Acta mater. VoL 46, No 9, pp. 3237-3245. 1998 Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain PI!:Sl359-6454(98)0008-1 1359-6454/98s19.00+0.00 INTERFACIAL SHEAR DEBONDING PROBLEMS IN FIBER-REINFORCED CERAMIC COMPOSITES CHUN-HWAY HSUEH and P. F BECHeR Metals and Ceramics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831,US.A. (Received 3 September 1997; accepted in revised form 5 December 1997) Abstract--Toughening of fiber-reinforced ceramic composites by fiber pullout relies on mode II debonding at the fiber/matrix interface. This mode Il debonding has been analyzed using the strength-based and the energy-based criteria, in which the interfacial shear strength and the interface debond energy are respect- ely adopted to characterize the debonding behavior. Using the concept of griffith theory, an effective cumferential defect at the interface is defined to account for the stress intensity due to the presence of the fiber in the matrix and the fiber-pullout geometry. This effective circumferential defect is then used to de- of interfacial debonding vs fiber fracture for a bridging fiber behind the crack tip is established using the energy-based criterion. C 1998 Acta Metallurgica Inc. 1 INTRODUCTION hence raised as to whether the initial debond stress rtant toughening mechanism in fiber for fiber pullout in a fiber-reinforced ceramic ce inforced ceramic composites is pullout of fibers posite can be related to any defect at the interface from the matrix during matrix cracking [1, 2. This Considering two semi-infinite elastic materials relies on mode Il (i.e. shear) debonding at the fiber/ bonded at the interface, the crack propagation pro- matrix interface which can be analyzed using either blem has been analyzed by He and Hutchinson [18] the strength-based or the energy-based criterion. In When a crack reaches the interface. the crack he strength-based approach (3-61. interfacial either deflects into the interface or penetrates into debonding occurs when the maximum interfacial the next layer depending upon the ratio of the shear stress induced by loading reaches the inter- energy release rate due to debonding to that due to facial shear strength, ts. In the energy-based crack penetration. This criterion [18] has been used approach [7-12], a sharp mode Il crack propagating extensively to predict interfacial debonding vs fiber along the interface is considered and interfacial fracture for a crack propagating in a fiber-re- debonding occurs when the energy release rate due inforced ceramic composite. However, the crack o crack propagation, Gi, reaches the interface propagation problem in fiber-reinforced composites debond energy, I Based on the above two debond- is three-dimensional. For an embedded fiber of a ing criteria, the required loading stress on the fiber finite radius, there are three options when a matrix during fiber pullout to initiate interfacial debonding crack reaches the interface: the interface can (i.e. the initial debond stress ), ad, has been derived. debond, the fiber can fracture, or the crack can Assuming that t, and Ti are intrinsic material cumvent the fiber. The analysis by He and properties, the predicted dependence of the initial Hutchinson focuses on the case that the matrix debond stress on the other material properties (i.e. crack does not circumvent the fiber. However, when the embedded fiber length. elastic constants and the matrix crack circumvents the fiber, the matrix dimensions of the fiber and the matrix) has been crack is bridged by intact fibers, and the fiber-pull- compared for the above two debonding criteria [12 ]. out geometry can be used as a representative For a given composite system, interfacial debonding volume element for this case. Hence, the second can be strength-governed or energy-governed [13] issue is how the condition of interfacial debonding and both criteria have been supported by different vs fiber fracture is modified for the case of a brid xperimental results [14-16. The first issue con fib elationship The purpose of the present study address between ts and Ti. Also, for a monolithic ceramic, the above two issues. First, some of the existing sol- the tensile strength can be related to its defect size utions of the initial debond stresses based on the Griffith theory [17]. a question is strength and the energy criteria are summarizedINTERFACIAL SHEAR DEBONDING PROBLEMS IN FIBER-REINFORCED CERAMIC COMPOSITES CHUN-HWAY HSUEH and P. F. BECHER Metals and Ceramics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831, U.S.A. (Received 3 September 1997; accepted in revised form 5 December 1997) AbstractÐToughening of ®ber-reinforced ceramic composites by ®ber pullout relies on mode II debonding at the ®ber/matrix interface. This mode II debonding has been analyzed using the strength-based and the energy-based criteria, in which the interfacial shear strength and the interface debond energy are respect￾ively adopted to characterize the debonding behavior. Using the concept of Grith theory, an e€ective cir￾cumferential defect at the interface is de®ned to account for the stress intensity due to the presence of the ®ber in the matrix and the ®ber-pullout geometry. This e€ective circumferential defect is then used to de￾rive the relation between the interfacial shear strength and the interface debond energy. Also, the condition of interfacial debonding vs ®ber fracture for a bridging ®ber behind the crack tip is established using the energy-based criterion. # 1998 Acta Metallurgica Inc. 1. INTRODUCTION An important toughening mechanism in ®ber-re￾inforced ceramic composites is pullout of ®bers from the matrix during matrix cracking [1, 2]. This relies on mode II (i.e. shear) debonding at the ®ber/ matrix interface which can be analyzed using either the strength-based or the energy-based criterion. In the strength-based approach [3±6], interfacial debonding occurs when the maximum interfacial shear stress induced by loading reaches the inter￾facial shear strength, ts. In the energy-based approach [7±12], a sharp mode II crack propagating along the interface is considered and interfacial debonding occurs when the energy release rate due to crack propagation, Gi, reaches the interface debond energy, Gi. Based on the above two debond￾ing criteria, the required loading stress on the ®ber during ®ber pullout to initiate interfacial debonding (i.e. the initial debond stress), sd, has been derived. Assuming that ts and Gi are intrinsic material properties, the predicted dependence of the initial debond stress on the other material properties (i.e. the embedded ®ber length, elastic constants and dimensions of the ®ber and the matrix) has been compared for the above two debonding criteria [12]. For a given composite system, interfacial debonding can be strength-governed or energy-governed [13] and both criteria have been supported by di€erent experimental results [14±16]. The ®rst issue con￾sidered in the present study is the relationship between ts and Gi. Also, for a monolithic ceramic, the tensile strength can be related to its defect size based on the Grith theory [17]. A question is hence raised as to whether the initial debond stress for ®ber pullout in a ®ber-reinforced ceramic com￾posite can be related to any defect at the interface. Considering two semi-in®nite elastic materials bonded at the interface, the crack propagation pro￾blem has been analyzed by He and Hutchinson [18]. When a crack reaches the interface, the crack either de¯ects into the interface or penetrates into the next layer depending upon the ratio of the energy release rate due to debonding to that due to crack penetration. This criterion [18] has been used extensively to predict interfacial debonding vs ®ber fracture for a crack propagating in a ®ber-re￾inforced ceramic composite. However, the crack propagation problem in ®ber-reinforced composites is three-dimensional. For an embedded ®ber of a ®nite radius, there are three options when a matrix crack reaches the interface: the interface can debond, the ®ber can fracture, or the crack can cir￾cumvent the ®ber. The analysis by He and Hutchinson focuses on the case that the matrix crack does not circumvent the ®ber. However, when the matrix crack circumvents the ®ber, the matrix crack is bridged by intact ®bers, and the ®ber-pull￾out geometry can be used as a representative volume element for this case. Hence, the second issue is how the condition of interfacial debonding vs ®ber fracture is modi®ed for the case of a brid￾ging ®ber. The purpose of the present study is to address the above two issues. First, some of the existing sol￾utions of the initial debond stresses based on the strength and the energy criteria are summarized. Acta mater. Vol. 46, No. 9, pp. 3237±3245, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain PII: S1359-6454(98)00008-1 1359-6454/98 $19.00 + 0.00 3237