A simple method for quantifying the size effect on fiber orientation distribution functions (ODFs) in fiber-reinforced concrete

Abstract

Fiber orientations are constrained by boundary effects (e.g. size effect), which play a significant role in the macroscopic rigidity of fiber-reinforced concrete (FRC). However, how to quantify the size effect on the fiber orientation distribution functions (ODFs) remain to be open issues. In this work, a simple method to quantify the sectional-size impact on fiber ODFs is proposed. By disassembling the fiber rotatable range and fiber location on the cross-section into several small facets and points, respectively, we draw out the fiber ODFs with different sectional sizes through superposition. Then, the calculation method of the fiber orientation factor based on the ODF is proposed, and the framework of applying an ODF to calculate the stiffness matrix is given. Our results revealed the influence of the cross-section size on the elastic properties of FRC, which can provide a sound guidance for the design and optimization of fiber-based cement composites.

Highlights

• 1. A practical method for discretizing the cross-section of fiber-reinforced concrete (FRC) into a point set is proposed.

• 2. A quantitative interplay between boundary constraints and size effects on fiber ODFs is developed.

• 3. The calculation framework of the fiber orientation factor and elastic modulus of the FRC based on the ODF is established.

• 4. The difference between the effective elastic modulus and Poisson’s ratio of FRCs with different boundary constraints is discussed.

Keywords:

• size effect
• fiber-reinforced concrete
• orientation distribution function
• orientation factor
• elastic properties

Credit authorship contribution statement

Qi Luo: Formal analysis, Conceptualization, Methodology, Software, Writing - review & editing. Fengjuan Wang: Formal analysis, Investigation, Methodology, Review & editing. Wenxiang Xu: Data curation, Review & editing. Jinyang Jiang: Conceptualization, Supervision, Methodology, Resoreces. Guowen Sun: Data curation, Review & editing. Liguo Wang: Data curation, Review & editing.

Additional information

Funding

The authors greatly acknowledge the General Program of National Natural Science Foundation of China (51878155). National Science Fund for Distinguished Young Scholars, China (51925903). National Postdoctoral Program for Innovative Talents (BX2021065). Science and Technology Research and Development Plan of China Railway Corporation “Research on key technology of design and construction and performance improvement of reinforced concrete in coastal environment with strong corrosion” (N2020G055).