1. No category

Comptest 2015
Effect of the adherent and adhesive
thickness on the fracture toughness and
cohesive law of FM300 adhesive
Carlos Sarrado, Albert Turon, Jordi Renart and Josep Costa
AMADE, University of Girona (Spain)
Objective
Comptest 2015
Bonded joints
Adherent thickness 𝑡"#$
Adhesive thickness 𝑡"%&
Mixed mode ratio
'((
'
Fracture toughness measurement
Cohesive law measurement
Model parameters
𝑡"#$
𝑡"%&
shown.
Background
Comptest 2015
The fracture of adhesive joint usually involves Fracture
Process Zones (FPZ) of a relevant length if compared to
specimen’s sizes
Figure 4.1: Representation of the load introduction in the three test types performed in this work.
During crack propagation
1
mm
Thirty-two tests in total were carried out. Two DCB, ENF, MMB 50%
and MMB 70% tests were performed for each material configuration in
Table 4.1. The experimental data were reduced using J -integral closedform solutions available in the literature. Details of the equations used can
Fracture
process
zone
be found in the description of each particular test.
Background
Ø Delamination: small FPZ
Comptest 2015
LEFM applies
Fracture process zone
on in the three test types perØ Adhesively bonded joints: large FPZ
NLFM
Two DCB, ENF, MMB 50%
ch material configuration in
uced using J -integral closedails of the equations used can
test.
Background – Data reduction methods
Comptest 2015
G
•
•
J
Energy release rate
•
J-integral approach
small FPZ (embedded within the Kdominant region of the singular
stress field)
•
Non-linear energy release rate
•
Large process zone
,
𝑃
𝜕𝐶
𝒢=
2𝐵 𝜕𝑎
When LEFM applies G
=J
x2
Crack tip
x1
Background – Data reduction methods – J-integral
Comptest 2015
J-integral closed-form solution
(Sarrado et al. CSTE 2015)
Background – Data reduction methods – J-integral
Comptest 2015
𝒢
𝐽
FPZ
a ??
(Sarrado et al. CSTE 2015)
Background – Data reduction methods – Experimental setup
Comptest 2015
Figure 4.2: Experimental setup for an MMB test and pictures taken by the cameras on either side of the specimen for monitoring the crack length (side A) and
measuring the crack opening displacement (side B).
shown.
Background – Data reduction methods
Comptest 2015
Delamination specimen (small FPZ)
Figure 4.1: Representation of the load introduction in the three test types performed in this work.
Thirty-two tests in total were carried out. Two DCB, ENF, MMB 50%
and MMB 70% tests were performed for each material configuration in
Table 4.1. The experimental data were reduced using J -integral closedform solutions available in the literature. Details of the equations used can
be found in the description of each particular test.
Background – Data reduction methods
Adhesive joint (large FPZ)
Similar results when the
FPZ is still small
Comptest 2015
Background – Data reduction methods
Comptest 2015
Adhesive joint (large FPZ)
J-integral approach chosen as a data reduction method
insert
location.
4.1.
Three
different
adherend
thicknesses
were
manufactured
by
stacking
a
Experimental characterisation of FM300 adhesive in T800S/M21 CFRP
different number of layers, whereas the two different adhesive thicknesses
were achieved by using one or two layers of adhesive.
4.2.2
Tests and data reduction method
Specimen total
Adhesive
Specimen
Layup
codes
thicknesses
(mm)
thickness
(mm)
Double Cantilever Beam (DCB) [67], End Notched Flexure (ENF) [68] and
A1T1
3.12 ± 0.06
[0]8 /d/[0]8
0.21 ± 0.02
Mixed Mode Bending (MMB) [19] tests were performed to characterize
A2T1
4.60 ± 0.08
[0]12 /d/[0]12
0.21 ± 0.02
the adhesive
under
pure
mode
I,
pure
mode
II
and
mixed
mode
loading,
A2T2
4.80 ± 0.10
[0]12 /d/[0]12
0.37 ± 0.01
respectively.
In
Figure
4.1,
the
configuration
of
each
test
is
schematically
A3T1
6.05 ± 0.23
[0]16 /d/[0]16
0.21 ± 0.02
shown.
Table 4.1: Specimen configurations tested. In the layup definition, d denotes the
insert location.
Figure 4.1: Representation of the load introduction in the three test types per4.2.2
Tests
and
data
reduction
method
formed in this work.
Adherent
thickness
𝑡
"#$
Double Cantilever Beam (DCB) [67], End Notched Flexure (ENF) [68] and
Thirty-two
tests
in
total
were
carried
out.
Two
DCB,
ENF,
MMB
50%
Fracture
toughness
measurement
Mixed Mode Bending (MMB) [19] tests were performed to characterize
Adhesive
thickness
𝑡
and
MMB
70%
tests
were
performed
for
each
material
configuration
in
"%&
the adhesive under pure mode I, pure mode II and mixed mode loading,
Table
4.1.
The
experimental
data
were
reduced
using
J
-integral
closedCohesive
law
measurement
respectively. In Figure
4.1,
the
configuration
of
each
test
is
schematically
'((
form
solutions
available
in
the
literature.
Details
of
the
equations
used
can
Mixed
mode
ratio
shown.
'
be found in the description of each particular test.
Comptest 2015
insert
location.
4.1.
Three
different
adherend
thicknesses
were
manufactured
by
stacking
a
Experimental characterisation of FM300 adhesive in T800S/M21 CFRP
different number of layers, whereas the two different adhesive thicknesses
were achieved by using one or two layers of adhesive.
4.2.2
Tests and data reduction method
Specimen total
Adhesive
Specimen
Layup
codes
thicknesses
(mm)
thickness
(mm)
Double Cantilever Beam (DCB) [67], End Notched Flexure (ENF) [68] and
A1T1
3.12 ± 0.06
[0]8 /d/[0]8
0.21 ± 0.02
Mixed Mode Bending (MMB) [19] tests were performed to characterize
A2T1
4.60 ± 0.08
[0]12 /d/[0]12
0.21 ± 0.02
the adhesive
under
pure
mode
I,
pure
mode
II
and
mixed
mode
loading,
A2T2
4.80 ± 0.10
[0]12 /d/[0]12
0.37 ± 0.01
respectively.
In
Figure
4.1,
the
configuration
of
each
test
is
schematically
A3T1
6.05 ± 0.23
[0]16 /d/[0]16
0.21 ± 0.02
shown.
Table 4.1: Specimen configurations tested. In the layup definition, d denotes the
insert location.
Figure 4.1: Representation of the load introduction in the three test types per4.2.2
Tests
and
data
reduction
method
formed in this work.
Adherent
thickness
𝑡
"#$
Double Cantilever Beam (DCB) [67], End Notched Flexure (ENF) [68] and
Thirty-two
tests
in
total
were
carried
out.
Two
DCB,
ENF,
MMB
50%
Fracture
toughness
measurement
Mixed Mode Bending (MMB) [19] tests were performed to characterize
Adhesive
thickness
𝑡
and
MMB
70%
tests
were
performed
for
each
material
configuration
in
"%&
the adhesive under pure mode I, pure mode II and mixed mode loading,
Table
4.1.
The
experimental
data
were
reduced
using
J
-integral
closedCohesive
law
measurement
respectively. In Figure
4.1,
the
configuration
of
each
test
is
schematically
'((
form
solutions
available
in
the
literature.
Details
of
the
equations
used
can
Mixed
mode
ratio
shown.
'
be found in the description of each particular test.
Comptest 2015
Fracture toughness measurement: Influence of adhesive thickness
Comptest 2015
Pure mode:
↑ 𝑡"%& ⟹ ↑ 𝐽6
Mixed-mode:
↑ 𝑡"%& ⟹ ≅ 𝐽6
.
Figure 4.4: Influence of the adhesive thickness on the fracture toughness of the
adhesive joint.
Fracture toughness measurement: Influence of adherent thickness
Comptest 2015
↓ 𝑡"#$ ⟹ ↑ 𝐽6
Higher increase when
increasing mode II
Figure 4.5: Influence of the adherend thickness on the fracture toughness of the
adhesive joint.
Fracture toughness measurement: Influence of mode mixity
Fracture toughness measurement
Adherent thickness 𝑡"#$
Adhesive thickness 𝑡"%&
Mixed mode ratio
'((
'
↓ 𝑡"#$ ⟹ ↑ 𝐽6
↑ 𝑡"%& ⟹ ↑ 𝐽6
𝐽99
↑ ⟹ ↑↑ 𝐽6
𝐽
Comptest 2015
insert
location.
4.1.
Three
different
adherend
thicknesses
were
manufactured
by
stacking
a
Experimental characterisation of FM300 adhesive in T800S/M21 CFRP
different number of layers, whereas the two different adhesive thicknesses
were achieved by using one or two layers of adhesive.
4.2.2
Tests and data reduction method
Specimen total
Adhesive
Specimen
Layup
codes
thicknesses
(mm)
thickness
(mm)
Double Cantilever Beam (DCB) [67], End Notched Flexure (ENF) [68] and
A1T1
3.12 ± 0.06
[0]8 /d/[0]8
0.21 ± 0.02
Mixed Mode Bending (MMB) [19] tests were performed to characterize
A2T1
4.60 ± 0.08
[0]12 /d/[0]12
0.21 ± 0.02
the adhesive
under
pure
mode
I,
pure
mode
II
and
mixed
mode
loading,
A2T2
4.80 ± 0.10
[0]12 /d/[0]12
0.37 ± 0.01
respectively.
In
Figure
4.1,
the
configuration
of
each
test
is
schematically
A3T1
6.05 ± 0.23
[0]16 /d/[0]16
0.21 ± 0.02
shown.
Table 4.1: Specimen configurations tested. In the layup definition, d denotes the
insert location.
Figure 4.1: Representation of the load introduction in the three test types per4.2.2
Tests
and
data
reduction
method
formed in this work.
Adherent
thickness
𝑡
"#$
Double Cantilever Beam (DCB) [67], End Notched Flexure (ENF) [68] and
Thirty-two
tests
in
total
were
carried
out.
Two
DCB,
ENF,
MMB
50%
Fracture
toughness
measurement
Mixed Mode Bending (MMB) [19] tests were performed to characterize
Adhesive
thickness
𝑡
and
MMB
70%
tests
were
performed
for
each
material
configuration
in
"%&
the adhesive under pure mode I, pure mode II and mixed mode loading,
Table
4.1.
The
experimental
data
were
reduced
using
J
-integral
closedCohesive
law
measurement
respectively. In Figure
4.1,
the
configuration
of
each
test
is
schematically
'((
form
solutions
available
in
the
literature.
Details
of
the
equations
used
can
Mixed
mode
ratio
shown.
'
be found in the description of each particular test.
Comptest 2015
Cohesive law measurement
Comptest 2015
[ Sørensen and Jacobsen (2003) ]
𝜎
∗
𝛿
𝜕𝐽
= ∗
𝜕𝛿
Cohesive law measurement
propagation than that of the standard, whereas the initial crack length
set to 40 mm. The MMB lever arm was set for each particular
test
acco
Comptest 2015
to the ASTM standard [19], depending on the specimen thickness an
aimed mixed-mode ratio. The term aimed here refers to the mode m
defined in an LEFM framework. Its definition is valid for, at least,
stages of crack growth, when the[ Sørensen
FPZ is still
small.
For
larger
FPZ
and Jacobsen (2003) ]
mode mixity becomes undefined in an LEFM sense and raises the discu
on how the mixed-mode ratio should be defined under large-scale frac
which is outside the scope of the current work.
Jc was computed using the J -integral closed-form solution for the M
test recently proposed by the authors [8] as
P
J=
b
!"
1
c
−
2 2L
#
θA +
"
c
1
+
2L 2
#
$c
c
θB + θC −
L
L
%
+ 1 θD
&
Closed
form
solution
where b is the specimen width, P is the applied load, c is the MMB
𝜎
∗
𝛿
𝜕𝐽
= ∗
𝜕𝛿
arm and θA , θB , θC and θD are the rotation angles at load introdu
points, as depicted in Figure 4.1. θA and θC refer to the lower and u
arms on the cracked end of the specimen, respectively, θB refers to
specimen’s uncracked end and θD refers to its mid-span length point.
4.2.3
Instrumentation
Crack length was visually monitored in order to have an approximate
for representation purposes only, as it is not required for the data redu
Cohesive law measurement
propagation than that of the standard, whereas the initial crack length
set to 40 mm. The MMB lever arm was set for each particular
test
acco
Comptest 2015
to the ASTM standard [19], depending on the specimen thickness an
aimed mixed-mode ratio. The term aimed here refers to the mode m
defined in an LEFM framework. Its definition is valid for, at least,
stages of crack growth, when the[ Sørensen
FPZ is still
small.
For
larger
FPZ
and Jacobsen (2003) ]
mode mixity becomes undefined in an LEFM sense and raises the discu
on how the mixed-mode ratio should be defined under large-scale frac
which is outside the scope of the current work.
Jc was computed using the J -integral closed-form solution for the M
test recently proposed by the authors [8] as
P
J=
b
!"
1
c
−
2 2L
#
θA +
"
c
1
+
2L 2
#
$c
c
θB + θC −
L
L
%
+ 1 θD
&
Closed
form
solution
where b is the specimen width, P is the applied load, c is the MMB
𝜎
∗
𝛿
𝜕𝐽
= ∗
𝜕𝛿
arm and θA , θB , θC and θD are the rotation angles at load introdu
points, as depicted in Figure 4.1. θA and θC refer to the lower and u
arms on the cracked end of the specimen, respectively, θB refers to
specimen’s uncracked endDIC
andas θaD refers to its mid-span length point.
virtual
4.2.3 Instrumentation
extensometer
at crack tip
Crack length was visually location
monitored in order to have an approximate
for representation purposes only, as it is not required for the data redu
(b) of the DCB tests conducted. Only 1 out of every 50 points is depicted for
by
Stigh
et
Cohesive law measurement:
Mode
IIal. [46] was used for computing Jc as
Comptest 2015
clarity.
P
J = (θA − 2θD + θB )
2b
where b is the specimen width, P is the applied load and
load introduction in the two
test
types
performed
the rotation angles at the load introduction points, as
3.1. θA refers to the arm on the cracked end of the spec
the specimen’s uncracked end and θD refers to its midwhere the load is applied.
plateau à plastic deformations
prior
to
damage
initiation.
Greater
when
↓
𝑡
𝑜𝑟 ↑
𝑡
"#$
"%& two
Figure 3.1: Representation of the load introduction
in the
remaining
àinfriction
Figure
4.8:traction
J vs. crack
tip
shear
displacement
(a)
and
measured
cohesive
laws
(b)
this work.
of the ENF tests conducted. Only 1 out of every 100 points is depicted for clarity.
was
used.
The
J
-integral
method
was
based
on
the
closed-form
s
68
of composite bonded joints in terms of cohesive laws
Cohesive law
measurement:
Mode
I
Comptest 2015
the DCB test proposed by Paris and Paris [43]
P
J =2 θ
b
where b is the specimen width, P is the applied load and θ is th
Figure 3.1:angle
Representation
of
the
load
introduction
in
the
two
test
types
performed
at the load introduction point. For the tests presented in
in this work.
the angles at both the upper and lower load introduction points o
specimen were monitored in order to remove the initial rigid bod
from the results (points A and C in the DCB specimen of Figur
ENF tests were done based on the procedure described i
method AITM 1.0006. The distance between supports was set t
for all the tests performed in order to achieve a longer crack p
than that of the standard, whereas the initial crack length was
mm. On one hand, the LEFM-based method described in the AI
test
method
was
used
to
obtain
G
.
Although
the
AITM
te
IIc
Low repeatability (limitations on measurement equip.) & Stick-slip à incomplete measurement
covers
only
initiation
values
of
the
mode
II
fracture
toughness
@cohesive laws
Figure
4.7:
J
vs.
crack
tip
opening
displacement
(a)
and
measured
Steep profile both prior to and after damage initiation à LEFM scope (large 𝜏 and Δ6 → 0)
(b) of the DCB
tests conducted.
1 out
of every 50values
points given
is depicted
forwo
equations
were usedOnly
for the
propagation
in this
Shape-dependence on the adhesive and adherent thicknesses might be of little relevance
clarity.
other hand, the J -integral closed-form solution for the ENF tes
by Stigh et al. [46] was used for computing Jc as
Jc was computed using the J -integral closed-form solution for th
testMixed
recently
proposed
Cohesive law measurement:
Mode
50% by the authors [8] as
Comptest 2015
4.3. Results
P
J=
b
!"
1
c
−
2 2L
#
θA +
"
c
1
+
2L 2
#
$c
c
θB + θC −
L
L
%
69
+ 1 θD
&
where b is the specimen width, P is the applied load, c is the MM
arm and θA , θB , θC and θD are the rotation angles at load intro
n the three test types perpoints, as depicted in Figure 4.1. θA and θC refer to the lower and
arms on the cracked end of the specimen, respectively, θB refers
specimen’s uncracked end and θD refers to its mid-span length poin
o DCB, ENF, MMB 50%
4.2.3 Instrumentation
material configuration in
Crack
length
was
visually
monitored
in
order
to
have
an
approximat
using J -integral closedfor representation purposes only, as it is not required for the data re
of the equations used can
t.
Figure 4.9: J vs. crack tip opening and shear displacements norm (a) and measured
cohesive laws (b) of the MMB 50% tests conducted. Only 1 out of every 100 points
is depicted for clarity.
Figure 4.9: J vs. crack tip opening
and shearusing
displacements
norm
(a) and measured
Jc was computed
the J -integral
closed-form
solution for th
testMixed
recently
proposed
by the Only
authors
[8] as
Cohesive
law(b)
measurement:
75%
Comptest 2015
cohesive
laws
of the MMB
50%Mode
tests
conducted.
1 out
of every 100 points
is depicted for clarity.
P
J=
b
!"
1
c
−
2 2L
#
θA +
"
c
1
+
2L 2
#
$c
c
θB + θC −
L
L
%
+ 1 θD
&
where b is the specimen width, P is the applied load, c is the MM
arm and θA , θB , θC and θD are the rotation angles at load intro
n the three test types perpoints, as depicted in Figure 4.1. θA and θC refer to the lower and
arms on the cracked end of the specimen, respectively, θB refers
specimen’s uncracked end and θD refers to its mid-span length poin
o DCB, ENF, MMB 50%
4.2.3 Instrumentation
material configuration in
Crack
length
was
visually
monitored
in
order
to
have
an
approximat
using J -integral closedfor representation purposes only, as it is not required for the data re
of the equations used can
t.
Effect of adherend or adhesive thickness less marked on the shape of the cohesive law
however a marked influence on the “path”
Figure 4.10: J vs. crack tip opening and shear displacements norm (a) and measured cohesive laws (b) of the MMB 75% tests conducted. Only 1 out of every 100
points is depicted for clarity.
can explain why the experimental observations for pure mode differ from
Cohesive
law
measurement:
Mixed
Mode
Comptest
2015
those for mixed mode.
The tractions of the fully damaged interface (for large crack opening
n of the load introduction in the three test types per-
otal were carried out. Two DCB, ENF, MMB 50%
were performed for each material configuration in
mental data were reduced using J -integral closedin the literature. Details of the equations used can
tion of each particular test.
First stagesà mode-II dominant and progressively changes to mode I as damage grows
Dependency on 𝑡"#$ but not in 𝑡"%&
Figure 4.11: Mode I (∆n ) against mode II (∆t ) crack tip opening displacements
for the MMB (a) 50% and (b) 75% tests (only 1 out of every 200 points is depicted
for clarity).
Cohesive law measurement
Comptest 2015
e 4.12: Idealized FM-300 cohesive laws as a function of the aimed
y. Mode I cohesive laws resemble the behavior of LEFM, which
Cohesive law measurement
Comptest 2015
I
e
d
o
M
e
Mod
II
e 4.12: Idealized FM-300 cohesive laws as a function of the aimed
y. Mode I cohesive laws resemble the behavior of LEFM, which
Summary
is not able to transfer loads after being damaged. Howeve
traction progressively increases for the MMB 75% (Figure
Comptest 2015
ENF (Figure 4.8 (b)) tests. Such remaining traction migh
of the presence of friction in the fractured interface, as i
for shear-dominated fracture.
In regards to the detailed modeling of adhesive joints
can be concluded from the previous observations that the
Adherend and the bondline thicknesses have a significant
impact
loading mode must be accurately accounted for in the tr
law that feeds the numerical model. The existing cohe
on the fracture toughness of the adhesive joint.
on the definition of initiation and propagation parameter
the mode mixity, but they do not take into account th
The shape of the measured cohesive laws is mainly defined by the
shape of the cohesive law [5]. This shape variation as a
mode mixity is qualitatively shown in Figure 4.12. It can
mode mixity.
the behavior of mode-I fracture resembles the behavior of
Cohesive law measurement is still a challenging research
topic
that this
behavior rapidly disappears as the mixed-mod
because of the difficulties that arise from the existing
measurement methods
Existing simulation methods should be addapted according to the
experimental observations
Figure 4.12: Idealized FM-300 cohesive laws as a function o
mixity. Mode I cohesive laws resemble the behavior of LEF
disappears as the interface plasticity increases for increasing m
References
Comptest 2015
C. Sarrado, A. Turon, J. Renart, J. Costa. An experimental data reduction method for the
Mixed Mode Bending test based on the J-integral approach. Submitted to Composite
Science and Technology; 2015.
C. Sarrado, A. Turon, J. Costa, J. Renart. On the validity of linear elastic fracture mechanics
methods to measure the fracture toughness of adhesive joints. Submitted to International
Journal of Solids and Structures; 2015.
C. Sarrado, A. Turon, J. Costa, J. Renart. An experimental analysis of the fracture behavior of
composite bonded joints in terms of cohesive laws. Submitted to Composite Science and
Technology; 2015.
Comptest 2015