OpenFOAM in Non-linear Stress Analysis_Modeling Adhesive JointsTropsaUniVarazdin

7/21/2019 OpenFOAM in Non-linear Stress Analysis_Modeling Adhesive JointsTropsaUniVarazdin

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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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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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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

-

Introduction Adhesives in Automotive Applications


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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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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



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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



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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



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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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( )( )[ ] !! ! +""++"=

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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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



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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)



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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



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Quasi-static crack growth

Programmed in OpenFoam library


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IWP Test Simulation

Transient crack growth

Programmed in OpenFoam library


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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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600 s

Examples of other FV Simulations

TDCB

TPB

RCP


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Thank [email protected]

OpenFOAM in Non-linear Stress Analysis_Modeling Adhesive JointsTropsaUniVarazdin

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