Abstract
Carbon-Fabric Reinforced Cementitious Matrix(C-FRCM)uses carbon fiber fabric as reinforcement,cement mortar as filler material,which has not only excellent mechanical strength,but also good electrical conductivity and formability.Researches have shown that the use of C-FRCM composites as anode material to retrofit reinforced concrete structures,which has the function of both anticorrosion and structural strengthening[1],therefore significantly improves the durability of coastal infrastructure.However,several factors af fect the durability of the C-FRCM anode.One of the major factors is the degradation of the bond strength caused by anodic polarization[2].Anodic polarization would cause decrease of the bonding strength between the carbon fiber fabric and the cement matrix,and also the tensile strength of the C-FRCM would be af fected.
In order to investigate the ef fect of anodic polarization on the tensile properties of the C-FRCM,Discrete element method(DEM)base model was developed.DEM is a numerical technique initially introduced by Cundall in 1971 for the study of rock mechanics[3].Compared to traditional finite element method(FEM),DEM has some advantages especially for modelling fracture of materials.There are no limits in displacement continuity or compatibility conditions.Along with the development of DEM and its advantages,nowadays researchers begin to extend DEM to model other materials such as soils,hot mix asphalt,Portland cement concrete,and polymer composites.
The DEM model developed in this article was based on geometric configuration of C-FRCM.Voronoi meshes were used to discretize the mortar matrix.Rectangular meshes were used for carbon fiber fabric.The constitutive behavior of mortar matrix and carbon fiber fabric was calibrated based on experimental results.The material properties of the cement matrix and carbon fiber fabric are shown in Table 1.Numerical uniaxial tensile tests were performed to study the decrease of the tensile strength of C-FRCM due to the decrease of bonding strength between carbon fiber fabrics and cement binder due to anodic polarization.
Figure 1 DEM model of C-FRCM composite and the corresponding material model
Table 1 Material properties of C-FRCM
The numerical simulation was performed with LMGC90 simulation software.LMGC90 is an open source platform developed by French lab LMGC using Fortran 90 language[4].It is capable of simulating composite materials using both FEM and DEM.The chosen numerical parameters of the simulation were listed in Table 2.An implicit integration scheme was used to ensure the convergence of the numerical scheme.
Table 2 Parameters of the numerical simulation
(https://www.daowen.com)
The results of the DEM simulation are shown in Figure 2.It can be seen from the figure that a weaker bonding strength would lead to a slippage of the carbon fiber bundle after cracking of the mortar.Therefore the tensile strength is greatly reduced.This is because the load is applied on the matrix.In order to transfer the applied load to the reinforced material,the carbon fiber fabric,the interface should be strong.When the strength of the interface decreases due to anodic polarization,this transfer mechanism becomes weaker.For very weak bond strength,the applied load cannot be transferred to the reinforced material;the failure mode is the cracking of the mortar matrix and slippage of the carbon fiber fabric.The low strength range at large deformation observed in Figure 2 referred to the slippage of the carbon fiber fabric.This strength depends on the friction coefficient between the carbon fabric and mortar matrix.
Figure 2 Effect of bonding strength on the tensile behavior of C-FRCM
Since anodic polarization would lead to a reduction on the bonding strength between carbon fiber fabric and mortar matrix,it would also affect the tensile strength of C-FRCM.In order to quantify this influence,a bond degradation parameterβis defined:
whereσ0 is the initial bond strength,σd is the bond strength after damage caused by anodic polarization.With this definition,the degradation of the bond strength is normalized by the initial bond strength.Figure 3 shows the relationship between the tensile strength of C-FRCM and bond degradation parameterβ.It could be seen from the figure that the tensile strength decreases with increasing damage of the interface.
With these results above,it's now possible to characterize the effect of the anodic polarization on the tensile strength of the C-FRCM when applied as both anode material and structure strengthening material for RC structures.Another numerical model was developed using Comsol Multiphysic software to compute the degradation of the bond strength regarding to input electric current density and duration of energization using FEM model[5].Therefore combining the results of FEM model and DEM model,it is possible to predict the tensile behavior of C-FRCM with input current density and duration of energization,which is critical for the design of ICCP-SS method using CFRCM composite[6].
Figure 3 Effect of bond degradation on the tensile strength of C-FRCM