Experimentally Calibrating Cohesive Zone Models for...
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Experimentally Calibrating Cohesive Zone
Models for Structural Automotive Adhesives
Mark Oliver
October 19, 2016
Adhesives and Sealants Council Fall Convention
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Outline
2
• Cohesive Zone Modeling (CZM) Introduction
• Experimental Measurement of Cohesive Laws
• Measuring Adhesive Joint Toughness at High Rates
• Rate dependent CZM
• Inverse Calibration Approach
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Cohesive Zone Modeling (CZM)
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Predicting Failure of Adhesive Joints
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Stress in Adhesive Layer
Bonded Joint
• Behavior of bonded joints
during crash events is a
significant concern
• Stresses in adhesive joints
can be highly complex
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δc
Cohesive Zone Modeling
5
Cohesive zone modeling is an approach for modeling failure of
adhesive joints in finite element analyses
The adhesive deformation/failure is defined by relating the applied
stress on the adhesive, σ, to the separation of the adhesive, δ :
Adhesive
σ
Adhesive
σ
δ
σ
Adhesive
σ
Adhesive
σ
δδC
σ(δ)
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Relationship to Material Properties
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σ
δδC
k J
Cohesive Zone Models captures several commonly measured
mechanical properties:
σmax
Material Property Related CZM
Parameter
Modulus, E Stiffness, k
Strength, σ Max Stress, σmax
Toughness, GC /JC J
Strain to Failure δc
Adhesive
σ
δ
Due to differences in the stress
state between a tensile specimen
and an adhesive joint, the
properties do not match exactly
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Measurement of Cohesive Zone Laws
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CZM Calibration
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• Cohesive Zone Models must be experimentally calibrated for
every adhesive
• Calibration can be done using standard test specimens widely
used in the adhesives industry
• For joint designers using finite element analysis, having the
cohesive zone model parameters allows them to predict
performance of joints made with different/new adhesives
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Measuring Traction-Separation Laws
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𝐽 = 0
𝛿𝑐
𝜎 𝛿 𝑑𝛿
𝜎 𝛿 =𝑑𝐽
𝑑𝛿
δ
J
σ
• The traction separation law is defined as the derivative of the J-
integral (J) with respect to the adhesive separation (δ).
• J and δ are both measureable using standard adhesive test
specimens.
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J-Integral
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𝐽 = Γ
𝑊𝑑𝑦 − 𝑇𝑖𝜕𝑢𝑖𝜕𝑥
𝑑𝑠
The J-integral is a measure of crack driving force and can be
applied to adhesive joints.
J has units of joules/meter2.
n
ds
P
P Γ
W = strain energy density
Ti = normal traction vector
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Measuring J-Integral for Adhesive Joints
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𝐽 =2𝑃𝑠𝑖𝑛( θ 2)
𝑏θ
Load, P
Load, P beam width, b
• The DCB specimen has a very simple J-Integral solution,
depending only upon the applied load, P, and the beam opening
angles, θ.
• The beam angles can be measured with digital image correlation.
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Measuring Crack Separation, δ
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• The crack separation, δ,
can be measured using
digital image correlation
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• Once we have
measured J as a
function of δ, we have
to differentiate:
• This is best done by
first fitting the data
with a smooth function
J vs. Adhesive Separation, δ
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0
500
1000
1500
2000
2500
3000
0 0.1 0.2 0.3 0.4
J I(J
/m2)
Adhesive Separation, δ (mm)
Experiment
Fit
𝜎 𝛿 =𝑑𝐽𝐼𝑑𝛿
Fit Parameters
E 1.5 GPa
σmax 28.4 MPa
JIC 2508 J/m2
δfail 0.12mm (48%)
Joint Toughness, JIC
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0
5
10
15
20
25
30
0
500
1000
1500
2000
2500
3000
0 0.1 0.2 0.3 0.4
Stre
ss (
MP
a)
J I(J
/m2)
Adhesive Separation, δ (mm)
Final Cohesive Zone Model
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Fit Parameters
E 1.5 GPa
σmax 28.4 MPa
JIC 2508 J/m2
δfail 0.12mm (48%)
Cohesive Zone Model
• The CZM for this
adhesive is shown
in red
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0
50
100
150
200
250
300
350
0 2 4 6 8 10
Load
(N
)
Load Line Displacement (mm)
Check – Simulated DCB Specimen
15
Experiment
CZM
We can check the cohesive
zone model accuracy by
simulating different tests to
compare the measured
and predicted
load/displacement profiles
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High Rate Measurement of Toughness
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Rate-Dependent Cohesive Zone Models
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δ
J
σ
• Adhesives can exhibit highly
rate-dependent properties.
• Rate-dependent Cohesive Zone
Models are required.
• MAT-240 in LS-DYNA is one
such model that is used in the
automotive industry
• To calibrate these models, we
need to measure toughness as a
function of loading rate
Increasing Rate
- J increases
- sigma max increasesσmax
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Impact-Rate Mode I Toughness
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θ1θ2
𝐽 =𝐸′𝑏3 𝜃1 −𝜃2 𝑠𝑖𝑛(𝜃1)
3𝐿2
L
2-7 m/s
• A dowel pin is driven into the sample at 2-7 m/s. The crack tip strain
rate is in the 100s per second.
• The J-Integral is calculated using the beam rotations measured by DIC
𝐸′ =𝐸
(1 − ν2)
width, b
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Impact-Rate Mode I Toughness
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• No measurement of load
• No measurement of crack length𝐽 =𝐸′𝑏3 𝜃1 −𝜃2 𝑠𝑖𝑛(𝜃1)
3𝐿2
θ1θ2
L width, b
Video duration = 14 ms
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0
1000
2000
3000
4000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
J I(J
/m2)
Normalized Test Time
휀 = 250 𝑠𝑒𝑐−1
휀 = 0.2 𝑠𝑒𝑐−1
휀 = 0.001 𝑠𝑒𝑐−1
Rate-Dependent Toughness
J curves for an
automotive adhesive
measured at three
loading rates
Impact DCB method
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0
1000
2000
3000
4000
0.0001 0.01 1 100 10000
Frac
ture
To
ugh
ne
ss, J
IC(J
/m2)
Crack Tip Strain Rate (s-1)
Rate Dependent Fracture Toughness
For finite element models,
the properties must be
provided as a function of
crack tip strain rate, which
can be experimentally
measured or simulated.
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Mode II Toughness: Elastic-Plastic ENF
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• Mode II ENF specimens for tough adhesives can be very large (~1 m in
length) if linear elasticity is to be guaranteed in the beams.
• Using the J-integral solution for the ENF specimen allows for some
plasticity in the beams during the experiment.
• The beam rotations, θ, at point A,B, C are measured with DIC.
𝐽 =𝑃
𝑏0.5𝜃𝐴 − 𝜃𝐵 + 0.5𝜃𝐶
P = applied load
b = specimen thickness
θA = beam rotation at point A
θB = beam rotation at point B
θC = beam rotation at point C
A C
B
• No measurement of crack length
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High Rate Mode II Toughness Measurement
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Video Duration = 7 msCrack location2.5 m/sec
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 1 2 3 4 5
J II(J
/m2)
Load Line Displacement (mm)
𝐽𝐼𝐼 =𝑃
𝑏0.5𝜃𝐴 − 𝜃𝐵 + 0.5𝜃𝐶
JIIC• This method can be done at
high rates using high speed
videography to capture the
specimen deformation
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Elastic-Plastic ENF J-Solution Validation
24
Using FEA, we can check that the test specimen dimensions are such that
the plastic deformation in the beams does influence the results.
0
5
10
15
20
25
30
35
40
45
50
0 0.1 0.2 0.3 0.4 0.5
Shea
r Tr
acti
on
(M
Pa)
Shear Displacement (mm)
Γ = 20kJ/m2
S = 45MPa
Assumed Cohesive Law
0
5
10
15
20
25
0 1 2 3 4 5 6 7 8 9 10
J-In
tegr
al (
kJ/m
2)
Displacement (mm)
Γ = 20.0 kJ/m2
JIC = 20.3 kJ/m2
𝐽 =𝑃
𝑏0.5𝜃𝐴 − 𝜃𝐵 + 0.5𝜃𝐶
“Measured” J value
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Inverse Calibration Approach
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Material Model Parameters
Parameter Mode I Value Mode II Value
Modulus (MPa) Experiment Experiment
Jo (J/m2) Experiment Experiment
Jinf (J/m2) Experiment Experiment
휀𝐺 Inverse calibration Inverse calibration
To/So (MPa) Inverse calibration Inverse calibration
T1/S1 (MPa) Inverse calibration Inverse calibration
휀𝑇/ 휀𝑆 Inverse calibration Inverse calibration
FG Inverse calibration Inverse calibration
26
• LS-DYNA MAT_240 has 16 parameters
• Measuring all of these accurately can be difficult
• One option is to measure a few parameters and use inverse
calibration methods to optimize the rest of the parameters
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Inverse Calibration Methodology
27
Fracture Experiment
Finite Element Model of
Experiment
Experiment
Model
Model Parameters to Be Solved For
Predicted Load-Displacement to
Experiment
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Model Parameter Optimization
28
Mode I
Mode II• Can optimize CZM to different
experiment types and loading rates
• The inverse calibration is done using
optimization software
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Summary
29
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Summary
30
• Cohesive zone modeling is an powerful method for predicting
adhesive joint failure that is becoming more widely used
• These models can be experimentally calibrated using industry-
standard test specimens
• High-rate toughness is particularly of interest for automotive
adhesives
• For joint designers using finite element analysis, having the
cohesive zone model parameters allows them to predict
performance of joints made with different/new adhesives