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

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

1.
东南大学　土木工程学院, 南京 210096
2.
中国海龙建筑科技有限公司, 深圳 518000
3.
金陵科技学院　建筑工程学院, 南京 211169

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
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- 文章访问数: 104
- HTML全文浏览量: 88
- 被引次数: 0
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

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

1.
School of Civil Engineering, Southeast University, Nanjing 210096, China
2.
China State Hailong Construction Technology Company Limited, Shenzhen 518000, China
3.
School of Architectural Engineering, Jinling Institute of Technology, Nanjing 211169, China

摘要

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。
- 超高延性水泥基复合材料 /
- 单根纤维拔出 /
- 拉伸应变硬化 /
- 多缝开裂 /
- 数值模拟 /
- 梁理论
Abstract: Based on the equivalent elastic foundation beam model describing the single fiber pullout behavior in engineered cementitious composites (ECC), an improved model was established by plane strain finite element analysis of the fiber-matrix system section, proposing an explicit calculation method for the spring restrained stiffness of the equivalent continuous beams. The model was applied to the numerical simulation analysis of uniaxial tensile strain hardening and multi-joint cracking behavior of ECC. The stress-strain relationship curves of ECC were calculated based on the frictional pulley model and the equivalent elastic foundation beam model, respectively, and compared with the experimental results. The results show that for polyethylene fiber (PE)-ECC, the calculation results based on the equivalent foundation beam model are in better agreement with the experimental results. It indicates that the improved equivalent foundation beam model proposed in this paper can well describe the pull-out behavior of fibers whose flexural stiffness cannot be neglected, and is of reference value for the force mechanism and design theory of such ECC materials and structures.
- engineering cementitious composites /
- single fiber pullout /
- tensile strain hardening /
- multiple cracking /
- numerical simulation /
- beam theory

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图 1 单根纤维拉拔模型

Figure 1. Diagram of single fiber pullout process

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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

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图 3 等效连续梁的离散化求解

Figure 3. Discretized solution of the equivalent continuous beam

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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

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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

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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

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图 7 K_m/E_m与h/r的关系曲线

Figure 7. Relation curve between K_m/E_m and h/r

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图 8 (K_m/E_m)_B曲线拟合结果对比

Figure 8. Comparison of (K_m/E_m)_B curve fitting result

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图 9 ECC单缝纤维桥接应力-裂缝开口宽度(σ_b-u)曲线

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

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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

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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

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图 12 ECC纤维体积掺量V_f和基体开裂强度σ_cr的威布尔分布直方图

Figure 12. Weibull distribution histogram of fiber volume content V_f and matrix cracking strength σ_crof ECC

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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

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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

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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 E_f/GPa	Matrix elastic modulus E_m/GPa	Frictional stress τ/MPa	Fiber Poisson's ratio ν_f	Matrix Poisson's ratio ν_m	Fiber embedded length L_e/mm
10	9.75	19.5	1.0	0.25	0.25	1.5
20	39		1.5			3
30	108		2.0			6

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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 type	Initial cracking stress/MPa	Initial cracking strain/%	Ultimate tensile strength/MPa	Ultimate tensile strain/%	Number of cracks
PVA/ECC	Frictional pulley model	3.10	0.08	4.64	3.59	36
PVA/ECC	Equivalent foundation beam model	3.05	0.09	5.61	7.44	46
PE/ECC	Frictional pulley model	5.25	0.03	8.96	2.91	45
PE/ECC	Equivalent foundation beam model	5.30	0.03	9.62	5.49	46

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