Determining the fracture energy of structural adhesives from wedge-peel tests
A.C. TAYLOR* & J.G. WILLIAMS
Department of Mechanical Engineering, Imperial College London, South Kensington Campus,
London SW7 2AZ, UK.
Abstract
Analytical solutions for calculating the adhesive fracture energy from wedge-peel tests, where
significant energy is absorbed by deformation of the substrates, are outlined. These are based on
the analysis by Williams [J. Mater. Sci. 33, 5351-5357 (1998)]. A range of structural adhesives,
with fracture energies between 600 and 5300 J/m2, were used to bond aluminium-alloy substrates
of thickness 1 or 2 mm, and tested using a range of pin diameters (i.e. wedge thicknesses). Three
analysis methods were used, based on measuring either the radii of curvature of the substrates,
the crack length or the force per unit width during the test. All three methods gave good agreement
with the independently-measured values of the fracture energies (via linear elastic fracture
mechanics). The methods were applied successfully to both cohesive and interfacial failure. The
method using the force per unit width was the easiest to apply, and gave the best agreement with
the independently-measured fracture energies.
Keywords
Epoxy polymers; Toughness; Fracture;
Short Title
Determining fracture energy from wedge-peel tests
* Corresponding author:
Tel.: +44 20 7594 7149
Fax.: +44 20 7594 7017
email: a.c.taylor@imperial.ac.uk
1
Nomenclature
Roman:
b
Width
C
Compliance
E
Modulus
F
Force
Gc
Fracture energy
Ĝ
Elastic energy of substrates
h
Thickness
k0
Non-dimensional radius of curvature including elastic deformation
k0
Non-dimensional radius of curvature excluding elastic deformation
l
Crack length
m
Geometry factor
n
Hardening exponent
R0
Radius of curvature including elastic deformation
R0
Radius of curvature excluding elastic deformation
u
Effective wedge half-thickness
u0
Wedge half-thickness or pin radius
Subscripts:
a
Adhesive
s
Substrate
y
Yield
Greek:

Angle of curvature

Crack length correction factor

Strain

Coefficient of friction

Stress

Constant,h
2
1. Introduction
The use of structural adhesives in industry is increasing steadily, as manufacturers have become
aware of the advantages that adhesives can offer, compared with conventional joining techniques,
in the assembly of engineering components and structures [1-2]. Fracture tests can be performed
to measure the toughness of these adhesives [3]. However, in many applications there is extensive
plastic deformation of the substrates during failure of the component, for example in a vehicle frontend during a crash [4]. Hence manufacturers often prefer to test adhesives using a method where
there is extensive plasticity of the substrates, such as the wedge-peel method, rather than use a
linear elastic fracture mechanics approach, e.g. [3].
Previous work by one of the present authors [5] has discussed the use of the impact wedge-peel
(IWP) test, for which an International Standard (ISO 11343) test method [6] is available. That work
discussed in detail the application of the IWP test method to measure the resistance to cleavage
fracture of structural adhesives. The results from IWP tests, using a range of commerciallyavailable structural epoxy adhesives to bond either aluminium-alloy or steel substrates, were
described. Secondly, the IWP results were shown to correlate with the values of the adhesive
fracture energies, Gc, of the various adhesives, measured using fracture mechanics methods.
Finally, a finite-element model was developed to predict the value of the IWP cleavage force as the
crack propagates through the specimen from the value of the adhesive fracture energy, Gc, which
was independently-measured using linear elastic fracture mechanics (LEFM). However, the finiteelement model was rather cumbersome.
Thouless et al [7] used an analytical model to predict the toughness of plastically-deforming
bonded joints, but the predictions were much lower than the fracture energies determined via
LEFM [5]. A modified version of the Thouless et al analysis, by one of the authors of the present
work, showed much closer agreement [8]. Thouless et al [9] have also considered asymmetric
joints, where one substrate is thicker than the other.
The analysis used in the present work is an extension of the analysis of the peeling of flexible
laminates from a stiff substrate by one of the authors [10-11], the analysis of which is now being
incorporated into draft standards. The present, modified, analysis predicts the fracture energy of
the adhesive using the curvature of the substrates during the wedge-peel test. Note that the
fracture energy of the adhesive is much smaller than the total energy absorbed during failure of the
specimen. Many times more energy is absorbed by the plastic deformation of the substrates than
by the fracture of the adhesive. (This is the principle behind the energy-absorbing zones used for
crash protection in automotive applications [4].) The predictions will be compared to the values of
the adhesive fracture energy measured by LEFM. The present paper applies this analysis to the
3
wedge-peel test for the first time, and compares the predictions with experimental data for a range
of structural adhesives.
2. Theoretical
2.1 Introduction
This analysis is based on the more detailed, and wider ranging, cases given in Williams [12], and
more details are given in Appendix A. The solutions given are for small  , see Fig. 1, i.e.
sin    
l
 1 , where l is the crack length which can be measured.  is determined by the
R0
deformation beyond the crack tip and is given by [13]:
2

h E
     0.2  0.058  a  s
6hs Ea
 hs 
2
(1)
where h is the thickness and E is the modulus. The numerical terms give the deformation in the
arms, and ha and Ea refer to the adhesive layer. Here it is assumed that the crack is in the centre
of the adhesive. For Ea   , i.e. the infinitely stiff case,   0.66 and for a typical set of
numbers, i.e. hs  1 mm , ha  0.4 mm , E  70 GPa , Ea  3 GPa then   1.5 . These values
represent upper bound behaviour as they assume the maximum deformation of the root region. For
the heavily plastically deforming cases the effective stiffness of the base is much higher and a
lower bound occurs when   0 [13].
(Fig. 1)
In experiments there are four parameters which are usually measured; l , u, R0 and F . The value
of l has to be measured during the test and is often difficult to determine as the position of the
crack tip can be hard to identify. Similarly, the measurement of u can be problematic unless the
edge of the wedge and specimen lie in the same plane. The value of R0 can also be measured
during the test, though in many cases the specimen fails in an asymmetric manner such that the
radii of curvature on each side of the wedge are not equal. The non-dimensional radius of
curvature can be calculated using:
k0 
hs
2 y R0
(2)
4
where y is the yield strain. It may be more convenient to determine the radius of curvature after
the test, from the radius of the bent arms as in Thouless et al [7]. This measured value, of R0 , is
thus not the value at the crack tip but that after elastic unloading. For large plastic deformations the
change is not large but a correction can be made, and the true value k 0 may be derived from the
measured value, k 0 , from:
k 0
3
n
k0  k0
2n
(3)
For small angles we may relate l and R0 since 2 ≈ 2u/R0 and hence,
l
hs
u
1
 1 
 y hs k 0 2

(4)
Note that:
 u 
1

k0  
2
 h 
 y s   l   
 hs

(5)
so that finding k 0 from l requires good accuracy in l and a knowledge of  . If both R0 and l are
known then  may be determined.
If k 0 and  are known then:
1

 hs  y  2 12 
n  

 u  k 0 
1 
 4  1 n
Gc




k

1
Gˆ  2  n  0
1  n  
 hs  y  2 12 
 1    u  k 0 




(6)
 y hs
Gˆ 
2Es
(7)
where
2
5
where y is the yield stress. [See Appendix A for details of the derivation]. Upper and lower bounds
are determined by  and the lower bound (  = 0) is,
Gc
1 n
4n k 0

Gˆ 2  n  1  n 
(8)
F
 is measured then, [see Appendix A],
b
If 
1

 hs  y  2
1
1   
 
1

 u  2 y k 0 2
 F   4  1 n 


k 0 
1
 bGˆ   2  n 

 hs  y  2
1
  k 0 2
 1   
 u 








(9)
where  is the coefficient of friction. If  and  are known then k 0 can be found and hence Gc
from Eqn. 6. The lower bound is for     0 and is,
 
 n F
Gc  

1 n  b
(10)
It should be noted that this analysis ignores the elastic deformation and the result may be
corrected by adding Ĝ to the value of Gc computed from Eqn. 6.
In the present work, most of the specimen failure was asymmetric, i.e. the radii of curvature of the
two arms were not identical. It is possible to average the radii of curvature prior to calculating the
fracture energy. Such a method has been used by various authors, e.g. [7,14]. However, the
contribution to the total fracture energy from each arm can alternatively be calculated individually,
and then summed. This latter approach is the one used in the present work.
3. Experimental procedure
3.1. Materials
Several rubber-toughened structural epoxy adhesives were tested, as listed in Table 1. These
were chosen to represent a wide variation in toughness. The curing conditions, and the resulting
glass transition temperatures, Tg, are also shown in Table 1.
(Table 1)
6
Aluminium alloy substrates (grade EN AW 5754), which were 1 or 2 mm thick, were used for the
wedge-peel tests. The substrates were guillotined from the sheet to the required size of 20 ± 0.25
mm wide by 190 ± 1 mm long.
Aluminium alloy substrates (grade EN AW 2014A) were used for the linear elastic fracture
mechanics tests, which used tapered double-cantilever beam (TDCB) specimens [3]. The high
yield strength of this grade is required when testing tough adhesives, to avoid plastic deformation
of the substrates during the test. The beams were 10 mm wide by 310 mm long.
3.2. Tensile Testing
Tensile dumbbell specimens were machined from the aluminium alloy substrates. The tensile
specimens were tested in compliance with the standard [15] at a constant displacement rate of 1
mm/min, using a clip-on extensometer to measure the engineering strain within the gauge length.
The values of true stress and true strain were calculated. The Young’s modulus was calculated for
each of the four replicate samples, and a linear plus power law hardening model was fitted to the
data.
3.3. Specimen preparation
The bonding surfaces of the substrates were abraded by grit-blasting using 180/220 mesh alumina
grit, and cleaned with acetone. A chromic acid etch treatment was then used, by placing the
substrates into a bath of chromic-sulphuric acid at 69°C for 20 minutes. (The composition of the
bath is 40 litres distilled water; 7.2 litres sulfuric acid (s.g. 1.84); 3.87 kg sodium dichromate; 0.06
kg powdered aluminium and 0.1 kg copper sulfate. All obtained from Sigma Aldrich, Gillingham,
UK.) The substrates were removed, rinsed with tap water, and placed in a bath of tap water for 10
minutes. They were then rinsed with distilled water and dried in an oven at 60°C for 10 minutes.
Adhesive was then applied to each substrate, and spread using a spatula. A piece of stainless
steel wire was placed in the adhesive layer at each end of the joint to ensure a constant adhesive
layer thickness of ha = 0.4 mm. Two pieces of polytetrafluoroethylene (PTFE) film (Aerovac,
Keighley, UK), 50 mm long, were placed at one end of the specimen to create a pre-crack. The
substrates were brought together and clamped in a bonding jig, and the excess adhesive was
removed using a spatula prior to curing. After curing the adhesive, any more excess adhesive
present around the sides of the specimen was removed with a chisel. The edges of the specimens
were sanded and polished to provide a smooth edge for photography.
7
3.4. TDCB Specimen Testing
The tapered double-cantilever beam (TDCB) test was used to measure the adhesive fracture
energy, Gc, of the structural epoxy adhesives listed in Table 1. Prior to testing, the adhesive layer
was painted with white paint and a crack length scale was adhered to the side of the specimen.
Tests were conducted on a universal testing machine at a constant displacement rate of 0.1
mm/min, at room temperature (21 ± 2 °C). The tests were conducted in compliance with the
standard method [3]. Force, displacement and crack length data were recorded. The values of the
adhesive fracture energy were calculated using corrected beam theory [3], using:
GIC 
Fc2 dC

2b dl
(11)
where Fc is the force at failure, b is the width of the beam, C is the compliance and:
1

1
dC 8m 
 3 3 3 

1  0.43  l
dl Esb 
m 


(12)
where Es is the substrate modulus (69 GPa), and m is the geometry factor (2 mm-1) which is
defined as [3]:
3l 2 1
m 3 
hs hs
(13)
3.5. Wedge-Peel Specimen Testing
Tests were conducted on a universal testing machine at a crosshead speed of 15 mm/min, at room
temperature (21 ± 2 °C). Prior to testing, the specimen thickness was measured at three different
locations using a micrometer to ensure a uniform bond-line thickness of 0.4mm had been
achieved. The specimen arms were bent outwards over the region containing the PTFE starter film
to provide room for the wedge. The specimen was placed vertically on a compression platen, to
provide a rigid and level base. The diameter of the wedge was varied from 3 to 10 mm using
precision-ground dowel pins which were attached to a V-groove in the tip of the wedge using
cyanoacrylate adhesive (Superglue, Henkel, Winsford, UK), see Fig. 2. A scale was adhered to the
wedge to calibrate the photographs. Digital photographs were taken during the test, and the
corresponding load and displacement noted. Tests were conducted until a maximum displacement
of 80 mm was reached, or until the unbonded ends of the specimen contacted the test rig or
8
specimen. At least two specimens were tested, and at least three images of each test were
analysed. Three or four pin diameters were used for each combination of adhesive type and
substrate thickness.
(Fig. 2)
3.6. Analysis
The photos taken during the test, see Fig. 2 for example, were analysed using Microsoft Paint or
Visio software to determine the values of R0, u, and l for both arms of the specimens. Firstly the
crack tip was located by magnifying the image, and the value of Δ was calculated using Eqn. 1.
Secondly, three points were identified on each substrate between the crack tip and the wedge, and
on the circumference of the pin. A circle was fitted to each of these sets of points. A straight line
was drawn between the centre of each substrate circle and the centre of the pin circle. Where this
line crosses the pin circle is the contact point between the pin (wedge) and the specimen, allowing
the values of l and u to be determined. The radius of each substrate circle is equal to the radius of
curvature plus half the substrate thickness, allowing values of R0 to be calculated.
4. Results
4.1. Tensile Testing
The true stress vs. true strain data for the 1 and 2 mm thick substrates are shown in Fig. 3, with the
fitted linear plus power law hardening relationship. The data were fitted over the range of up to 6%
strain, as in Kawashita et al [16], which is larger than the maximum strains seen in the wedge peel
test. As both thicknesses of aluminium alloy showed very similar stress vs. strain characteristics,
the same relationship was used for both. The Young’s modulus of the fitted relationship is Es = 69
GPa, the work-hardening coefficient is n = 0.157, and the yield stress σy = 130 MPa, as shown in
Table 2.
(Fig. 3)
(Table 2)
4.2. TDCB Specimen Testing
All the linear elastic fracture mechanics specimens failed by stable crack growth, and the fractures
were always cohesive within the adhesive layer. For all the adhesives, a mean fracture energy is
quoted. For most of the adhesives, the measured value of the fracture energy, GC, was constant
with crack length. A fracture energy of 930 J/m2 was measured for ESP110, as shown in Table 3,
9
which agrees well with the values quoted by Kawashita et al [16] of 1050 J/m2, and by Blackman et
al [5] of 1060 J/m2. For the AV4600 adhesive, a fracture energy of 2940 J/m2 was measured, which
agrees well with the value of 3090 J/m2 quoted by Kawashita et al [16]. For the 4555B adhesive, a
fracture energy of 2630 J/m2 was measured. A fracture energy of 5300 J/m2, as measured by
Georgiou [17], was used for the 1493 adhesive. Significantly, this is one of the toughest structural
adhesives available.
(Table 3)
The specimens bonded with the E32 adhesive showed a rising resistance-curve (R-curve), where
GC increased from approximately 500 to 700 J/m2 over 100 mm of crack growth. This R-curve
behaviour is commonly observed for structural adhesives. A mean fracture energy of 610 J/m 2 was
measured for E32, as shown in Table 3. This value agrees well with the 650 J/m 2 quoted by
Blackman et al [5].
Thus the adhesives tested possess fracture energies from 610 to 5300 J/m2, which covers the
range of fracture energies typical of structural adhesives.
4.3. Wedge-Peel Testing
4.3.1 Introduction
Wedge-peel tests were performed using both 1 mm and 2 mm thick substrates. Buckling was
observed for the thinner substrates with the tougher adhesives. Reducing the specimen length
allowed tests to be performed successfully in many cases. Many of the wedge-peel specimens
failed in an asymmetric manner, i.e. the radii of curvature of the two arms were not identical.
Hence, for the analysis discussed above, the total fracture energy from each arm was calculated
individually, and then summed.
Note that the total energy absorbed during the test is equal to the peel force per unit width. For
example, for a 2 mm thick specimen bonded with the AV4600 adhesive the total energy is
approximately 20000 N/m = 20000 J/m2. By comparison, the fracture energy from LEFM is much
smaller, a Gc of 2940 J/m2 being measured. Therefore approximately 15% of the energy goes into
fracture of the adhesive, and approximately 85% into the plastic deformation of the substrates.
Hence the corrections are large, and so it may be expected that the errors from the analysis will
also be relatively large.
As discussed above, the analysis is valid for small angles of α. The values of α were calculated for
the wedge-peel tests, and varied from 0.15 to 0.46. Hence all of the angles comply with the
10
requirement. The dependence of the wedge-peel results on varying the power-law fits employed
was also investigated. It was found that although the experimental true stress vs. true strain data
could be modelled by a number of slightly different values for the power-law coefficients n and σy,
the resultant values of toughness generated by the models were not significantly altered.
From the equations presented above, three solutions will be used. In all cases Gc is calculated
using Eqn. 6, and as the data are measured during the test the elastic deformation is included.
Hence Ĝ is added to the result to allow for this. (For example, Ĝ is typically 255 J/m2 for the
AV4600 adhesive, which is less than 10% of Gc.) Firstly,  is calculated using Eqn. 1, and k0 from
Eqn. 2. Secondly,  is calculated using Eqn. 4, and k0 from Eqn. 2. Both of these methods require
image analysis of photographs taken during the test. The first method requires measurement of the
radius of curvature of the substrate, and the second requires that the distance from the crack tip to
the wedge contact point is measured.
Finally,  is calculated using Eqn. 1, and k0 from Eqn. 9. This method uses the measured force
per unit width, rather than requiring image analysis. However, values of the coefficient of friction, µ,
and of the effective wedge thickness, 2u, are required. A value of µ = 0.25 is assumed, which is a
reasonable value for contact between polished steel and polymer [18]. Analysis of the images from
the tests showed that u ≈ u0. This assumption is very reasonable for the less tough adhesives and
thinner substrates. For the tougher adhesives, such as AV4600, used with the thicker substrates
then the value of u tends to be about 10% less than u0.
To test the robustness and reproducibility of the analysis method, the sets of specimens have been
manufactured, tested and analysed by different people. As such the scatter in the experimental
data may be expected to be relatively large.
4.3.2 Fracture energy predictions from wedge-peel analysis
The predictions of the adhesive fracture energy for the specimens using 2 mm thick substrates will
be considered first. All failures were cohesive within the adhesive. The predicted values are shown
in Fig. 4, where the graphs are ordered by increasing adhesive fracture energy.
(Fig. 4)
The predictions of Gc from the wedge-peel tests agree well with the LEFM values from the TDCB
tests for all of the adhesives used. The worst agreement is for the ESP110 adhesive, which is
probably due to operator dependence.
11
The predicted Gc is approximately constant with pin diameter. Note that the complete range of pin
diameters is not available for all the adhesives for two possible reasons. The problems occur
mostly with larger pin diameters, especially for the 10 mm diameter pin. Firstly, interfacial failure
may occur in some cases, for example for the E32 adhesive with 2 mm substrates. Secondly, the
bending of the arms may be so asymmetric that it is not possible to calculate Ro for one arm, i.e. Ro
is very large. In this latter case, method 2 predicts a fracture energy that is small compared to the
other methods and the LEFM value. Inspection of the photographs shows that this is due to the
centreline of the adhesive not being aligned with the centre of the wedge, as the whole specimen
moves across so one substrate appears to deform only elastically. Hence the value of u used is
incorrect, as the assumption of u = u0 is no longer correct. Indeed good predictions are possible if a
value of u = 2u0 (i.e. the diameter of the pin or thickness of the wedge) is used.
The method that calculates Gc using k0 from Eqn. 9, i.e. from the measured F/b shows the best
agreement with the LEFM value. The other two methods give comparable results. The methods do
not consistently over- or under-predict Gc.
For the specimens using 1 mm thick substrates for the wedge-peel tests, the predicted values are
shown in Fig. 5. The specimens bonded with the tougher adhesives such as 4555B and 1493
tended to buckle during testing, so no data are available for these systems with 1 mm thick
substrates. The use of short specimens enabled some data to be obtained for the AV4600
adhesive, see Fig. 5b.
(Fig. 5)
For the E32 and AV4600 adhesives, failure was visually interfacial using the 1 mm substrates. For
cohesive failure, the predictions of Gc agreed well with the LEFM value as discussed above.
However, where interfacial failure occurs, the predictions would be well below the LEFM value.
This is because the full plastic zone is unable to form during interfacial failure; only half of the zone
can form due to the presence of the substrate. Hence it should be expected that the Gc of the
adhesive will be half that for cohesive failure. Fig. 5a shows the predicted values, with Gc/2 from
the LEFM tests. The agreement between the predicted and measured Gc values is good. This
shows that the analysis can be applied successfully to interfacial as well as cohesive failure.
Further, the value of fracture energy is independent of the thickness of the substrate.
It is thought that the higher stiffness of the thicker substrates maintains the crack more centrally
than for the thinner substrates, and hence encourages cohesive rather than interfacial failure as
observed in the present work. The T-stress has an effect on the stability of the crack; when the Tstress is higher, as will be the case with thicker substrates, then the crack path is more stable [19].
12
4.3.3 Comparison of analysis methods
The three analysis methods used are as follows. Firstly,  is calculated using Eqn. 1, and k0 from
Eqn. 2. Secondly,  is calculated using Eqn. 4, and k0 from Eqn. 2. Thirdly,  is calculated using
Eqn. 1, and k0 from Eqn. 9. All the methods use Eqn. 6, which is dependent on  , k0 and the
substrate properties (Es, y, y, n & hs).
The mean and standard deviation of the predicted fracture energies for each adhesive, for each of
the three methods, were calculated using the data for all the pin diameters and substrate
thicknesses available. These values are compared with the LEFM values in Fig. 6. The predictions
using all of the methods show good agreement with the independently-measured LEFM values,
and the standard deviations generally overlap. As expected, the standard deviations of the fracture
energies calculated from the wedge-peel data are greater than those from the LEFM tests. There is
some operator dependence, for example with the ESP110 adhesive, where the data show much
poorer agreement than for the other adhesives. However, when sufficient care is taken then very
good agreement is achieved.
(Fig. 6)
The analysis is not adversely affected by asymmetric failure, when the two radii of curvature are
not equal, which was commonly observed. However, when failure is so asymmetric that it is not
possible to calculate R0 for one arm, i.e. R0 is very large, then method 2 cannot be used in the form
outlined above.
The analysis can be applied successfully to interfacial failure, when Gc/2 is predicted, as well as
cohesive failure, when Gc is predicted. It is therefore important to identify the locus of failure from
the wedge-peel tests prior to using the predicted values.
Of these methods, generally the second method gives the worst agreement. From Fig. 6 it can be
seen that the standard deviations using this method are also relatively large. Equation 4 is used in
this method, which uses the value of the crack length, l. Hence it appears that the variability is
introduced to the predictions via the calculation of  via Eqn. 4. Here the value of l/h is used, and
squared to calculate k0. As the crack in the adhesive is fine close to the crack tip it can be difficult
to determine the value of l accurately, leading to errors and the relatively poor predictions. Other
work has shown that determining the crack length accurately is a general problem *ref. This
method requires careful lighting of the test and good focussing to ensure that the proper crack
length can be measured. Careful polishing of the specimen edge is also required.
13
The second-best agreement tends to be from the first approach. Here the value of  is calculated
using the geometry and the elastic properties of the materials (i.e. hs, ha, E & Ea). The value of k0 is
calculated from the measured curvature, R0, the specimen thickness, hs, and the yield strain of the
substrates, y. Hence only a single value, which is R0, needs to be measured during the test. As R0
is relatively large and clear compared to, say, the crack length, then it can be determined relatively
accurately. Indeed, Thouless et al [7] have also shown that the radius of curvature can be
successfully used to calculate the fracture energy of adhesives where there is extensive plastic
deformation of the substrates. This method does also require careful polishing of the specimen
edge, plus good alignment between the edge of the specimen and the end of the pin to ensure that
both are in focus.
The third method, which calculates Gc from the measured F/b shows the best agreement with the
LEFM values. This is not surprising as the value of the force, F, is the easiest to measure, as it is
recorded by the universal testing machine. It can also be considered to be accurate as the loadcell
is calibrated, and there will be no operator uncertainty as long as the force is zeroed before the
specimen is placed in the test fixture. If the values of F/b used are instantaneous values
corresponding to when the photograph is taken, then as the value of F/b is not constant, this may
lead to some uncertainty; though this tends to vary by only about 5% of the mean value during the
test. This uncertainty can also be overcome by using the F/b value averaged over the test. The
value of the coefficient of friction is unknown for the contact between the fracture surface and the
wedge, which will add uncertainty to the results. However, the assumption of µ = 0.25 works very
well.
5. Conclusions
An analytical model has been outlined which allows the adhesive fracture energy to be calculated
from wedge-peel tests, where much more energy is absorbed by deformation of the substrates
than by fracture of the adhesive. A range of structural adhesives were used, with fracture energies
between 600 and 5300 J/m2. These were tested using two thicknesses of aluminium-alloy
substrates and a range of pin diameters (i.e. wedge thicknesses). Three analysis methods were
used, based on measuring either the radii of curvature of the substrates, the crack length or the
force per unit width. All three methods gave good agreement with the independently-measured
values of the fracture energies (via linear elastic fracture mechanics). For example, the extent of
the correction required was from a total energy of 20000 J/m2 to a fracture energy of 2940 J/m2, i.e.
a correction of 85%.
14
The method which uses the force per unit width was the easiest to apply, and gave the best
agreement with the independently-measured fracture energies. The methods were applied
successfully to both cohesive and interfacial failure, where Gc/2 is predicted due to the restriction of
the plastic zone by the substrate. The predictions are unaffected by asymmetry in the test, except
where one of the radii of curvature is too large to measure.
Acknowledgements
The authors would like to thank the following final-year project students for their help with collection
of the experimental data and its analysis: Charles Betts, David Branton, Tom Ehrman, Nasir Ilyas,
Herwig Peters and Navdeep Riarh.
15
References
[1]
Petrie, E. M. Handbook of Adhesives and Sealants, (McGraw-Hill Professional, New York,
2007).
[2]
Kinloch, A. J. Proc. Inst. Mech. Engrs. G 211, 307-335 (1997).
[3]
BS-7991 Determination of the mode I adhesive fracture energy, GIC, of structural
adhesives using the double cantilever beam (DCB) and tapered double cantilever beam (TDCB)
specimens, (BSI, London, 2001).
[4]
Fay, P. A., and Suthurst, G. D. Int. J. Adhesion Adhesives 10, 128-138 (1990).
[5]
Blackman, B. R. K., Kinloch, A. J., Taylor, A. C., and Wang, Y. J. Mater. Sci. 35, 1867-1884
(2000).
[6]
BS-EN-ISO-11343 Adhesives - Determination of Dynamic Resistance to Cleavage of HighStrength Adhesive Bonds Under Impact Conditions - Wedge Impact Method, (ISO, Geneva, 2005).
[7]
Thouless, M., Adams, J., Kafkalidis, M., Ward, S., Dickie, R., and Westerbeek, G. J. Mater.
Sci. 33, 189-197 (1998).
[8]
Kinloch, A. J., and Williams, J. G. J. Mater. Sci. Lett. 17, 813-814 (1998).
[9]
Thouless, M., Kafkalidis, M., Ward, S., and Bankowski, Y. Scripta Materialia 37, 1081-1087
(1997).
[10]
Williams, J. G. J. Adhesion 41, 225-239 (1993).
[11]
Kinloch, A. J., Lau, C. C., and Williams, J. G. Int. J. Frac. 66, 45-70 (1994).
[12]
Williams, J. G. J. Mater. Sci. 33, 5351-5357 (1998).
[13]
Williams, J. G., Hadavinia, H., and Cotterell, B. Int. J. Solids Struct. 42, 4927-4946 (2005).
[14]
Pardoen, T., Ferracin, T., Landis, C. M., and Delannay, F. J. Mech. Phys. Solids 53, 19511983 (2005).
[15]
BS-EN-10002-1 Tensile testing of metallic materials. Part 1. Method of test at ambient
temperature, (BSI, London, 2001).
[16]
Kawashita, L. F., Moore, D. R., and Williams, J. G. J. Mater. Sci. 40, 4541-4548 (2005).
[17]
Georgiou, I., The fracture of adhesively-bonded aluminium joints for automotive structures,
(PhD, Imperial College London, London, 2003).
[18]
Greer, A., and Hancock, D. J. Tables, Data and Formulae for Engineers, (Stanley Thornes,
Cheltenham, 1984).
[19]
Chen, B., and Dillard, D. A. Int. J. Adhesion Adhesives 21, 357-368 (2001).
16
Figure Captions
Fig. 1: Wedge peel geometry and parameters used.
Fig. 2: Photograph of wedge peel test using 8 mm diameter pin, 4555B adhesive and 2 mm thick
substrates.
Fig. 3: True stress versus strain for aluminium alloy substrates, for substrate thickness of 1 and 2
mm.
Fig. 4: Predicted Gc versus wedge diameter for substrate thickness of 2 mm (cohesive failure) for
adhesives (a) E32, (b) ESP110, (c) 4555B, (d) AV4600, and (e) 1493.
Fig. 5: Predicted Gc versus wedge diameter, for substrate thickness of 1 mm (interfacial failure) for
adhesives (a) E32, and (b) AV4600.
Fig. 6: Predicted and measured Gc for adhesives used.
Fig. A1: Geometry of half of the wedge-peel test.
Fig. A2: Non-dimensional bending moment versus radius of curvature.
17
Tables
Table 1: Adhesives used in the current work
Adhesive
Manufacturer
Cure temperature
Cure time
(°C)
Glass transition,
Tg (°C)
E32
Permabond
60
60 min
56
ESP110
Permabond
150
45 min
104
4555B
Henkel
180
30 min
n/d
AV4600
Huntsman
180
30 min
91
1493
Dow
180
30 min
91
Notes: 1. Tg of 1493 from Georgiou [17].
2. Suppliers: Permabond, Eastleigh, UK; Henkel, Dusseldorf, Germany; Huntsman,
Duxford, UK; Dow, Nuneaton, UK.
Table 2: Fitted tensile stress-strain data for aluminium-alloy substrates
Substrate
EN AW 5754
Modulus, Es
Yield stress,
Yield strain, εy
(GPa)
σy (MPa)
(%)
69
130
0.19
n
0.157
Table 3: Fracture energy, Gc, from LEFM for adhesives used in the current work, for failure that is
cohesive within the adhesive.
Adhesive
Gc CBT (J/m2)
E32
610
ESP110
930
4555B
2630
AV4600
2940
1493
5300
18
Figures

R0
 
   y  
y 
hsh
u
n
(F/b)
u0
ha

l
Fig. 1: Wedge peel geometry and parameters used.
19
Fig. 2: Photograph of wedge peel test using 8 mm diameter pin, 4555B adhesive and 2 mm thick
substrates.
20
250
True Stress (MPa)
200
150
100
1 mm
2 mm
Fitted Curve
50
0
0
0.02
0.04
0.06
True Strain (mm/mm)
0.08
0.1
Fig. 3: True stress versus strain for aluminium alloy substrates, for substrate thickness of 1 and 2
mm.
21
700
600
GC (J/m2)
500
400
300
200
Method 1, chi eqn. 1, k0 eqn. 2
100
Method 2, chi eqn. 4, k0 eqn. 2
Method 3, chi eqn. 1, k0 eqn. 9
Gc LEFM (Cohesive)
0
3
4
5
6
7
Pin diameter (mm)
8
9
10
(a)
2500
2000
GC (J/m2)
1500
1000
500
Method 1, chi eqn. 1, k0 eqn. 2
Method 2, chi eqn. 4, k0 eqn. 2
Method 3, chi eqn. 1, k0 eqn. 9
Gc LEFM (Cohesive)
0
3
4
5
6
7
Pin diameter (mm)
8
9
10
(b)
22
3000
2500
GC (J/m2)
2000
1500
1000
Method 1, chi eqn. 1, k0 eqn. 2
500
Method 2, chi eqn. 4, k0 eqn. 2
Method 3, chi eqn. 1, k0 eqn. 9
Gc LEFM (Cohesive)
0
3
4
5
6
7
Pin diameter (mm)
8
9
10
(c)
4500
4000
3500
GC (J/m2)
3000
2500
2000
1500
1000
Method 1, chi eqn. 1, k0 eqn. 2
Method 2, chi eqn. 4, k0 eqn. 2
500
Method 3, chi eqn. 1, k0 eqn. 9
Gc LEFM (Cohesive)
0
3
4
5
6
7
Pin diameter (mm)
8
9
10
(d)
23
6000
5000
GC (J/m2)
4000
3000
2000
Method 1, chi eqn. 1, k0 eqn. 2
1000
Method 2, chi eqn. 4, k0 eqn. 2
Method 3, chi eqn. 1, k0 eqn. 9
Gc LEFM (Cohesive)
0
3
4
5
6
7
Pin diameter (mm)
8
9
10
(e)
Fig. 4: Predicted Gc versus wedge diameter for substrate thickness of 2 mm (cohesive failure) for
adhesives (a) E32, (b) ESP110, (c) 4555B, (d) AV4600, and (e) 1493.
24
700
600
GC (J/m2)
500
400
300
200
Method 1, chi eqn. 1, k0 eqn. 2
100
Method 2, chi eqn. 4, k0 eqn. 2
Method 3, chi eqn. 1, k0 eqn. 9
Gc LEFM (Interfacial)
0
3
4
5
6
7
Pin diameter (mm)
8
9
10
(a)
4500
4000
3500
GC (J/m2)
3000
2500
2000
1500
1000
Method 1, chi eqn. 1, k0 eqn. 2
Method 2, chi eqn. 4, k0 eqn. 2
500
Method 3, chi eqn. 1, k0 eqn. 9
Gc LEFM (Interfacial)
0
3
4
5
6
7
Pin diameter (mm)
8
9
10
(b)
Fig. 5: Predicted Gc versus wedge diameter, for substrate thickness of 1 mm (interfacial failure) for
adhesives (a) E32, and (b) AV4600.
25
6000
Method 1, chi eqn. 1, k0 eqn. 2
Method 2, chi eqn. 4, k0 eqn. 2
Method 3, chi eqn. 1, k0 eqn. 9
Gc LEFM (Cohesive)
5000
Gc (J/m2)
4000
3000
2000
1000
0
E32
ESP110
4555B
AV4600
1493
Fig. 6: Predicted and measured Gc for adhesives used.
26