Niobium/alumina bicrystal interface fracture: A theoretical interlink between local adhesion capacity and macroscopic fracture energies A. Siddiq a, * , S. Schmauder a , M. Ruehle b a Institut fu ¨ r Materialpru ¨ fung, Werkstoffkunde und Festigkeitslehre (IMWF), Universita ¨ t Stuttgart, Pfaffenwaldring 32, 70569 Stuttgart, Germany b Max-Planck Institute for Metal Research, Heisenberg Strasse 3, 70569 Stuttgart, Germany Received 14 July 2006; received in revised form 4 September 2007; accepted 10 September 2007 Abstract In the presented work, an effort has been put to clear up the theoretical interlink between local adhesion capacity and macroscopic fracture energies by bridging different length scales, such as nano-, meso-, and macro-scale. Crystal plasticity theory along with a cohesive modelling approach has been used during this work. The influence of different cohesive law parameters (cohesive strength, work of adhesion) on the macroscopic fracture energies for three different orientations of niobium/alumina bicrystal specimens has been presented. It is found that cohesive strength has a stronger effect on macroscopic fracture energies as compared to work of adhesion. In the last part a generalized correlation among macro- scopic fracture energy, cohesive strength, work of adhesion and yield stress is derived. The presented results can provide a great help to experimentalists in order to design better metal/ceramic interfaces. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Metal/ceramic interface; Crystal plasticity; Cohesive model; Fracture mechanics; Work of adhesion 1. Introduction Interfaces between metal and ceramic play an important role in many applications, because they combine the properties of metals like ductility, high electrical and thermal conductivity and the properties of ceramics like high hardness, corrosion resistance and capacity of resistance to wear. Some of the applications of metal/ ceramic joints include automotive industry, turbine blades, high pressure sodium lamps, squid magnetometers and dental implants. The fracture at or near such interfaces often limits the reliability of these joints. In the past, niobium/alumina interfaces have been studied experimentally [1–5] and numerically [6–8]. Single crystal- line alumina/niobium/alumina joints were investigated in [1,2] for different orientations of single crystalline 0013-7944/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2007.09.005 * Corresponding author. Tel.: +44 114 22 28874; fax: +49 711 685 62365. E-mail addresses: a.siddiq@shef.ac.uk, amir.siddiq@gmail.com (A. Siddiq). Available online at www.sciencedirect.com Engineering Fracture Mechanics xxx (2007) xxx–xxx www.elsevier.com/locate/engfracmech ARTICLE IN PRESS Please cite this article in press as: Siddiq A et al., Niobium/alumina bicrystal interface fracture: ..., Engng Fract Mech (2007), doi:10.1016/j.engfracmech.2007.09.005