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A four-point bending test for the bonding evaluation of

composite pavement

Manitou Hun, Armelle Chabot, Ferhat Hammoum

To cite this version:

Manitou Hun, Armelle Chabot, Ferhat Hammoum. A four-point bending test for the bonding eval-

uation of composite pavement. 7th Rilem International Conference on Cracking in Pavements, Jun

2012, France. p.51-60, g., graphiques, ill. en couleurs, bibliogr., �10.1007/978-94-007-4566-7_6�.

�hal-00845902�

A four-point bending test for the bonding evaluation of

composite pavement

M. Hun

1

, A. Chabot

1

, F. Hammoum

1

1

LUNAM Université, IFSTTAR, Route de Bouaye, CS4, F-44344

Bouguenais Cedex, France

Abstract. The aim of this paper is to present a specific four-point bending test with

a specific model to help investigate the crack initiation and propagation at the

interface between layers of composite pavements. The influence of the geometry

on the delamination phenomenon in specimens is analyzed. Considering the

deflection behavior of specimens, both experimental and analytical results are

compared. Two different types of interface (concrete / asphalt and asphalt /

concrete) are tested in static conditions. Different failure mechanisms whose

mainly delamination is observed. The crack mouth opening displacement is

monitoring by means of linear variable differential transducer (LVDT). The strain

energy release rate is provided and compared successfully to the literature.

Introduction

Due to shrinkage phenomenon occurred in cement materials, the existing vertical

crack through the cement concrete layer combined to environmental and traffic

loadings affects the durability of composite pavements made with asphalt and

cement materials. Two main problems have to be investigated: i) debonding

mechanisms at the interface between two layers; ii) reflective cracking

phenomenon through asphalt overlay or corner cracks in concrete overlay. This

paper deals with the study of debonding. Previous research works have proposed

some experimental devices to characterize the bond strength of asphalt-concrete

interface in mode I [1]. But the combined normal and shear stresses near the edge

of the layer as the vertical crack usually initiates and propagates the delamination

[1]. The optimum design incorporating these variables has not been done yet.

Mixed mode test to evaluate the delamination resistance is needed. On site, only

few devices [4-5] allow testing the bond strength in mixed-mode. The literature

review offers interesting ideas especially those on reinforced concrete beams and

on concrete beams strengthened with composite materials [6].

M. Hun, A. Chabot, F. Hammoum

2

In this paper, we propose to adapt existing four-point bending test (4PB) to bi-

material specimens made with asphalt and cement material layers as illustrated in

Figure 1. By using a specific elastic model, the influence of the specimen geometry

and the material characteristics on internal stresses is presented. Then,

experimental program is described and a discussion on static results is given.

x

z

o

a

L/3

L

L-a

2L/3

2

1

a

x1

f

1

f

2

a

x2

a

a

2

z

F/2F/2 F/2F/2

e

2

e

1

b

F

L

F

L

FF

L

2

1

x

o

a

L

L-a

2

1

1

Zone I Zone II Zone III

Asphalt concrete

Cement concete

A B C D

Asphalt concrete

Cement concete

(a)

(b)

Figure 1. (a) Schematic of test configuration, (b) Schematic adapted for calculating

strain energy release rate calculation

Quasi-analytical investigation

The Multi-particle Model of Multi-layer Materials with 5 equilibrium equations

per layer (M4-5n, n: total number of layers) [2] used to calculate stress and strain

energy release rate on the 4PB test (Figure 1.b) is briefly presented. Considering

homogenous, elastic and isotropic material assumptions, the specimen design is

studied in order to optimize stresses to cause delamination between layers.

Introduction to the M4-5n

The M4-5n has five kinematic fields per layer i (

{

}

ni ,...,1∈

): the average plane

displacement

(

)

yxU

i

,

α

, the average out of plane

(

)

yxU

i

,

3

and the average rotations

(

)

yx

i

,

α

Φ

{

}

(

)

2,1∈

α

. Stress field is assumed to be written with polynomial

approximation in z (vertical direction) per layer i (characterized by

iii

Ee

υ

,,

, its

thickness, Young modulus and Poisson ratio parameters). Its coefficients are

expressed with the use of the classical Reissner generalized stress fields in

(

)

yx,

per layer i. These polynomial approximations have the advantage to define the

normal stresses

(

)

yx

ii

,

1, +

ν

and the shear stresses

(

)

yx

ii

,

1, +

α

τ

at the interface

between i and i+1 layers. Theses stress fields are responsible for the delamination

between layers at the edge or cracking location points. Hellinger-Reissner's

formulation reduces the real 3D problem to the determination of regular plane

fields (x,y) per layer i and interface i, i+1 (and i-1, i). This model can be viewed as

superposition of n Reissner’s plates, connected by means of an elastic energy that

depends on the interlaminar stress fields [2]

.

The M4-5n advantage is to

give finite

value of stresses near the edge or crack permitted to identify easily delamination

criteria [3].

A four-point bending test for the bonding evaluation of composite pavement

3

In order to simplify the analysis, the 4PB test presented in Figure 1.a is simulated

under the assumption of plane strain. Then, the mechanical fields depend only on

the variable x. The problem is divided in three zones (see Figure 1.b). By mean of

shear forces

(

)

xQ

i

1

of layers 1 and 2, linking conditions of displacements, forces

and moments between zones, the first and last single layer zone (

],0[

1

ax ∈

and

],[

2

LaLx

−

∈

) allow to pass on the support conditions of the beam at the

bilayer zone

(

)

],[

21

aLax −∈

. On this central zone (where

2

=

n

), different

manipulations of M4-5n equations let to put finally into a system of second order

differential equations in function of x only with the form Eqn. (1)

( ) ( ) ( )

(

)

( )

( )

( )

( )

Φ

Φ

==+

x

xU

xQ

x

xU

xXwithCxBXxAX

2

1

2

1

1

1

1

1

1

1

"

(1

)

where A, B, and C are the analytical matrices functions of geometric parameters,

elastic characteristics of material behaviors and loading conditions specified

(Figure 1.a). The expression of A, B, and C are given in Eqn. (2-4):

( ) ( )

( )

( )

( )

( )

( )

( )

( ) ( )

−−

−−

−

+−

−

+

−

+

−

+

+

+

−−

−

=

0

1

00

1

112

000

12

00

35

13

0

15

1

15

0000

1

1

1

15

4

000

11212

22

2

3

2

2

2

2

2

3

2

2

2

22

1

11

2

22

1

121

2

2

1

1

12

211

1

1

12

2121

1

1

2

11

1

11

υυ

υυ

υ

υ

υ

υ

υ

υ

υυ

EeEe

EeEee

E

e

E

e

E

Eee

E

Eeee

EeEe

A

(2

)

( ) ( )

( )

∈

×

×

+

×

+

−

=

+

+

+

−

−

+

−

+

−−

−

=

3

,,

0

10002

100025

112

100025

1

0

;

00000

00100

10

5

112

5

112

10

2

1

5

1

5

1

2

1

00100

1

22

2

2

2

22

2

11

1

2

2

2

1

11

L

axif

F

F

Ee

F

E

C

EeEe

e

EE

e

B

υ

υ

υυ

υυ

(3

)

( )

−∈

×

−

×

+

−

×

+

=

∈

=

2

22

2

2

2

,

3

2

,

0

10002

100025

112

100025

1

0

;

3

2

,

3

,

0

0

0

0

0

aL

L

xif

F

F

Ee

F

E

C

LL

xifC

υ

υ

(4

)

M. Hun, A. Chabot, F. Hammoum

4

The shear stresses

(

)

x

2,1

1

τ

and normal stresses

(

)

x

2,1

ν

of M4-5n at the interface

between layer 1 and 2, are obtained analytically in function, respectively, of the

unknowns of the system of Eqn. (1) and their derivative by the Eqn. (5) of interface

behavior, and the equilibrium equation of shear forces of Eqn. (6). The sum of

shear force of layers has to verify the condition as indicating in Eqn. (7).

( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( )( )

212121

2

1

2

2

1

1

1

1

2

1

2

1

1

1

1

1

2

1

212,1

1

114

5

1

5

1

22

15

υυ

υυ

τ

+++

+

+

+

+Φ−Φ−−

=

EeEe

xQ

E

xQ

E

x

e

x

e

xUxU

EEx

(5)

(

)

(

)

xQx

'1

1

2,1

−=

ν

(6)

( ) ( )

−∈

×

−

∈

∈

×

=+

21

2

1

1

1

,

3

2

10002

;

3

2

,

3

0;

3

,

10002

aL

L

xif

FLL

xif

L

axif

F

xQxQ

(7)

Eqn. (8) gives the M4-5n elastic energy W

e

. According to linear elasticity theory

for a system under constant applied load, the energy release rate can be expressed

as in Eqn. (9) in case of the crack propagation along the interface (Figure 1.b).

(

)

(

)

( )

[ ]

( )

[ ]

( )

[ ]

( )

[ ]

[ ]

( )

( )

( )

[ ]

( )

[ ]

( ) ( )

( ) ( )

( )

( )

( )

( )

−+

+−

−

+

−

+

+

+

+

−

+

+

+

+

+

+

+

+

+

+

++

Φ

−

+

−

++Φ

−

+

−

+

+

+

−

=

∫

∫∫∫

∫∫

∫∫∫

∫

2

22

2

2

3

2

2

22

2

2

"1

1

1

11

2

22

1

11

"1

1

1

11

2

1

2

2

1

1

1

1

2

2

1

22

2

2

1

1

11

1

2

'2

1

2

'2

1

'1

1

2

2

2

'1

1

1

1

2

'2

1

2

2

22

2

'2

1

2

22

2

'1

1

2

1

11

2

'1

1

1

11

2

22

1

2

3

1

2

22

2

1000

10

13

1000

2

1

1

11

15

2

1

11

5

1

5

16

5

16

140

17

4

2

270

13

112

12

112

12

1000

10

13

1000

2

1

3

2

2

1

2

2

1

2

2

1

2

1

2

1

2

1

2

1

2

3

2

1

2

2

1

2

3

2

1

23

2

F

Ee

aL

aL

F

Ee

dxU

Ee

E

e

E

e

dxU

Ee

Q

E

Q

E

dxQ

Ee

dxQ

Ee

dxQ

QQ

E

e

dxQ

E

e

dx

Ee

dxU

Ee

dx

Ee

dxU

EeF

Ee

a

a

F

Ee

W

x

x

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

x

x

e

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

υ

υ

υ

υυ

υ

υυυυ

υ

υ

υ

υ

υ

υ

(8)

A

W

G

e

∂

∂

=

(9)

Both the methods of adimentionalisation and numerical resolution of equations by

the Newmark finite difference scheme used by Pouteau [4] and Le Corvec [7] are

adapted to this test. This method is programmed under the free software Scilab. For

a symmetrical case, the excellent convergence of normal and shear stresses at the

interface between layers at

1

ax =

and

2

ax =

is obtained in [8]. It has shown that

the discretization of the x variable into 1200 elementary segments is sufficient.

One simulation takes few seconds (CPU time). Interface ruptures are expected in

mixed mode (mode I and II). The results have been compared successfully with

finite element calculations and different static tests on Alu/PVC structure [8].