聚酰亚胺的动静态压缩力学性能及本构模型

于文峰 李金柱 姚志彦 黄风雷

于文峰, 李金柱, 姚志彦, 黄风雷. 聚酰亚胺的动静态压缩力学性能及本构模型[J]. 高压物理学报, 2022, 36(4): 044101. doi: 10.11858/gywlxb.20210922
引用本文: 于文峰, 李金柱, 姚志彦, 黄风雷. 聚酰亚胺的动静态压缩力学性能及本构模型[J]. 高压物理学报, 2022, 36(4): 044101. doi: 10.11858/gywlxb.20210922
YU Wenfeng, LI Jinzhu, YAO Zhiyan, HUANG Fenglei. Mechanical Behaviors and Constitutive Model of Polymide under Quasi-Static and Dynamic Compressive Loading[J]. Chinese Journal of High Pressure Physics, 2022, 36(4): 044101. doi: 10.11858/gywlxb.20210922
Citation: YU Wenfeng, LI Jinzhu, YAO Zhiyan, HUANG Fenglei. Mechanical Behaviors and Constitutive Model of Polymide under Quasi-Static and Dynamic Compressive Loading[J]. Chinese Journal of High Pressure Physics, 2022, 36(4): 044101. doi: 10.11858/gywlxb.20210922

聚酰亚胺的动静态压缩力学性能及本构模型

doi: 10.11858/gywlxb.20210922
基金项目: 国家自然科学基金(11472052)
详细信息
    作者简介:

    于文峰(1996—),男,硕士,主要从事材料与结构冲击动力学研究. E-mail:ywf996@outlook.com

    通讯作者:

    李金柱(1972—),男,博士,副教授,主要从事爆炸与冲击动力学研究. E-mail:lijinzhu@bit.edu.cn

  • 中图分类号: O347.3

Mechanical Behaviors and Constitutive Model of Polymide under Quasi-Static and Dynamic Compressive Loading

  • 摘要: 为研究聚酰亚胺在动静态压缩载荷作用下的力学特性,采用材料试验机(material testing system, MTS)和分离式霍普金森压杆(split Hopkinson pressure bar, SHPB)进行压缩实验,得到了材料在不同应变率下的应力-应变曲线。通过分析回收试样的形貌,得到了聚酰亚胺在裂纹形式、尺寸变形等方面的特性。聚酰亚胺屈服强度的动态增强因子与应变率的关系具有明显的双线性特性,可采用多元线性方程或Cowper-Symonds模型描述。针对聚酰亚胺的动态力学响应特性,阐述了从低应变率到高应变率范围内的压缩变形机理。采用考虑$\,\beta $转变的唯象本构模型,描述了聚酰亚胺在大应变率范围内的弹塑性大变形响应,包括初始黏弹性、屈服、应变软化和应变硬化在内的力学行为。通过贝叶斯方法拟合模型参数,拟合结果与实验结果在各应变率下都具有较好的一致性。

     

  • 图  聚酰亚胺试样

    Figure  1.  PI specimens

    图  SHPB实验装置示意图

    Figure  2.  Schematic diagram of SHPB experiment device

    图  试样的裂纹角度

    Figure  3.  Crack angles of samples

    图  准静态实验中不同样品的应力-应变曲线

    Figure  4.  Stress-strain curves of different samples in the quasi-static experiment

    图  $\varnothing $10.00 mm×4.00 mm试样动态压缩回收后的形貌

    Figure  5.  Morphology of the recovered samples with the initial size of $\varnothing $10.00 mm×4.00 mm

    图  $\varnothing $10.00 mm×4.00 mm试样的应变率随时间的变化曲线

    Figure  6.  Strain rate of the $\varnothing $10.00 mm×4.00 mm specimen versus time

    图  $\varnothing $10.00 mm×4.00 mm试样的应力-应变曲线

    Figure  7.  Stress-strain curves of the specimens with the size of $\varnothing $10.00 mm×4.00 mm

    图  “鼓状”示意图

    Figure  8.  Schematic diagram of “drum”

    图  $\varnothing$6.00 mm×2.00 mm试样的应力-应变曲线

    Figure  9.  Stress-strain curves of the specimens with the size of $\varnothing$6.00 mm×2.00 mm

    图  10  多模型拟合实验动态增强因子随应变率的变化

    Figure  10.  Two models’ fitting results of the dynamic increase factor versus strain rate

    图  11  贝叶斯方法预测本构模型材料参数流程图

    Figure  11.  Flow chart of predicting material parameters in the constitutive model by Bayesian approach

    图  12  准静态加载下模型拟合结果与实验数据的对比

    Figure  12.  Comparison between the model fitting results and the experimental data under quasi-static loading

    图  13  动态加载下模型拟合结果与实验数据的对比

    Figure  13.  Comparison between the model fitting results and the experimental data under dynamic loading

    表  1  准静态压缩实验后回收试样的形貌

    Table  1.   Morphology of the recovered samples after quasi-static experiment

    No.Strain rate/s−1Specimens after quasi-static compressionSize/(mm×mm×mm)Crack
    10.0016.02×5.83×2.78No
    20.0016.15×5.72×2.74No
    30.0016.18×5.80×2.75No
    40.0106.13×5.83×2.71No
    50.0106.25×5.78×2.72No
    60.0106.46×5.70×2.72Yes
    70.1006.64×5.86×2.58Yes
    80.1006.76×5.69×2.59Yes
    90.1006.54×5.89×2.59Yes
    下载: 导出CSV

    表  2  动态压缩后$\varnothing $6.00 mm×2.00 mm试样的形貌

    Table  2.   Morphology of the recovered $\varnothing $6.00 mm×2.00 mm samples after dynamic compression

    No.Load pressure/MPaStrain rate/s−1Size/(mm×mm)Specimens after dynamic compressionCrack
    10.053388$\varnothing $6.13×1.91No
    20.085195$\varnothing $6.75×1.61No
    30.106137$\varnothing $7.08×1.48No
    40.137627$\varnothing $7.72×1.29No
    50.178496$\varnothing $8.48×1.10No
    60.2010371$\varnothing $8.99×1.00No
    下载: 导出CSV

    表  3  两种模型的拟合方程与判定系数

    Table  3.   Two models’ fitting equations and their determination coefficients

    ModelEquationsR2
    Cowper-Symonds${ D_{ {\text{IF} } } } = {(1 + \dot \varepsilon /3\,396)^{1/3.22} }$0.99067
    Poly-linear fitting${ D_{ {\text{IF} } } } = \left\{ \begin{gathered} 1.065{ {\dot \varepsilon }^{0.009\,3} }\;\;{\text{ } }\dot \varepsilon \leqslant 0.100{\text{ } }{\text{s}^{ - 1} } \\ 0.275{ {\dot \varepsilon }^{0.185\,5} }\;\;{\text{ } }\dot \varepsilon \geqslant 3\,388{\text{ } }{\text{s}^{ - 1} } \\ \end{gathered} \right.$0.99206
    0.98288
    下载: 导出CSV

    表  4  αβ转变相关的材料参数

    Table  4.   Material parameters related to the α and β transformations

    $ {K_\alpha } $$ {\alpha _1} $$ {\alpha _2} $$ {\alpha _3} $$ {\alpha _4} $$ {\alpha _5} $$ {K_\beta } $${\,\beta _1}$${\,\beta _2}$${\,\beta _3}$${\,\beta _4}$${\,\beta _5}$
    51.0694.142−0.30615.4641.4640.0110.00420.0470.83781.889−1.5191.192
    下载: 导出CSV

    表  5  预测屈服强度与实验屈服强度之间的误差

    Table  5.   Error between the predicted yield stresses and the experimental results

    Strain rate/s−1$\text{ }{\sigma }_{\text{y, exp} }$/MPa$\text{ }{\sigma }_{\text{y, pred} }$/MPaError/%
    0.001128.55126.96−1.23
    0.010 130.89130.29−0.45
    0.100 134.16133.62−0.40
    3388155.84161.923.90
    5195172.32171.81−0.29
    6137177.28176.71−0.32
    7627185.43181.14−2.31
    8496190.08191.450.72
    10371197.88217.539.93
    下载: 导出CSV
  • [1] 李敏, 张佐光, 仲伟虹, 等. 聚酰亚胺树脂研究与应用进展 [J]. 复合材料学报, 2000, 17(4): 48–53. doi: 10.3321/j.issn:1000-3851.2000.04.010

    LI M, ZHANG Z G, ZHONG W H, et al. Study and application development of polyimides [J]. Acta Materiae Compositae Sinica, 2000, 17(4): 48–53. doi: 10.3321/j.issn:1000-3851.2000.04.010
    [2] 汪家铭. 聚酰亚胺薄膜技术进展与市场前景 [J]. 合成技术及应用, 2012, 27(3): 24–29. doi: 10.3969/j.issn.1006-334X.2012.03.011

    WANG J M. Technology advances and market prospects of polyimide film [J]. Synthetic Technology and Application, 2012, 27(3): 24–29. doi: 10.3969/j.issn.1006-334X.2012.03.011
    [3] 楚晖娟, 朱宝库, 徐又一. 聚酰亚胺泡沫材料在航空航天飞行器中应用进展 [J]. 宇航材料工艺, 2006, 36(3): 1–3. doi: 10.3969/j.issn.1007-2330.2006.03.001

    CHU H J, ZHU B K, XU Y Y. Application of polyimide foam materials in aerospace vehicles [J]. Aerospace Materials & Technology, 2006, 36(3): 1–3. doi: 10.3969/j.issn.1007-2330.2006.03.001
    [4] 徐立志, 高光发, 赵真, 等. 不同应变率下聚乙烯材料的压缩力学性能 [J]. 爆炸与冲击, 2019, 39(1): 013301.

    XU L Z, GAO G F, ZHAO Z, et al. Compressive mechanical properties of polyethylene at different strain rates [J]. Explosion and Shock Waves, 2019, 39(1): 013301.
    [5] WANG J, XU Y J, ZHANG W H. Finite element simulation of PMMA aircraft windshield against bird strike by using a rate and temperature dependent nonlinear viscoelastic constitutive model [J]. Composite Structures, 2014, 108: 21–30. doi: 10.1016/j.compstruct.2013.09.001
    [6] 张龙辉, 张晓晴, 姚小虎, 等. 高应变率下航空透明聚氨酯的动态本构模型 [J]. 爆炸与冲击, 2015, 35(1): 51–56. doi: 10.11883/1001-1455(2015)01-0051-06

    ZHANG L H, ZHANG X Q, YAO X H, et al. Constitutive model of transparent aviation polyurethane at high strain rates [J]. Explosion and Shock Waves, 2015, 35(1): 51–56. doi: 10.11883/1001-1455(2015)01-0051-06
    [7] ROLAND C M, TWIGG J N, VU Y, et al. High strain rate mechanical behavior of polyurea [J]. Polymer, 2007, 48(2): 574–578. doi: 10.1016/j.polymer.2006.11.051
    [8] 胡文军, 张方举, 田常津, 等. 聚碳酸酯的动态应力应变响应和屈服行为 [J]. 材料研究学报, 2007, 21(4): 439–443. doi: 10.3321/j.issn:1005-3093.2007.04.019

    HU W J, ZHANG F J, TIAN C J, et al. Dynamic stress-strain response and yield behavior of polycarbonate [J]. Chinese Journal of Materials Research, 2007, 21(4): 439–443. doi: 10.3321/j.issn:1005-3093.2007.04.019
    [9] CHOU S C, ROBERTSON K D, RAINEY J H. The effect of strain rate and heat developed during deformation on the stress-strain curve of plastics [J]. Experimental Mechanics, 1973, 13(10): 422–432. doi: 10.1007/BF02324886
    [10] WALLEY S M, FIELD J E. Strain rate sensitivity of polymers in compression from low to high rates [J]. DYMAT Journal, 1994, 1(3): 211–227.
    [11] GOGLIO L, PERONI L, PERONI M, et al. High strain-rate compression and tension behaviour of an epoxy bi-component adhesive [J]. International Journal of Adhesion and Adhesives, 2008, 28(7): 329–339. doi: 10.1016/j.ijadhadh.2007.08.004
    [12] 于鹏, 姚小虎, 张晓晴, 等. 聚碳酸酯类非晶聚合物力学性能及其本构关系 [J]. 力学进展, 2016, 46(1): 201603. doi: 10.6052/1000-0992-15-016

    YU P, YAO X H, ZHANG X Q, et al. Mechanical behaviors and constitutive models of polycarbonate amorphous polymers [J]. Advances in Mechanics, 2016, 46(1): 201603. doi: 10.6052/1000-0992-15-016
    [13] 陈春晓, 彭刚, 冯家臣, 等. 聚甲醛动态力学性能及本构行为研究 [J]. 塑料工业, 2018, 46(2): 137–139, 53. doi: 10.3969/j.issn.1005-5770.2018.02.031

    CHEN C X, PENG G, FENG J C, et al. The research of dynamic mechanical properties and constitutive behavior of POM [J]. China Plastics Industry, 2018, 46(2): 137–139, 53. doi: 10.3969/j.issn.1005-5770.2018.02.031
    [14] WANG H T, ZHANG Y, HUANG Z G, et al. Experimental and modeling study of the compressive behavior of PC/ABS at low, moderate and high strain rates [J]. Polymer Testing, 2016, 56: 115–123. doi: 10.1016/j.polymertesting.2016.09.027
    [15] WANG H T, ZHOU H M, HUANG Z G, et al. Constitutive modeling of polycarbonate over a wide range of strain rates and temperatures [J]. Mechanics of Time-Dependent Materials, 2017, 21(1): 97–117. doi: 10.1007/s11043-016-9320-1
    [16] 王海涛. 聚合物大变形及断裂行为的建模与模拟 [D]. 武汉: 华中科技大学, 2017.

    WANG H T. Modeling and simulation of the large deformation and fracture behavior of polymers [D]. Wuhan: Huazhong University of Science and Technology, 2017.
    [17] 宋力, 胡时胜. SHPB数据处理中的二波法与三波法 [J]. 爆炸与冲击, 2005, 25(4): 368–373. doi: 10.3321/j.issn:1001-1455.2005.04.014

    SONG L, HU S S. Two-wave and three-wave method in SHPB data processing [J]. Explosion and Shock Waves, 2005, 25(4): 368–373. doi: 10.3321/j.issn:1001-1455.2005.04.014
    [18] LU F Y, LIN Y L, WANG X Y, et al. A theoretical analysis about the influence of interfacial friction in SHPB tests [J]. International Journal of Impact Engineering, 2015, 79: 95–101. doi: 10.1016/j.ijimpeng.2014.10.008
    [19] BAUWENS-CROWET C, BAUWENS J C, HOMÈS G. The temperature dependence of yield of polycarbonate in uniaxial compression and tensile tests [J]. Journal of Materials Science, 1972, 7(2): 176–183. doi: 10.1007/BF02403504
    [20] JONES N. Structural impact [M]. Cambridge: Cambridge University Press, 1989.
    [21] PANCHENKO D. Introduction to probability and statistics [M]. Cambridge: Cambridge University Press, 1980.
    [22] BAR-SHALOM Y, LI X R, KIRUBARAJAN T. Estimation with applications to tracking and navigation [M]. New York: Wiley, 2001.
  • 加载中
图(13) / 表(5)
计量
  • 文章访问数:  171
  • HTML全文浏览量:  95
  • PDF下载量:  26
出版历程
  • 收稿日期:  2021-12-23
  • 修回日期:  2022-01-11
  • 录用日期:  2022-01-11
  • 网络出版日期:  2022-06-24
  • 刊出日期:  2022-07-28

目录

    /

    返回文章
    返回