Engineering Fracture Mechanics PERGAMON Engineering Fracture Mechanics 65(2000)15-28 On crack-wake debonding in fiber reinforced ceramics Yih-Cherng Chiang ring, Chinese Culture University, No 55. Hua-Kang Road, Taipei, Taiwan Received 6 March 1999: received in revised form 4 September 1999: accepted 8 November 1999 Abstract In this paper, the effect of interfacial debonding in the wake of a crack on the stress for matrix cracking is studied for unidirectional fiber reinforced ceramics. A simple shear-lag model is adopted to calculate the stress and strain fields in the fiber and the matrix. a criterion for crack-wake debonding is proposed by treating the debonding process as a particular crack propagation problem. Then, by using an energy balance approach the formulation of the matrix cracking stress of an infinite fiber-bridged crack is derived. The theoretical results are compared with experimental data of Sic/borosilicate, SiC/LAS and C/borosilicate ceramic composites. C 2000 Elsevier Science Ltd. All rights reserved Keywords: Interfacial debonding: Matrix cracking: Ceramics; Composites 1. Introduction Studies, both from theoretical analyses and experimental observations, have indicated that interfacial properties are the key factors to developing a successful fiber reinforced brittle matrix composite. For analytical modeling, both the energy balance approach suggested by Aveston, Cooper and Kelly(ACK) [1, 2] and the fracture mechanics approach proposed by Marshall et al. [3] and McCartney [4] have been used to investigate the influence of interfacial properties on the matrix cracking stress. In these analyses, the fiber/matrix interface was assumed to be either perfectly bonded or unbonded but susceptible to weak frictional resistance. For the perfectly bonded composite, the fiber and matrix deform elastically above the crack plane and no relative fiber/matrix slippage occurs as the matrix crack propagates. The analytical expression of the matrix cracking stress by Aveston and Kelly [2] relates to the elastic properties and the geometrical constants of the fiber and the matrix; no specific interfacial property appears in the analytical expression of the matrix cracking stress. As the interface is unbonded and Fax:+886-2-2861-5241 E-mailaddress.johnycc(@gmail.gcn.net.tw(.-C.Chiang) 0013-794400/S- see front matter 2000 Elsevier Science Ltd. All rights reserved PI:S0013-7944(99)00130-7On crack-wake debonding in ®ber reinforced ceramics Yih-Cherng Chiang* Department of Mechanical Engineering, Chinese Culture University, No. 55, Hua-Kang Road, Taipei, Taiwan Received 6 March 1999; received in revised form 4 September 1999; accepted 8 November 1999 Abstract In this paper, the e€ect of interfacial debonding in the wake of a crack on the stress for matrix cracking is studied for unidirectional ®ber reinforced ceramics. A simple shear-lag model is adopted to calculate the stress and strain ®elds in the ®ber and the matrix. A criterion for crack-wake debonding is proposed by treating the debonding process as a particular crack propagation problem. Then, by using an energy balance approach the formulation of the matrix cracking stress of an in®nite ®ber-bridged crack is derived. The theoretical results are compared with experimental data of SiC/borosilicate, SiC/LAS and C/borosilicate ceramic composites. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Interfacial debonding; Matrix cracking; Ceramics; Composites 1. Introduction Studies, both from theoretical analyses and experimental observations, have indicated that interfacial properties are the key factors to developing a successful ®ber reinforced brittle matrix composite. For analytical modeling, both the energy balance approach suggested by Aveston, Cooper and Kelly (ACK) [1,2] and the fracture mechanics approach proposed by Marshall et al. [3] and McCartney [4] have been used to investigate the in¯uence of interfacial properties on the matrix cracking stress. In these analyses, the ®ber/matrix interface was assumed to be either perfectly bonded or unbonded but susceptible to weak frictional resistance. For the perfectly bonded composite, the ®ber and matrix deform elastically above the crack plane and no relative ®ber/matrix slippage occurs as the matrix crack propagates. The analytical expression of the matrix cracking stress by Aveston and Kelly [2] relates to the elastic properties and the geometrical constants of the ®ber and the matrix; no speci®c interfacial property appears in the analytical expression of the matrix cracking stress. As the interface is unbonded and Engineering Fracture Mechanics 65 (2000) 15±28 0013-7944/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 3 - 7 9 4 4 ( 9 9 ) 0 0 1 3 0 - 7 www.elsevier.com/locate/engfracmech * Fax: +886-2-2861-5241. E-mail address: johnycc@gmail.gcn.net.tw (Y.-C. Chiang)