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8/6/2019 vercelli06 Pirondi
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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
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AGENDA
•Introduction
•Objectives
•Modelling
•Results and discussion
•Conclusions
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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
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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)
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INTRODUCTION
...AND SOME POTENTIAL APPLICATIONS IN ENGINEERING DESIGN
•Stiffener delamination
•Crash and collapse
(including joints)
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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
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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
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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.
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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
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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
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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)
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MODELLING
Adherend
Cohesive Zone
Adhesive
CZA models
CZ only models
DCB
T-peel
DCB
T-peel
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RESULTSEXAMPLE OF SIMULATION RUN ON DCB
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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
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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
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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
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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
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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
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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
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• 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