Nonlinear Semianalytical Prediction of Debonding at the FRP–Generic Material Interface with Mechanical End Anchorages

Acknowledgments

Notation

A

constant to be calibrated from the experimental bond–slip curve;

A_c

cross-sectional area of the substrate;

A_p

cross-sectional area of the FRPs;

AF, RF

axial forces transmitted to the FRP at the loading end and the anchoring end, respectively;

B

constant to be calibrated from the experimental bond–slip curve;

B_f

bonding force;

B_fmax

maximum bonding force;

b_c, b_p

width of the substrate and the FRP laminate;

c₁, c₂

integral constants that can be determined from the boundary conditions of this problem;

du_c(x)/dx, du_p(x)/dx

axial strain in the substrate and the FRPs;

E_c, E_p

elastic moduli of the substrate and the FRP laminate, respectively;

K

axial stiffness of the bare FRP laminate;

L_b

bond length;

L_db

debonding length;

L_eff

effective bond length;

L_tri

load transfer length;

P

tension load applied on the FRP laminate;

P_L, P_A

axial force in the FRPs at the loading end and at the anchoring end, respectively;

P_db

debonding resistance;

$P_0^b$

axial force in FRP composite at the origin of the bonded interface;

$P_d^{db}$

dimensionless axial force in FRPs at the extremity of the debonded interface;

R

reaction force;

t_c, t_p

thickness of the substrate and the FRP laminate;

u_c(x), u_p(x)

displacement in the substrate and FRPs induced by the tension loads applied on the FRPs;

δ_L, δ_A

relative slips in the FRPs at the loading end and at the anchoring end, respectively;

δ_u

ultimate slip;

γ

ratio of residual bonding shear stress to maximum bond shear stress;

σ_c, σ_p

longitudinal stresses of the substrate and the FRP laminate, respectively;

τ_c, τ_p

bonding shear stresses of the substrate and the FRP laminate, respectively;

τ_max

maximum bonding shear stress;

τ_res

residual bonding shear stress;

${\varphi }_0^b,{\varphi }_A^b$

dimensionless relative slips at the origin and extremity of the remaining bonded interface, respectively;

${\varphi }_d^{db}$

dimensionless relative slip in FRPs at the extremity of the debonded interface;

ϕ_L, ϕ_A

nondimensionalized boundary conditions of the slip in the interface at the loading end and the anchoring end, respectively;

ϕ_tri

dimensionless relative slip at the extremity of the load transfer length; and

η

ratio of ultimate slip to the slip corresponding to the maximum bonding shear stress.

References