PHYSICS OF SOLIDS Pergamon outa or tn48 (2000)2137-216] s or son www.elsevier.com/locate/jmps Interface debonding ahead of a primary crack D. Leguillon a, .C. Lacroix a. E. Martin b Laboratoire de Modelisation en Mecanique, CNRS UMR 7607, Universite Pierre et Marie Curie, Paris 6.8 rue du Capitaine Scott, 75015 Paris, France Laboratoire de genie Mecanique, UPRES 496, IUT A, Universite de bordeaux I, 33405 Talence, Received 2 July 1999; received in revised form 18 November 1999 Abstract The debonding of an interface between two elastic materials is assumed to occur ahead of a primary crack lying in material 1. Conditions for such a mechanism are derived from an asymptotic analysis and depend on the elastic mismatch between the two materials as well as on material I and interface toughnesses. The ligament width between the primary crack tip and the interface and the debond nucleation length can be determined if the interface strength is known. A similar mechanism involving a crack nucleation ahead of the primary crack in material 2 is also examined. Deflection prediction is derived from an energetic criterion which is in general more favourable to deflection than the He and Hutchinson one. The former decreases asymptotically towards the latter. Moreover, if the crack lies in the stiffest material esults show that these nucleation mechanisms are highly improbable. If material 2 and inter- face strengths are known, a stress criterion is naturally derived. The presented analysis is independent of the applied loads and of the geometry of the specimen. 2000 Elsevier Science Ltd. All rights reserved Keywords: A Crack branching and bifurcation; B Ceramic material; C. Asymptotic analysis 1. Introduction Fibre reinforced ceramic matrix composites and ceramic laminates are increasingly considered for various applications because their fabrication can be tailored to meet ecific properties like high strength at high temperatures(Moya, 1995; Evans author.Fax:+33-1-4427-5259 dol@ccr jussieu. fr (D. Leguillon) 0022-5096/00/S- see front matter 2000 Elsevier Science Ltd. All rights reserved PI:S0022-5096(99)00101-5Journal of the Mechanics and Physics of Solids 48 (2000) 2137–2161 www.elsevier.com/locate/jmps Interface debonding ahead of a primary crack D. Leguillon a,*, C. Lacroix a , E. Martin b a Laboratoire de Mode´lisation en Me´canique, CNRS UMR 7607, Universite´ Pierre et Marie Curie, Paris 6, 8 rue du Capitaine Scott, 75015 Paris, France b Laboratoire de Ge´nie Me´canique, UPRES 496, IUT A, Universite´ de Bordeaux I, 33405 Talence, France Received 2 July 1999; received in revised form 18 November 1999 Abstract The debonding of an interface between two elastic materials is assumed to occur ahead of a primary crack lying in material 1. Conditions for such a mechanism are derived from an asymptotic analysis and depend on the elastic mismatch between the two materials as well as on material 1 and interface toughnesses. The ligament width between the primary crack tip and the interface and the debond nucleation length can be determined if the interface strength is known. A similar mechanism involving a crack nucleation ahead of the primary crack in material 2 is also examined. Deflection prediction is derived from an energetic criterion which is in general more favourable to deflection than the He and Hutchinson one. The former decreases asymptotically towards the latter. Moreover, if the crack lies in the stiffest material, results show that these nucleation mechanisms are highly improbable. If material 2 and inter￾face strengths are known, a stress criterion is naturally derived. The presented analysis is independent of the applied loads and of the geometry of the specimen.  2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Crack branching and bifurcation; B. Ceramic material; C. Asymptotic analysis 1. Introduction Fibre reinforced ceramic matrix composites and ceramic laminates are increasingly considered for various applications because their fabrication can be tailored to meet specific properties like high strength at high temperatures (Moya, 1995; Evans, * Corresponding author. Fax: +33-1-4427-5259. E-mail address: dol@ccr.jussieu.fr (D. Leguillon). 0022-5096/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 00 22 -5096(99)00101-5