r - The Hong Kong Polytechnic University

Figure 3 Idealised bonded joint model
Figure 4 Softening local bond-slip model
Local Deformation (bond-slip) Model
The actual local FRP-to-concrete bond-slip behaviour can be closely approximated by a bilinear bond-slip
model (Yuan et al., 2004; Lu et al., 2005). However, Chen et al. (2007) have demonstrated that using a
rigid-linear softening bond-slip model as shown in Figure 4 and retaining the fracture energy G f of a bilinear
model leads to almost the same final predictions while significantly simplifying the calculation process. This
linear softening bond-slip model is adopted in the present formulation where δ is the longitudinal slip at the
interface, τ f is the peak bond stress (bond strength) and δ f is the ultimate slip when shear stress reduces to zero
and the plate is considered to be debonded. Friction and aggregate interlock in the debonded area is ignored,
leading to the absence of any residual shear strength after debonding. The bond-slip model in Figure 4
represents a constitutive relation that can be described mathematically by the following equation:
⎧ 0 when δ ( x)
= 0
⎪
τ ( x)
= f ( δ ) = ⎨
τ f
[ δ f − δ ( x)]
when 0 < δ ( x)
≤ δ
(1)
f
⎪
⎩δ
f
Failure Process and States of Interface
Figure 5 shows the sequence of debonding propagation for a typical failure process and the corresponding
interfacial shear stress distribution for the bonded joint shown in Figure 3. A point on the interface can be in a
rigid, softening, or debonded state. Letters R (rigid), S (softening) and D (debonding) are used to describe the
states of the interface from the plate end to mid-length. The entire interface is initially in a rigid state as the
adopted local bond–slip model neglects elastic deformations. Softening initiates at the plate ends as soon as any
loading is applied, resulting in micro-cracking and interfacial slip. The softening length of the interface a
increases with increases in loading and reaches a d when debonding (macro-cracking) initiates at a slip of δ f . The
interface ahead of the softening front remains rigid and has no interfacial stresses in the present analysis (Figure
5a-c), which makes the softening front abrupt. When the more accurate bilinear bond-slip model is used the
actual stress distribution would be smooth ahead of the softening front throughout the whole loading process
(Teng et al., 2006).
Figure 5 Failure progression and interfacial shear stress distribution at different states of the bonded joint
interface
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