TESTING, MATERIAL DATA AND IDENTIFICATION OF MODEL
PARAMETERS FOR TOUGHENED STRUCTURAL ADHESIVES
Dominik Teutenberg1), Gerson Meschut1), Michael Schlimmer2), Ulrich Kroll3), Anton Matzenmiller3)
1) University of Paderborn, 2) WWV Consulting GmbH, 3) University of Kassel
Paderborn, D-33098, Germany
dominik.teutenberg@lwf.upb.de
Introduction
Structural adhesives are widely used in industrial
applications to join components of different materials in
lightweight design. Therefore, it is mandatory to provide
reliable numerical simulations of the bondings in such
multi-material-designed components under various loading
conditions.
When calculating adhesive bonds, two basic tasks arise:

determining stresses in the adhesive layer in relation
to external loads and other constraints,

and determining stress limits that lead to functional or
structural failure of the joint.
Generally, a non-homogenous, multiaxial state of stress
exists in the adhesive layer. Therefore, an appropriate
material equation, yield stress hypothesis and failure
conditions are required for a FE-analysis. Material
equations and failure conditions for multiaxial loaded
adhesive layers can only be determined by testing
adhesively joined specimens under homogenous stress
conditions. This means a great deal of experimental effort.
A nearly homogenous shear stress distribution exists in the
so-called double hollow cylinder sample as described in
ASTM E 229 and ISO 11003-1. First known experiments
with these types of adhesively bonded samples can be
traced back to MÜLLER (1959) [1], KUENZI and
STEVENS (1963) [2] and BOSSLER among others (1968)
[3]. ENGASSER and PUCK conducted combined tensiontorsion experiments (1980) [4], and SCHLIMMER
published a yield stress hypothesis for adhesively bonded
joints based on the invariants of stress tensors (1982) [5].
Based on this work, the first research project in Germany
[6] began with the cooperation of the automobile industry
in 2000. These research projects of the research association
Forschungsvereinigung Stahlanwendung (FOSTA) were
founded by the AiF under the program for the promotion
of joint industrial research and development (IGF) by the
federal ministry of economics and technology and Stiftung
Stahlanwendungsforschung. Affiliated research continued
[7,8] with the goal of FE-simulating the mechanical
behaviour of large adhesively bonded structures in
automobile manufacturing under a variety of loads, from
crash to fatigue to temperature change conditions.
Experimental System
The stress–strain behaviour of an adhesively bonded joint
under quasi-static load can be determined on bluntly
bonded cylinder samples under shear and tension load
according to ISO 11003-1. When compared with the thick
adherend shear specimen (ISO 11003-2), the cylinder
sample can be tested under torsion load. This loading
results in an almost homogenous shear stress distribution
within the adhesive layer between the cylinder halves. That
is why this experiment provides the best and most
reproducible results for testing the mechanical behaviour
of adhesive bonds.
In order to compile a material equation for adhesives, a
shear stress-shear strain correlation as well as a tensile
stress-strain correlation is needed. In contrast to the tension
test of bulk adhesive specimen, the thin adhesive layer is in
a uniaxial strain state, which results in a high hydrostatic
tensile stress. SCHLIMMER developed testing equipment
in the 1990’s to determine the strain behaviour of thin
adhesive layers in a cylinder specimen with uniaxial and
combined shear-/normal stress (Figure 1a). It was possible
to determine the complex mechanical behaviour of an
adhesively bonded joint. The adhesive layer’s reaction to
exterior load is measured using a biaxial deformation
sensor (Figure 1b). Adherend deformations are eliminated
by measurement software in order to measure and control
tension and shear strains within the adhesive layer.
Constant adhesive layer strain rates under tension and/or
shear loads are controlled with a PID feedback control
system.
Figure 1: a) Testing machine for tension / torsion loads
b) Cylinder specimen with biaxial deformation
sensor [9]
Results and Discussion
50
A flexibilized and toughened heat curing epoxy adhesive
for car body structure is investigated: Betamate 1496V
from DOW. The experimental results of tests with four
different strain proportions are displayed in Figure 2: pure
shear strain, pure tensile strain as well as two combined
strains. The slopes of the curves within the linear elastic
course are similar, regardless of the strain combination.
This permits the determination of elastic material
parameters for shear modulus, tensile modulus and
POISSON’s ratio, whereas the yield points and maximum
stresses depend on the strain combination.
40
40
40
30
30
xy [MPa]
x [MPa]
20
10
Zug- / Torsionsversuche
tension
and shear tests
d
10-3-3s-1s-1
d11 // dt
dt==11·10
epoxy
adhesive
Klebstoff: EP 13
adhesive
layer
thickness: 0.2 mm
Fügeteile:
Stahl
tensile
strain:
Klebschichtdicke:
0,2 mm
xy / 2x = 0
Zugbeanspruchung:
20
xy / 2x = 0
combined strain:
Kombinierte
xy / 2x Beanspruchung
= 0.5
2xx ==20,5
xy
// 2
xy
10
xy / 2x = 2
0
0,00
0.00
0,25
0.25
0,50
0.50
x [-]
0
0,0
0.0
0,5
0.5
1,0
1.0
xy / 2x = 
Figure 2: Stress-strain behaviour of a toughened EPadhesive with uniaxial and combined shear/normal strain. [6]
Figure 2 shows the results of the uniaxial and combined
shear-/normal strain tube specimens’ yield stress and
maximum strength and their dependence on one another. A
curve drawn through these points is labelled as yield
strength curve or maximum stress curve and is in general a
state of stress function.
𝐹 = 𝐹(𝜎𝑥 , 𝜎𝑦 , 𝜎𝑧 , 𝜏𝑥𝑦 , 𝜏𝑦𝑧 , 𝜏𝑥𝑧 )
(1)
Because the yield condition at isotropy is invariant against
coordination transformation, the following applies:
𝐹(𝐽1 , 𝐽2 , 𝐽3 )
(2)
𝐽1 , 𝐽2 and 𝐽3 are the stress tensor’s invariants. The tensor’s
split into deviator and spherical tensor leads to the
invariants 𝐽2′ , 𝐽3′ of the stress deviator. For slightly plastic
compressible materials the yield potential can be written as
𝐹(𝐽1 , 𝐽2′ , 𝐽3′ ). The invariants 𝐽1 , 𝐽2′ are determined for the
experimental yield strengths and maximum strengths from
Figure 2 by
𝐽1 =
1+𝑣
1−𝑣
1 1−2𝑣 2
𝜎𝑥 , 𝐽2′ = (
3
1−𝑣
) 𝜎𝑥 2 + 𝜏𝑥𝑦 2
Spannungsmaximum
maximum stress
1/2
(J2')
20
yield
strength
Fließgrenze
10
0
0
25
50
75
(3a,b)
by taking into consideration the prevention of transverse
strain within the experiment. This leads to Figure 3.
100
125
J1 [MPa]
Figure 3: Description of yield strength and maximum
strength as invariants of the toughened EP. [6]
Non-linear relationships between the stress tensor’s first
invariant 𝐽1 and the stress deviator’s second invariant 𝐽2′ are
shown for yield strength and stress maximum. These can
be described using the following equation taken from [10]:
1
1
3
3
(4)
𝑎1 and 𝑎2 are free parameters to be experimentally
determined, 𝜎𝐹 is the yield stress. The shear-based
equivalent stress condition is obtained by redefining the
yield limit as
1
1
3
3
𝜏𝐹 2 = 𝐽2′ + 𝑎1 𝜎𝐹 𝐽1 + 𝑎2 𝐽1 2
Yield condition and strength diagram
13
30
𝐹 = 𝐽2′ + 𝑎1 𝜎𝐹 𝐽1 + 𝑎2 𝐽1 2
shear strain
xy / 2x = ∞
Schubbeanspruchung
xy [-]
[MPa]
Klebstoff:
EP
epoxy
adhesive
(5)
A physical explanation for this yield condition is outlined
in [6]. Based on these results, a rate-dependent I1-J2plasticity theory with continuum damage is chosen to
describe the inelastic mechanical behaviour of the
adhesive. The constitutive equations comprise in addition a
non-associated flow rule, a non-linear hardening
assumption and an isotropic damage model of the
KACHANOV-RABOTNOV type with plasticity driven damage
evolution [06, 07, 11] to account for stiffness and strength
degradation of the adhesive layer. For use in
crashworthiness analysis, the rate-dependency of the yield
strength is modeled with the JOHNSON-COOK approach.
The material equations for toughened adhesive polymers
(TAPO) are implemented into the commercial finite
element (FE) software LS-DYNA [12], verified as shown
below in Figure 6, and validated at various experimentally
based test examples. The TAPO-model is available for
large-scale simulations in research and industrial
applications. With regard to the identification of the model
parameters pi, the best characteristic values pi,opt may be
even determined by hand or numerically optimized with
the help of the commercial optimization tool LS-OPT [13]
by minimizing the mean square error between the
computed results from the FE-simulation and the test data
for some chosen quantities of the bluntly glued, thinwalled specimen at hand.
Figure 4: FE-model of
two bluntly glued,
thin- walled cylinders
Due to the high stiffness of the bonded steel parts
compared to the adhesive layer, only an excerpt is modeled
for the FE-analysis. While the adhesive (blue) is
represented by a single layer of 32 eight-node-solid
elements along the circumference and one hexahedron in
radial direction, 160 fully integrated linear bricks are used
for the adherends (red). The loading is applied by a rigid
ring (green) connected to the upper adherend’s free end,
whereas the lower boundary of the bonded cylinder is
fixed. The shear and normal strain in the bond
𝜀 = ln (1 +
∆𝑁
𝑑𝑘
) and 𝛾 = arctan (
∆𝑇
𝑑𝑘 +∆𝑁
)
(6)
depend on either the measured ( )exp or computed ( )fem
values of the displacement jumps ΔT,N across the adhesive
layer in tangential and normal direction. In order to
regulate the jumps ΔT,c and ΔN,c for the feedback control
testing system close to the target value αtar, the error eexp is
minimized between a given, desired strain proportion αtar=
0.0, 0.5, 2.0, or ∞ and its experimental output αexp for the
strain ratio α=γ ∕ 2ε.
Figure 6: Verification of model and identified param. pi,opt
Conclusions
The bluntly glued, thin-walled cylindrical specimen is
presented to investigate the mechanical behavior of
structural adhesives. A nearly homogenous state of stress
due to defined torsion, tension or compression and any
combination may be achieved in the bonding layer. The
double hollow cylinder provides valid test data for the
determination of the adhesive’s model parameters and for
the numerical simulation of joint failure in bonded
components. As a result of verification and validation of
the computational model, it may be concluded that the
specimen at hand allows for a robust computer aided
design of adhesively assembled components to predict
deformation and failure of their bonds.
Acknowledgements
The authors gratefully acknowledge financial support of
AiF under the program for the promotion of joint industrial
research and development (IGF) by the federal ministry of
economics and technology through FOSTA together with
Stiftung Stahlanwendungsforschung.
Figure 5: Feedback control system and loop dashed line
for identification of model parameters pi
References
The output variables yi={ΔT ,ΔN, F, M, α} comprise either
the experimental yi,exp or the computed values yi,fem. From
the axial force F and the torsional moment M, the
engineering shear and normal stress of the FE-analysis and
the experiment are computed as τxy=M/W and σx=F∕A0,
where A0 denotes the initial cross-sectional area and W the
section modulus of the specimen. The model error efem
between the FEM simulation yi,fem and the output yi,exp of
the testing system may be reduced up to a minimum by
feeding improved estimates pi for the material parameters
into the FEM model with the help of LS-OPT. The
procedure may be repeated until the identification method
provides the final model parameters pi,opt for the best fit.
Note, the feedback in the control system uses purely
experimental data. The model is only unilaterally coupled
to the loop of the controlled testing system. The normal
and tangential stress-displacement output of the FEsimulation and the testing system are displayed in figure 6
- taken from [14] - for the various strain proportions α
given above.
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