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基于梁理论的ECC拉伸应变硬化与多缝开裂行为的数值模拟

吴畅 王欣汝 许铭纹 姚杰 陈明糠 金辰华

吴畅, 王欣汝, 许铭纹, 等. 基于梁理论的ECC拉伸应变硬化与多缝开裂行为的数值模拟[J]. 复合材料学报, 2022, 40(0): 1-12
引用本文: 吴畅, 王欣汝, 许铭纹, 等. 基于梁理论的ECC拉伸应变硬化与多缝开裂行为的数值模拟[J]. 复合材料学报, 2022, 40(0): 1-12
Chang WU, Xinru WANG, Mingwen XU, Jie YAO, Minkang CHEN, Chenhua JIN. Numerical simulation of the tensile strain hardening and multiple cracking behavior of ECC based on beam theory[J]. Acta Materiae Compositae Sinica.
Citation: Chang WU, Xinru WANG, Mingwen XU, Jie YAO, Minkang CHEN, Chenhua JIN. Numerical simulation of the tensile strain hardening and multiple cracking behavior of ECC based on beam theory[J]. Acta Materiae Compositae Sinica.

基于梁理论的ECC拉伸应变硬化与多缝开裂行为的数值模拟

基金项目: 国家自然科学基金 (52108119);江苏省自然科学基金(BK20200376);江苏省高等学校基础科学(自然科学)研究项目(21KJB560005)
详细信息
    通讯作者:

    吴畅,博士,讲师,研究方向为高性能混凝土及预应力混凝土结构 E-mail: changwu@seu.edu.cn

  • 中图分类号: TB332

Numerical simulation of the tensile strain hardening and multiple cracking behavior of ECC based on beam theory

  • 摘要: 基于描述超高延性水泥基复合材料(Engineered cementitious composites, ECC)中单根纤维拔出行为的等效弹性地基梁模型,通过纤维-基体系统切面的平面应变有限元分析,提出了等效连续梁弹簧约束刚度的显式计算方法,建立了改进的等效弹性地基梁模型,并将模型应用于ECC单轴拉伸应变硬化与多缝开裂行为的数值模拟分析。分别基于摩擦滑轮模型和等效弹性地基梁模型计算ECC应力-应变关系曲线,并与试验结果进行对比。结果表明:对于聚乙烯(PE)/ECC,大部分情况下基于等效地基梁模型的计算结果与试验结果相比于聚乙烯醇(PVA)/ECC更加吻合。表明本文提出的改进的等效地基梁模型能够很好地描述抗弯刚度无法忽略的纤维的拔出行为,对于此类ECC材料和结构的受力机理和设计理论具有一定的参考价值。

     

  • 图  1  单根纤维拉拔模型

    Figure  1.  Diagram of single fiber pullout process

    图  2  纤维-基体等效地基梁模型的离散化

    Figure  2.  Discretization of fiber-matrix equivalent foundation beam model

    Δ—Length of a discrete segment

    图  3  等效连续梁的离散化求解

    Figure  3.  Discretized solution of the equivalent continuous beam

    图  4  拔出段纤维的约束端等效弹簧

    Figure  4.  Equivalent spring at the restrained end of the extracted fiber

    图  5  弹性地基平面应变模型

    Figure  5.  Plane strain model of elastic foundation

    X—Location from the fracture plane; h(x): distance from the fiber bottom to the fracture plane at x; γ—Inclination angle; H—Distance from the fiber center to the top edge; r—Radius of the fiber; B—Distance from the fiber center to the side edge

    图  6  纤维-基体系统的平面应变有限元模型

    Figure  6.  Plane strain finite element model of the fiber-matrix system

    图  7  Km/Emh/r的关系曲线

    Figure  7.  Relation curve between Km/Em and h/r

    图  8  (Km/Em)B曲线拟合结果对比

    Figure  8.  Comparison of (Km/Em)B curve fitting result

    图  9  ECC单缝纤维桥接应力-裂缝开口宽度(σb-u)曲线

    Figure  9.  Fiber bridging stress-crack opening width(σb-u) curve of a single crack of ECC

    图  10  ECC拉伸试件离散裂缝随机分布数值模型

    Figure  10.  Numerical model of discrete crack random distribution of ECC tensile specimens

    图  11  ECC单轴拉伸的应力-应变曲线编程流程图

    Figure  11.  Programming flow chart of stress-strain curve of ECC under uniaxial tension

    图  12  ECC纤维体积掺量Vf和基体开裂强度σcr的威布尔分布直方图

    Figure  12.  Weibull distribution histogram of fiber volume content Vf and matrix cracking strength σcr of ECC

    图  13  ECC单轴拉伸试验应力-应变模拟曲线

    Figure  13.  Stress-strain simulation curves of ECC specimens under uniaxial tensile tests

    图  14  ECC试验结果与数值模拟结果对比

    Figure  14.  Comparison between test results and numerical results of ECC

    表  1  摩擦滑轮模型和等效弹性地基梁模型主要参数的选取

    Table  1.   Selection of the main parameters in the frictional pulley model and equivalent foundation beam model

    Fiber radius
    r/μm
    Fiber elastic modulus
    Ef/GPa
    Matrix elastic modulus
    Em/GPa
    Frictional stress
    τ/MPa
    Fiber Poisson's ratio
    νf
    Matrix Poisson's ratio
    νm
    Fiber embedded length
    Le/mm
    109.7519.51.00.250.251.5
    20391.53
    301082.06
    下载: 导出CSV

    表  2  ECC单轴拉伸数值模拟平均结果

    Table  2.   average results of numerical simulation of ECC uniaxial tension

    Fiber
    type
    Model typeInitial cracking
    stress/MPa
    Initial cracking
    strain/%
    Ultimate tensile
    strength/MPa
    Ultimate tensile
    strain/%
    Number of
    cracks
    PVA/ECCFrictional pulley model3.100.084.643.5936
    Equivalent foundation
    beam model
    3.050.095.617.4446
    PE/ECCFrictional pulley model5.250.038.962.9145
    Equivalent foundation
    beam model
    5.300.039.625.4946
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-11-26
  • 录用日期:  2022-01-30
  • 修回日期:  2022-01-28
  • 网络出版日期:  2022-02-26

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