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
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
Cohesive Zone Modeling (CZM)
3
Predicting Failure of Adhesive Joints
4
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
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)
Relationship to Material Properties
6
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
Measurement of Cohesive Zone Laws
7
CZM Calibration
8
• 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
Measuring Traction-Separation Laws
9
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.
J-Integral
10
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
Measuring J-Integral for Adhesive Joints
11
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.
Measuring Crack Separation, δ
12
• The crack separation, δ,
can be measured using
digital image correlation
• 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
13
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
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
14
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
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
High Rate Measurement of Toughness
16
Rate-Dependent Cohesive Zone Models
17
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
Impact-Rate Mode I Toughness
18
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
Impact-Rate Mode I Toughness
19
• No measurement of load
• No measurement of crack length𝐽 =𝐸′𝑏3 𝜃1 −𝜃2 𝑠𝑖𝑛(𝜃1)
3𝐿2
θ1θ2
L width, b
Video duration = 14 ms
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
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.
Mode II Toughness: Elastic-Plastic ENF
22
• 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
High Rate Mode II Toughness Measurement
23
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
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
Inverse Calibration Approach
25
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
Inverse Calibration Methodology
27
Fracture Experiment
Finite Element Model of
Experiment
Experiment
Model
Model Parameters to Be Solved For
Predicted Load-Displacement to
Experiment
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
Summary
29
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