Skip to main content
SpringerLink
Log in

Strengthening mechanism of steel fiber in UHPC: A new fracture phase field model

UHPC 中钢纤维的增强机理:一种新的断裂相场模型

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

The engineering optimization of ultra-high strength concrete (UHPC) requires urgent exploration of the strengthening mechanism of steel fiber in UHPC and the establishment of an effective simulation model. In this study, we propose a new fracture phase field model that considers the fracture energy of the interface between steel fiber and UHPC matrix. The model is utilized to conduct uniaxial tensile numerical simulations of 3D UHPC incorporating steel fibers, and a comparative experiment is conducted to validate the proposed model. The results display a notable agreement between the simulation and experiment. It is found that the tensile strength and residual strength of UHPC increase with steel fiber volume content and decrease with steel fiber diameter. The inclusion of steel fibers in UHPC results in more intricate crack patterns during the fracture process. The above results can be attributed to the debonding occurring at the interface between the steel fiber and the UHPC matrix which dissipates additional energy and thus enhances the UHPC. This work establishes a theoretical foundation for UHPC performance design and the development of effective simulation methods.

摘要

超高性能混凝土(UHPC)是一种具有巨大潜力的复合材料。为了降低UHPC 的成本并获得更好的 性能, 有必要研究钢纤维在UHPC 中的增强机理, 实践中也需要一个有效的数值模型来促进UHPC 的 应用。钢纤维从UHPC 中拔出时会产生新的裂纹面, 进而需要消耗更多的能量。基于此, 推导了新裂 纹及其裂纹表面能的公式, 提出了一种考虑钢纤维与UHPC 基体之间界面断裂能的断裂相场模型。利 用该模型, 对含钢纤维的三维UHPC 试样进行了单轴拉伸数值模拟; 开展对比实验验证了所提模型的 正确性。结果表明, 模拟结果与实验结果吻合较好。通过分析不同试样的新裂纹面与拉伸强度间的关 系, 发现UHPC 的抗拉强度和残余强度随钢纤维体积含量的增加而增加, 随钢纤维直径的增加而降低。 进一步分析发现, UHPC 的抗拉强度与钢纤维的侧表面积成正比。理论分析、数值模拟和实验表明, 钢纤维在UHPC 中的增强机理为: 钢纤维的加入使UHPC 基体与钢纤维在断裂过程中产生了一些新的 裂纹, 这些新裂纹消耗了更多的能量。本文研究工作可为UHPC 的性能设计和开发有效的UHPC 数值 模型提供理论依据。

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. GONG Ji-hao, MA Yu-wei, FU Ji-yang, et al. Utilization of fibers in ultra-high performance concrete: A review [J]. Composites Part B: Engineering, 2022, 241: 109995. DOI: https://doi.org/10.1016/j.compositesb.2022.109995.

    Article  CAS  Google Scholar 

  2. GRAYBEAL B, BRÜHWILER E, KIM B S, et al. International perspective on UHPC in bridge engineering [J]. Journal of Bridge Engineering, 2020, 25(11): 04020094. DOI: https://doi.org/10.1061/(asce)be.1943-5592.0001630.

    Article  Google Scholar 

  3. SIVA C R, PANKAJ A. Flexural behavior of reinforced concrete beams with high performance fiber reinforced cementitious composites [J]. Journal of Central South University, 2019, 26(9): 2609–2622. DOI: https://doi.org/10.1007/s11771-019-4198-0.

    Article  CAS  Google Scholar 

  4. WEN Cheng-cheng, ZHANG Peng, WANG Juan, et al. Influence of fibers on the mechanical properties and durability of ultra-high-performance concrete: A review [J]. Journal of Building Engineering, 2022, 52: 104370. DOI: https://doi.org/10.1016/j.jobe.2022.104370.

    Article  Google Scholar 

  5. CHEN Xuan, WAN Dong-wei, JIN Ling-zhi, et al. Experimental studies and microstructure analysis for ultra high-performance reactive powder concrete [J]. Construction and Building Materials, 2019, 229: 116924. DOI: https://doi.org/10.1016/j.conbuildmat.2019.116924.

    Article  CAS  Google Scholar 

  6. HASSAN A M T, JONES S W, MAHMUD G H. Experimental test methods to determine the uniaxial tensile and compressive behaviour of ultra high performance fibre reinforced concrete (UHPFRC) [J]. Construction and Building Materials, 2012, 37: 874–882. DOI: https://doi.org/10.1016/j.conbuildmat.2012.04.030.

    Article  Google Scholar 

  7. ZHAO Qiu, HUANG Jin-ju, YANG Jian-ping, et al. Experimental study on the tensile behavior of ultra-high performance concrete fiber continuous joints [J]. Structural Concrete, 2022, 23(1): 207–219. DOI: https://doi.org/10.1002/suco.202100415.

    Article  Google Scholar 

  8. YANG Jian, CHEN Bao-chun, NUTI C. Influence of steel fiber on compressive properties of ultra-high performance fiber-reinforced concrete [J]. Construction and Building Materials, 2021, 302: 124104. DOI: https://doi.org/10.1016/j.conbuildmat.2021.124104.

    Article  Google Scholar 

  9. GUO Xiao-lu, LI Hua-bing, WANG Si-jia. Effects of precorroded steel fibers on mechanical properties and interface bond behavior of ultra-high performance concrete-normal concrete [J]. Construction and Building Materials, 2022, 356: 129234. DOI: https://doi.org/10.1016/j.conbuildmat.2022.129234.

    Article  CAS  Google Scholar 

  10. FENG Jun, GAO Xu-dong, LI Ji-zheng, et al. Influence of fiber mixture on impact response of ultra-high-performance hybrid fiber reinforced cementitious composite [J]. Composites Part B: Engineering, 2019, 163: 487–496. DOI: https://doi.org/10.1016/j.compositesb.2018.12.141.

    Article  CAS  Google Scholar 

  11. LE HOANG A, FEHLING E. Influence of steel fiber content and aspect ratio on the uniaxial tensile and compressive behavior of ultra high performance concrete [J]. Construction and Building Materials, 2017, 153: 790–806. DOI: https://doi.org/10.1016/j.conbuildmat.2017.07.130.

    Article  Google Scholar 

  12. ROMUALDI J P, BATSON G B. Mechanics of crack arrest in concrete [J]. Journal of the Engineering Mechanics Division, 1963, 89(3): 147–168. DOI: https://doi.org/10.1061/jmcea3.0000381.

    Article  Google Scholar 

  13. YANG Jian, CHEN Bao-chun, SU Jia-zhan, et al. Effects of fibers on the mechanical properties of UHPC: A review [J]. Journal of Traffic and Transportation Engineering (English Edition), 2022, 9(3): 363–387. DOI: https://doi.org/10.1016/j.jtte.2022.05.001.

    Article  Google Scholar 

  14. TENG Le, HUANG Huang-huang, KHAYAT K H, et al. Simplified analytical model to assess key factors influenced by fiber alignment and their effect on tensile performance of UHPC [J]. Cement and Concrete Composites, 2022, 127: 104395. DOI: https://doi.org/10.1016/j.cemconcomp.2021.104395.

    Article  CAS  Google Scholar 

  15. AYDIN L, ARTEM H S, ÖTERKUŞ E, et al. Fiber reinforced composites [C]// Dobrzański L A. Composite materials engineering. Cambridge: Woodhead Publishing, 2017: 5–50.

    Google Scholar 

  16. WANG Shun-feng, YU Long, YANG Fei, et al. Effect of steel fiber distribution on the mechanical properties of UHPC caused by vehicle-bridge coupling vibration [J]. Composites Part B: Engineering, 2022, 245: 110201. DOI: https://doi.org/10.1016/j.compositesb.2022.110201.

    Article  CAS  Google Scholar 

  17. TALREJA R, WAAS A M. Concepts and definitions related to mechanical behavior of fiber reinforced composite materials [J]. Composites Science and Technology, 2022, 217: 109081. DOI: https://doi.org/10.1016/j.compscitech.2021.109081.

    Article  CAS  Google Scholar 

  18. TSAI J H, PATRA A, WETHERHOLD R. Finite element simulation of shaped ductile fiber pullout using a mixed cohesive zone/friction interface model [J]. Composites Part A: Applied Science and Manufacturing, 2005, 36(6): 827–838. DOI: https://doi.org/10.1016/j.compositesa.2004.10.025.

    Article  Google Scholar 

  19. YU R C, CIFUENTES H, RIVERO I, et al. Dynamic fracture behaviour in fibre-reinforced cementitious composites [J]. Journal of the Mechanics and Physics of Solids, 2016, 93: 135–152. DOI: https://doi.org/10.1016/j.jmps.2015.12.025.

    Article  CAS  ADS  Google Scholar 

  20. WU Guo-zheng, WANG Hui-ming. Numerical simulation of steel fiber pull-out process based on cohesive zone model and unified phase-field theory [J]. Sustainability, 2023, 15(5): 4015. DOI: https://doi.org/10.3390/su15054015.

    Article  CAS  Google Scholar 

  21. LIU Qiang, GORBATIKH L, LOMOV S V. A combined use of embedded and cohesive elements to model damage development in fibrous composites [J]. Composite Structures, 2019, 223: 110921. DOI: https://doi.org/10.1016/j.compstruct.2019.110921.

    Article  Google Scholar 

  22. BITENCOURT L A G, MANZOLI O L, BITTENCOURT T N, et al. Numerical modeling of steel fiber reinforced concrete with a discrete and explicit representation of steel fibers [J]. International Journal of Solids and Structures, 2019, 159: 171–190. DOI: https://doi.org/10.1016/j.ijsolstr.2018.09.028.

    Article  Google Scholar 

  23. ZHANG Jin-hua, LIU Xin-guo, WU Zhang-yu, et al. Fracture properties of steel fiber reinforced concrete: Size effect study via mesoscale modelling approach [J]. Engineering Fracture Mechanics, 2022, 260: 108193. DOI: https://doi.org/10.1016/j.engfracmech.2021.108193.

    Article  Google Scholar 

  24. MAHMUD G H, YANG Zhen-jun, HASSAN A M T. Experimental and numerical studies of size effects of Ultra High Performance Steel Fibre Reinforced Concrete (UHPFRC) beams [J]. Construction and Building Materials, 2013, 48: 1027–1034. DOI: https://doi.org/10.1016/j.conbuildmat.2013.07.061.

    Article  Google Scholar 

  25. SHAFIEIFAR M, FARZAD M, AZIZINAMINI A. Experimental and numerical study on mechanical properties of Ultra High Performance Concrete (UHPC) [J]. Construction and Building Materials, 2017, 156: 402–411. DOI: https://doi.org/10.1016/j.conbuildmat.2017.08.170.

    Article  Google Scholar 

  26. ZHAO Bing, XU Ya-xing, PENG Hui, et al. Experiment and phase-field simulation of uniaxial compression of ultra-high-performance concrete with coarse aggregate [J]. Advances in Structural Engineering, 2022, 25(10): 2121–2136. DOI: https://doi.org/10.1177/13694332221088947.

    Article  Google Scholar 

  27. BILGEN C, HOMBERGER S, WEINBERG K. Phase-field fracture simulations of the Brazilian splitting test [J]. International Journal of Fracture, 2019, 220(1): 85–98. DOI: https://doi.org/10.1007/s10704-019-00401-w.

    Article  Google Scholar 

  28. DONNINI J, LANCIONI G, CHIAPPINI G, et al. Uniaxial tensile behavior of ultra-high performance fiber-reinforced concrete (UHPFRC): Experiments and modeling [J]. Composite Structures, 2021, 258: 113433. DOI: https://doi.org/10.1016/j.compstruct.2020.113433.

    Article  CAS  Google Scholar 

  29. WU Jian-ying. A unified phase-field theory for the mechanics of damage and quasi-brittle failure [J]. Journal of the Mechanics and Physics of Solids, 2017, 103: 72–99. DOI: https://doi.org/10.1016/j.jmps.2017.03.015.

    Article  MathSciNet  ADS  Google Scholar 

  30. PAN Jun, WANG Hong, ZHAO Bing, et al. Phase field fracture simulation of concrete: factors affecting crack width [J]. Journal of Transport Science And Engineering, 2022, 38: 8–14. DOI: https://doi.org/10.3969/j.issn.1674-599X.2022.01.002. (in Chinese)

    Google Scholar 

  31. SU Yu-tai, ZHU Jia-qi, LONG Xu, et al. Statistical effects of pore features on mechanical properties and fracture behaviors of heterogeneous random porous materials by phase-field modeling [J]. International Journal of Solids and Structures, 2023, 264: 112098. DOI: https://doi.org/10.1016/j.ijsolstr.2022.112098.

    Article  Google Scholar 

  32. HIRSHIKESH, NATARAJAN S, ANNABATTULA R K. A FEniCS implementation of the phase field method for quasi-static brittle fracture [J]. Frontiers of Structural and Civil Engineering, 2019, 13(2): 380–396. DOI: https://doi.org/10.1007/s11709-018-0471-9.

    Article  Google Scholar 

  33. MIEHE C, WELSCHINGER F, HOFACKER M. Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations [J]. International Journal for Numerical Methods in Engineering, 2010, 83(10): 1273–1311. DOI: https://doi.org/10.1002/nme.2861.

    Article  MathSciNet  ADS  Google Scholar 

  34. WEINBERG K, DALLY T, SCHU S, et al. Modeling and numerical simulation of crack growth and damage with a phase field approach [J]. GAMM-Mitteilungen, 2016, 39(1): 55–77. DOI: https://doi.org/10.1002/gamm.201610004.

    Article  MathSciNet  Google Scholar 

  35. ABU-LEBDEH T, HAMOUSH S, HEARD W, et al. Effect of matrix strength on pullout behavior of steel fiber reinforced very-high strength concrete composites [J]. Construction and Building Materials, 2011, 25(1): 39–46. DOI: https://doi.org/10.1016/j.conbuildmat.2010.06.059.

    Article  Google Scholar 

  36. WANG De-hui, SHI Cai-jun, WU Ze-mei, et al. A review on ultra high performance concrete: Part II. Hydration, microstructure and properties [J]. Construction and Building Materials, 2015, 96: 368–377. DOI: https://doi.org/10.1016/j.conbuildmat.2015.08.095.

    Article  Google Scholar 

  37. ZHANG Rui, YAN Xiao-feng, GUO Li. Pullout damage analysis of steel fiber with various inclination angles and interface states in UHPC through acoustic emission and microscopic observation [J]. Journal of Building Engineering, 2022, 51: 104271. DOI: https://doi.org/10.1016/j.jobe.2022.104271.

    Article  Google Scholar 

  38. BHOWMICK S, LIU Gui-rong. Three dimensional CS-FEM phase-field modeling technique for brittle fracture in elastic solids [J]. Applied Sciences, 2018, 8(12): 2488. DOI: https://doi.org/10.3390/app8122488.

    Article  Google Scholar 

  39. MSEKH M A, SARGADO J M, JAMSHIDIAN M, et al. Abaqus implementation of phase-field model for brittle fracture [J]. Computational Materials Science, 2015, 96: 472–484. DOI: https://doi.org/10.1016/j.commatsci.2014.05.071.

    Article  Google Scholar 

  40. LIU Jian-zhong, HAN Fang-yu, CUI Gong, et al. Combined effect of coarse aggregate and fiber on tensile behavior of ultra-high performance concrete [J]. Construction and Building Materials, 2016, 121: 310–318. DOI: https://doi.org/10.1016/j.conbuildmat.2016.05.039.

    Article  Google Scholar 

  41. TCECS 10107—2020. China Association for Engineering Construction Standardization. Technical requirements for ultra high performance concrete [S]. Beijing: Standards Press of China, 2020. (in Chinese)

    Google Scholar 

  42. BUJNAKOVA P, JOST J, FARBAK M, et al. Experimental study of the modulus of elasticity of concrete at different ambient temperature [J]. IOP Conference Series: Materials Science and Engineering, 2019, 549(1): 012049. DOI: https://doi.org/10.1088/1757-899x/549/1/012049.

    Article  CAS  Google Scholar 

  43. LE HOANG A, FEHLING E. Influence of steel fiber content and aspect ratio on the uniaxial tensile and compressive behavior of ultra high performance concrete [J]. Construction and Building Materials, 2017, 153: 790–806. DOI: https://doi.org/10.1016/j.conbuildmat.2017.07.130.

    Article  Google Scholar 

  44. NIU Yan-fei, HUANG Hao-liang, WEI Jiang-xiong, et al. Investigation of fatigue crack propagation behavior in steel fiber-reinforced ultra-high-performance concrete (UHPC) under cyclic flexural loading [J]. Composite Structures, 2022, 282: 115126. DOI: https://doi.org/10.1016/j.compstruct.2021.115126.

    Article  CAS  Google Scholar 

  45. KANG S T, LEE Yun, PARK Y D, et al. Tensile fracture properties of an Ultra High Performance Fiber Reinforced Concrete (UHPFRC) with steel fiber [J]. Composite Structures, 2010, 92(1): 61–71. DOI: https://doi.org/10.1016/j.compstruct.2009.06.012.

    Article  Google Scholar 

  46. ZHOU Zhi-gang, CAI Yang-fa, TAN Jun. Effect of polyester fiber on performance of rubber modified asphalt concrete [J]. Journal of Changsha University of Science & Technology (Natural Science), 2021, 18(2): 1–8. DOI: https://doi.org/10.19951/j.cnki.cslgdxxbzkb.2021.02.001. (in Chinese)

    Google Scholar 

  47. HE Zhi-yong, YANG Jie-ying, ZOU Li-mei. Research on the effect of the double-horizontal-shaft vibrating mixing on the performance of ultra-high performance concrete [J]. Journal of Changsha University of Science & Technology (Natural Science), 2023, 20(5): 154–162. DOI: https://doi.org/10.19951/j.cnki.1672-9331.20220401001. (in Chinese)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering, Changsha University of Science and Technology, Changsha, 410004, China

    Bing Zhao  (赵冰), Xian-zheng Li  (李先正), Jun Pan  (潘军), Hui Peng  (彭晖), Xu-long Peng  (彭旭龙) & Zhen-hao Zhang  (张振浩)

  2. College of Civil Engineering, Xi’ an University of Architecture & Technology, Xi’an, 710055, China

    Zhan-ping Song  (宋战平)

  3. School of Materials Science and Engineering, Northeastern University, Shenyang, 110167, China

    Mo-yu Zhao  (赵漠雨)

Authors
  1. Bing Zhao  (赵冰)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xian-zheng Li  (李先正)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun Pan  (潘军)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hui Peng  (彭晖)
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xu-long Peng  (彭旭龙)
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhen-hao Zhang  (张振浩)
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Zhan-ping Song  (宋战平)
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Mo-yu Zhao  (赵漠雨)
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

ZHAO Bing and LI Xian-zheng provided the concept and edited the draft of manuscript. PAN Jun, PENG Hui, PENG Xu-long and ZHANG Zhenhao conducted the literature review and wrote the first draft of the manuscript. SONG Zhan-ping and ZHAO Mo-yu edited the draft of manuscript.

Corresponding author

Correspondence to Bing Zhao  (赵冰).

Ethics declarations

ZHAO Bing, LI Xian-zheng, PAN Jun, PENG Hui, PENG Xu-long, ZHANG Zhen-hao, SONG Zhan-ping and ZHAO Mo-yu declare that they have no conflict of interest.

Additional information

Foundation item: Project(2022JJ30583) supported by the Natural Science Foundation of Hunan Province, China; Project(21B0315) supported by the Natural Science Research Project of Hunan Education Department, China; Project(18ZDXK04) supported by the Civil Engineering Key Discipline Innovation Project of Changsha University of Science and Technology, China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, B., Li, Xz., Pan, J. et al. Strengthening mechanism of steel fiber in UHPC: A new fracture phase field model. J. Cent. South Univ. 31, 225–236 (2024). https://doi.org/10.1007/s11771-023-5531-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-023-5531-1

Key words

关键词

Search

Navigation