A. Morales-Rodriguez et al. Journal of the European Ceramic Sociery 27(2007)3301-3305 where A is a m-dependent prefactor that has been taken for a value equal to 1 based on and r is the mean radius of the fiber (r=7.25 um for NM 202 Nicalon fibers) The difference in fiber pull-out lengths measured results in apparent interfacial shear stress values of 80 and 120 MPa for MTT- and RTT-specimens, respectively. There is no phys- 0.6 ical explanation of such increase of interfacial shear stress due to static fatigue. On the other hand during RTT an additional matrix multicracking can be introduced leading to a saturation of the matrix cracking: in that case. the pull-out length is not representative of the actual value of #2 the interfacial shear stress. Complementary tests are now in #4 progress, using the microindentation technique, to confirm this hypothesis 4.2. A fiber tows-based approach to explain the 2D-SiCrSic composites tensile strengt Fig. 6. Statistical distributions of in situ fiber tensile strength Although the in situ properties of fibers and fiber/matrix interfaces in the composite material is commonly used to infer et al. 8 By plotting the cumulative distribution of of(Fig. 6) the macroscopic mechanical properties of CMcs as the tensile measured on many fibers(more than 20 fibers/specimen), the strength, UTS, from the strength of the fibers and the shear stress shape factor, m, and the scale parameter of the fibers, o, has developed during fiber/matrix sliding before the final fracture, 6 been ascertained from the Weibull function given by Eq (2): the previous analysis of our results is not sufficient to describe the UTS experimentally obtained P(or)=1-exp o Regarding Figs. I and 2, the final linearity of a-E curves (except for #2 case)and the large final strains achieved suggest that fiber tows could be the entity responsible These statistical parameters have been used to predict the ulti- mate failure in these composites, better than individual fiber mate strength of composites following Eq. (3)proposed by characteristics. The extensive fiber/matrix debonding stated at microstructural observations supports the previous hypoth esis. Debonding phenomena could be strongly determined by (3) matrix-intercracking distances after static loading: the shorter intercracking level, the stronger debonding. Then, the final where Ve is the volume fraction of fibers in the loading direc- unloading-reloading performed on fatigued-specimens favours ion(in this study V=0. 2). A comparison between predicted fill fiber/matrix debonding in high-stress fatigued-specimens and measured values of oUTS is presented in Table 3. Even if a achieving larger deformations Under lower loading conditions significant fraction of the fibers exhibit well-defined mirror su it is expected to achieve higher matrix-intercracking distances faces, it seems that the fracture mirror approach overestimates making more difficult the full fiber/matrix debonding and, the UTs values experimentally obtained. therefore, hindering the tows or individual fibers elonga The in situ scale parameter, o, has been also used to cal- tion. The previous argument justifies the improvement in final culate the fiber/matrix shear stress, t, using the pull-out length strength obtained after static fatigue at 90%o respect to 70%OR measured on fractured specimens by means of the following Case expression Recently, Calard and Lamon have presented a model for the oUTs of composites considering the force-strain curves 入(m)roo (4) for Nicalon NLM 202 fiber bundles. The final tensile strength of composites, oUTS, is approximately given by the following Table 3 Comparison between ultimate strengths predictions obtained from in sin fiber strength, single fibers and fiber tows approaches PUTS (MPa) arTs(MPa) OUTS (MPa) (MPa) 34 24 The statistical parameters obtained from data plotted in Fig. 6 are included.3304 A. Morales-Rodr´ıguez et al. / Journal of the European Ceramic Society 27 (2007) 3301–3305 Fig. 6. Statistical distributions of in situ fiber tensile strength. et al.8 By plotting the cumulative distribution of σf (Fig. 6) measured on many fibers (more than 20 fibers/specimen), the shape factor, m, and the scale parameter of the fibers, σ0, has been ascertained from the Weibull function given by Eq. (2): P(σf) = 1 − exp − σf σ0 m . (2) These statistical parameters have been used to predict the ulti￾mate strength of composites following Eq. (3) proposed by Curtin6: σmirror UTS = Vfσ0 2 m + 2 1/m+1 m + 1 m + 2  , (3) where Vf is the volume fraction of fibers in the loading direc￾tion (in this study Vf = 0.2). A comparison between predicted and measured values of σUTS is presented in Table 3. Even if a significant fraction of the fibers exhibit well-defined mirror sur￾faces, it seems that the fracture mirror approach overestimates the UTS values experimentally obtained. The in situ scale parameter, σ0, has been also used to cal￾culate the fiber/matrix shear stress, τ, using the pull-out length measured on fractured specimens by means of the following expression6: τ = λ(m)rσ0 4l , (4) where λ is a m-dependent prefactor that has been taken for a value equal to 1 based on6 and r is the mean radius of the fiber (r = 7.25m for NLM 202 Nicalon fibers). The difference in fiber pull-out lengths measured results in apparent interfacial shear stress values of 80 and 120 MPa for MTT- and RTT-specimens, respectively. There is no phys￾ical explanation of such increase of interfacial shear stress due to static fatigue. On the other hand during RTT an additional matrix multicracking can be introduced leading to a saturation of the matrix cracking; in that case, the pull-out length is not representative of the actual value of the interfacial shear stress. Complementary tests are now in progress, using the microindentation technique, to confirm this hypothesis. 4.2. A fiber tows-based approach to explain the 2D-SiCf/SiC composites tensile strength Although the in situ properties of fibers and fiber/matrix interfaces in the composite material is commonly used to infer the macroscopic mechanical properties of CMCs as the tensile strength, UTS, from the strength of the fibers and the shear stress developed during fiber/matrix sliding before the final fracture,6 the previous analysis of our results is not sufficient to describe the UTS experimentally obtained. Regarding Figs. 1 and 2, the final linearity of σ–ε curves (except for #2 case) and the large final strains achieved suggest that fiber tows could be the entity responsible for the ulti￾mate failure in these composites, better than individual fiber characteristics.9 The extensive fiber/matrix debonding stated at microstructural observations supports the previous hypoth￾esis. Debonding phenomena could be strongly determined by matrix-intercracking distances after static loading: the shorter intercracking level, the stronger debonding. Then, the final unloading-reloading performed on fatigued-specimens favours full fiber/matrix debonding in high-stress fatigued-specimens, achieving larger deformations. Under lower loading conditions it is expected to achieve higher matrix-intercracking distances making more difficult the full fiber/matrix debonding and, therefore, hindering the tow’s or individual fiber’s elonga￾tion. The previous argument justifies the improvement in final strength obtained after static fatigue at 90% respect to 70% σR case. Recently, Calard and Lamon10 have presented a model for the σUTS of composites considering the force–strain curves for Nicalon NLM 202 fiber bundles. The final tensile strength of composites, σtows UTS, is approximately given by the following Table 3 Comparison between ultimate strengths predictions obtained from in situ fiber strength,6 single fibers and fiber tows10 approaches Specimen σexp UTS (MPa) m σ0 (GPa) σmirror UTS (MPa) σtows UTS (MPa) σfiber UTS (MPa) #1 228 3.2 2.3 298 265 238 #2 202 3.6 2.0 262 192 172 #4 225 4.2 2.1 286 221 216 #5 265 3.4 2.4 312 292 324 The statistical parameters obtained from data plotted in Fig. 6 are included.