Materials and Structures

, Volume 41, Issue 10, pp 1613–1621 | Cite as

Numerical simulation of rebar/concrete interface debonding of FRP strengthened RC beams under fatigue load

Original Article


The aim of this paper is to simulate the rebar/concrete interface debonding of FRP strengthened RC beams under fatigue load and also, to ascertain the influence of design parameters such as the elastic modulus, thickness and length of the FRP plate on the debonding performance. In order to simplify the simulation, some basic equilibrium equations are formulated and then the stresses of the rebar and FRP plate are numerically solved, and stress intensity factor is avoided in the simulation by fundamentals of fracture mechanics because of its complexity around the crack tip of bi-material interface. With the combination of finite element method and difference approximation, authors program the degradation model of coefficient of friction, debond criterion, propagation law and loop of load process into a commercial finite element code to investigate the fatigue debonding. The relationships between the debond length as well as other fatigue parameters and number of cyclic load are obtained and discussed.


FRP plate RC beam Finite element method Difference approximation Interface fracture 



Interfacial area per unit length


Radius of rebar


Width of concrete beam


Width of FRP plate


Volume fraction of concrete of ERR calculation zone


Volume fraction of rebar of ERR calculation zone


Parameter of Paris law


Concrete cover measured to center of rebar closest to tensile face of concrete


Elastic modulus of ERR calculation zone when treated as an isotropic material


Tensile Young’s modulus of concrete


Young’s modulus of FRP plate


Young’s modulus of rebar


External cyclic load


Energy release rate


Height of beam


Height of ERR calculation zone


Step length in difference approximation


Distance from FRP plate end to the nearest support


Length of beam


Current debond length


Initial debond length


Parameter of Paris law


Fatigue cyclic number


Elapsed cycle when μ(0) attains the value (μ0 + μf)/2


Number of integration points


Parameter describing the degradation velocity of coefficient of friction


Residual fiber compressive stress in the radial direction


Distance between neutral axis of concrete and x axis


Thickness of FRP plate


Strain energy of ERR calculation zone


Strain energy of one element


Volume of integration point i


Strain of compression concrete when the stress gets σ0


Strain of concrete


Ultimate strain of compression concrete


Strain of FRP plate


Strain of rebar


Elastic strain vector


Coefficient of friction on the debonded interface


Original value of the coefficient of friction before reduction


Steady state or final value of the coefficient of friction where there is no further degradation on μ


Stress of concrete


Yield stress of compression concrete


Stress of FRP plate


Stress of rebar


Elastic stress vector


Frictional stress



This research project is funded by the National Nature Science Foundation of China (No. 50378001) and the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education institutions of MOE, P.R. China.


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Copyright information

© RILEM 2008

Authors and Affiliations

  1. 1.School of Civil Engineering & ArchitectureBeijing Jiaotong UniversityBeijingP.R. China

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