混杂纤维增强水泥基复合材料弯曲韧性与纤维增强指数的定量关系

基于掺加CaCO₃晶须的混杂纤维增强水泥基复合材料梁和板四点弯曲试验，提出了确定弯曲韧性指标与纤维增强指数（S）关系的数学公式。S考虑了纤维抗拉强度和机械锚固性能对混杂纤维/水泥复合材料弯拉性能的影响，物理意义明确。公式为二次函数形式，可以反映混杂纤维体系对混杂纤维/水泥复合材料增韧效果，而通过确定二次函数极值，能对纤维配比进行优化。该数学模型对钢-合成纤维和钢-植物纤维增强水泥复合材料均有良好的适用性，且无需考虑基体（水泥砂浆或混凝土）和试件形状（梁或板）。另外，该公式不仅适用于指定挠度处弯曲韧性和等效抗弯强度表征的韧性指标，对ASTM C1018规定的弯曲韧性指标，如I₅、I₁₀、I₃₀和I₅₀等也同样适用。

Quantitative relationship between flexural toughness and fiber reinforcing index of hybrid fiber reinforced cementitious composites

On the basis of the four point bending experiments of beams and slabs of hybrid fiber reinforced cementitious composites with CaCO₃ whisker, a mathematical formula was proposed to determine the relationship between flexural toughness index and fiber reinforcing index (S). The S takes into account of the effect of the fiber tensile strength and mechanical anchorage on the flexural tensile properties of hybrid fiber/concrete, which has clear physical meaning. The quadratic function can reflect the toughness reinforcing effect of hybrid fiber system on the hybrid fiber/concrete, and it can be used to optimize fiber composition by determining the extreme value of the quadratic function. The mathematical model has good applicability on steel-synthetic and steel-plant fibers reinforced concrete, without considering the matrix (mortar or concrete) and specimen shape (beam or slab). In addition, the formula can be applied not only to the flexural toughness and equivalent flexural strength, but also to the flexural toughness index based on ASTM C1018, e.g. I₅, I₁₀, I₃₀ and I₅₀.