Numerical Simulation Method For The Fatigue Behavior Of Unidirectional Fiber-reinforced Polymers

To resolve the durability problems of coastal reinforced concrete bridges,the use of Fiber-Reinforced Polymer(FRP)wires instead of steel rebars and prestressed steel wires becomes the inexorable trend in the construction of coastal reinforced concrete bridges in the future because of their excellent properties,such as high specific strength,good resistance to corrosion and fatigue.As the reinforcement of concrete bridges,FRP wire is subjected to the repetitive loading caused by traffic,and its ability to resist fatigue loading is crucial to the safety of the bridge over its operational life.FRP wire is the unidirectional FRP(UD FRP)and generally is manufactured by the pultrusion process from continuous long fibers embedded in the matrix.Therefore,research on the fatigue life and fatigue residual strength of UD FRP can provide reference basis for assessing the fatigue behavior of FRP wires,which is crucial for the successful design and wider usage of FRP wires for bridge applications.To this end,this paper focuses on the study of numerical simulation method for the fatigue behavior of UD FRP.A representative volume element is established considering the influence of boundary effects,and both the static strength failure and fatigue failure of fiber elements are considered as the damage mechanism of UD FRP.This paper analyzes the intrinsic damage mechanisms and failure processes of UD FRP under longitudinal cyclic tensile loading,as well as develops the mechanistic model and numerical simulation method for predicting the fatigue life and the residual tensile strength of the UD FRP.Besides,the impact of factors affecting the fatigue behavior of the UD FRP is explored,including the fiber fatigue property,the fiber volume fraction,and the fiber/matrix interfacial shear stress,as well as an in-depth analysis of the mechanism of action and the reasons for the impact are provided.This research can provide a theoretical basis for evaluating and improving the fatigue performance of unidirectional glass fiberreinforced polymer and can also provide a reference for the numerical simulation of the fatigue performance of unidirectional carbon fiber-reinforced polymer.The main works of the dissertation are as follows:First,a two-dimensional simplified model is proposed for studying the fatigue behavior of the UD FRP under longitudinal cyclic tensile loading.With the assumption of hexagonal fiber packing,the UD FRP cross-section is regarded as a hexagon.Due to the symmetry in the hexagonal cross-section,only 1/6 part of the wire cross-section is selected to form the two-dimensional representative volume element,considering the boundary effect in the UD FRP fatigue behavior.The fatigue strength coefficient of fiber element follows a two-parameter Weibull distribution.Combining the assigned Weibull fatigue strength coefficient,the corresponding initial fatigue life of a fiber element can be calculated by S-N curves.Additionally,each fiber element is assigned a Weibull static strength according to the strength-life equal rank assumption.The single fiber breakage at four different locations are preset to calculate SCFs,and the stress redistribution caused by multifiber breakages is addressed using the principle of superposition.The accumulated fatigue damage of fiber elements is assessed using the Palmgren-Miner law,and both the static strength failure and fatigue failure of fiber elements are considered in the two-dimensional simplified model.To consider the effect of the scatter of the static strength and fatigue properties of the single fibers,Monte Carlo simulation is performed.The proposed model is implemented to explore the fatigue behavior of the UD GFRP and validated against experimental results.Secondly,a three-dimensional progressive fatigue damage model is developed to study the fatigue behavior of the UD FRP under longitudinal cyclic tensile loading,considering both the stress recovery of the fiber in which the broken element resides and the stress concentration on adjacent fiber elements within the ineffective length.Based on the two-dimensional simplified model,the threedimensional characteristic representative volume element is established first as the foundation of the progressive fatigue damage model.A damage indicator describing the recovery of load carrying capacity of fiber elements is introduced and combined with the principle of superposition to realize the stress redistribution caused by fiber breakage.To improve computational performance of the progressive fatigue damage model,an adaptive block-by-block strategy is proposed;this adaptive algorithm is based on the speed of damage growth concerning the fiber breakages within the UD FRP.Combining Monte Carlo method,the progressive fatigue damage model is implemented to predict the fatigue life and stiffness degradation of the UD GFRP and validated against experimental results.Thirdly,a multi-parameter Weibull model of the probabilistic stress-life curve is deduced to describe the variability in the predicted fatigue life,in which fatigue life and the applied maximum fatigue stress are compatible.The parameters of the multi-parameter Weibull model are determined using the maximum likelihood estimation(MLE)approach,and an improved expectation maximization(EM)algorithm is employed to deal with the censored data.Based on the progressive fatigue damage model,the impact of factors affecting the fatigue behavior of the UD FRP is explored,including the Weibull shape parameter and scale parameter corresponding to fiber fatigue strength coefficient,the fiber volume fraction,and the fiber/matrix interfacial shear stress.Finally,a mechanistic model for predicting the residual tensile strength of the UD FRP is developed.The mechanistic residual strength model is an extension of the progressive fatigue damage model.The state of damage in the UD FRP for a specific maximum fatigue stress level and number of cycles is first assessed and then taken as input to simulate the post-fatigue static tensile behavior of the UD FRP.The post-fatigue static tensile simulation is conducted under strain-control,and the stress redistribution caused by fiber breakages is calculated based on the conditions of displacement coordination and static equilibrium.Based on the proposed mechanistic model,Monte Carlo simulation is conducted to explore the influence of the fatigue loading conditions on the post-fatigue static tensile behavior of UD GFRP,such as the residual stress-strain response,residual strength,the kinetics of fiber element breaks,and the critical damage cluster.To assess the predictive capability of the proposed model,the prediction in terms of residual strength is compared with the experimental data from the literature.