A micromechanical bridging law model for CFCCs Konstantinos G. Dassios a, * , Vassilis Kostopoulos b , Marc Steen c a Foundation of Research and Technology Hellas, Institute of Chemical Engineering and High Temperature Chemical Processes, Stadiou Street, Platani, Patras GR 26504, Achaia, Greece b Department of Mechanical Engineering and Aeronautics, University of Patras, Rio GR 26500, Greece c Institute for Energy, Joint Research Centre, European Commission, Westerduinweg 4, 1755 LE Petten, The Netherlands Received 2 June 2006; received in revised form 17 July 2006; accepted 17 July 2006 Available online 7 November 2006 Abstract In the present work, a methodology is presented for the assessment of bridging laws for continuous fibre-reinforced ceramic matrix composites based on material properties as well as micromechanics of fibre deformation and failure. A load–displacement model is ini- tially formulated that utilizes weakest-link statistical concepts to analyse and relate the individual contributions of matrix, intact/bridg- ing and failed/pull-out fibres during the composite fracture process. The total and individual contributions to the bridging law and crack growth resistance of the material are determined by identifying the non-elastic part of displacement as crack opening. The model is val- idated against the experimentally recorded load–displacement behaviour of a notched SiC-fibre-reinforced glass–ceramic matrix compos- ite tested under monotonic tension. The output parameters of the converged regression procedure remain within a small scattering range from the corresponding mean values that compare favourably with known material properties. A parametric analysis of the effect of fibre volume fraction, Weibull modulus of fibres and interfacial shear stress in overall composite performance is presented in view of the ability of the model to serve as an a priori fracture prediction tool. Ó 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Ceramic matrix composites; Fiber reinforced composites; Fracture 1. Introduction The brittle nature of ceramics has hindered the use of these materials in high-temperature applications with increased mechanical demands for many decades. The development, in the 1970s, of ceramic matrix composite (CMC) materials, consisting of a bulk ceramic phase, the matrix, reinforced by an embedded phase in the form of particulates, whiskers or fibres, unleashed the potential of these materials to equip a structure with a unique combina- tion of properties to withstand simultaneous thermal and mechanical loading and pushed up the limits. A specially designated class of CMCs that evolved during the 1990s, continuous fibre-reinforced ceramic matrix composites (CFCCs), with fibres of high length- to-diameter ratios, has become established as the strongest and toughest of all types of ceramic composites. CFCCs are used today as structural components in commercial and military aircraft and high-speed vehicles (e.g. braking systems, stabilizers), in aerospace applications (e.g. mechanical parts and thermal barriers for space shuttles, rocket nozzles), and in incinerators, heat exchangers and many other high-temperature applications. Among the admirable characteristics of CFCCs are their increased crack growth resistance and improved damage tolerance compared with monolithic ceramics, their notch insensitiv- ity and their ability to effectively redistribute stresses around notches, voids and cracks. These prominent prop- erties stem from the energy dissipation mechanisms acti- vated during CFCC fracture that temper the fatal work of crack propagation at the crack front (crack process zone) by consuming a part of the externally applied energy. The two major energy dissipation mechanisms in CFCCs 1359-6454/$30.00 Ó 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.07.039 * Corresponding author. Tel.: +30 2610 965277; fax: +30 2610 965228. E-mail address: kdassios@iceht.forth.gr (K.G. Dassios). www.actamat-journals.com Acta Materialia 55 (2007) 83–92