梯度密度黏弹性材料的波传播研究

李毅 苗春贺 徐松林 张金咏 王鹏飞

李毅, 苗春贺, 徐松林, 张金咏, 王鹏飞. 梯度密度黏弹性材料的波传播研究[J]. 爆炸与冲击, 2021, 41(1): 013202. doi: 10.11883/bzycj-2020-0313
引用本文: 李毅, 苗春贺, 徐松林, 张金咏, 王鹏飞. 梯度密度黏弹性材料的波传播研究[J]. 爆炸与冲击, 2021, 41(1): 013202. doi: 10.11883/bzycj-2020-0313
LI Yi, MIAO Chunhe, XU Songlin, ZHANG Jinyong, WANG Pengfei. Wave propagation in density-graded viscoelastic material[J]. Explosion And Shock Waves, 2021, 41(1): 013202. doi: 10.11883/bzycj-2020-0313
Citation: LI Yi, MIAO Chunhe, XU Songlin, ZHANG Jinyong, WANG Pengfei. Wave propagation in density-graded viscoelastic material[J]. Explosion And Shock Waves, 2021, 41(1): 013202. doi: 10.11883/bzycj-2020-0313

梯度密度黏弹性材料的波传播研究

doi: 10.11883/bzycj-2020-0313
基金项目: 高压物理与地震科技联合实验室室开放基金(2019HPPES01);国家自然科学基金(11672286,11602267,11872361);安徽省自然科学基金(1708085MA05)
详细信息
    作者简介:

    李 毅(1996- ),男,硕士,ustcliyi@mail.ustc.edu.cn

    通讯作者:

    徐松林(1971- ),男,博士,研究员,博士生导师,slxu99@ustc.edu.cn

  • 中图分类号: O347.4

Wave propagation in density-graded viscoelastic material

  • 摘要: 梯度密度黏弹性材料中波的传播比较复杂。为了研究其在冲击载荷作用下黏弹性响应特征,基于控制方程的Euler形式,利用Laplace变换,得到了这种材料中的波传播规律的一个理论公式;并据此分析了双层周期性黏弹性介质中的应力情况。选择具有梯度密度特性的钛-硼化钛(Ti-TiB2)材料和碳纤维树脂材料,采用不同的叠合方向和方式,利用分离式霍普金森压杆(split Hopkinson pressure bar,SHPB)加载装置进行了动态冲击实验,并用三波法对得到的实验结果进行处理。同时,采用数值Laplace逆变换方法,结合SHPB测得的入射波与透射波数据,使用推导的理论公式计算出理论解,并与实验结果进行了比较。结果表明:(1)梯度钛-硼化钛材料由于内界面和叠层界面的存在,表现出一定的黏性特性;单层Ti-TiB2材料的计算结果和三波法分析得到的结果基本一致,双层Ti-TiB2材料叠合后的计算结果与三波法分析结果存在一定的差异。(2)双层碳纤维树脂材料表现出较强的黏弹性特征,应力波的衰减幅度较大,三波法分析结果与该材料的冲击性能有较大的差异。由此可知,无论是细微观结构特征产生的黏性,还是材料本身的黏性,对材料动力学行为的影响都不可忽略。。
  • 图  1  垂直入射双层周期性叠合介质示意图

    Figure  1.  Schematic diagram of a two-layer periodically-superimposed medium with normal incidence

    图  2  梯度钛-硼化钛样品中密度和硬度[16]分布

    Figure  2.  Distributions of density and hardness[16] in gradient Ti-TiB2 specimen

    图  3  梯度钛-硼化钛实验波形

    Figure  3.  Recorded wave profiles in the gradient Ti-TiB2 specimens

    图  4  单层试件中的应力波形

    Figure  4.  Stress-time curves in single-layer specimens

    图  5  双层叠合试件中的应力波形

    Figure  5.  Stress-time curves in two-layer superimposed specimens

    图  6  制备的碳纤维增强树脂复合材料的密度随碳纤维质量分数的变化

    Figure  6.  Density change of prepared carbon-fiber reinforced resin composites with carbon fiber mass fraction

    图  7  双层碳纤维增强树脂叠合试件中的应力波形

    Figure  7.  Stress-time curves in two-layer superimposed specimens of carbon fiber reinforced resin

    图  8  等效梯度密度材料和双层叠合试件中的应力波形的对比

    Figure  8.  Comparison of stress-time curves in the equivalent gradient-density materials with those in two-layer superimposed specimens

  • [1] 徐松林, 刘永贵, 席道瑛, 等. 弹性波在含双裂纹岩体中的传播分析 [J]. 地球物理学报, 2012, 55(3): 944–952. DOI: 10.6038/j.issn.0001-5733.2012.03.024.

    XU S L, LIU Y G, XI D Y, et al. Analysis of propagation of elastic wave in rocks with double-crack model [J]. Chinese Journal of Geophysics, 2012, 55(3): 944–952. DOI: 10.6038/j.issn.0001-5733.2012.03.024.
    [2] 谭子翰, 徐松林, 刘永贵, 等. 含多种尺寸缺陷岩体中的弹性波散射 [J]. 应用数学和力学, 2013, 34(1): 38–48. DOI: 10.3879/j.issn.1000-0887.2013.01.005.

    TAN Z H, XU S L, LIU Y G, et al. Scattering of elastic waves by multi-size defects in rock mass [J]. Applied Mathematics and Mechanics, 2013, 34(1): 38–48. DOI: 10.3879/j.issn.1000-0887.2013.01.005.
    [3] 胡时胜, 王礼立, 宋力, 等. Hopkinson压杆技术在中国的发展回顾 [J]. 爆炸与冲击, 2014, 34(6): 641–657. DOI: 10.11883/1001-1455(2014)06-0641-17.

    HU S S, WANG L L, SONG L, et al. Review of the development of Hopkinson pressure bar technique in China [J]. Explosion and Shock Waves, 2014, 34(6): 641–657. DOI: 10.11883/1001-1455(2014)06-0641-17.
    [4] ZHAO H, GARY G, KLEPACZKO J R. On the use of a viscoelastic split Hopkinson pressure bar [J]. International Journal of Impact Engineering, 1997, 19(4): 319–330. DOI: 10.1016/S0734-743X(96)00038-3.
    [5] BACON C. An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar [J]. Experimental Mechanics, 1998, 38(4): 242–249. DOI: 10.1007/BF02410385.
    [6] 王宝珍, 胡时胜. 猪肝动态力学性能及本构模型研究 [J]. 力学学报, 2017, 49(6): 1399–1408. DOI: 10.6052/0459-1879-17-238.

    WANG B Z, HU S S. Research on dynamic mechanical response and constitutive model of porcine liver [J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(6): 1399–1408. DOI: 10.6052/0459-1879-17-238.
    [7] 朱珏, 胡时胜, 王礼立. SHPB试验中粘弹性材料的应力均匀性分析 [J]. 爆炸与冲击, 2006, 26(4): 315–322. DOI: 10.11883/1001-1455(2006)04-0315-08.

    ZHU J, HU S S, WANG L L. Analysis on stress uniformity of viscoelastic materials in split Hopkinson bar tests [J]. Explosion and Shock Waves, 2006, 26(4): 315–322. DOI: 10.11883/1001-1455(2006)04-0315-08.
    [8] 王礼立. 应力波基础[M]. 2版. 北京: 国防工业出版社, 2005: 148−177.

    WANG L L. Foundation of stress waves [M]. 2nd ed. Beijing: National Defense Industry Press, 2005: 148−177.
    [9] TING T C T, MUKUNOKI I. A theory of viscoelastic analogy for wave propagation normal to the layering of a layered medium [J]. Journal of Applied Mechanics, 1979, 46(2): 329–336. DOI: 10.1115/1.3424550.
    [10] TEDESCO J W, LANDIS D W. Wave propagation through layered systems [J]. Computers & Structures, 1989, 32(3/4): 625–638. DOI: 10.1016/0045-7949(89)90351-9.
    [11] HAN C, SUN C T. Attenuation of stress wave propagation in periodically layered elastic media [J]. Journal of Sound and Vibration, 2001, 243(4): 747–761. DOI: 10.1006/jsvi.2000.3420.
    [12] MUKERJI T. Waves and scales in heterogeneous rocks [D]. Stanford: Stanford University, 1995.
    [13] 周风华, 陈亮. SHPB实验中粘弹性试件内部应力波的传播 [J]. 固体力学学报, 2010, 31(2): 149–156. DOI: 10.19636/j.cnki.cjsm42-1250/o3.2010.02.006.

    ZHOU F H, CHEN L. Stress wave propagations in viscoelastic specimen during SHPB tests [J]. Chinese Journal of Solid Mechanics, 2010, 31(2): 149–156. DOI: 10.19636/j.cnki.cjsm42-1250/o3.2010.02.006.
    [14] 郑宇轩, 陈亮, 周风华, 等. Laplace变换法研究SHPB实验中试件的黏弹性波传播问题 [J]. 力学学报, 2014, 46(6): 843–852. DOI: 10.6052/0459-1879-14-002.

    ZHENG Y X, CHEN L, ZHOU F H, et al. Using Laplace transform to solve the viscoelastic wave problems in the SHPB experiments [J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(6): 843–852. DOI: 10.6052/0459-1879-14-002.
    [15] 张鸣, 王道荣, 单俊芳, 等. 石英纤维布叠层材料冲击性能研究 [J]. 实验力学, 2018, 33(2): 183–193. DOI: 10.7520/1001-4888-17-201.

    ZHANG M, WANG D R, SHAN J F, et al. Investigation on impact properties of quartz fiber cloth laminated material [J]. Journal of Experimental Mechanics, 2018, 33(2): 183–193. DOI: 10.7520/1001-4888-17-201.
    [16] 柯文轩. TiB2-TiB-Ti梯度材料的制备与力学性能研究[D]. 武汉: 武汉理工大学, 2013.

    KE W X. Fabrication and mechanical properties of TiB2-TiB-Ti functionally gradient materials [D]. Wuhan: Wuhan University of Technology, 2013.
    [17] 张鸣. 变密度粘弹性介质中弹性波传播的理论和实验研究[D]. 合肥: 中国科学技术大学, 2018.

    ZHANG M. Theoretical and experimental study on the propagation of stress wave in viscoelastic medium with variable density [D]. Hefei: University of Science and Technology of China, 2018.
    [18] 周光泉, 刘孝敏. 粘弹性理论[M]. 合肥: 中国科学技术大学出版社, 1996.

    ZHOU G Q, LIU X M. Viscoelastic theory [M]. Hefei: University of Science and Technology of China Press, 1996.
  • 加载中
图(8)
计量
  • 文章访问数:  694
  • HTML全文浏览量:  412
  • PDF下载量:  92
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-08-31
  • 修回日期:  2020-10-20
  • 刊出日期:  2021-01-05

目录

    /

    返回文章
    返回