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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