Availableonlineatwww.sciencedirect.com Science Direct E噩≈RS ELSEVIER Joumal of the European Ceramic Society 28(2008)1551-1556 www.elsevier.comlocate/jeurceramsoc fracture statistics of ceramic laminates strengthened by compressive residual stresses Javier Pascual Tanja Lube a, * Robert Danzer a, Institut fiir Struktur- und Funktionskeramik, Montanuniversitit Leoben, Peter Tinner StraBe 5. A-8700 Leoben, austria Materials Center Leoben Forschung GmbH, Franz Josef StraBe 13. A-8700 Leoben, Austria Received 25 August 2007; accepted 12 October 2007 Available online 27 December 2007 Ceramic multilayer composites have been developed in recent years to enhance toughness and reliability of ceramics. It has been demonstrated by theoretical as well as experimental means, that surface compressive stresses protect the composite against the negative action of surface flaws. The behaviour of an alumina-aluminazirconia laminate having significant compressive residual stresses at its alumina surface is investigated pared to alumina specimens its strength is increased by the amplitude of the residual compressive surface stress, which is also a lower threshold value for strength. The consequences of that behaviour for the fracture statistics and reliability are discussed 2007 Elsevier Ltd. All rights reserved. Keywords: Strength: Fracture: Al2O3: ZrO2: Laminate Introduction distribution function, which, in its simplest form and for volume general-starts from small flaws, which are distributed in the given by,d mogene specimen of volume V and loaded in a t flaws distributed in Ceramic materials suffer from brittle fracture. which -in axial and he ous tensile stress state with amplitude, o, is materialoron its surface. The strength of a specimen is defined by the major flaw, i. e. by its shape, size, orientation and its posi- F(o. V)=1-exP[vo(0o tion in the specimen. 4 In general it is assumed that flaws behave similarly to cracks. Thus a fracture mechanical failure crite- The Weibull modulus m depends on the distribution of the flaw can be defined, which correlates the strength of the specimen sizes. ,0 It describes the scatter of the strength data: the smaller Griffith/Irwin criterion the strength(or) is inverse proportional volume. The characteristic strength oo is the stress at whic, a with the size of the crack. For example, following the well known is m, the larger is the scatter. Vo is an arbitrary normalise to the square root of the size(a) of the crack-: or a 1/va. for specimen of volume V=Vo-the probability of failure is 63% Since the size and position of flaws are statistically distributed (F=63%). ao and Vo are not independent. The two independent the strength of ceramic specimens shows a large scatter and parameters are m and Voo Even for very small tensile stresses design with ceramic materials has to be performed with statisti- being only a little above zero some probability of fracture exists. cal means Strength tests show that the probability of failure, F, All specimens tested in this study had a nominally identical increases with the applied load and the size of the specin size and were tested under nominally identical conditions. In the This behaviour is well described by the two-parameter Weibull following, the normalising volume in Eq (1) is set equal to the pecimens volume(v=vo). If surface flaws are important an analogous weibull distribution for surface flaws can be found Corresponding author. Tel:+4338424024100: fax: +43 38424024102. and the analogous simplification will be used E-mail addresses: javier. pascual @rhi-ag com(. Pascual), The probability of failure depends sensibly on the parameters Now with RHI AG Technology Center, Standort Leoben, 8700 Leoben, in the Weibull distribution which must therefore be determined MagnesitstraBe 2, Austria. with the highest possible precision. Yet, the experimental deter 2Tel:+433842459220;fax:+433842459225 mination of a Weibull distribution is expensive and laborious 0955-2219/S-see front matter o 2007 Elsevier Ltd. All rights reserved. doi: 10.1016/j-jeurceramsoc 2007 10.005Available online at www.sciencedirect.com Journal of the European Ceramic Society 28 (2008) 1551–1556 Fracture statistics of ceramic laminates strengthened by compressive residual stresses Javier Pascual a,1, Tanja Lube a,∗, Robert Danzer a,b,2 a Institut f ¨ur Struktur- und Funktionskeramik, Montanuniversit ¨at Leoben, Peter Tunner Straße 5, A-8700 Leoben, Austria b Materials Center Leoben Forschung GmbH, Franz Josef Straße 13, A-8700 Leoben, Austria Received 25 August 2007; accepted 12 October 2007 Available online 27 December 2007 Abstract Ceramic multilayer composites have been developed in recent years to enhance toughness and reliability of ceramics. It has been demonstrated by theoretical as well as experimental means, that surface compressive stresses protect the composite against the negative action of surface flaws. The behaviour of an alumina–alumina/zirconia laminate having significant compressive residual stresses at its alumina surface is investigated. Compared to alumina specimens its strength is increased by the amplitude of the residual compressive surface stress, which is also a lower threshold value for strength. The consequences of that behaviour for the fracture statistics and reliability are discussed. © 2007 Elsevier Ltd. All rights reserved. Keywords: Strength; Fracture; Al2O3; ZrO2; Laminate 1. Introduction Ceramic materials suffer from brittle fracture, which – in general – starts from small flaws, which are distributed in the material or on its surface.1,2 The strength of a specimen is defined by the major flaw, i.e. by its shape, size, orientation and its posi￾tion in the specimen.3,4 In general it is assumed that flaws behave similarly to cracks.1–6 Thus a fracture mechanical failure crite￾rion can be defined, which correlates the strength of the specimen with the size of the crack. For example, following the well known Griffith/Irwin criterion the strength (σf) is inverse proportional to the square root of the size (a) of the crack1–6: σf ∝ 1/ √a. Since the size and position of flaws are statistically distributed the strength of ceramic specimens shows a large scatter and design with ceramic materials has to be performed with statisti￾cal means. Strength tests show that the probability of failure, F, increases with the applied load and the size of the specimen.2,5,6 This behaviour is well described by the two-parameter Weibull ∗ Corresponding author. Tel.: +43 3842 402 4100; fax: +43 3842 402 4102. E-mail addresses: javier.pascual@rhi-ag.com (J. Pascual), tanja.lube@mu-leoben.at (T. Lube). 1 Now with RHI AG Technology Center, Standort Leoben, 8700 Leoben, Magnesitstraße 2, Austria. 2 Tel.: +43 3842 45922 0; fax: +43 3842 45922 5. distribution function, which, in its simplest form and for volume flaws distributed in a specimen of volume V and loaded in a uni￾axial and homogeneous tensile stress state with amplitude, σ, is given by7,8: F(σ, V) = 1 − exp − V V0 σ σ0 m (1) The Weibull modulus m depends on the distribution of the flaw sizes.9,10 It describes the scatter of the strength data: the smaller is m, the larger is the scatter. V0 is an arbitrary normalising volume. The characteristic strength σ0 is the stress at which – for specimen of volume V = V0 – the probability of failure is 63% (F = 63%). σ0 and V0 are not independent. The two independent parameters are m and V0σm 0 . Even for very small tensile stresses being only a little above zero some probability of fracture exists. All specimens tested in this study had a nominally identical size and were tested under nominally identical conditions. In the following, the normalising volume in Eq. (1) is set equal to the specimens’ volume (V = V0). If surface flaws are important an analogous Weibull distribution for surface flaws can be found and the analogous simplification will be used. The probability of failure depends sensibly on the parameters in the Weibull distribution, which must therefore be determined with the highest possible precision. Yet, the experimental deter￾mination of a Weibull distribution is expensive and laborious. 0955-2219/$ – see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2007.10.005