JOURNAL DE PHYSIQUE Colloque C5, supplkment au nolO, Tome 49, octobre 1988 ON THE INTERFACE CRACK MODELS T. SUGA('), S. SCHMAUDER and G. ELSSNER Max-Planck-Institut fiir Metallforschung, Institut fiir Werkstoffwissenschaften, 0-7000 Stuttgart, F.R.G. Resume - Les modeles du continu pour une fissure dans l'interface sont discutes. Les incompatiblites logiques presentes dans le champ de tension du modele conventionnel, cornme par exemple les singularites d'oscillation et les interpenetrations de la sur- face de fissure, sont dleminees en modifiant les conditions de joints a la pointe de fissure. Un modele de la pointe de fissure est presente et discute par rapport a la dispersion inelastique de l'energie et le manque d'interfaces de materiaux hetero- genes . Abstract - The continuum models for an interface crack are reviewed. The logical in- consistencies present in the local stress field of the conventional model, such as the oscillatory singularities and the interpenetration of the crack surfaces, are re- moved by modifying the boundary conditions at the crack tip. An interpretation of the crack tip models is given and discussed with respect to inelastic energy dissipation during interfacial failure of heterogeneous materials. I - INTRODUCTION Semibrittle fracture along interfaces of heterogeneous materials (such as solid state bonded ceramic-metal jqints or composites) can occur when the energy stored in the specimen by external work becomes sufficient to supply the fracture energy needed for creating new surfaces. The term "semibrittle" means that the region in which the en- ergy is consumed by the failure process is limited to the crack tip. The ideal frac- ture energy of an interface corresponds to the thermodynamic work of adhesion WA which is the difference between the sum of surface energies and the interfacial ener- gy of the materials bonded: WA=7n+7c-7nc. Any failure process is accompanied by irre- versible inelastic energy dissipation. Therefore, denoting its contribution to the fracture energy by WP, the thermodynamic criterion for an interface fracture is writ- ten as /I/: where GC is the critical value of the generalized strain energy release rate C. This equation is a rational generalization of the Griffith-Orowan formula for the semi- brittle failure of homogeneous materials. If the inelastic deformation of the speci- men is limited to a narrow region in the vicinity of the crack, the generalized strain energy release rate corresponds to Irwin's elastic strain energy release rate G which can be calculated by an elastic analysis of the cracked material. If the load-deformation relationship of the specimen is not linear, can also be obtained by modifying the elastic strain energy release rate G,by the experimentally estimated nonlinearity coefficient /2/. Experimental verification of the energy criterion for interfacial fracture is given in early works by Malyshev and Salganik /3/, Mulville /4/, and Saxena 151, followed by the extensive experiments by Suga and Elssner /1.6,7/. The most important result in /1/ is that the dissipated work Wp is dependent on the reversible work WA. There- '')low at: The University of Tokyo, Faculty of Engineering, Department of Precision Engineering, 113 Tokyo, Japan. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988565