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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

Abstract

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.

Keywords

FRP plate RC beam Finite element method Difference approximation Interface fracture 

Nomenclature

A

Interfacial area per unit length

a

Radius of rebar

b

Width of concrete beam

bp

Width of FRP plate

Cc

Volume fraction of concrete of ERR calculation zone

Cs

Volume fraction of rebar of ERR calculation zone

c

Parameter of Paris law

d

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

E

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

Ec

Tensile Young’s modulus of concrete

Ep

Young’s modulus of FRP plate

Es

Young’s modulus of rebar

F

External cyclic load

G

Energy release rate

h

Height of beam

\(\tilde{h}\)

Height of ERR calculation zone

hd

Step length in difference approximation

kd

Distance from FRP plate end to the nearest support

L

Length of beam

l

Current debond length

l0

Initial debond length

m

Parameter of Paris law

N

Fatigue cyclic number

\(\overline{N}\)

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

Nint

Number of integration points

n

Parameter describing the degradation velocity of coefficient of friction

q0

Residual fiber compressive stress in the radial direction

r

Distance between neutral axis of concrete and x axis

t

Thickness of FRP plate

U

Strain energy of ERR calculation zone

Ue

Strain energy of one element

voli

Volume of integration point i

ɛ0

Strain of compression concrete when the stress gets σ0

ɛc

Strain of concrete

ɛcu

Ultimate strain of compression concrete

ɛp

Strain of FRP plate

ɛs

Strain of rebar

el}

Elastic strain vector

μ(N,z)

Coefficient of friction on the debonded interface

μ0

Original value of the coefficient of friction before reduction

μf

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

σc

Stress of concrete

σc0

Yield stress of compression concrete

σp

Stress of FRP plate

σs

Stress of rebar

{σ}T

Elastic stress vector

τ

Frictional stress

Notes

Acknowledgements

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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