MECHANI MATERIALS ELSEVIER Mechanics of Materials 29(1998)111-121 Effect of microstructural parameters on the fracture behavior of fiber-reinforced ceramics Yu-Fu Liu a*, Chitoshi Masuda Ryoji Yuuki b National Research Institute for Metals, 1-2-1 Sengen, Tsukuba 305, Japan nstitute of Industrial Science, University of Tokyo, Tokyo, Japan Received 30 May 1997 Abstract A bridging law which includes both interfacial debonding and sliding properties in fiber-rei ceramics is applied to fiber bridging analysis and crack growth problems by treating bridging fibers as a distribution of closure stress. A numerical method to solve distributed spring model of a penny-shaped crack is provided to determine the bridging stress, debond length, crack opening displacement and stress intensity factor. By introducing fracture criteria of the composite and fiber, crack growth behavior in R-curve for the penny-shaped crack are simulated and the effects of such microstructural parameters as interface debonding toughness, compressive residual stress, frictional sliding stress, and fiber volume fraction on the R-curve are quantified in an explicit manner. On the basis of R-curve results, the toughening mechanism of fiber-reinforced ceramics is discussed. @1998 Elsevier Science Ltd. All rights reserved Keywords: Microstructural parameters; Fracture behavior; Fiber-reinforced ceramics 1. Introduction approximation levels exist with regards to bridging laws(Marshall and Cox, 1985; Budiansky et al The contribution of fiber bridging in fiber-rein- 1986 Budiansky and Amazigo, 1989, Budiansky et forced ceramics to toughness enhancement is widely al., 1995; Meda and Steif, 1994), inter facial proper accepted and the toughness increment due to fiber ties( Gao et al., 1988; Hutchinson and Jensen, 1990), bridging is governed by the constitutive relation fiber and composite anisotropy(Hutchinson and between the fiber bridging stress and crack opening Jensen, 1990; Marshall, 1992; Luo and Ballarini, isplacement, ie, bridging law. In the bridging law, 1994), among arguments on bridging length scales the mechanical properties of the fiber-matrix inter-(Bao and Suo, 1992; Cox, 1993; Cox and Marshall face play an important role. Various treatment and 1994), initial flaw size and specimen geometrical effect( Cox and Marshall, 1991; Budiansky and Cui, 1994). Early studies (for example, Aveston et al 1971) used one parameter, i. e, constant shear fric- tional stress. to deal with the interfacial resistance (formerly Associate Professor) effect, which is presumably applicable to composite 0167-6636/98/S19.00@ 1998 Elsevier Science Ltd. All rights reserved PS0167-6636(98)00009XMechanics of Materials 29 1998 111–121 Ž . Effect of microstructural parameters on the fracture behavior of fiber-reinforced ceramics Yu-Fu Liu a,), Chitoshi Masuda a , Ryoji Yuuki b,1 a National Research Institute for Metals, 1-2-1 Sengen, Tsukuba 305, Japan b Institute of Industrial Science, UniÕersity of Tokyo, Tokyo, Japan Received 30 May 1997 Abstract A bridging law which includes both interfacial debonding and sliding properties in fiber-reinforced ceramics is applied to fiber bridging analysis and crack growth problems by treating bridging fibers as a distribution of closure stress. A numerical method to solve distributed spring model of a penny-shaped crack is provided to determine the bridging stress, debond length, crack opening displacement and stress intensity factor. By introducing fracture criteria of the composite and fiber, crack growth behavior in R-curve for the penny-shaped crack are simulated and the effects of such microstructural parameters as interface debonding toughness, compressive residual stress, frictional sliding stress, and fiber volume fraction on the R-curve are quantified in an explicit manner. On the basis of R-curve results, the toughening mechanism of fiber-reinforced ceramics is discussed. q 1998 Elsevier Science Ltd. All rights reserved. Keywords: Microstructural parameters; Fracture behavior; Fiber-reinforced ceramics 1. Introduction The contribution of fiber bridging in fiber-rein￾forced ceramics to toughness enhancement is widely accepted and the toughness increment due to fiber bridging is governed by the constitutive relation between the fiber bridging stress and crack opening displacement, i.e., bridging law. In the bridging law, the mechanical properties of the fiber–matrix inter￾face play an important role. Various treatment and ) Corresponding author. 1 Deceased formerly Associate Professor . Ž . approximation levels exist with regards to bridging laws Marshall and Cox, 1985; Budiansky et al., Ž 1986; Budiansky and Amazigo, 1989; Budiansky et al., 1995; Meda and Steif, 1994 , interfacial proper- . ties Gao et al., 1988; Hutchinson and Jensen, 1990 , Ž . fiber and composite anisotropy Hutchinson and Ž Jensen, 1990; Marshall, 1992; Luo and Ballarini, 1994 , among arguments on bridging length scales . ŽBao and Suo, 1992; Cox, 1993; Cox and Marshall, 1994 , initial flaw size and specimen geometrical . effect Cox and Marshall, 1991; Budiansky and Cui, Ž 1994 . Early studies for example, Aveston et al., . Ž 1971 used one parameter, i.e., constant shear fric- . tional stress, to deal with the interfacial resistance effect, which is presumably applicable to composite 0167-6636r98r$19.00 q 1998 Elsevier Science Ltd. All rights reserved. PII S0167-6636 98 00009-X Ž