Finite Element Simulation for Nonlinear Finite Element Analysis of FRP Strengthened RC Beams with Bond-Slip Effect

PATHAK Prabin a, ZHANG Y. X. b * School of Engineering and Information Technology, University of New South Wales, Australian

Defence Force Academy, Canberra, ACT 2600, Australia

E-mail: aPrabin.Pathak@student.adfa.edu.au; by.zhang@adfa.edu.au

Keywords: Bond-slip; Fibre Reiforced Polymer; Nonlinear Finite Element Analysis; RC Beams.

Abstract. A new simple, efficient and accurate finite element model denoted as FEM-B is

developed for the analysis of structural behavior of FRP strengthened RC beams with bond-slip

effect. Geometric nonlinearity and material nonlinear properties of concrete and steel rebar are

accounted for this model. Concrete, steel, FRP and adhesive are modelled as Solid 65, Link 180,

Shell181 and Solid 45 respectively. Concrete is modelled using Nitereka and Neal’s model for

compression, isotropic and linear elastic model before cracking for tension and strength gradually

reduces to zero after cracking, whereas steel is assumed to be elastic perfectly plastic material. The

material of FRP is considered to be linearly elastic until rupture, and adhesive is assumed to be

linearly elastic. The bond slip between concrete, adhesive and FRP is based on the bilinear law,

which is modelled using spring element Combin 39.The developed new finite element model FEM-

B is validated against experimental results, and demonstrates to be effective for the structural

analysis of FRP strengthened RC beams.

Introduction

In recent decades, there is an increasing interest in using high strength composites for the

strengthening of concrete structures. Steel-rebar reinforced structures are subjected to structural

deterioration, which might be caused by design and construction defects, environmental effects,

extreme loadings such as earthquake, fire, impact loadings. Fiber reinforced polymers are of

superior characteristics such as high strength to weight ratio, ease of application, immunity to

corrosion, fatigue resistance, good durability, and are being used increasingly to reinforce and

strength the concrete structures [1].

A large number of experimental and numerical studies have been carried out on FRP

strengthened RC beams and many finite element models have been developed and employed for the

structural analysis of FRP strengthened RC beams. However, majority of these models focused on

the structural behavior of FRP strengthened RC beam with perfect bonding between FRP and

concrete interface [2-6], and the debonding failure between FRP and concrete, which is the one of

the typical failure mode [7], was neglected. In fact, as a result of the debonding, the strength

utilization ratios are sometimes only 15–35%, depending on the cause of debonding due to the FRP

debonding failures [8]. So, consideration of bond slip effect between FRP, adhesive and concrete is

utmost important for accurate prediction of the structural behavior of FRP strengthened RC beams.

Several finite element models considering the bond-slip effect were reported. For example, Wu

et al. [9] conducted a finite element analysis of FRP strengthened RC beam under three point load

using DIANA where material properties of concrete was based on Drucker-Prager plasticity model,

and steel rebar and FRP were assumed as linear elastic–perfectly plastic material and linear elastic

material until rupture respectively. Concrete was modelled as four-node plane stress element, and

the steel rebar and FRP were modelled as two-node linear truss elements. A zero thickness interface

element was used to model the bond slip between FRP and concrete according to bond-slip law

developed by Niu et al. [10]. Sayed et al. [11] analyzed the structural behavior of FRP strengthened

RC beams using ANSYS under four-point loading. The concrete, steel reinforcement and FRP were

modelled as SOLID65, LINK8 and SOLID46 elements respectively. The material properties of

concrete was based on the Mac Gregor and Plight’s model [12] for concrete in compression,

whereas in tension the stress and strain relation was assumed to be linear and elastic until the

maximum tensile strength is reached, after which it gradually reduced to zero. Steel rebar was

modelled as isotropic, elastic and perfectly plastic material that behaves identically in tension and

compression, and the FRP was assumed to be linear and elastic. The contact between FRP and

concrete was modeled using a set of TARGE170 and CONTA174 contact elements, which

functioned on the basis of Coulomb’s friction model, and the bond-slip was modelled based on of

the model by Lu et al. [13]. However, the modelling of adhesive has been neglected in most of the

developed finite element models leading to inaccurate prediction of structural behavior of FRP

strengthened RC beams. Molina et al. [14] stated that the effect of adhesive could not be neglected

in a finite element model because it can be susceptible to damage. Gao et al. [7] mentioned that the

efficient analysis of FRP strengthened RC beams depends upon proper bonding of FRP and

concrete with an epoxy adhesive.

In this paper, a simple finite element model with bond-slip effect is developed for accurate and

effective numerical modelling of the structural behavior of FRP strengthened RC beams. A finite

element model (FEM-P) assuming perfect bond between adhesive, FRP and concrete interfaces was

developed by the authors[15]. The FEM-P element is further developed in this paper to form the

new finite element model FEM-B, with bond slip between concrete, adhesive and FRP accounted

for. To model the bond slip between FRP, adhesive and concrete, spring elements are used with the

nonlinear bond stress-slip relationship developed by Lu et al. [13]. The developed finite element

model is validated by comparing the computed results with available experimental results.

Finite Element Model

A finite element model FEM-B is developed using finite element package ANSYS under static

loading which includes the bond-slip between FRP, adhesive and concrete. Concrete, steel, FRP are

modelled as solid, link, shell elements respectively and FRP/adhesive/concrete interfaces are

modelled using spring element with appropriate bond stress slip law. A perfect bond is assumed

between steel rebar and concrete.

The three-dimensional eight-node Solid65 element, which is characterized by three translational

(translation in the x, y and z directions) degree of freedom at each node, is used to represent the

concrete. This element is capable of modelling concrete cracking in tension and compression.

Link180 element with three degrees of freedom (translation in the x, y and z directions) at each

node is used to model steel reinforcement. The FRP strips are smeared as thin plates and four-node

SHELL181 element with six degrees of freedom at each node, i.e. translations in the x, y, and z

directions, and rotations about the x, y, and z axes is used for modelling the FRP plate. Solid45

element, which has three degrees of freedom at each node, i.e. translation in the x, y and z

directions are used to model epoxy adhesive. Two-node nonlinear spring element COMBIN39,

which has no physical mass and dimension, is used to model FRP, adhesive and concrete interfaces.

Material Model

Concrete is a quasi-brittle material with different behavior in tension and compression. The

nonlinear stress-strain relationship by Nitereka and Neal [16] is used for compressive uniaxial

stress–strain relationship of concrete, which consists of an ascending curve and linear descending

branch as shown in Fig. 1(a) and Eq. (1).

𝜎𝑐=fc [𝜀𝑐

𝜀0(2 −

𝜀𝑐

𝜀0)] for (𝜀 ≤ 𝜀0)

𝜎𝑐=fc [1 − 0.15 × (𝜀𝑐−𝜀0

𝜀𝑐𝑢−𝜀0)] for ( 𝜀0 ≤ 𝜀 ≤ 𝜀𝑐𝑢) (1)

Where fc is the compressive strength of the concrete and 𝜀𝑐𝑢 is the ultimate compressive strain of

the concrete. The corresponding compressive strain ε0 at the compressive strength is calculated by

the equation proposed by Coronado and Lopez [17] as

ε0= 1.71 × (fc/Ec) (2)

in which Ec is the Young’s modulus of concrete.

The stress-strain curve of concrete in tension is assumed to be isotropic, linear and elastic up to

the maximum tensile strength after which concrete crack occurs and strength gradually reduces to

zero as shown in Fig.1(b) in which, Tc is the multiplier for the amount of tensile stress relaxation

whose default value is 0.6 in ANSYS.

The required input data to describe the material properties of concrete in ANSYS are elastic

modulus (Ec), Poisson’s ratio, uniaxial compressive stress, shear transfer coefficient (βt), uniaxial

tensile stress (ft). The value of βt can vary from zero to one and zero refers to a smooth crack

whereas one refers to a rough crack. These factors are used to determine how much shear force can

be transferred across open or closed cracks. For this model, closed crack is assumed as 1 and open

crack is assumed as 0.3.

Fig. 1. Stress-strain relationship of concrete: (a) compression [14]; (b) tension [18]

The steel rebar is assumed to be bilinear, isotropic, elastic and perfectly plastic material which

behaves identically in tension and compression with stiffness only in axial direction. FRPs are

assumed to be linear and elastic until the tension stress reaches its ultimate strength which causes

brittle rupture and then reduces to zero. The epoxy is assumed to be linearly elastic.

A bilinear bond-slip model under static developed by Lu et al. [13] as shown in Fig. 2 is adopted

for the bond slip behaviour between FRP, concrete and adhesive where 𝜏𝑚𝑎𝑥 is the maximum local

bond stress, 𝑠0 is a local slip at 𝜏𝑚𝑎𝑥 , 𝑠𝑓 is a local slip .

Fig. 2. A bilinear bond stress-slip model [13]

Numerical Validation

A FRP strengthened RC beam is analysed using the developed FE model and the computed load-

central deflection relationship is compared to that obtained from the experimental study. Due to

𝜏𝑚𝑎𝑥(MPa)

𝑠0 𝑠𝑓 Slip (mm)

Bond stress

(unit(MPa)

Stress

Strain ε0

fc

𝜀𝑐𝑢

Stress

Strain ε0 6ε0

ft

Tc ft

symmetry, only a quarter of the beam is analysed. A convergence study is carried out to study the

mesh sensitivity of the developed model.

A CFRP Strengthened RC Beam Tested by Arduini et al. [2]

A CFRP strengthened RC beam of size 320 mm 160 mm 1500 mm strengthened with FRP under

four-point bending loading is modelled using the developed finite element model. The details of

steel reinforcement and FRP are shown in Fig. 3. The tension face of the RC beam is externally

strengthened with 1000 mm long, 300 mm wide and 1.2 mm thick CFRP plates using epoxy

adhesive. The material parameters of concrete, steel, FRP and epoxy are given in Table 1.

(a) Longitudinal section

(b) Cross-section

Fig 3. A CFRP-strengthened RC beam tested by Arduini et al. [2] (Dimensions: mm)

Table 1: Material parameters

Material Young modulus [GPa]

Compressive strength [MPa]

Tensile strength [MPa]

Yield strength [MPa]

Poisson’s ratio

Concrete 27 36 2.7 0.2

Steel 200 550 0.3

CFRP 235 3510 0.35

Epoxy 2.0 0.38

The load-deflection relationship of the FRP strengthened RC beam under static loading obtained

from FEM-P [15] and FEM-B and experiment [2] is shown in Fig. 4. Very good agreement between

numerical results from developed finite element model and the experiment is achieved. The two

curves obtained from FEM-B and FEM-P are nearly identical before the load reaching 80 kN where

no obvious bond slip occurs, but after that when bond slip occurs, the FEM-B model predicts the

structural behavior of FRP strengthened RC beam more accurately. At 112 kN, the maximum

central deflection of the beam obtained from the FEM-B model and FEM-P [16] is 4.098 mm and

3.886 mm respectively, while the central deflection obtained from the experiment [2] is 4.45 mm.

This demonstrates the effectiveness and accuracy of the model in the nonlinear finite element

analysis of the FRP-RC beams and the capability of the FEM-B to model the structural behavior of

the beams with bond-slip effect.

Fig 4. Load-central deflection of the FRP strengthened RC beam

Conclusion

A new and simple finite element model FEM-B is developed with bond slip effect between

concrete, adhesive and FRP considered in this paper. In the finite element model, material

nonlinearities are considered, and concrete, steel, FRP components and adhesive are modeled using

Solid65 element, Link180 element, Shell181 elements, and Solid45 element respectively. Concrete

is modelled using Nitereka and Neal’s model for compression, isotropic and linear elastic model

before cracking for tension and strength gradually reduces to zero after cracking. Material property

of steel is assumed to be elastic-perfectly plastic, whereas the FRP is assumed to be linearly elastic

until rupture occurs, and adhesive is assumed to be linearly elastic. Spring element Combin39 is

used for the bond-slip behavior of concrete, FRP and adhesive based on a bilinear bond stress-slip

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6

Lo

ad

(KN

)

Central Deflection(mm)

FEM-P

Experiment

FEM-B

law. The computed results agree very well with those obtained from experimental results, and the

numerical results from FEM-B model are closer to the experimental results than those obtained

from finite element model FEM-P with perfect bond, especially after the load reaches certain value

where bond slip starts to occur. This demonstrates the efficiency, accuracy and capability of the

developed finite element model in the finite element analysis of FRP strengthened RC beams with

bond-slip effect.

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