OpenFOAM in Non-linear Stress Analysis Modelling of ...powerlab.fsb.hr/ped/kturbo/OpenFOAM/WorkshopZagrebJan2006/... · (velocity) Free End G C t t max δ CODδ Numerical crack tip

Dr Vlado Tropša

Current Position: Lecturer of Solid Mechanics, VELSPrevious Position Held: Research Associate 1999-2004

Imperial CollegeLondon

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 SCHOOL HIGH ELECTROTECHNICAL SCHOOL –– VELS VELSVISOKA ELEKTROTEHNIVISOKA ELEKTROTEHNIČČKA KA ŠŠKOLAKOLAVARAVARAŽŽDINDINCROATIACROATIA

2January 2006 3rd Progress Meeting

Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE

“OpenFoam” Workshop, Zagreb, Croatia

VELS, Varaždin, Croatia

• Introduction – Adhesives in Automotive Applications

• Experimental Procedures• IWP method (Impact Wedge Peel)

• Numerical Simulations (Finite Volume Method)

• Conclusions

Outlines





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:Prediction of their performance under impact loading

-

Introduction – Adhesives in Automotive Applications





• 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

AdhesiveWedge Retaining Shackle Substrates

Bolt

RamMotion

MachineRam

Rubber Washersfor

DampingContact

LostMotionDevice

Specimen

Wedge

StaticLoad-Cell

Piezo-Electric

Load-Cell

Strain Gauges

Fixed Base

Experimental Procedures: IWP





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






• 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

Fo

rce

[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






• Quasi-static crack growth: Large plastic deformation

• Transient crack growth: Low plastic deformation

A.A. 5754, 1 mm thick, XD1493, 2 m/s, 23°C

A.A. 6111, 2 mm thick, XD4600, 2 m/s, 23°C






• Characteristic of IWP numerical systems:• Highly dynamic (stress wave propagation, inertia)• Non-linear numerical systems:

• boundary conditions (cohesive zone model, surfaces infrictional contact)

• material properties (elasto-plastic constitutive model)• large deformations

• Large numerical systems (high resolution required in thecontact and the fracture process regions – local refinements)

Can be solved using the FINITE VOLUME METHOD

Numerical Procedures: IWP





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

00 0

00000

1

vv a

TTdvt

dt

dvdt

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:

( ) d

eq

d

p SES

ESIEES

2

2:

3

9 tr2

!

µ

µ"!#µ!!

+$+=

( ) ( )[ ] ( )TTTI uuuuuIuIE !!!!!!! "#"+"+"=$"+#"+=

2

1

2

1





A.A. 5754, 1 mm thick, XD1493, 2 m/s, 23°C

A.A. 6111, 2 mm thick, XD4600, 2 m/s, 23°C

3D Numerical Model for IWP Test

Fixed End

SpecifiedDisplacement (velocity)

Free End

GC

ttmax

δCOD δ

Numerical cracktip position

t δCOD

Symmetry Plane

Contact EventCrack Propagation Event

Numerical Simulations (Finite Volume Method)





800 µs

700 µs650 µs600 µs

δt

t

δ

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)






Test parameters:• Aluminium arms + adhesive XD4600 + Titanium wedge• Test speed = 2 m/s• Dugdale CZM curve: Gc = 2000 J/m2, σmax = 50 MPa• Arm thickness = 1, 2 mm

A.A. 5754, 1 mm thick, XD1493, 2 m/s, 23°C

A.A. 6111, 2 mm thick, XD4600, 2 m/s, 23°C

16800 Finite Volumes1 mm IWP specimen












Quasi-static crack growth

Programmed in OpenFoam library





IWP Test Simulation

Transient crack growth

Programmed in OpenFoam library





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.





600 µs

Examples of other FV Simulations

• TDCB

• TPB

• RCP





Thank [email protected]

Documents

OpenFOAM in Non-linear Stress Analysis Modelling of ...powerlab.fsb.hr/ped/kturbo/OpenFOAM/WorkshopZagrebJan2006/... · (velocity) Free End G C t t max δ CODδ Numerical crack tip