水泥基材料中倾斜端钩型钢纤维拔出力学性能计算模型

王照耀; 毕继红; 赵云; 霍琳颖

doi:10.13801/j.cnki.fhclxb.20210207.003

水泥基材料中倾斜端钩型钢纤维拔出力学性能计算模型

doi: 10.13801/j.cnki.fhclxb.20210207.003

王照耀^1,,
毕继红^{1, 2, ,},
赵云^1,,
霍琳颖^1,

1.
天津大学　建筑工程学院，天津 300072
2.
天津大学　滨海土木工程结构与安全教育部重点实验室，天津 300350

基金项目: 国家自然科学基金(51227006)

详细信息

通讯作者:
毕继红，博士，教授，博士生导师，研究方向为钢纤维混凝土材料力学性能　E-mail：jihong_bi@163.com

中图分类号: TU528.572
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- 被引次数: 0
出版历程
- 收稿日期: 2020-12-10
- 录用日期: 2021-01-25
- 网络出版日期: 2021-02-07
- 刊出日期: 2021-12-01

Calculation model for pullout behavior of inclined hooked-end steel fiber in cement-based materials

WANG Zhaoyao^1
,,
BI Jihong^{1, 2
, ,},
ZHAO Yun^1
,,
HUO Linying^1
,

1.
School of Civil Engineering, Tianjin University, Tianjin 300072, China
2.
Key Laboratory of Coast Civil Structure Safety of Ministry of Education, Tianjin University, Tianjin 300350, China

摘要

摘要: 端钩型钢纤维是结构工程中应用最广泛的钢纤维品类之一，单根钢纤维拔出力学性能对于确定钢纤维混凝土的受拉本构及受拉韧性具有重要意义。为了得到能够有效预测倾斜端钩型钢纤维拔出荷载-端部位移曲线的理论模型，首先将倾斜端钩型钢纤维拔出过程分为完全黏结、脱黏和拔出滑移阶段三种受力状态，考虑不同拔出阶段及基体孔道损伤，建立了钢纤维黏结应力与纤维端部位移之间的关系，同时考虑钢纤维塑性变形、附加摩擦力及纤维拔出角度导致的基体剥落和挤压摩擦效应，建立了一种可以预测倾斜端钩型钢纤维拔出全过程的理论计算模型，在此基础上提出形式简单的简化模型，选取已有试验数据对提出的计算模型进行验证，结果表明：本文提出的两种模型均能够有效预测端钩型钢纤维拔出全过程，具有较高的计算精度且变异系数小，为进一步分析钢纤维对水泥基材料受拉性能的增强作用提供了理论依据。
- 端钩型钢纤维 /
- 拔出力学性能 /
- 倾斜纤维 /
- 附加摩擦力 /
- 基体剥落 /
- 挤压摩擦效应
Abstract: It is well-known that the hooked-end steel fiber is one of the most widely-used type of steel fiber in structural engineering, and the pullout behavior of a single steel fiber is significant for determining the tensile constitutive and the tensile toughness of steel fiber reinforced concrete. In order to obtain a theoretical analysis method which can effectively predict the pullout load-end displacement curves of inclined hooked-end steel fiber, the inclined pullout process of the hooked-end steel fiber was divided into three states: fully bonding stage, debonding stage and pullout slipping stage. A novel bond shear stresses-end displacement model was established considering the different steel fiber pullout stages and the damage of the matrix hole. A theoretical analysis model that can predict the load-slip curve of the pullout behavior of inclined hooked-end steel fiber was proposed by considering the plastic deformation of the steel fiber, the additional friction, spalling and snubbing effects of the matrix caused by the fiber pullout inclination. A simplified model was also proposed based on the theoretical model. The existing experimental data were selected to verify and evaluate the proposed calculation model. The results show that the two models proposed in this paper can effectively predict the process of hooked-end steel fiber inclined pullout. And the two models have high calculation accuracy and low coefficient of variation, which provide a theoretical reference for further analysis of the effect of steel fiber on the enhancement of tensile properties of cement-based materials.
- hooked-end steel fiber /
- pullout behavior /
- inclined fiber /
- additional friction /
- spalling of matrix /
- snubbing effect

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图 1 倾斜端钩型钢纤维拔出三个阶段

Figure 1. Three stages of pullout behavior of inclined hooked-end steel fiber

a—Debonding length of steel fiber; P—Pullout force

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图 2 端钩型钢纤维几何尺寸

Figure 2. Geometric dimensions of hooked-end steel fiber

α—Hook angle; l₁ and l₂—Segment length of the end-hook; L—Embedded length of steel fiber; d_f—Diameter of steel fiber

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图 3 钢纤维黏结应力-端部位移关系

Figure 3. Relationship between fiber bond stress and end displacement

δ₁, δ₂—Maximum end-displacement in the completely bonding stage and debonding stage, respectively; τ_max—Bond shear strength; τ_s—Bond shear stress corresponding to the end of the debongding stage; g_f—Interfacial shear fracture energy

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图 4 表示孔道损伤的系数κ_s与端部位移δ关系曲线

Figure 4. Relationship curves between the coefficient κ_s indicating the damage of the hole and the end displacement δ

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图 5 钢纤维微单元受力分析

Figure 5. Stress analysis of steel fiber segment

τ—Bond shear stress; d_x—Infinitesimal length; σ_f—Normal stress of steel fiber; dσ_f—Increment of the normal stress

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图 6 钢纤维锚固端截面受力分析

Figure 6. Stress analysis of steel fiber anchorage end

σ_m—Normal stress of the matrix; D_m—Diameter of the influenced section in matrix; x—Distance from the end of fiber

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图 7 钢纤维端钩部分受力分析及截面应力分布

Figure 7. Mechanical analysis and stress distribution of hooked-end of steel fiber

T₁, T₂ and T₁'—Tensile force for the end-hook; f₁ and f₂—Bond force of the end-hook; T_p—Tensile force required for plastic deformation; β—Angle of the normal force; N₁ and N₂—Normal force; r_f—Radius of steel fiber; A_p—Area of the plastic region; y—Distance between the neutral axis and the plastic zone centroid; γ—Angle between the plastic zone and the vertical axis

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图 8 钢纤维产生塑性变形时拉力-弯矩关系曲线

Figure 8. Tensile force-moment curves corresponding to the plastic deformation of steel fiber

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图 9 附加摩擦力与钢纤维端部位移关系

Figure 9. Relationship between additional friction and end displacement of steel fiber

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图 10 基体剥落示意图

Figure 10. Diagram of matrix spalling

θ—Pullout orientation angle; A_fta and A_ftb—Area of the cracking interface; l_ft—Spalling length; F_fn—Compressive force; F_fb—Spalling force

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图 11 基体剥落长度与加载角度、荷载之间关系

Figure 11. Relationship between the spalling length of matrix, inclination and load

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图 12 基体剥落长度试验值与预测值对比

Figure 12. Comparison between experimental and predicted values of spalling length of matrix

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图 13 计算流程图

Figure 13. Calculation flow chart

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图 14 钢纤维拔出最大黏结应力与基体抗压强度关系

Figure 14. Relationship between maximum bond stress during steel fiber pullout and compressive strength of matrix

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图 15 钢纤维拔出荷载-位移曲线简化模型

Figure 15. Simplified model of steel fiber pullout load-end displacement curve

A₁-A₆—Six key-points of the simplified model; L_e—Effective embedded length of steel fiber

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图 16 Soetens等^[12]试验荷载-端部位移曲线对比

Figure 16. Comparison of load-end displacement curves with test data of Soetens et al^[12]

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图 17 Breitenbücher等^[29]的试验荷载-端部位移曲线对比

Figure 17. Comparison of load-end displacement curves with test data of Breitenbücher et al^[29]

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表 1 用于预测端钩型钢纤维拔出力学性能的参数取值

Table 1. Parameters used to predict the pullout behavior of hooked-end steel fiber

Parameter	Value
Elastic modulus of matrix E_m/MPa	3.2×10⁴
Elastic modulus of fiber E_f/MPa	2×10⁵
Diameter of matrix D_m	10d_f
Fiber Poisson's ratio v_f	0.3
Matrix Poisson's ratio v_m	0.2
Curvature radius of hooked fiber ρ	2d_f
End hook angle α/(°)	50

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表 2 钢纤维拔出峰值荷载预测值与试验值对比

Table 2. Comparison between predicted and experimental values of steel fiber pullout peak load

Reference	Specimen	P_pre/N	P_ex/N	P_pre/P_ex
Soetens et al^[12]	HHH-80-30-00	725.91	736.63	0.98
	HHH-80-30-15	810.56	818.18	0.99
	HHH-80-30-30	838.71	885.96	1.07
	HHH-80-30-45	796.03	869.45	1.08
Breitenbücher et al^[29]	BP-80/60-00	637.51	633.88	1.01
	BP-80/60-15	684.43	670.84	1.02
	BP-80/60-30	739.01	744.76	0.99
	BP-80/60-45	753.37	768.79	0.97
	BP-80/60-60	675.96	615.40	1.10
μ				1.02
C_OV				0.05
Notes: P_pre and P_ex—Predicted and the experimental value of the peak load, respectively; μ—Ratio of P_pre and P_ex; C_OV—Coefficient of variation; “HHH” in notation system of the first series of tests represents the high strength matrix and hooked-end fiber with high carbon content. Figures in the second, third and fourth symbol represent fiber diameter (mm/100), embedded length (mm) and pullout inclination (°), respectively. For example, the notation of “HHH-80-30-30”—Pullout specimen with high strength matrix, 0.8 mm of fiber diameter, 30 mm of embedded length and 30° of pullout inclination. “BP” in notation system of the second series of tests represents a type of hooked-end fiber with tensile yield strength 2600 MPa. Figures in the second, third and fourth symbol represent fiber aspect ratio (-), fiber length (mm) and pullout inclination (°), respectively. For example, the notation of “BP-80/60-15”—Pullout specimen with 80 of fiber aspect ratio, 60 mm of fiber length and 15° of pullout inclination.

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