1882 Journal of the American Ceramic Society'Kerans et al. Vol 81. No. 7 7000+++rTT 6000 R5000 3000 °m15 2000 000 cement (um) Fig. 1. Reported typical push-out curve, with elastic deformation removed, for high-strength NicalonTM/C/SiC (After Rebillat et al. 2) see Parthasarathy et al. 7)Briefly, a fiber that is pulling out of this work was to examine the rough-interface formalism for a matrix under axial loading is subjected to radial stresses that suitability in describing the behavior of such composites differ along the length of the fiber The interfacial normal stress in the unslipped region ahead of the crack tip(Region I of Fig 2)is determined by the residual stresses and the applied axial IL. Procedure tress through differences in the poisson's ratios of the con he approach to analysis was based on the following tituents In Region lll of Fig. 2, the normal stress is defined as pothesis. The fine, highly branched, diffuse the sum of those stresses plus the stresses that result from the ing reported via TEM analysis of tensile specimens, 3, I is full effect of the topographical misfit. The roughness-induced considered to be characteristic of the early stages of stresses may be larger than the thermal stresses. As shown in and small displacements. A push-out test imposes Fig 2, Region Il extends, with increasing misfit, from the crack ments between the fiber and the matrix that are larg tip to the beginning of Region Ill. This area complicates analy those that generally develop in a composite in regions away sis and results in many interesting effects. A full solution of the from the final failure site, and such large displacements require problem for one simple form of roughness has shown that the the resolution of the diffuse cracking into a single crack or into friction in Region Il actually can be very much larger than that rubble. It is imagined that the early growth of the debonding treated-fiber Nicalon TM/C/SiC A s Co f debonding p ward crack is in the diffuse, multiple-branched form; however, a in Region Ill, and calculated push-out curves show some critical displacement, it resolves into a single crack feature suggests that roughness may contribute to the unusual Hence, two stages of cracking are assumed; each stage has the curvature observed in push-out load-deflection curves of same fracture energy (G)but different roughness parameters posites. The objective of that describe the two types of crack surfaces. The roughness T R+2A Fig. 2. isfit strain created by a rough fiber, of radius R and roughness amplitude 4, sliding in a matching matrix hole, the shape drawn and unrelated to the model or experiment. In practice, the roughness is assumed to be asymmetric and small, compared to the fiber dimensions (After Parthasarathy and Kerans. s)see Parthasarathy et al.17) Briefly, a fiber that is pulling out of a matrix under axial loading is subjected to radial stresses that differ along the length of the fiber. The interfacial normal stress in the unslipped region ahead of the crack tip (Region I of Fig. 2) is determined by the residual stresses and the applied axial stress through differences in the Poisson’s ratios of the con￾stituents. In Region III of Fig. 2, the normal stress is defined as the sum of those stresses plus the stresses that result from the full effect of the topographical misfit. The roughness-induced stresses may be larger than the thermal stresses. As shown in Fig. 2, Region II extends, with increasing misfit, from the crack tip to the beginning of Region III. This area complicates analy￾sis and results in many interesting effects. A full solution of the problem for one simple form of roughness17 has shown that the friction in Region II actually can be very much larger than that in Region III, and calculated push-out curves show upward curvature in the Region II-only portion of debonding.18 This feature suggests that roughness may contribute to the unusual curvature observed in push-out load–deflection curves of treated-fiber Nicalon™/C/SiC composites. The objective of this work was to examine the rough-interface formalism for suitability in describing the behavior of such composites. II. Procedure The approach to analysis was based on the following hy￾pothesis. The fine, highly branched, ‘‘diffuse’’ multiple crack￾ing reported via TEM analysis of tensile specimens2,3,11 is considered to be characteristic of the early stages of cracking and small displacements. A push-out test imposes displace￾ments between the fiber and the matrix that are larger than those that generally develop in a composite in regions away from the final failure site, and such large displacements require the resolution of the diffuse cracking into a single crack or into rubble. It is imagined that the early growth of the debonding crack is in the diffuse, multiple-branched form; however, at some critical displacement, it resolves into a single crack. Hence, two stages of cracking are assumed; each stage has the same fracture energy (G) but different roughness parameters that describe the two types of crack surfaces. The roughness Fig. 1. Reported typical push-out curve, with elastic deformation removed, for high-strength Nicalon™/C/SiC. (After Rebillat et al.12) Fig. 2. Schematic of misfit strain created by a rough fiber, of radius R and roughness amplitude A, sliding in a matching matrix hole; the shape is arbitrarily drawn and unrelated to the model or experiment. In practice, the roughness is assumed to be asymmetric and small, compared to the fiber dimensions. (After Parthasarathy and Kerans.18) 1882 Journal of the American Ceramic Society—Kerans et al. Vol. 81, No. 7