Inverse Identification of Constitutive Models for Structural Adhesives

Transcription

1 Inverse Identification of Constitutive Models for Structural Adhesives 1 Pierre Jousset,, Zürich, Switzerland Mohamed Rachik, Lab. Roberval, UTC, Compiègne, France

2 Sika: Presentation 2 Sika: International company, specialist in polymer chemistry 12 employees, 4.6 billion CHF turnover Core competencies: Bonding, sealing, reinforcing, protecting, damping

3 Introduction 3 General trends in the automotive industry: Finite Element (FE) Simulation is intensively used during design phases Structural Adhesives: Even more used to assemble car body structures Esi Group: Comparison of Real and Simulated frontal Crash with PAM-CRASH 2G, courtesy of Wolkswagen AG Ph-D Report: Cornelis Wirth, Berechnungskonzept für die Klebflanschfestigkeit in Gesamtkarosseriemodellen, TU München, 24 Consequence: Structural Adhesives must be taken into account in non linear FE-Analysis of car body structures

4 Structural adhesive SikaPower 4 1 component Adhesive: Epoxy base Applied in thin layers:.3mm Class of products considered in this presentation: SikaPower -49: structural adhesive for spot welding bonding Weld point Schweisspunkt Karosserieblech Substrate Adhesive Klebstoff Typical adhesive/welding hybrid application

5 Specimen for the validation of material models 5 The butt bonded hollow cylinder: Can superimpose any combination of traction and shear loading in the adhesive layer Steel substrates Length half cylinder=12mm Internal radius=5mm External Radius=6mm Joint thickness=.2mm Adhesive Test data availale for 4 different load cases with SP49 (from projcet AIF P593)

6 Material constitutive models 6 General mechanical behavior of structural adhesives: elasto-plastic Nominal Stress (Mpa test Nominal Strain (%) Structural adhesives under multi-axial loading: cannot be described by classical material constitutive models in FE Analysis Steel substrates Adhesive F (KN) test Only traction test test simu von Mises simu von Mises u2 (mm) Implementation of a new material model is required

7 Implementation of a new material constitutive model for structural adhesives in FE Simulation 7 New material model: inspired from Mahnken/Schlimmer (25) implemented at Sika under Abaqus/Standard and Abaqus/Explicit Goal: To predict the behavior of the adhesive under multi-axial loading in quasi-static load-cases Material s parameters must be identified Example: Elastic limit or yield function: Where I 1 and J 2 are stress invariants: a 1 and a 2 : parameters to identify 2 = 3J + a Y I + a I Y = Resolving the above equation to find a 1 and a 2 suppose: - To have an homogeneous stress state in the adhesive layer - To know the stresses values in the adhesive layer f y

8 Stress state in an adhesive layer under traction 8 Stress (MPA) Stresses along node path node path - true distance(mm) S11 S22 S33 S12 S13 S23 Simple traction load but: multi-axial stress state in the adhesive layer. These stress are not known and cannot be used for direct identification of parameters a 1 and a 2 f y 2 = 3J + a Y I + a I Y = Consequence: Development of an alternative method based on inverse identification to compute material parameters

9 Principe of inverse identification 9 Inverse identification: curve fitting through an iterative optimisation process Goal: to find the set of material parameters bringing the best fit between the simulation and the measured (test) response 5 4 Force (KN) Measured response (Test) FEM Iteration 1 FEM Iteration disp (mm) Power of the inverse identification method: No assumption has to be made on the stress/strain state in the adhesive layer

10 Description of the optimisation problem 1 Design variables: Material parameters Objective function: Difference between the computed and the measured response, using a least square f ( x ) = n i = 1 [ m i ( x ) c i ( x )] 2 m i : measured response in the test c i : computed response in the FE Simulation i: global number of points on the two curves f must be minimised Constraints: can be defined on c i to prevent the solution diverging from the measured response

11 Development of the inverse identification procedure 11 Altair HyperStudy Parameterised input file Variables=material Parameters Abaqus/Standard Job 1 Job 2.. Job n Python Script Abaqus/CAE Experimental data Computed response Measured response Objective function: Least square function Altair HyperStudy New material parameter set Final identified parameters set yes no Convergence Test Minimisation of the objective fonction

12 Optimisation algorithm (HyperStudy) Adaptive Response Surface Method 12 Adaptive Response Surface Method: - requires only one computation per iteration - many iterations needed due to oscillations of the response Adaptive Response Surface Method Origin of oscillations: - local approximation of the objective function at each iteration Short time/iteration Oscillations Many iterations needed

13 Optimisation algorithm (HyperStudy) Genetic Algorithm Method 13 Genetic Algorithm Method: - based on global approximation of the objective function - requires many computations per iteration - Converge in less iterations than gradient methods to a solution Genetic Algorithm Method No oscillation Few iterations needed Long time/iteration

14 Application: Material parameters identification 14 New material constitutive model developed at Sika: - contains 6 parameters - must describe the adhesive under mixed-mode loading Use of the butt bonded hollow cylinder for inverse identification under mixed-mode loading Length half cylinder=12mm Internal radius=5mm External radius=6mm Adhesive thickness=.2mm

15 Parameter identification results 15 alpha=.5 traction alpha=2 traction traction only γ xy α = 2. ε x F (KN) 2 1 Test FEM.E+ 4.E-3 8.E-3 u2 (mm) alpha=.5 torsion F (KN) 15 1 Test 5 FEM.E+ 4.E-3 8.E-3 u2 (mm) alpha=2 torsion F (KN) 2. Test FEM..E+ 4.E-3 8.E-3 u2 (mm) torsion only Mt (KN.mm) E+ Test FEM 5.E-3 u3 (mm) Mt (KN.mm) E+ Test FEM 2.E-2 u3 (mm) Moment (KN.mm) Test 2 FEM.E+ 4.E-2 8.E-2 u3 (mm)

16 Conclusion 16 Implementation of a new material constitutive models at Sika to predict the behaviour of structural adhesives under multi-axial loading in quai-static FE Simulation An inverse identification procedure combining HyperStudy and Abaqus/Standard resp. explicit has been developed to find material parameters The inverse identification method has been succesfully used to find a satisfactory set of material parameters

17 17 Thank you for your attention