Key Engineering Materials Vols 488-489 (2012) pp 537-540
© (2012) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/KEM.488-489.537
Online: 2011-09-21
Finite Element Simulation on Failure Assessment of toughened epoxy
adhesives
P. Akbarzadeh a, Kh. Farhangdoostb
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Iran
a
po_akbarzadeh@yahoo.com, bfarhang@um.ac.ir,
Keywords: adhesive joints, Finite-element, energy release rate, R-Curve
Abstract. The prediction of the strength of adhesively bonded joints has been investigated using a
variety of failure criteria such as maximum stress or strain, and fracture mechanics approaches.
Fracture mechanics approaches based on the critical strain energy release rate, for crack propagation
are applicable to highly cross-linked structural adhesives and have the advantage of avoiding the
explicit consideration of the bi-material singularities inherent in adhesive joints.
In the present work, the finite-element simulation of such adhesive joint has been performed and the
R-curves of two different rubber-toughened epoxy adhesives were measured using double
cantilever beam (DCB) specimens. The FE results are applied to be compared with the experimental
results which were reported in the literature.
Introduction
The use of structural adhesives to bond composites and light weight alloys is now well established
within the aerospace and automotive industries. The characterization of adhesive joints using a
fracture mechanics approach is well established for mode I (the tensile opening mode) at slow rates
in a British Standard [1] and an International Standard [2].
The prediction of the strength of adhesively bonded joints has been investigated using a variety
of failure criteria such as maximum stress or strain, and fracture mechanics approaches. Fracture
mechanics approaches based on the critical strain energy release rate, for crack propagation are
applicable to highly cross-linked structural adhesives and have the advantage of avoiding the
explicit consideration of the bi-material singularities inherent in adhesive joints.
Crack extension in rubber toughened adhesive joints begins with the cavitation of rubber
particles followed by void growth and induced shear yielding of the matrix. These processes lead to
the progressive development of a damage zone consisting of yielded material and distributed microcracks. As the load on the joint increases, the largest micro-cracks coalesce to form a macro-crack,
which then grows as new micro-cracks and the damage zone advance into the adhesive layer.
During these early stages of fracture, the damage zone continues to expand ahead of the growing
macro-crack, leading to a progressive toughening of the joint as increasing amounts of strain energy
are dissipated by the plastic deformation and micro-cracking. This process results in the fracture
resistance curve (R-curve) of Gc versus the crack length. Eventually, the damage zone reaches a
steady-state size and the Gc becomes constant, no longer increasing with macro-crack length. This
steady-state value of Gc has been used to predict the ultimate strength of a wide range of adhesive
joints [3].
In the present work, the finite-element simulation of such adhesive joint has been performed and
the R-curves of two different rubber-toughened epoxy adhesives were measured using double
cantilever beam (DCB) specimens. The FE results are applied to be compared with the experimental
results which were reported in the paper by Ameli et al[4].
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Advances in Fracture and Damage Mechanics X
Finite element modeling
The DCB joint of Fig. 1 were modeled using finite elements (FE). Finite element analyses were
performed to calculate steady-state energy release rate values, Gc.
Fig. 1. Geometry of DCB (mode-I) specimen. All dimensions in mm.
The commercial code ABAQUS CAE (V 6.9) was used to create the finite element models.
Taking advantage of symmetry it was sufficient to model one half of DCB specimen only as shown
in Fig.2. The 24,000 element two-dimensional (2D) model used four-node bilinear plane strain
quadrilateral element with reduced integration (CPE4R). The finite element mesh was refined
within the region ahead of crack tip. Mesh sensitivity test was performed based on its influence on
variation of stress strain distribution ahead of the crack front.
The analyses were performed for two different adhesives (Table 1) and the AA6061-T6
adherends were modeled as elastic. The load pin displacement at the onset of propagation of each
crack length obtained from experimental test programme [4] were applied to the corresponding FE
models.
Fig. 2. Two-dimensional finite element model of a DCB specimen with a magnification of the adhesive elements in the
crack tip region.
Table 1. Mechanical and physical properties of adhesives 1 and 2 [4]
The load versus load pin displacement curves for five different crack growth events obtained
from FE analyses has been shown in Figure 3.
Key Engineering Materials Vols. 488-489
539
Fig. 3. Load vs. pin displacement up to adhesive crack extension with different initial crack lengths
corresponding to the steady-state Gc.
The steady-state energy release rate values obtained from FE analyses and its comparison
experimental results that reported by Ameli et al.[4] has been shown (Figs. 4 and 5).
Conclusion
The R-curves for two different toughened epoxy adhesive systems were measured using FE
modeling. The data could be fit to a bilinear model representing the rising part and steady-state
region of the R-curve. Figures 4 and 5 suggest that the results obtained from the FE analyses are in
good agreement with the experiments. Therefore it can be concluded that the FE modeling could be
applied to achieve reliable fracture prediction in adhesive joint structures and hence decrease the
need for extensive fracture test experiments over a wide range of cases.
Fig. 4. Typical R-curve of adhesive systems 1.
Fig. 5. Typical R-curve of adhesive systems 2.
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Advances in Fracture and Damage Mechanics X
References
[1] BSI. 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; 2001 [BS 7991].
[2]
ISO, Adhesives – determination of the mode I adhesive fracture energy GIC of structural
adhesive joints using double cantilever beam and tapered double beam specimens. ISO; 2009
[25217].
[3]
G.C. Jacob, J.F. Fellers, J.M. Starbuck, S. Simunovic. Crashworthiness of automotive
composite material systems. J Appl Polymer Sci. 92(5) (2003) 3218–25.
[4] A. Ameli, M. Papini, J.A. Schroeder, J.K. Spelt. Fracture R-curve characterization of toughened
epoxy adhesives. Engng Fract Mech. 77 (2010) 521–534
Advances in Fracture and Damage Mechanics X
10.4028/www.scientific.net/KEM.488-489
Finite Element Simulation on Failure Assessment of Toughened Epoxy Adhesives
10.4028/www.scientific.net/KEM.488-489.537
DOI References
[4] A. Ameli, M. Papini, J.A. Schroeder, J.K. Spelt. Fracture R-curve characterization of toughened epoxy
adhesives. Engng Fract Mech. 77 (2010) 521–534.
doi:10.1016/j.engfracmech.2009.10.009