Accurate and continuous adhesive fracture energy determination using an
instrumented wedge test
M. Budzik
a,b
, J. Jumel
a
, K. Imielin
´
ska
b
, M.E.R. Shanahan
a,
Ã
a
Universite
´
Bordeaux 1, Laboratoire de Me
´
canique Physique (LMP)—UMR CNRS 5469, 351 Cours de la Libe
´
ration, 33405 Talence Cedex, France
b
Technical University of Gdansk, Faculty of Mechanical Engineering, Department of Material Science and Engineering, Narutowicza 11/12, 80-952 Gdansk, Poland
article info
Article history:
Accepted 23 November 2008
Available online 30 January 2009
Keywords:
Aluminium and alloys
Fracture
Strain gauges
Wedge tests
abstract
The wedge test and the related double cantilever beam test are practical methods of assessing structural
adhesive fracture energy. In the former, and to a lesser extent the latter, a recognised problem is the
difficulty of following the length of the growing crack, required to calculate fracture energy with any
accuracy. We present a novel method of measurement of crack length that has the advantages of being
accurate and allowing continuous assessment of crack-length evolution during the failure process.
It is based on the attachment of a series of strain gauges to the outer surface of one of the beams
constituting the adhesive assembly. Surface strain measurements are interpreted directly using simple
beam theory. The method has been validated both with adhesive assemblies under failure conditions
and by tests undertaken on ‘‘artificial’’ joints, where ‘‘bonding’’ is effected by clamping adherends
together.
& 2009 Elsevier Ltd. All rights reserved.
1. Introduction
Of the various adhesion tests available for evaluating the
fracture strength of structural adhesive joints, the double
cantilever beam (DCB) and its close relative, the (so-called Boeing)
wedge test, are amongst the most versatile, and generally yield
the most reliable information about fracture energy (e.g. [1–11]).
With a judicious choice of test geometry, these systems lead to
relatively small adherend strains near the crack front [10,11].
As a result, local plastic strain, which leads to supplementary
energy dissipation, is relatively limited. The main difference
between the DCB and the wedge test is that in the former, fracture
occurs at an imposed rate of separation and in the latter, at
imposed separation. (The DCB also tends to be used with thicker
adherends.) Two adherends are bonded along (most of) their
length and with the DCB, a force is applied to each (for example in
a tensile testing machine), at the open end and perpendicular
to the joint, in order to force debonding [2]. The separation rate of
the two points of application of the force is maintained constant.
If the length of the opening crack (either within the adhesive or at
the interface adherend/adhesive, depending on type of failure) is
represented by a, it may be shown that the energy release rate,
equivalent to fracture energy, G
c
, follows a scaling rule of the form
G
c
$a
2
. Beam analysis based on the opening displacement and the
force applied allows a, and therefore G
c
, to be evaluated.
However, since the bending moment leading to failure
increases linearly with a, at constant applied force, crack growth
may accelerate and become unstable in certain cases. This
problem has been countered by the development of the more
refined, tapered double cantilever beam (TDCB) test, in which
stability is restored by using profiled adherends with thickness
increasing away from the region of force application (e.g. [4,12]).
(Also, in principle, crack length need not be measured directly.)
Notwithstanding, it is not always convenient, or even possible, to
use profiled adherends (for instance, when testing the adhesion
properties of automotive body assembly materials) and so an
alternative set-up is the so-called wedge test, which uses the
same geometry, generally of thin plates bonded together, but
the opening displacement is maintained constant by insertion of
the ‘‘wedge’’ [11]. Crack growth is then ‘‘driven’’ by the restitution
of stored, elastic, strain energy stored in the bent adherends,
mainly from the wedge up to the crack front [13]. A considerable
advantage is that the scaling relation becomes G
c
$a
À4
, leading
to stable crack growth at decreasing rate [14,15]. The disadvantage
is that, since the force exerted on the adherends by the wedge is
unknown, direct measurement of the crack length, a, is necessary
to calculate G
c
.
Adherend lengths are typically of the order of 10 cm, and
wedge thickness of the order of a few millimetres, and as a
consequence, the relatively small curvature of the beams means
that the evaluation of crack length may be delicate. Various
techniques have been used to study crack lengths in adhesion
tests. The most basic techniques rely on direct, or microscopic,
observations of the position of the crack tip, sometimes with the
ARTICLE IN PRESS
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/ijadhadh
International Journal of Adhesion & Adhesives
0143-7496/$ - see front matter & 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijadhadh.2008.11.003
Ã
Corresponding author. Tel.: +33 5 40 00 6611; fax: +33 5 40 00 69 64.
E-mail address: m.shanahan@lmp.u-bordeaux1.fr (M.E.R. Shanahan).
International Journal of Adhesion & Adhesives 29 (2009) 694–701