plate

    图  6  速度冲击比例模型与原型圆板中点处应变响应曲线对比

    Figure  6.  Comparison of strain response between the velocity impact scale model and the prototype at the midpoint of the circular plate

    图  7  速度冲击比例模型与原型圆板中点处应力响应曲线对比

    Figure  7.  Comparison of stress response between the velocity impact scale model and the prototype at the midpoint of the circular plate

    图  8  质量冲击比例模型与原型圆板中点处位移响应曲线对比

    Figure  8.  Comparison of displacement response between the mass impact scale model and the prototype at the midpoint of the circular plate

    图  9  质量冲击比例模型与原型圆板中点处动能响应曲线对比

    Figure  9.  Comparison of kinetic energy response between the mass impact scale model and the prototype at the midpoint of the circular plate

    图  10  质量冲击比例模型与原型圆板中点处力响应曲线对比

    Figure  10.  Comparison of strain response between the mass impact scale model and the prototype at the midpoint of the circular plate

    图  11  质量冲击比例模型与原型圆板中点处应变响应曲线对比

    Figure  11.  Comparison of stress response between the mass impact scale model and the prototype at the midpoint of the circular plate

    图  12  不同冲击速度下圆板沿直径方向的位移

    Figure  12.  Displacement of circular plate along the diameter direction under different impact velocities

    图  13  不同冲击速度下圆板沿直径方向的Mises应力

    Figure  13.  Mises stress of circular plate along the diameter direction under different impact velocities

    图  14  不同冲击速度下圆板沿直径方向的等效应变

    Figure  14.  Equivalent strain of the circular plate along the diameter direction under different impact velocities

    表  1  刚塑性结构相似性缩放因子[6, 8]

    Table  1.   Scaling factors of rigid-plastic structure [6, 8]

    变量缩放因子变量缩放因子
    长度,$ L $$ \lambda ={L}_{\mathrm{m}}/{L}_{\mathrm{p}} $位移,$ \delta $$ {\lambda }_{\delta }=\lambda $
    密度,$ \rho $$ {\lambda }_{\rho }={\rho }_{\mathrm{m}}/{\rho }_{\mathrm{p}} $应力,$ \sigma $$ {\lambda }_{\sigma }={\lambda }_{\rho }{\lambda }_{v}^{2} $
    速度,$ v $$ {\lambda }_{v}={v}_{\mathrm{m}}/{v}_{\mathrm{p}} $应变,$ \varepsilon $$ {\lambda }_{\varepsilon }=1 $
    质量,$ m $$ {{\lambda }_{m}={\lambda }_{\rho }\lambda }^{3} $应变率,$ \dot{\varepsilon } $$ {\lambda }_{\dot{\varepsilon }}={\lambda }_{v}/\lambda $
    时间,$ t $$ {\lambda }_{t}=\lambda /{\lambda }_{v} $力,$ F $$ {{\lambda }_{F}={\lambda }_{\rho }\lambda }^{2}{\lambda }_{v}^{2} $
    加速度,$a$${\lambda }_{a}={\lambda }_{v}^{2}/\lambda$能量,${E}_{{\rm{n}}}$${ {\lambda }_{ {E}_{{\rm{n}}} }={\lambda }_{\rho }\lambda }^{3}{\lambda }_{v}^{2}$
     注:在表中,比例模型与原型相关的物理量分别用下标m和p表示,$ {\lambda }_{K}={K}_{\mathrm{m}}/{K}_{\mathrm{p}} $表示缩比模型和原型相关物理量的比值,例如${\lambda }_{v}={v}_{\mathrm{m} }/{v}_{\mathrm{p} }$表示比例模型和原型速度的比值,比例模型和原型的几何缩放系数$ \mathrm{\lambda }={L}_{\mathrm{m}}/{L}_{\mathrm{p}} $。
    下载: 导出CSV

    表  2  理想弹塑性薄板结构冲击载荷作用下缩放因子

    Table  2.   Scaling factors of theideal elastic-plastic thin-plates under impact loading

    变量缩放因子变量缩放因子
    x, y$ {\lambda }_{x}={\lambda }_{y}={\left({L}_{x}\right)}_{\mathrm{m}}/{\left({L}_{x}\right)}_{\mathrm{p}} $t$ {\lambda }_{t}={\lambda }_{\zeta }/{\lambda }_{{v}_{\textit{z}}} $
    z$ {\lambda }_{\textit{z}}={\lambda }_{x}{\left({\lambda }_{{\sigma }_{\mathrm{Y}}}/{\lambda }_{E}\right)}^{1/2} $χ, η$ {\lambda }_{\chi }={\lambda }_{\eta }={\lambda }_{x}{\lambda }_{{\sigma }_{\mathrm{Y}}}/{\lambda }_{E} $
    $ \rho $$ {\lambda }_{\rho }={\rho }_{\mathrm{m}}/{\rho }_{\mathrm{p}} $ζ$ {\lambda }_{\zeta }={\lambda }_{x}{\left({\lambda }_{{\sigma }_{\mathrm{Y}}}/{\lambda }_{E}\right)}^{1/2} $
    m$ {{\lambda }_{m}=\mathrm{\lambda }}_{\rho }{\lambda }_{x}{\lambda }_{y}{\lambda }_{\textit{z}} $$ {v}_{\textit{z}} $$ {\lambda }_{{v}_{\textit{z}}}={\lambda }_{{\sigma }_{\mathrm{Y}}}{\left({\lambda }_{\rho }{\lambda }_{E}\right)}^{-1/2} $
    E$ {\lambda }_{E}={E}_{\mathrm{m}}/{E}_{\mathrm{p}} $$ {F}_{\textit{z}} $$ {\lambda }_{{F}_{\textit{z}}}={\lambda }_{M}{\lambda }_{{A}_{\textit{z}}} $
    $ {\sigma }_{\mathrm{Y}} $${\lambda }_{ {\sigma }_{\mathrm{Y} } }={\left({\sigma }_{{\rm{Y}}}\right)}_{\mathrm{m} }/{\left({\sigma }_{\mathrm{Y} }\right)}_{\mathrm{p} }$$ {a}_{\textit{z}} $${\lambda }_{ {a}_{\textit{z} } }= {\lambda }_{ {v}_{\textit{z} } } ^{2}/{\lambda }_{\zeta }$
    $ {\sigma }_{x},{\sigma }_{y} $$ {\lambda }_{{\sigma }_{x}}={\lambda }_{{\sigma }_{y}}={\lambda }_{{\sigma }_{\mathrm{Y}}} $$ {\varepsilon }_{x}{,\varepsilon }_{y} $$ {\lambda }_{{\varepsilon }_{x}}{,\lambda }_{{\varepsilon }_{y}}={\lambda }_{{\sigma }_{\mathrm{Y}}}/{\lambda }_{E} $
    $ {\tau }_{xy} $$ {\lambda }_{{\tau }_{xy}}={\lambda }_{{\sigma }_{\mathrm{Y}}} $$ {\gamma }_{xy} $${\lambda }_{ {\gamma }_{xy} }={\lambda }_{ {\sigma }_{{\rm{Y}}} }/{\lambda }_{E}$
    下载: 导出CSV

    表  3  圆板材料属性

    Table  3.   Material properties of circular plate

    材料密度/(kg·m−3弹性模量/GPa屈服强度/MPa
    原型铝2.7072.4265
    Ti-6Al-4V4.431141104
    1006钢7.89200350
    黄铜8.52110112
    钨合金17.04001506
    下载: 导出CSV

    表  4  模型缩放系数

    Table  4.   Scaling factors of themodels

    $ {\lambda }_{x} $模型材料$ {\lambda }_{\rho } $$ {\lambda }_{E} $$ {\lambda }_{\sigma } $${\lambda }_{\varepsilon }$$ {\lambda }_{\textit{z}} $$ {\lambda }_{{v}_{\textit{z}}} $$ {\lambda }_{t} $
    1原型铝1111111
    1/50Ti-6Al-4V1.641.574.172.650.03252.590.0126
    1/501006钢2.922.761.320.480.01380.460.0298
    1/50黄铜3.161.520.420.280.01060.190.0547
    1/50钨合金6.305.525.681.030.02030.960.0211
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-10-09
  • 修回日期:  2020-04-22
  • 网络出版日期:  2021-09-30
  • 刊出日期:  2021-11-23

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