Debonding Analysis Model and Experimental Investigations on FRP Plates Reinforced SHCC Beams Under Three-point Bending - HU Jihong; SUN Mingqing; WANG Yingjun; CHEN Jianzhong; HUANG Wei (工程科学与技术)
ObjectiveStrain-hardening cement-based composites (SHCC) exhibit inherent characteristics of multiple microcracking under uniaxial tension and bending, which reduces stress concentration at the crack mouth and delays debonding failure between SHCC and externally bonded FRP plates during the bending of FRP plate-strengthened SHCC beams. This study conducts experimental investigation and theoretical analysis on SHCC beams reinforced with externally bonded FRP plates to examine their debonding behavior, providing guidance for the engineering application of such structural systems.MethodsThe mechanical model based on composite beam theory was developed by satisfying the requirements of force equilibrium and strain compatibility while simultaneously allowing for interfacial partial slip at the FRP-concrete interface. The theoretical analysis included two loading stages: before SHCC cracked and after SHCC cracked. Before SHCC cracked, SHCC and FRP were treated as Euler‒Bernoulli beams and were connected based on reasonable interface rules; the interfacial shear stress was then obtained using the linear elastic mechanics method. After SHCC cracked, to quantify the effect of SHCC multiple fine cracks on interfacial bond stress, segmental stiffness reduction was conducted based on the moment-curvature relation, which combined interface stress analysis and equations on sectional internal force balance to construct the mechanical analysis model. First, the cracked FRP‒SHCC beams were divided into two parts: the elastic part and the SHCC cracked part. Then, the SHCC cracked part was subdivided into several segments. Second, the bending stiffness and the height of the compression zone of SHCC at the joint between the elastic zone and cracked zone and at midspan were obtained by solving the equilibrium equation of the cross-section force system. Third, the bending stiffness and the height of the compressive zone of each segment were assumed to change linearly from the midspan to the elastic part. Finally, the simplified linear interface bond-slip relation, the constitutive relations of FRP and SHCC, and the control differential equations on the axial force of FRP were utilized to establish the analysis model for FRP-reinforced SHCC beams. The solution was programmed using MATLAB software. Three-point bending tests of FRP‒SHCC beams with different geometric dimensions and different FRP thicknesses were performed to verify the validity of the analysis model. Single-side shear tests on the FRP‒SHCC interface were performed to obtain the interfacial bond stress-slip relationship. The typical interface bond stress-slip curve included an ascending branch and a descending branch, which was similar to that of the FRP‒RC interface. Based on the fine finite element analysis by Lu et al., the interfacial shear stress near the crack zone exhibited a highly brittle descent after reaching its peak value. Further studies showed that the calculated results were only 3.7% lower than the test results when the curve with only the ascending branch was applied to the whole beam. The bond stress-slip relationship indicated by Lu et al. was a curve, and the shear stress dropped sharply to 0 after reaching the peak value. This study simplified the ascending curve to a straight line to simplify the calculationResults and DiscussionsThe deviations of the calculated peak load from the test values were in the range of -7.79% to 7.45%, the deviations of the calculated FRP strain from the test values were in the range of -11.52% to 8.13%, and the deviations of the calculated mid-span deflection from the test values were in the range of -7.33% to -22.03%. The calculation results showed that the tensile strain of FRP decreased linearly from the mid-span to the support during the elastic stage, and after the SHCC cracked, the distribution of FRP strain from the mid-span to the beam end indicated that its decreasing rate transitioned from slow to fast and then to slow. The strain of FRP did not reach its fracture strain, which implied that the failure of the composite beams was not due to the strength failure of FRP. The calculated deformation-load curve of the FRP-SHCC beam showed that the elastic stage was short, and the slope of the curve gradually decreased with the increase of the load, indicating that the stiffness of the composite beam gradually decreased as the crack opening of the SHCC increased. The calculated mid-span deflection results aligned with the test results for most of the loading process, except for a short segment near the peak load. In the test, when approaching the peak load, the slope of the load-deformation curve gradually decreased, indicating the occurrence of interface debonding. It was likely that the linear interface bonding stress-slip relationship adopted in the model used in this study could not reflect this process, which remained an issue requiring further investigation. The slope of the FRP strain-load relationship curve significantly decreased when the SHCC initially cracked and then approached a constant. The slope of the curve was also larger when the thickness of the FRP plate increased. The calculated values were in reasonable agreement with the test results. The calculated interface shear stress showed that during the elastic stage, the interfacial shear stress gradually increased from mid-span to the plate end. After the SHCC cracked, the interfacial shear stress first increased and then decreased from mid-span to the end of the plate. The interface shear stress reached its maximum at a position corresponding to the height of the beam from the mid-span, initiating FRP debonding. These results were consistent with the phenomena observed in the test.ConclusionsThis study quantifies the process of crack opening and development in different regions of cracked SHCC through segmental stiffness reduction, and the debonding failure load of FRP-reinforced SHCC beams is determined by combining internal force balance equations with interface stress analysis. The results showed reasonable agreement with the experimental data, indicating that the approach can be applied to the analysis of this type of new civil engineering structure.