Scaling laws for the adhesive composite butt joint strength derived by finite fracture mechanics. (15th January 2019) - Felger, J.; Stein, N.; Frey, C.; Becker, W.
Abstract: The effective strength of butt joints under uniaxial tensile loading significantly depends on the adhesive thickness as well as on the elastic contrast of adhesive and adherend. For an assessment of their impact using sensitivity analysis, for joint design optimisation, or for an efficient evaluation of butt joint test data, a suitable modelling approach is desired. In the present work, the joint's failure is modelled assuming a spontaneous formation of finite cracks along the interface between adhesive and adherend. A coupled stress and energy approach is used requiring only two fundamental material parameters, that is, material strength and toughness. Presuming the length of initiating cracks to be small compared to the adhesive thickness, the method of matched asymptotic expansions in combination with a complex potential formalism is applied. This enables an efficient description of the stress distribution in the vicinity of the bi-material notch tip and the derivation of scaling laws for the energy dissipation during crack nucleation. The joint strength is calculated for a varying adhesive thickness and for different layups of the composite adherends. The theoretical predictions based on the asymptotic coupled stress and energy approach are validated against numerical cohesive zone data and experimental findings from literature.