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Dr Vlado Trop!a
Current Position: Lecturer of Solid Mechanics, VELS
Previous Position Held: Research Associate 1999-2004
Imperial College
London
Co-Authors: I. Georgiou, A. Ivankovic, A.J. Kinloch, J.G. Williams
OpenFOAM Workshop, Zagreb, Croatia, January 26-28, 2006
OpenFOAM in Non-linear Stress Analysis:Modelling of Adhesive Joints
HIGH ELECTROTECHNICAL SCHOOLHIGH ELECTROTECHNICAL SCHOOLVELSVELS
VISOKA ELEKTROTEHNIVISOKA ELEKTROTEHNI""KAKA ##KOLAKOLA
VARAVARA$$DINDIN
CROATIACROATIA
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7/21/2019 OpenFOAM in Non-linear Stress Analysis_Modeling Adhesive JointsTropsaUniVarazdin
2/18
2January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Introduction Adhesives in Automotive Applications
Experimental Procedures IWP method (Impact Wedge Peel)
Numerical Simulations (Finite Volume Method)
Conclusions
Outlines
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7/21/2019 OpenFOAM in Non-linear Stress Analysis_Modeling Adhesive JointsTropsaUniVarazdin
3/18
3January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Adhesive bonding - alternative method for automotive manufacturers?
Efficient for joining thin-sheet materials Light-weight structures Applicable for joining dissimilar materials Cost effective joining method
Failures of joints during the impacts Low dissipation of energy during impact Propagation of impact loads into passenger area Strain rate sensitivity of adhesive materials Aging of the adhesive
Lack of design information
Major requirement for widespread use of adhesives:
Predictionof their performance under impact loading
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Introduction Adhesives in Automotive Applications
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7/21/2019 OpenFOAM in Non-linear Stress Analysis_Modeling Adhesive JointsTropsaUniVarazdin
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4January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Materials tested A.A. 5754 (1, 2 & 3 mm) / A.A. 6111 (1 & 2 mm) XD4600, single part adhesive
Test conditions Room temperature
Test rate of 0.4 - 12 m/s
Equipment Servo-hydraulic Instron machine
Specimen GripWedge
Adhesive
Wedge Retaining Shackle Substrates
Bolt
Ram
Motion
MachineRam
Rubber Washers
forDampingContact
LostMotionDevice
Specimen
Wedge
StaticLoad-Cell
Piezo-Electric
Load-Cell
Strain Gauges
Fixed Base
Experimental Procedures: IWP
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5January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Quasi-static crack growth
High speed photography, 4500 f/s of an IWP test exhibitedquasi-static crack growth. Al. Substrates, 1mm thick,A.A.5754 bonded with XD4600 adhesive and tested at 2.1m/s, 23 C
High speed photography, 4500 f/s of an IWP test exhibitedquasi-static crack growth. Al. Substrates, 2mm thickA.A.6111 bonded with XD4600 adhesive and tested at 2.1m/s, 23 C
Transient crack growth
Experimental Procedures: IWP
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6January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Types of crack growth Quasi-static (stable) Transient (unstable)
Quasi-static crack growth Initial high-peaks region !Plateau"region
Transient crack growth Initial high-peaks region No !Plateau"region
Causes for the initial peaks Dynamic effects, from initial contact between the wedge - specimen Crack initiation
Within !plateau"region: Quasi-static Velocity of the crack = Test rate
Transient Crack Velocity > Test rate
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Time [ms]
0
250
500
750
1000
1250
1500
1750
2000
2250
2500
Force[N]
Quasi-Static Crack Growth (1 mm thick specimen)
Transient Crack Growth (2 mm thick specimen)
Start
End End
-5754-0/XD4600 adhesive
- 6111-T4/XD4600 adhesive
Experimental Procedures: IWP
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7January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Quasi-static crack growth: Large plastic deformation
Transient crack growth: Low plastic deformation
A.A. 5754, 1 mm thick, XD1493, 2 m/s, 23C
A.A. 6111, 2 mm thick, XD4600, 2 m/s, 23C
Experimental Procedures: IWP
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8January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Characteristic of IWP numerical systems:
Highly dynamic (stress wave propagation, inertia)
Non-linear numerical systems:
boundary conditions (cohesive zone model, surfaces in
frictional contact)
material properties (elasto-plastic constitutive model)
large deformations
Large numerical systems (high resolution required in the
contact and the fracture process regions local refinements)
Can be solved using the FINITE VOLUME METHOD
Numerical Procedures: IWP
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9January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
( )( )[ ] !! ! +""++"=
00 0
00000
1
vv a
TTdv
td
tdv
dt
d
t #
#$###
#
#$
#
# baFSSFS
u&
Numerical Procedures (Finite Volume Method)
Governing equation for linear momentum (incremental formulation):
Inertia Surface Bodyforces forces forces
Constitutive relation for elastic-plastic solid (Prandtl-Reuss flow rule):
scalar multiplier Green strain tensor:
( ) deq
d
p SES
ESIEES
2
2:
3
9tr2
!
"!#!!
+$+=
( )( )[ ] ( TTT I uuuuuIuIE !!!!!!! "#"+"+"=$"+#"+=2
1
2
1
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10January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
A.A. 5754, 1 mm thick, XD1493, 2 m/s, 23C
A.A. 6111, 2 mm thick, XD4600, 2 m/s, 23C
3D Numerical Model for IWP Test
Fixed End
SpecifiedDisplacement(velocity)
Free End
GC
t
tmax
COD
Numerical cracktip position
t COD
Symmetry Plane
Contact EventCrack Propagation Event
Numerical Simulations (Finite Volume Method)
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11January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
800 s
700 s650 s600 s
!t
t
!
GC
Traction-separation law (Cohesive Zone Model) Governs the local fracture process Experimentally determined (?) Widespread and numerically effective method Predictive model
(crack initiation and propagation results from the analysis)
Numerical Simulations (Finite Volume Method)
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12January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Test parameters:
Aluminium arms + adhesive XD4600 + Titanium wedge
Test speed = 2 m/s
Dugdale CZM curve: Gc= 2000 J/m2, "
max= 50 MPa
Arm thickness = 1, 2 mm
A.A. 5754, 1 mm thick, XD1493, 2 m/s, 23C
A.A. 6111, 2 mm thick, XD4600, 2 m/s, 23C
16800 Finite Volumes
1 mm IWP specimen
Numerical Simulations (Finite Volume Method)
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13/18
13January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Numerical Simulations (Finite Volume Method)
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14January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Numerical Simulations (Finite Volume Method)
Quasi-static crack growth
Programmed in OpenFoam library
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15January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
IWP Test Simulation
Transient crack growth
Programmed in OpenFoam library
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16January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Conclusions
Finite Volume Method suitable for modelling small scale testsinvolving adhesively bonded joints loaded statically and dynamically.
Quasi-static and dynamic crack growth predicted in IWP specimens.
Good transferability of cohesive properties between different tests.
Developing FV elasto-plastic shell model.
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17January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
600 s
Examples of other FV Simulations
TDCB
TPB
RCP
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18January 2006 3rdProgress Meeting
Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE
OpenFoamWorkshop, Zagreb, Croatia
VELS, Vara!din, Croatia
Thank [email protected]