FINITE ELEMENT SIMULATION OF STRUCTURAL
ADHESIVES AND ADHESIVELY BONDED JOINTS AND
EXPERIMENTAL VERIFICATION BY NONCONTACTING STRESS-STRAIN ANALYSIS
P. L. Geiss, S. Gramsch, D. Vogt
University of Kaiserslautern, Workgroup for Materials and Surface Technologies,
Gottlieb-Daimler-Strasse, D-67663 Kaiserslautern, Germany, [email protected]
ABSTRACT
The thick-adherend tensile–shear test according to ISO 11003-2 is widely used to
characterize adhesively bonded joints. However, the accurate measurement of
deformations close to the bondline is still a challenge, especially for structural adhesives
with high moduli. In this paper a method of using finite element simulation to evaluate
and adjust data from non-contacting video extensometry strain-measurements is
discussed.
FEM, simulation of adhesives, bonded joints, non-contacting stress-strain-analysis,
compensation
INTRODUCTION
A widely used method to analyze the shear-stress strain behaviour of adhesives is the
thick-adherend tensile-shear test according to ISO 11003-2. To determine shear strains,
optical or mechanical extensometers are usually applied on the front side of both parts
of the specimen close to the end of the overlap area. The overall extension reading thus
includes deformation of the adhesive as well as deformation of the adherend. In this
paper a new method (dot measurement) is used and the results are compared to the
strain measurement using simple gauge marks. The finite element simulation (FEM) is
applied to correlate the results of both different measurement methods and to derive a
correction function.
EXPERIMENTAL METHODS
Non-contacting videoextensometry
To measure shear strain the non-contacting video extensometry is used. This technique
is based on an optical displacement-measurement using high resolution CCD-cameras.
The deformation of a sample can either be measured by the application of gauge marks
at the joints edges or the application of a grit of dots close to the adhesive layer (fig. 1).
Fig. 1: Gauge mark and dot measurement – measuring point positions
FE-simulation
The finite element simulation (FEM) is a widely spread and effective tool to analyze
and predict stress-strain distributions. Its use related to adhesive joints is already
discussed in [1] and [2]. In this study the MARC/Mentat 2005r software package from
MSC was used. The mesh was composed of 10 hexahedral 8-node elements across the
thickness of the adhesive layer (d=0.2mm), 50 elements covering the width of the joint
(25mm) and 400 elements in the longitudinal direction of the overlap area (12.5mm). To
avoid mesh-dependent effects the number of elements in the cross section of the
adhesive layer varies to maintain a constant element size independent of the bondline
thickness. On the basis of data obtained from bulk specimen the material properties of a
one-component epoxy based structural adhesive were characterized by Young’s
modulus and the Poisson ratio. For plasticity a workhardening function σ = σ(εplastic) is
determined from shear tests, using the dot measurement variant. The bonded parts are
simulated as linear-elastical applying the von Mises yield criterion.
RESULTS AND DISCUSSION
Experimental results
Depending on the measurement method
different results are obtained leading to
differences in the τ-γ-behaviour (fig. 2).
Linear gauge marks result in a lower shear
modulus (GGM = 206 MPa) compared to the
use of the dot measurement (GDM = 640 MPa).
A comparison with the shear modulus G =
E/2(1+µ) = 615 MPa determined from
uniaxial tensile tests (bulk specimen) reveals
the dot measurement to be more accurate
because the measurement takes place closer to
Fig. 2: τ-γ-behaviour at different
the bondline. Despite this advantage the gauge
strain measurements variants
mark variant is more popular due to the
easiness in application and less scattering
leading to a higher resolution due to the possibility of integration along the length of the
marker.
Simulation results and validation
Fig. 3 compares experimental and simulated σ-ε-curves from uniaxial tension tests. Fig.
4 displays experimental and simulated τ-γ-curves from thick-adherend tensile sheartests for two different bondline thicknesses (d=0.2mm and d=3mm). Correlating with
[3] the shear modulus increases with an increasing bondline thickness (fig 4).
Furthermore the results feature a good correlation between simulation and experiment.
Fig. 3: Correlation experiment/simulation
at uniaxial tension
Fig. 4: Correlation experiment/simulation
at different bondline strength (shear)
Correction of the experimental shear strain data by FE-simulation
Simulated τ-γ-curves are determined at marker positions (fig. 5) similar to the
experimental measurement via gauge marks and dots. Fig. 6 illustrates how simulated τγ-curves correlate with the experimental data for different positions of the marker.
Fig. 5: Positions of the markers
Fig. 6: Correlation experiment/simulation at
different positions of the markers
The simulated results allow the generation of a correction function as follows:
ξ (τ ) =
γ GM (τ )
γ DM (τ )
γDM(τ): shear strain, analogue to dot measurement
γGM(τ): shear strain, analogue to gauge mark measurement
The function ξ( τ) depends on the thickness
of the adhesive layer, so a FE-based
correction function can be derived for
various bondline thicknesses (see fig. 7).
Below the yield point the correction factors
remain constant. After the yield point they
decline linearly until reaching a threshold
value ξ( τmax) = 1. By this approach it is
possible to reduce the FE-model to a
simple linear-elastic model with a single
load step correlating to a shear stress within
the range 0<τ<τyield and to approximate the
Fig. 7: Correction functions
complete correction function by a bilinear
function. In return only Young’s modulus,
Poisson ratio, the yield point and bond
strength need to be experimentally
predetermined. The thickness dependent
value of ξ( τ<τyield) is derived directly
from the FE-simulation. The function
above the yield point can be derived by
linear regression between the starting point
(ξ( τ<τyield); τyield) and the end point (1;
τmax). As depicted in fig. 8 the application
of the correction function with the
Fig. 8: Corrected characteristics
experimental data from gauge mark
measurements leads to a similar
characteristics, as using the dot measurement variant.
CONCLUSION
In this paper a method of using finite element simulation to evaluate and adjust data
from non-contacting video extensometry strain-measurements is discussed and applied
to data from thick-adherend tensile–shear tests. By using sample specific correction
functions obtained from finite element simulation the accuracy of measurements with
linear markers on the surface of the specimen could be enhanced to match the results of
more sophisticated but more laborious dot-measurements on the edge of the specimen
close to the bondline.
References
[1] Adams, R. D.; Wake, W. C.: “Structural Adhesive Joints in Engineering”; Elsevier
Applied Science Publishers, 1984
[2] Schlimmer, M. u.a.; „Berechnung und Auslegung von Klebverbindungen“; Teil 19, Adhäsion – Kleben & Dichten, Jahrgang 2004 Heft 5-12, Jahrgang 2005 Heft 1-3
[3] Habenicht, G.; „Kleben - Grundlagen, Technologie, Anwendung“; Springer-Verlag
2006