G N. Morscher, J. D. Cawley/Journal of the European Ceramic Society 22(2002)2777-2787 pristine weakly bonded fibers cannot be carried by the for a fiber failure originating in the region exposed by a remaining fibers, then the composite fails. Two criteria matrix crack. The number of fibers per tow, number of must be met in order for a composite to fail according tows in a composite cross-section, and the size of the to this process: specimen for a given volume fraction of fibers will affect the total number of fibers in a matrix crack. The effec- 1. A critical number of fibers in a given matrix tive gage length of fibers will be controlled by the ability crack must be strongly bonded to one another or of the fibers to transfer load to the matrix, i. e. interfacial to the matrix. When these fibers fail in a matrix shear strength, the amount of interfacial recession that crack, the stress increase to the remaining may occur, and the number of matrix cracks that are unbroken fibers is sufficient to cause them to fail. exposed in the " hot zone""of the furnace. An increase in 2. An event has to occur to fail one or more of the effective length of fully-loaded fibers will increase those strongly bonded fibers to cause unbridged the likelihood that a strongly bonded fiber will fail in or crack growth. Most likely, this event is caused by near a matrix crack beginning the process of unbridged the failure of one strongly bonded fiber due to crack growth intrinsic fiber strength degradation(flaw growth) of a fiber that is relatively weak in the distribu tion of fiber strengths. It is also possible that 3. A model for intermediate temperature stress rupture fiber-degradation could occur from fiber oxida- of SiC/BN/SiC composites tion depending on the fiber-type and oxidizing environment In order to model this process, an approach con ceptually similar Curtin and coworkers 18-2 approach to model composite strength and individual The kinetics for fiber fusion or the depth into a matrix fiber fracture was employed. Only the simple case of rack away from the exposed surface that fibers are through-thickness cracks was considered. The model strongly bonded depends on the ingress of oxidizing was applied to two SiC fiber Bn interphase MI SiC duction, and the shortest distance between two fibers, for these systems. 4.I g available property information species into the matrix crack, i.e. the rate of oxide pro- matrix systems by usi i.e. the gap that must be filled by oxide. Ingress of oxi- dizing species can only occur if matrix cracks are pre 3. The model sent which intersect load-bearing fibers; therefore, fiber fusion will be dependent on the presence of matrix The stress on the fibers in a bridged matrix cracl cracks, and whether or not those cracks are through the can be found from the applied far-field composite stress, thickness of the specimen. The durability of the inter- 0, and the volume fraction of fibers in the loading phase will affect the rate for fiber-to-fiber fusion. It was direction, f. found for the woven Hi-Nicalon(Nippon Carbon, Co Japan)fiber(HN)reinforced, BN interphase, melt-infil trated (MI) SiC matrix composite of Ref. 14 that the thin carbon layer that exists between the fiber and the bn due to fiber decomposition during matrix processing 7 enhances crack growth and interphase oxidation I5 Also the closer fibers are to one another or the thinner Transfer e interphase coating and the method of interphase used in u= crack coating will be critical. It was found in the earlier study 4 model that over 95% of all the fibers were nearly in contact openIng with one another, i.e. are separated by less than 100 nm R displacement even though the average thickness of the interphase was 0.5 This is nce of woven structures, where the act of weaving tightens tows and forces fibers into intimate contact with one another oeo=o/f Fiber failure depends on the strength-distribution of the fibers in a matrix crack. the number of fibers in a Fig. 2. Schematic representation of stress-profile at and around a matrix crack, and the effective gage length of loaded a composite. sf. m fibers and the matri fibers. A wider distribution of fiber strengths for the rule of The model assumes same average strength will mean a greater probability [Eq(7)pristine weakly bonded fibers cannot be carried by the remaining fibers, then the composite fails. Two criteria must be met in order for a composite to fail according to this process: 1. A critical number of fibers in a given matrix crack must be strongly bonded to one another or to the matrix. When these fibers fail in a matrix crack, the stress increase to the remaining unbroken fibers is sufficient to cause them to fail. 2. An event has to occur to fail one or more of those strongly bonded fibers to cause unbridged crack growth. Most likely, this event is caused by the failure of one strongly bonded fiber due to intrinsic fiber strength degradation (flaw growth) of a fiber that is relatively weak in the distribu￾tion of fiber strengths. It is also possible that fiber-degradation could occur from fiber oxida￾tion depending on the fiber-type and oxidizing environment. The kinetics for fiber fusion or the depth into a matrix crack away from the exposed surface that fibers are strongly bonded depends on the ingress of oxidizing species into the matrix crack, i.e. the rate of oxide pro￾duction, and the shortest distance between two fibers, i.e. the gap that must be filled by oxide. Ingress of oxi￾dizing species can only occur if matrix cracks are pre￾sent which intersect load-bearing fibers; therefore, fiber fusion will be dependent on the presence of matrix cracks, and whether or not those cracks are through the thickness of the specimen. The durability of the inter￾phase will affect the rate for fiber-to-fiber fusion. It was found for the woven Hi-Nicalon (Nippon Carbon, Co., Japan) fiber (HN) reinforced, BN interphase, melt-infil￾trated (MI) SiC matrix composite of Ref. 14 that the thin carbon layer that exists between the fiber and the BN due to fiber decomposition during matrix processing 17 enhances crack growth and interphase oxidation.15 Also, the closer fibers are to one another or the thinner the interphase, the faster fibers will fuse to one another or to the matrix, respectively. Therefore, the uniformity of the interphase coating and the method of interphase coating will be critical. It was found in the earlier study 14 that over 95% of all the fibers were nearly in contact with one another, i.e. are separated by less than 100 nm, even though the average thickness of the interphase was 0.5 mm. This is especially a consequence of woven structures, where the act of weaving tightens tows and forces fibers into intimate contact with one another. Fiber failure depends on the strength-distribution of the fibers in a matrix crack, the number of fibers in a matrix crack, and the effective gage length of loaded fibers. A wider distribution of fiber strengths for the same average strength will mean a greater probability for a fiber failure originating in the region exposed by a matrix crack. The number of fibers per tow, number of tows in a composite cross-section, and the size of the specimen for a given volume fraction of fibers will affect the total number of fibers in a matrix crack. The effec￾tive gage length of fibers will be controlled by the ability of the fibers to transfer load to the matrix, i.e. interfacial shear strength, the amount of interfacial recession that may occur, and the number of matrix cracks that are exposed in the ‘‘hot zone’’ of the furnace. An increase in the effective length of fully-loaded fibers will increase the likelihood that a strongly bonded fiber will fail in or near a matrix crack beginning the process of unbridged crack growth. 3. A model for intermediate temperature stress rupture of SiC/BN/SiC composites In order to model this process, an approach con￾ceptually similar to Curtin and coworkers 1820 approach to model composite strength and individual fiber fracture was employed. Only the simple case of through-thickness cracks was considered. The model was applied to two SiC fiber BN interphase MI SiC matrix systems by using available property information for these systems.14,15 3.1. The model The stress on the fibers in a bridged matrix crack, sf, can be found from the applied far-field composite stress, s, and the volume fraction of fibers in the loading direction, f. Fig. 2. Schematic representation of stress-profile at and around a matrix crack in a composite. sf,m would represent the stress on the fibers where the fibers and the matrix share the load according to the rule of mixtures. The model assumes d/2 extends to sf=0 for simplicity [Eq. (7)]. G.N. Morscher, J.D. Cawley / Journal of the European Ceramic Society 22 (2002) 2777–2787 2779