On the Toughness of Ductile Adhesive Joints

Crack propagation along one of the interfaces between a thin ductile adhesive layer and the elastic substrates it joins is considered. The layer is taken as being elastic-plastic, and the fracture process of the interface is modeled by a traction-separation law, characterized by the peak separation stress 6 and the work of separation per unit area To. Crack growth resistance curves for mode I loading of the adhesive joint are computed, with emphasis on steady-state toughness, as a function of three extrinsic effects : layer thickness, layer-substrate modulus mismatch, and initial residual stress in the layer. Conditions under which separation first occurs well ahead of the initial crack tip are discussed. 1. SPECIFICATION OF THE MODEL This paper continues the study begun by Tvergaard and Hutchinson (1994) in which an embedded fracture zone model is applied to the mode I fracture of an adhesive joint comprised of a thin elastic-plastic metal layer joining two elastic substrates. The present work employs the model to investigate the influence on joint toughness of both the elastic mismatch between the layer and the substrates and the residual stress in the layer. As in the earlier study, the thickness of the ductile layer is another extrinsic variable which comes into play. The approach adopted was first introduced by Needleman (1987) to study particle debonding in metal matrices and subsequently by Tvergaard and Hutchinson (1992, 1993) to model crack growth resistance in homogeneous solids and along interfaces. A traction-separation law simulating the fracture process is embedded within an elastic-plastic continuum as a boundary condition along the line extending ahead of the crack. In the case of an interface joining dissimilar materials, the separation law necessarily involves both the normal and shear tractions and the two associated relative displacements of the surfaces across the interface.