OpenFOAM in Non-linear Stress Analysis: Modelling of Adhesive Joints

Transcription

1 HIGH ELECTROTECHNICAL SCHOOL VELS VISOKA ELEKTROTEHNIČKA KA ŠKOLA VARAŽDIN CROATIA OpenFOAM in Non-linear Stress Analysis: Modelling of Adhesive Joints Dr Vlado Tropša Current Position: Lecturer of Solid Mechanics, VELS Previous Position Held: Research Associate London Co-Authors: I. Georgiou, A. Ivankovic, A.J. Kinloch, J.G. Williams OpenFOAM Workshop, Zagreb, Croatia, January 26-28, 2006

2 Outlines VELS, Varaždin, Croatia Introduction Adhesives in Automotive Applications Experimental Procedures IWP method (Impact Wedge Peel) Numerical Simulations (Finite Volume Method) Conclusions 2

3 Introduction Adhesives in Automotive Applications 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 3

4 Experimental Procedures: IWP Materials tested A.A (1, 2 & 3 mm) / A.A (1 & 2 mm) XD4600, single part adhesive Test conditions Room temperature Test rate of m/s Equipment Servo-hydraulic Instron machine Wedge Bolt Specimen Grip Adhesive Wedge Retaining Shackle Substrates Machine Ram Rubber Washers for Damping Contact Lost Motion Device Wedge Strain Gauges Specimen Piezo- Electric StaticLoad-Cell Load-Cell Ram Motion Fixed Base 4

5 Experimental Procedures: IWP Quasi-static crack growth Transient crack growth High speed photography, 4500 f/s of an IWP test exhibited quasi-static crack growth. Al. Substrates, 1mm thick, A.A.5754 bonded with XD4600 adhesive and tested at 2.1 m/s, 23 C m/s, 23 C High speed photography, 4500 f/s of an IWP test exhibited quasi-static crack growth. Al. Substrates, 2mm thick A.A.6111 bonded with XD4600 adhesive and tested at 2.1 5

6 Experimental Procedures: IWP 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 Force [N] Quasi-Static Crack Growth (1 mm thick specimen) /XD4600 adhesive Transient Crack Growth (2 mm thick specimen) T4/XD4600 adhesive End End Causes for the initial peaks Crack initiation Within plateau region: Quasi-static Dynamic effects, from initial contact between the wedge - specimen Transient 250 Start Time [ms] Velocity of the crack = Test rate Crack Velocity > Test rate 6

7 Experimental Procedures: IWP Quasi-static crack growth: Large plastic deformation A.A. 5754, 1 mm thick, XD1493, 2 m/s, 23 C Transient crack growth: Low plastic deformation A.A. 6111, 2 mm thick, XD4600, 2 m/s, 23 C 7

8 Numerical Procedures: IWP 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 OF SCIENCE, the TECHNOLOGY fracture AND MEDICINE process regions local refinements) Can be solved using the FINITE VOLUME METHOD 8

9 v Green strain tensor: VELS, Varaždin, Croatia Numerical Procedures (Finite Volume Method) Governing equation for linear momentum (incremental formulation): ( ) # d # u& 1!![ T = " + ( + ) T " ] # $ " +! 0 dv0 # S F S # S # F da0 $ b 0 dv # t dt # t # t a v0 Inertia Surface Body forces forces forces 0 0 Constitutive relation for elastic-plastic solid (Prandtl-Reuss flow rule):! 9µ 2 d S = 2µ! E + # tr! E I $ " p 2 E + 3µ Seq ( ) d S :! E scalar multiplier 1 1! E = " 2 2 [( ) ( T ) ] ( T T I + "! u # I + "! u $ I = "! u + "! u + "! u#! u ) S 9 0

10 Numerical Simulations (Finite Volume Method) 3D Numerical Model for IWP Test A.A. 5754, 1 mm thick, XD1493, 2 m/s, 23 C Specified Displacement (velocity) Free End Fixed End Symmetry Plane Numerical crack tip position t t max A.A. 6111, 2 mm thick, XD4600, 2 m/s, 23 C t G δ C COD δ COD δ Crack Propagation Event Contact Event 10

11 Numerical Simulations (Finite Volume Method) Traction-separation law (Cohesive Zone Model) t Governs 600 µs the local fracture process 650 µs 700 µs Experimentally determined (?) Widespread and numerically effective method Predictive model (crack initiation and propagation results from the analysis) 800 µs G C δ t δ 11

12 Numerical Simulations (Finite Volume Method) Test parameters: A.A. 5754, 1 mm thick, XD1493, 2 m/s, 23 C Aluminium arms + adhesive XD Titanium wedge Test speed = 2 m/s Dugdale CZM curve: G c = 2000 J/m 2, σ max = 50 MPa Arm thickness = 1, 2 mm A.A. 6111, 2 mm thick, XD4600, 2 m/s, 23 C 1 mm IWP specimen Finite Volumes 12

13 Numerical Simulations (Finite Volume Method) 13

14 Numerical Simulations (Finite Volume Method) Quasi-static crack growth Programmed in OpenFoam library 14

15 IWP Test Simulation Transient crack growth Programmed in OpenFoam library 15

16 Conclusions VELS, Varaždin, Croatia Finite Volume Method suitable for modelling small scale tests involving 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. 16

17 Examples of other FV Simulations 600 µs TDCB TPB RCP 17

18 Thank you! 18