Acta mater. VoL 46, No 5, pp. 1657-1667, 1998 8y丿 Pergamon Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain PI!:Sl359-6454(97)00347-9 1359-6454/98s19.00+0.00 THE GENERATION OF MULTIPLE MATRIX CRACKING AND FIBER-MATRIX INTERFACIAL DEBONDING IN A GLASS COMPOSITE YONGJIAN SUN and RAJ N SINGHT Department of Materials Science and Engineering, University of Cincinnati, P O. Box 210012, Cincinnati. OH 45221-0012. U.S.A 7 Received 17 June 1997, accepted 10 September 1997) Abstract-The phenomena of multiple matrix cracking and fiber-matrix interfacial debonding are directly observed and analyzed in a transparent SiC fiber-reinforced borosilicate glass composite. Under a certain load, the number of matrix cracks and the length of interfacial debonding are directly measured because of the availability of this transparent glass composite. These observations on the interfacial debonding accom- nying the multiple matrix cracking, and their comparison with the theoretical analyses of the acking and debonding behaviors are presented. The micromechanics of matrix cracking, interfacial debonding, and associated matrix crack saturation/saturation stress are also analyzed. C 1998Acta Metallurgica Inc. 1 INTRODUCTION Ceramic materials exhibit superior mechanical increased because of the reinforcing fibers [2/are stress. ultimate strength. and work of fracture properties at high temperature. But, their use as Most research workers focused their interests on structural components is severely limited because of the study of first matrix cracking stress, ultimate their brittleness. Fiber-reinforced ceramic compo- strength of composites, and the significant role of sites, by incorporating fibers in ceramic matrices he interface on these two properties [2-5]. The however, not only exploit their attractive high-tem- study of the initial non-linear behavior of the com- perature strength but also enhance their toughness. posite after FMC. however, is not that extensive A typical load-displacement curve for a ceramic Firstly in early 1970s, from the consideration of composite subjected to tensile loading parallel to the maximum shear stress at the fiber-matrix inter- the fiber direction is shown in Fig. 1 [ At th face, Aveston and Kelly [6(Ak) proposed the fun- point A, the first matrix crack initiates when the damental concepts and relationships among matrix matrix reaches its elastic limit. If the fibers and crack spacing, interfacial debonding (or sliding) matrix are weakly-bonded or frictionally coupled, ength, and interfacial shear stress of a continuous he matrix crack propagates transversely across the fiber-reinforced composite. Since then Zok and fibers thus creating bridged-fibers to carry ad- Spearing [7 developed a model for multiple matrix ditional load. When this happens, the matrix crack crack spacing showing both the periodic and ran- deflects at the fiber/coating/matrix interfaces dom cracking patterns. Weitsman and Zhu [8] because of the interfacial debonding and sliding the increase of the applied load, more matrix TTTTTTTTTTTTTTTTTTTTTTTH cracks are generated and interfacial debonding pro- agates with a larger sliding zone. This process Fig.I. Point B indicates the saturation of the 3 80 leads to a non-linear curve between a and b in matrix cracking behavior. Beyond point B, the curve shows additional non-linear behavior until the onset of fiber failures and fiber pull-out at point C. This point C represents the strength of the com- posite, at which the breakage of a large number of ⊥⊥ fibers leads to decreased load-bearing capacity of 00.5 3.03.54.0 the composite. The first matrix cracking (FMC) Displacement (mm) Fig. 1. A typical load-displacement curve for a Sic fiber To whom all correspondence should be addressed.THE GENERATION OF MULTIPLE MATRIX CRACKING AND FIBER±MATRIX INTERFACIAL DEBONDING IN A GLASS COMPOSITE YONGJIAN SUN and RAJ N. SINGH{ Department of Materials Science and Engineering, University of Cincinnati, P.O. Box 210012, Cincinnati, OH 45221-0012, U.S.A. (Received 17 June 1997; accepted 10 September 1997) AbstractÐThe phenomena of multiple matrix cracking and ®ber±matrix interfacial debonding are directly observed and analyzed in a transparent SiC ®ber-reinforced borosilicate glass composite. Under a certain load, the number of matrix cracks and the length of interfacial debonding are directly measured because of the availability of this transparent glass composite. These observations on the interfacial debonding accom￾panying the multiple matrix cracking, and their comparison with the theoretical analyses of the matrix cracking and debonding behaviors are presented. The micromechanics of matrix cracking, interfacial debonding, and associated matrix crack saturation/saturation stress are also analyzed. # 1998 Acta Metallurgica Inc. 1. INTRODUCTION Ceramic materials exhibit superior mechanical properties at high temperature. But, their use as structural components is severely limited because of their brittleness. Fiber-reinforced ceramic compo￾sites, by incorporating ®bers in ceramic matrices, however, not only exploit their attractive high-tem￾perature strength but also enhance their toughness. A typical load±displacement curve for a ceramic composite subjected to tensile loading parallel to the ®ber direction is shown in Fig. 1 [1]. At the point A, the ®rst matrix crack initiates when the matrix reaches its elastic limit. If the ®bers and matrix are weakly-bonded or frictionally coupled, the matrix crack propagates transversely across the ®bers thus creating bridged-®bers to carry ad￾ditional load. When this happens, the matrix crack de¯ects at the ®ber/coating/matrix interfaces because of the interfacial debonding and sliding. With the increase of the applied load, more matrix cracks are generated and interfacial debonding pro￾pagates with a larger sliding zone. This process leads to a non-linear curve between A and B in Fig. 1. Point B indicates the saturation of the matrix cracking behavior. Beyond point B, the curve shows additional non-linear behavior until the onset of ®ber failures and ®ber pull-out at point C. This point C represents the strength of the com￾posite, at which the breakage of a large number of ®bers leads to decreased load-bearing capacity of the composite. The ®rst matrix cracking (FMC) stress, ultimate strength, and work of fracture are increased because of the reinforcing ®bers [2]. Most research workers focused their interests on the study of ®rst matrix cracking stress, ultimate strength of composites, and the signi®cant role of the interface on these two properties [2±5]. The study of the initial non-linear behavior of the com￾posite after FMC, however, is not that extensive. Firstly in early 1970's, from the consideration of the maximum shear stress at the ®ber±matrix inter￾face, Aveston and Kelly [6] (AK) proposed the fun￾damental concepts and relationships among matrix crack spacing, interfacial debonding (or sliding) length, and interfacial shear stress of a continuous ®ber-reinforced composite. Since then Zok and Spearing [7] developed a model for multiple matrix crack spacing showing both the periodic and ran￾dom cracking patterns. Weitsman and Zhu [8] Acta mater. Vol. 46, No. 5, pp. 1657±1667, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain PII: S1359-6454(97)00347-9 1359-6454/98 $19.00 + 0.00 Fig. 1. A typical load±displacement curve for a SiC ®ber {To whom all correspondence should be addressed. reinforced borosilicate glass composite. 1657