This paper provides a contribution to such methods and focuses on a widely used joint type, the single lap joint (SLJ). Currently typical approaches for the assessment of failure loads of adhesive joints are basically: strength of materials approaches, fracture mechanics approaches and cohesive zone modelling. But strength of materials approaches cannot be directly applied to stress fields containing singularities because they occur at the edges of adhesive layers and fracture mechanics approaches depend on information concerning existing defects or on assumptions for such. Cohesive zone modeling has proven to be a versatile tool for failure load assessment at the expense of numerical issues in the complex modelling and the difficulties in obtaining an appropriate traction-separation law.

In this work the hybrid criterion by Leguillon [1] in the framework of finite fracture mechanics is applied to the assessment of failure loads of adhesively bonded joints. In the hybrid criterion the spontaneous formation of cracks of finite size is postulated, if a stress and an energy criterion are fulfilled simultaneously. The stress criterion must be fulfilled on the complete area of the crack considered and the incremental energy release rate must reach the fracture toughness of the material. Only two essential material parameters are needed to formulate the hybrid criterion: a characteristic strength and a fracture toughness.

On the basis of classical linear-elasticity solutions for adhesively bonded single lap joints, two closed-form analytical formulations of the hybrid criterion are derived and allow for an assessment of the failure load of the adhesive joints. The classical solutions of Goland and Reissner [2] and of Ojalvo and Eidinoff [3] are used to formulate the criterion. The solution by Goland and Reissner considers shear and peel stresses in the adhesive layer that occur arising from shear-lag and bending of the joint. The Ojalvo-Eidinoff solution uses extended kinematics to fully cover the effect of the adhesive layer thickness.

The results of a parameter study show that the effects of the geometrical parameters predicted by the present criterion correspond well to the effects that are known from experimental investigations. Furthermore a direct comparison of the given criterion with experimental results is shown in the work. It can be seen that the given criterion gives good predictions of the failure loads of the single lap joints and even the effect of the adhesive layer thickness is incorporated. The latter effect cannot be covered by linear-elasticity solutions for single lap joints [4]. The paper closes with a discussion of the results obtained and the hybrid criterion.

1

D. Leguillon, "Strength or toughness? A criterion for crack onset at a notch", European Journal of Mechanics-A/Solids, 21(1), 61-72, 2002. doi:10.1016/S0997-7538(01)01184-6

2

M. Goland, E. Reissner, "The stresses in cemented joints", Journal of Applied Mechanics, 11(1), A17-A27, 1944.

3

I. Ojalvo, H. Eidinoff, "Bond thickness effects upon stresses in single-lap adhesive joints", AIAA Journal, 16(3), 204-211, 1978. doi:10.2514/3.60878

4

L. da Silva, P. das Neves, R. Adams, A. Wang, J. Spelt, "Analytical models of adhesively bonded joints - Part II: Comparative study", International Journal of Adhesion and Adhesives, 29(3), 331-341, 2009. doi:10.1016/j.ijadhadh.2008.06.007

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