International Journal of Adhesion & Adhesives 29 (2009) 67–76
Stress analysis in a classical double lap, adhesively bonded joint
with a layerwise model
Alberto Diaz Diaz
, Gilles Foret
, Alain Ehrlacher
Centro de Investigacio
n en Materiales Avanzados (CIMAV), Miguel de Cervantes 120, Complejo Industrial Chihuahua, 31109 Chihuahua, Chih, Mexico
Paris-Est - Institut Navier Ecole Nationale des Ponts et Chausse
es - LAMI 6-8 Avenue Blaise Pascal, Cite
Accepted 24 January 2008
Available online 16 February 2008
This paper focuses on stress analysis in classical double lap, adhesively bonded joints having constant layer thicknesses.
Several analytical methods found in the literature do not provide adequate information on stresses at the adherend/adhesive
interfaces. In these methods, the adhesive thickness is assumed to be small compared to that of the adherends and the stresses to be
uniform through the adhesive thickness. Herein, the model proposed by the authors can be considered as a stacking of Reissner–Mindlin
plates (six plates for a double lap joint). The equations based on stacked plates were applied to the geometry of a symmetrical, double-
lap, adhesively bonded joint. Finally, the model has been validated by comparing the model results with those of a ﬁnite element
r 2008 Elsevier Ltd. All rights reserved.
Keywords: Stress analysis; Peal; Layerwise model
Structural designers are interested in the strength
evaluation under service conditions. A reliable prediction
of stresses at locations where a high risk of crack initiation
exists is thus a necessary step in designing mechanical
structures. Simpliﬁed models [1–5] and solid ﬁnite element
calculations [6,7] show that in an adhesive joint, both
shear and normal stresses reach their maximum value
in the vicinity of the bond edges. These stress concentra-
tions often lead to the joint failure. In an adhesive joint,
three kinds of failure are possible. The ﬁrst is adhesive
failure, which occurs at the adherend/adhesive interface.
The second is cohesive failure, which occurs in the
adhesive. The last kind of failure is mixed: it starts out as
an adhesive crack and then quickly becomes a cohesive
In the majority of models employed for adhesive
joints, stresses are considered constant through the
layer thickness [1,8–10]. In addition, the shear stress
in the adhesive layer is often taken as a linear function of
the difference between the displacement of the outer
adherend and the displacement of the inner adherend
(see Fig. 1). These models, in classical terms are called
shear lag models. Their constitutive equations are detai-
led in Appendix A. In order, to correctly estimate the
failure in the adhesive layer, a more complex model is
needed for calculating the stresses at the adhesive/adherend
A more complex model is the layerwise model called
M4-5N (multi-particle model of multi-layered materials
with ﬁve kinematic ﬁelds per layer for an N layer laminate).
This model belongs to the family of multi-particle models
developed in [11–17].In, Hadj-Ahmed et al. used
a layerwise model to analyse the variations on the
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