Mixed-Mode FRP–Concrete Bond Failure Analysis Using a Novel Test Apparatus and 3D Nonlinear FEM

Acknowledgments

Notation

A_f

FRP cross-sectional area;

b_f

FRP width;

d_m

parameter controlling the debonding process in the bond–slip relation;

E_frp

FRP tensile modulus;

$f_c^{\mathrm{\prime }}$

compressive strength of concrete;

f_frp

tensile stress in each FRP arm;

G_cn

critical normal fracture energy in the bond–slip relation;

G_ct

critical tangential fracture energy in the bond–slip relation;

G_n

normal fracture energy in the bond–slip relation;

G_n

tangential fracture energy in the bond–slip relation;

i

index of discrete point for strain measurement;

K_n

normal contact stiffness in the bond–slip relation;

K_t

tangential contact stiffness in the bond–slip relation;

L

initial bonded length of FRP strip;

L_bonded

L_b = instantaneous bonded length of FRP strip during partial debonding;

L_unbonded

unbonded length of FRP strip;

P

Load applied to the bonded FRP–concrete specimen;

P₀

Peak load of the pure shear (Mode II) specimen;

P_max

maximum load for the FRP-bonded concrete specimen;

t

FRP sheet thickness;

u_x

lateral displacement in the x-axis;

β

tangent of the peel angle between the FRP plate/sheet and the concrete substrate;

β₀

initial value of β prior to debonding initiation;

ΔL

spacing between the strain gauges;

δ

relative movement between the apparatus and the concrete block;

δ_0.75

relative movement between the apparatus and the concrete specimen having β = 0.75;

δ_n

normal slip in the bond–slip relation;

${\delta }_n^{\ast }$

normal slip accompanying σ_max, in the bond–slip relation;

${\delta }_n^c$

maximum normal slip in the bond–slip relation;

δ_t

tangential slip in the bond–slip relation;

${\delta }_t^{\ast }$

tangential slip accompanying τ_max in the bond–slip relation;

${\delta }_t^c$

maximum tangential slip in the bond–slip relation;

ɛ

strain gauge reading;

θ

peel angle between the FRP plate/sheet and the concrete substrate;

σ

normal stress in the bond–slip relation;

σ_max

maximum normal stress in the bond–slip relation;

τ

FRP–concrete bond shear stress;

τ_max

maximum shear stress in the bond–slip relation;

(τ_max.aver.)₀

average bond shear strength under a pure shear (Mode II) condition; and

(τ_max.aver.)_mixed-mode

average bond shear strength under a mixed-mode condition.

References