Availableonlineatwww.sciencedirect.co ScienceDirect Acta materialia ELSEVIER Acta Materialia 55(2007)409-421 www.actamat-journals.com Prediction of the fracture toughness of a ceramic multilayer composite Modeling and experiments C R Chen a. Pascual b F D. Fischer .o. Kolednik d, *R. Danzer b Materials Center Leoben Forschung GmbH, Franz-Josef-Strasse 13, A-8700 Leoben, austria truktur und Funktionskeramik. Montanumiversitat Leoben. Peter. Tunner. Strasse 5.A-8700 Leoben. austria Institute of Mechanics, Montanumirersitat Leoben, Franz-Josef-Strasse 18, A-8700 d erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Jahnstrasse 12, 4-8700 Leoben, Austria Received 24 March 2006: received in revised form 28 June 2006: accepted 2 July 2006 Available online 7 November 2006 Abstract equires experiments to measure the intrinsic fracture toughness of the phases and to determine the required material data. The numerical modeling includes a conventional finite element stress analysis and the calculation of the crack driving force based on the concept of configurational(material)forces. The procedure yields the fracture toughness of the composite as a function of the crack length. a bend- bar consisting of layers made of alumina and an alumina-zirconia composite is investigated The bar has a crack perpendicular to the interfaces. The spatial variations of both the thermal residual stresses and the elastic modulus induce shielding and anti-shielding effects on the crack, which are quantified. The numerically predicted fracture toughness is compared with the experimental values. o 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved Keywords: Ceramics: Multilayer; Fracture toughness; Crack tip shielding: Thermal residual stresses 1. Introduction oxide fuel cells [8] but also in structural applications such as dental restorations or hip replacements [5] To improve the performance against brittle failure in A prerequisite for the application of multilayer ceramic materials, strategies have been developed in recent is the understanding of their resistance against crack initi- years to design tough and strong ceramics consisting of ation and propagation. Different authors have predicted multilayers. These strategies include the tailoring of weak the toughening effect of the residual stress state by means interfaces for crack deflection or the design of multilayers of the weight function method [1, 3, 9, 10]. They used the with compressive residual stresses in the outer layers [1]. classical weight function concept to calculate the stress The beneficial consequences of compressive stresses at the intensity factor, considering an inhomogeneous distribu rface are well known: increases in strength, fracture tion of the residual stresses in a homogeneous body (mostly oughness and reliability [2, 3]. Additionally, the wear resis- with the elastic modulus of the first layer). According to tance is enhanced [4]. Therefore, such ceramics receive seri- Fett et al. [11, 12] an approximate weight function method ous consideration for structural application [5-7]. Ceramic can also be applied to heterogeneous, graded or laminated multilayers have already found functional applications in materials with a variable Youngs modulus. substrates for low-load-bearing integrated circuits or solid The immanent inhomogeneity of the material, however causes implications which are not taken into account by the weight function method: spatially varying material proper- Tel: +43 114: fax: +43 3842804116. ties induce an additional crack driving force term. The nik(aunileoben ac at(O. Kolednik ) propagation of a crack in a direction orthogonal to the 1359-6454/$30.00 O 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:l0.1016 actant200607.046Prediction of the fracture toughness of a ceramic multilayer composite – Modeling and experiments C.R. Chen a , J. Pascual b , F.D. Fischer c , O. Kolednik d,*, R. Danzer b a Materials Center Leoben Forschung GmbH, Franz-Josef-Strasse 13, A-8700 Leoben, Austria b Institut fu¨r Struktur- und Funktionskeramik, Montanuniversita¨t Leoben, Peter-Tunner-Strasse 5, A-8700 Leoben, Austria c Institute of Mechanics, Montanuniversita¨t Leoben, Franz-Josef-Strasse 18, A-8700 Leoben, Austria d Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Jahnstrasse 12, A-8700 Leoben, Austria Received 24 March 2006; received in revised form 28 June 2006; accepted 2 July 2006 Available online 7 November 2006 Abstract A procedure to predict the fracture toughness of a ceramic multilayer composite made of different phases is presented. The procedure requires experiments to measure the intrinsic fracture toughness of the phases and to determine the required material data. The numerical modeling includes a conventional finite element stress analysis and the calculation of the crack driving force based on the concept of configurational (material) forces. The procedure yields the fracture toughness of the composite as a function of the crack length. A bend￾ing bar consisting of layers made of alumina and an alumina–zirconia composite is investigated. The bar has a crack perpendicular to the interfaces. The spatial variations of both the thermal residual stresses and the elastic modulus induce shielding and anti-shielding effects on the crack, which are quantified. The numerically predicted fracture toughness is compared with the experimental values. 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Ceramics; Multilayer; Fracture toughness; Crack tip shielding; Thermal residual stresses 1. Introduction To improve the performance against brittle failure in ceramic materials, strategies have been developed in recent years to design tough and strong ceramics consisting of multilayers. These strategies include the tailoring of weak interfaces for crack deflection or the design of multilayers with compressive residual stresses in the outer layers [1]. The beneficial consequences of compressive stresses at the surface are well known: increases in strength, fracture toughness and reliability [2,3]. Additionally, the wear resis￾tance is enhanced [4]. Therefore, such ceramics receive seri￾ous consideration for structural application [5–7]. Ceramic multilayers have already found functional applications in substrates for low-load-bearing integrated circuits or solid oxide fuel cells [8], but also in structural applications such as dental restorations or hip replacements [5]. A prerequisite for the application of multilayer ceramics is the understanding of their resistance against crack initi￾ation and propagation. Different authors have predicted the toughening effect of the residual stress state by means of the weight function method [1,3,9,10]. They used the classical weight function concept to calculate the stress intensity factor, considering an inhomogeneous distribu￾tion of the residual stresses in a homogeneous body (mostly with the elastic modulus of the first layer). According to Fett et al. [11,12], an approximate weight function method can also be applied to heterogeneous, graded or laminated materials with a variable Young’s modulus. The immanent inhomogeneity of the material, however, causes implications which are not taken into account by the weight function method: spatially varying material proper￾ties induce an additional crack driving force term. The propagation of a crack in a direction orthogonal to the 1359-6454/$30.00 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.07.046 * Corresponding author. Tel.: +43 3842 804 114; fax: +43 3842 804 116. E-mail address: kolednik@unileoben.ac.at (O. Kolednik). www.actamat-journals.com Acta Materialia 55 (2007) 409–421