Abstract This study aimed to analytically develop tensile stress-crack width constitutive relationships for hybrid fibre reinforced concrete (HFRC). An inverse analysis was performed based on the fictitious crack hinge model to derive the stress-crack width relationship through careful calibrations of model parameters with the digital image correlation (DIC) measurements. The studied parameters included fibre types, volume fraction (Vf) and their combinations. Multilinear stress-crack width relationships for steel, polyolefin and hybrid fibre reinforced concrete with three different fibre volume fractions of 0.50%, 0.75% and 1.00% were derived. The hinge parameters assumed in the inverse analysis were validated with the help of full-field strain measurements using the DIC technique. The relationship between the crack tip opening displacement (CTOD) and the crack mouth opening displacement (CMOD) was verified with the help of the developed equations through the inverse analysis. Afterwards, the simplified equations for predicting the stress-crack width relationships for various types of hybrid FRC were proposed.

中文翻译：

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使用逆分析和数字图像相关的混合纤维增强混凝土的多线性拉伸应力-裂缝宽度关系

摘要 本研究旨在分析开发混合纤维增强混凝土 (HFRC) 的拉伸应力-裂缝宽度本构关系。基于虚构的裂纹铰链模型进行逆向分析，通过使用数字图像相关 (DIC) 测量仔细校准模型参数来推导出应力-裂纹宽度关系。研究的参数包括纤维类型、体积分数 (Vf) 及其组合。导出了三种不同纤维体积分数为 0.50%、0.75% 和 1.00% 的钢、聚烯烃和混合纤维增强混凝土的多线性应力裂纹宽度关系。在使用 DIC 技术的全场应变测量的帮助下，对逆分析中假设的铰链参数进行了验证。借助所建立的方程，通过逆分析验证了裂纹尖端张开位移（CTOD）与裂纹嘴张开位移（CMOD）之间的关系。随后，提出了预测各种混合FRC应力裂纹宽度关系的简化方程。