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A.A. PirondiPirondi

DepartmentDepartment ofof IndustrialIndustrial EngineeringEngineering

University of Parma,University of Parma, ItalyItaly

Meeting sul tema

Gli Adesivi StrutturaliL'incollaggio all'origine dell'innovazioneindustriale del futuro

26-27 Giugno 2006

Vercelli

COHESIVE ZONE MODELLINGCOHESIVE ZONE MODELLINGOF TOF T--peel JOINTS FAILUREpeel JOINTS FAILURE



AGENDA

•Introduction

•Objectives

•Modelling

•Results and discussion

•Conclusions



INTRODUCTION

COHESIVE ZONE MODEL

Cohesive fracture mechanisms

Atomic bonds Yield strip Intergranular bridging

Fibre bridging Multiple crackingGearing and friction

Cohesive Zone Description

σ(δ)δ

a



INTRODUCTION

EXAMPLES OF ADHESIVE JOINT FAILURE SIMULATION WITH CZM…

• T-peel joint (Thouless et al., 1999)

• Separation from interface corners (Liechti, Mohammed, 2000)

• Rate-dependent fracture of DCB joints (Siegmund et al., 2002)

• Ceramic-to-ceramic metal adhesives (Tvergaard, Hutchinson, 1996)

• Internal flaws (Jensen, Feraren, 2004)



INTRODUCTION

...AND SOME POTENTIAL APPLICATIONS IN ENGINEERING DESIGN

•Stiffener delamination

•Crash and collapse

(including joints)



INTRODUCTION

Cohesive Zone Model of adhesive joint

Intrinsic fracture

properties of theadhesive layer

Adherend contribution

(elastic and plastic)

From: Hutchinson, Evans, Acta Mater. 48, 2000, 125-135



INTRODUCTION

Viscoplastic dissipation

Decohesion work(intrinsic propertyof the adhesive)

Adhesive behaviour

“Constraint” to deformation

= plasticzone

i n c r e a s i n g

a d h e r e n d

t h i

c k n e s s

h

h/2

crack tip

From: Martiny et al., Proc. Adh. Sociecty, USA, 2005

Cohesive Zone Model + adhesive layer



OBJECTIVES

• Calibration of the CZ parameters on DCB joints fracture experiments

• CZ and CZ + adhesive layer (CZA)

• Simulation of T-peel tests and comparison with experiments.



EXPERIMENTS

DCB

•Loctite Multibond 330 ®

ta = 0.25mm•Aluminum alloyt = 15mm

T-peel•Loctite Multibond 330 ®

ta = 0.1mm•Unalloyed steel

t = 1.5mm(courtesy Prof. M. Rossetto,Polytechnic of Turin, Italy)

Δ’= 1mm/min Δ’= 2.5mm/min



EXPERIMENTS

Loctite Multibond 330 ® bulk tensile behaviour

0

1

2

3

4

5

6

7

8

9

10

0 0.005 0.01 0.015 0.02 0.025

Strain (mm/mm)

S t r e s s ( M

y = -0.149x - 8E-06

-4.00E-04

-3.00E-04

-2.00E-04

-1.00E-04

0.00E+00

0 0.001 0.002

εx (mm/mm)

ε y ( m m / m

E = 878MPa

ν = 0.15

Rp0.2 = 5.6MPa

R = 8.6MPa

A% = 2.14%

F

F

x

y

28

22

55

thickness = 1mm

From: Pirondi, Nicoletto, Proc.IGF 2000, Bari, 2000



MODELLING

•Adherend8 node, plane stress,

reduced integration

•Cohesive Zone4 node cohesive element

•Adhesive (CZA modelsonly)4 node, plane strain(hybrid formulation)

F, δ

F, δ

F,δ

F,δ

•Failure within adhesive(cohesive failure)



MODELLING

Adherend

Cohesive Zone

Adhesive

CZA models

CZ only models

DCB

T-peel

DCB

T-peel



RESULTSEXAMPLE OF SIMULATION RUN ON DCB



CZM calibration

RESULTS

0

200

400

600

800

1000

1200

1400

1600

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Opening, δ (mm)

L o a d ,

F (

Experiment

Triangular law, c1=0.01, sm=10MPa

Triangular law, c1=0.01, sm=5MPa

Triangular law, c1=0.01, sm=2.5MPa

Γ0 = GIc = 550J/m2

partial unloading to evaluatethe compliance (crack length)

bounds for CZ calibration



CZM calibration

RESULTS

0

200

400

600

800

1000

1200

1400

1600

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Opening, δ (mm)

L o a d ,

F (

Experiment

Trapezoidal law, c1=0.2, c2=0.5

Triangular law, c1=0.01

Exponential law

σm = 5MPa



CZM calibration

RESULTS

0

200

400

600

800

1000

1200

1400

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Opening, δ (mm)

L o a d ,

F

(

Experiment

CZ + adhesive layer

CZ only

Γ

0

= 450J/m2

σm = 6MPa

Γ0 = 550J/m2

σm = 5MPa



T-peel simulation: CZ only

RESULTS

0

100

200

300

400

500

600

700

800

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Displacement (mm)

L o a d (

Experiment

Simulation

• Lower adhesive layer thickness (0.1mm) compared to DCB (0.25mm)

- increase of stiffness → σm = 5*0.25/0.1 = 12.5MPa- possible influence on Γ0 not considered

Γ0 = 550J/m2

σm = 5*0.25/0.1 = 12.5MPa



T-peel simulation: CZA

RESULTS

0

100

200

300

400

500

600

700

800

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Displacement (mm)

L o a d (

Experiment

Simulation

Γ0 = 550J/m2

σm = 5MPa

• Adhesive layer modelled in addition to the cohesive zone

- Γ0 and σm as calibrated on DCB



0

100

200

300

400

500

600

700

800

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Displacement (mm)

L o a d (

Experiment

Simulation

6

8

10

12

14

16

18

0 1 2 3 4 5

Distance [mm]

σ m [ M P a

T-peel simulation: CZA

RESULTS

Γ0 = 550J/m2

• Transient initial cohesive strength = peel stress for tensile failure (FE analysis)

• Steady-state fracture cohesive strength = DCB-calibrated*(influence of adherend

material)*(influence of ahesive thickness) ⇒ σm = 5*1.18*1.4 = 8.3MPa



• The CZ parameters have been calibrated on DCB experiments. CZ only an CZ

+ adhesive layer didn’t give in this case significantly different parameters.

•The simulation of fracture of T-peel joints with CZ only showed that the

propagation phase was well matched, while the maximum stress has to be

increased to get closer to the experimental peak load.

•The simulation of T-peel joints with CZ + adhesive layer needs recalibration in

the same way as with CZ to match the experimental peak load. A way to

perform recalibration was evaluated.

• It is worth to underline that the shape of the adhesive layer root in T-peel

joints may affect the results: careful control is needed.

CONCLUSIONS

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