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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].