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Deformation and failure modelling of high strength adhesives for crash simulation

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Abstract

The deformation and failure mechanisms of toughened high strength adhesives used in the automotive industry are very complex and require advanced numerical models for crashworthiness simulation. The theoretical background of two new modelling approaches for thin adhesive layers is presented: firstly, a simplified elastic damaging node-to-element tied interface model approach for convenient and efficient modelling, and secondly a detailed modelling approach for improved accuracy using an elasto-viscoplastic solid element representation of the adhesive layer. The material model parameters required for both approaches are determined by a comprehensive set of experiments, including quasi-static and dynamic adhesive coupon testing, fracture toughness testing, and quasi-static tension/shear (and combined) testing of thin adhesive layers. A more complex adhesively joined assembly of two aluminium extrusions subjected to quasi-static (QS) and dynamic loading serves as the final validation example for both modelling approaches. Good agreement of experiments and numerical predictions was observed for both modelling approaches.

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Abbreviations

G IC , G IIC :

Critical strain energy release rate for Mode I and Mode II loading

\({\delta_{I}, \delta_{II}}\) :

Relative out-of-plane (Mode I) and in-plane (Mode II) interface element displacements

\({{\sigma_{I}, {\sigma_{II}}}}\) :

Out-of-plane (Mode I) and in-plane (Mode II) interface element stresses

E, G :

Young’s modulus, shear modulus

dA, dW :

Infinitesimal area and energy

d I , d II :

Out-of-plane (Mode I) and in-plane (Mode II) damage functions

 < x > + :

Operator returns ‘x’ if x > 0 and 0 otherwise

sup t≤ τ (x):

Supremum of x: Maximum of x within the range 0 ≤ t≤ τ

I 1, J 2 :

First invariant of the stress tensor and second invariant of the stress deviator

σ m :

Hydrostatic stress

σ e :

Equivalent von Mises stress

I :

Identity matrix

\({\sigma,\varepsilon^{e},\varepsilon ^{p}}\) :

Stress tensor, elastic and plastic strain tensor

E :

Elasticity matrix

σ x , τ xy :

Axial stress and torque shear stress

\({\sigma _T \left( {\varepsilon _T^p } \right)}\) :

Tensile strain hardening curve

Φ:

Yield function

α, β :

Shape parameters for the yield function and the flow potential

σ0 :

Shift stress value representing the centre of the yield locus

\({\tilde{\sigma}}\) :

Special effective equivalent stress

\({\dot{\varepsilon}_T^{p}}\) :

Plastic strain rate threshold

C :

Fitting parameter for the strain rate model

\({\dot{\lambda}}\) :

Plastic multiplier

DCB:

Double Cantilever Beam

DF:

Deshpande and Fleck

DYN:

Dynamic

Exp, Sim:

Experiment and Simulation

FE:

Finite Element

JC:

Johnson and Cook

QS:

Quasi-static

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Authors and Affiliations

  1. Volkswagen AG, 38436, Wolfsburg, Germany

    Lars Greve

  2. Fraunhofer Institut für Werkstoffmechanik, Woehlerstr. 11, 79108, Freiburg, Germany

    Florence Andrieux

Authors
  1. Lars Greve
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  2. Florence Andrieux
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Correspondence to Lars Greve.

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Greve, L., Andrieux, F. Deformation and failure modelling of high strength adhesives for crash simulation. Int J Fract 143, 143–160 (2007). https://doi.org/10.1007/s10704-007-9054-9

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  • DOI: https://doi.org/10.1007/s10704-007-9054-9

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