PSI - Issue 72

Thomas Steffen Methfessel et al. / Procedia Structural Integrity 72 (2025) 105–112

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Beyond this, also a comparison has been performed to the results of the well-established Ojalvo-Eidinoff model for larger thicknesses of the adhesive. From Fig. 5 it can be seen that the analytic sandwich-type model (midplane) results agree well to comparative finite element analyses also for larger thicknesses of the adhesive layer but the predictions of Ojalvo and Eidinoff get inaccurate. This means a significant improvement of the extended model presented here for larger thicknesses of the adhesive layer.

Fig. 5. Shear stresses and peeling stresses of the analytic model (AM) in comparison to finite element analyses (FEA) and the model of Ojalvo and Eidinoff (OE). Beyond single-lap joints the introduced sandwich-type model can also be applied to other kinds of structural situations with applied cross-sectional forces determined from corresponding equilibrium conditions. 5. Assessment of effective strength A given adhesive joint is overloaded when a debonding crack is generated that typically starts at the edges between the adhesive layer and the adherends where the high stress concentrations occur. As suggested by Leguillon (2002) in a pioneering paper according to the concept of Finite Fracture Mechanics, such a debonding crack of finite length will form instantaneously when a stress and energy criterion as a so- called “coupled criterion”, are satisfied simultaneously. For the stress subcriterion here the following quadratic criterion is taken: f(  ) = ( / ) 2 +( / ) 2 ≥1 . (8) Herein the quantities  c and  c denote the tensile and shear strength of the given material. For the energy subcriterion the so-called incremental energy release rate ̅ is employed which for a crack length  a and surface area  A=d  a (where d is the depth of the considered joint) is defined as ̅ = - = 1 ∫ ( ) 0 . (9) To enable crack initiation, this incremental energy release rate must be larger than the fracture toughness G c of the adhesive layer or of the interface to the adherends which means ̅ ≥ G c . (10) The energy release rate is composed of a mode I and mode II part and can be calculated through the so-called virtual crack closure integrals from the crack opening displacements in the following manner: ̅ = ̅ I + ̅ II with