Availableonlineatwww.sciencedirect.com SCIENCE DIRECT E噩≈S ELSEVIER Journal of the European Ceramic Society 26(2006)343-349 www.elsevier.com/locate/jeurceran Prediction of crack deflection in porous/dense ceramic laminates D. Leguillona*,S.Tariolleb, E. Martin, T. Chartier, J.L. Besson a LMM, CNRS UMR7607, Universite P et M. Curie, case 162, 4 place Jussieu. 75252 Paris Cedex 05, france b CES CNRS UMR 5146. Ecole des mines de saint-Etienne. St Etienne. france c LCTS. CNRS UMR 5801 Universite bordeaux Pessac france d sPCTS, CNRS UMR 6638, E. N.S. de Ceramique Industrielles, Limoges, france Received 24 June 2004; received in revised form 4 November 2004; accepted 12 November 2004 Abstract The arrangement of ceramic layers in laminated structures is an interesting way to enhance the flaw tolerance of brittle ceramic materials The interfaces are expected to deflect cracks, increasing the fracture energy of the laminate compared to a monolithic material and thus raising Laminates have been fabricated with alternating dense and porous layers of the same material, i.e. SiC or B. C, in order to obtain a good chemical compatibility between the laminas and almost no thermal residual stresses. Porosity, in the porous layers, is achieved by incorporating organic particles which are removed during the debinding step. In this context, the target of this study is to predict the volume fraction of pores, in the porous layer, required to cause crack deflection. The proposed criterion derives from an energy balance. It relies on a two-scale analysis taking into account the laminated structure of the material. It can be written in terms of two relevant material parameters: the ratio of Youngs moduli of the dense and porous materials and toughness ratios. a unique function depending on the volume fraction of pores can be used to express the two above-mentioned ratios Assuming a cubic lattice of spherical voids, the parameters of the porous ceramic depend linearly on the porosity and vanish at the point of percolation of pores. As a consequence, the criterion can be rewritten in term of a single parameter: the porosity. Crack deflection is permitted only for very high values of the porosity. Predicted values agree satisfactorily with experiments on Sic and B.C. The comparison with the He and hutchinson criterion shows that this latter underestimates the correct value C 2004 Elsevier Ltd. All rights reserved Keywords: Fracture; Toughness and toughening: Laminates; Porosity 1. Introduction ally fabricated by stacking layers of different compositions in a suitable sequence. Alternating dense and porous layer Laminated structures with weak interfaces or interphases of the same material offers the best chemical compatibility constitute one strategy to improve the flaw tolerance of brit- and almost no thermal residual stresses. Crack deflection ha tle ceramic materials. These structures have proved to be ef- been observed within such systems as the result of the pres- ficient in increasing fracture energy by promoting crack de- ence of porous interlayers. - The question is thus to predict flection mechanisms at interfaces between layers: cracks that the volume fraction of pores, in the porous layers, required form in one layer are deflected along the interface with adja- to cause crack deflection nt layers which increases the fracture energy of the laminate Two kinds of ceramic laminates are analysed silicon car- compared to that of a monolithic material and thus raises the bide(Sic)2-7 and boron carbide(B4C).7, 8 The specimens apparent toughness. Laminar ceramic composites are gener- are fabricated by stacking layers obtained by tape-casting and then by lamination, debinding and sintering. Porosity of Corresponding author. Tel. +33 144 275 322; fax: +33 144 275 259 porous layers is introduced by adding pore-forming agents E-mail address: dol(@ccr, jussieu. fr(D. Leguillon) such as corn starch or polymer particles. These organic par- 0955-2219/S-see front matter c 2004 Elsevier Ltd. All rights reserved doi: 10.1016/j. jeurceramsoc 2004.1 1.003Journal of the European Ceramic Society 26 (2006) 343–349 Prediction of crack deflection in porous/dense ceramic laminates D. Leguillona,∗, S. Tariolleb, E. Martinc, T. Chartierd, J.L. Bessond a LMM, CNRS UMR7607, Universit´e P. et M. Curie, case 162, 4 place Jussieu, 75252 Paris Cedex 05, France b CES, CNRS UMR 5146, Ecole des Mines de Saint-Etienne, St Etienne, France c LCTS, CNRS UMR 5801, Universit´e Bordeaux 1, Pessac, France d SPCTS, CNRS UMR 6638, E.N.S. de C´eramiques Industrielles, Limoges, France Received 24 June 2004; received in revised form 4 November 2004; accepted 12 November 2004 Available online 19 January 2005 Abstract The arrangement of ceramic layers in laminated structures is an interesting way to enhance the flaw tolerance of brittle ceramic materials. The interfaces are expected to deflect cracks, increasing the fracture energy of the laminate compared to a monolithic material and thus raising the toughness. Laminates have been fabricated with alternating dense and porous layers of the same material, i.e. SiC or B4C, in order to obtain a good chemical compatibility between the laminas and almost no thermal residual stresses. Porosity, in the porous layers, is achieved by incorporating organic particles which are removed during the debinding step. In this context, the target of this study is to predict the volume fraction of pores, in the porous layer, required to cause crack deflection. The proposed criterion derives from an energy balance. It relies on a two-scale analysis taking into account the laminated structure of the material. It can be written in terms of two relevant material parameters: the ratio of Young’s moduli of the dense and porous materials and toughness ratios. A unique function depending on the volume fraction of pores can be used to express the two above-mentioned ratios. Assuming a cubic lattice of spherical voids, the parameters of the porous ceramic depend linearly on the porosity and vanish at the point of percolation of pores. As a consequence, the criterion can be rewritten in term of a single parameter: the porosity. Crack deflection is permitted only for very high values of the porosity. Predicted values agree satisfactorily with experiments on SiC and B4C. The comparison with the He and Hutchinson criterion shows that this latter underestimates the correct value. © 2004 Elsevier Ltd. All rights reserved. Keywords: Fracture; Toughness and toughening; Laminates; Porosity 1. Introduction Laminated structures with weak interfaces or interphases constitute one strategy to improve the flaw tolerance of brit￾tle ceramic materials. These structures have proved to be ef- ficient in increasing fracture energy by promoting crack de- flection mechanisms at interfaces between layers: cracks that form in one layer are deflected along the interface with adja￾cent layers which increases the fracture energy of the laminate compared to that of a monolithic material and thus raises the apparent toughness. Laminar ceramic composites are gener- ∗ Corresponding author. Tel.: +33 144 275 322; fax: +33 144 275 259. E-mail address: dol@ccr.jussieu.fr (D. Leguillon). ally fabricated by stacking layers of different compositions in a suitable sequence.1 Alternating dense and porous layers of the same material offers the best chemical compatibility and almost no thermal residual stresses. Crack deflection has been observed within such systems as the result of the pres￾ence of porous interlayers.2–9 The question is thus to predict the volume fraction of pores, in the porous layers, required to cause crack deflection. Two kinds of ceramic laminates are analysed: silicon car￾bide (SiC)2–7 and boron carbide (B4C).7,8 The specimens are fabricated by stacking layers obtained by tape-casting, and then by lamination, debinding and sintering. Porosity of porous layers is introduced by adding pore-forming agents such as corn starch or polymer particles. These organic par- 0955-2219/$ – see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2004.11.003