Hi-Nicalon/BN/a-Si,N, ceramic-matrix composites 1485 that(1)the ultimate tensile stress, ou, and the ultimate bending stress of the composite are equal and(2) to the ultimate stress of the composite, all the fibers are still bearing the load, then the ultimate tensile Load (N) stress of the fibers in the composite, o can be calculated by using eqn(4). The value so calculated can be viewed as an upper limit of the ultimate stress of the fiber tested under tensile mode: 0000050.100.15020025 With u=b=672 MPa, o, is 1400 MPa. This value is much lower than that measured by Nippon Carbon for ngn0ithic silicon nitride and the hi-nicalon /silicon-nitride virgin Hi-Nicalon fibers(a =1940 MPa)2,and this composite tested under four-point flexure point must be emphasized Otherwise, from eqn(2), the longitudinal Youngs correctly transferred at the fiber/matrix interface. modulus is E=206 GPa and 164 GPa for the Observation after flexural tests shows that the crack monolithic matrix and the composite, respectively. As starts propagating from the notch tip and its noted, the modulus of the monolithic silicon nitride is progression is tortuous owing to the extensive fiber ligher than that of the composite. This surprising bridging mechanism. In the case of linear elastic result would suggest that there is no enhancement in behavior, the matrix fracture energy could be the stiffness of the monolithic matrix by the estimated by assuming that the matrix crack starts incorporation of these high-tnodulus fibers(E=250 propagating at the end of the proportional limit GPa). In fact, when inserting the values of the characterized by the proportional load, PI(corre- longitudinal Young s modulus and the volume fraction ponding to a displacement ui), by using the following of the matrix [Em =193 GPa(see the next paragraph relationship G=Pu,2B(W-h) where B and w are the dimensions of the specimens and h the height of the notch( Fig. 1). The calculated matrix fracture energy valucs arc similar for both thc monolithic silicon nitride and the composite: G=345J m. Such a value is reasonable compared with others reported in the literature. Otherwise, since this energy value corresponds to initiation of the matrix crack. it Hi-Nicaion/BN/SI3N4 would be interesting, as a further investigation, to calculate the increasing crack growth resistance values B-curve). Because of a lack of larger specimens (compact tension ones, for example), such a study has not been conducted vet deflection(um) Fig. 5(a)Three-point flexure test of unnotched monolithic 3.2.2 Unnotched specimens silicon nitride and Hi-Nicalon/BN/silicon-nitride composite Figure 5 shows the load/displacement relationshi tained in a three- point bend flexure test performed on two unnotched specimens of monolithic silicon xy一 from the follow classical beam theory PeO E=P/48Bw3 where P is the applied load and 8 the deflection from these relationships, the ultimate bending stress is Tb=538 and 672 MPa for the matrix and the Three-point flexure test of unnotched monolithic composite, respectively. Making the crude assumptions itride and Hi-Nicalon/BN/silicon-nitride compositHi-Nicalon/BN/c-u-Si,N, ceramic-matrix composites 1485 0 SiN4(M) l Hi-NicalodSiiN4 I I I I I 1 I ! , I I I 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 040 Displacement (mm) Fig. 4. Load/displacement curves of notched specimens of monolithic silicon nitride and the Hi-Nicalonkilicon-nitride composite tested under four-point flexure. correctly transferred at the fiber/matrix interface. Observation after flexural tests shows that the crack starts propagating from the notch tip and its progression is tortuous owing to the extensive fiber￾bridging mechanism. In the case of linear elastic behavior, the matrix fracture energy could be estimated by assuming that the matrix crack starts propagating at the end of the proportional limit, characterized by the proportional load, Pi (corre￾sponding to a displacement CL,), by using the following relationship: G = P,uiI[2B(W - h)] (1) where B and W are the dimensions of the specimens and h the height of the notch (Fig. 1). The calculated matrix fracture energy values are similar for both the monolithic silicon nitride and the composite: G = 34.5 J m -2. Such a value is reasonable compared with others reported in the literature.4 Otherwise, since this energy value corresponds to initiation of the matrix crack, it would be interesting, as a further investigation, to calculate the increasing crack growth resistance values (R-curve). Because of a lack of larger specimens (compact tension ones, for example), such a study has not been conducted yet. 3.2.2 Urmotched specimens Figure 5 shows the load/displacement relationships obtained in a three-point bend flexure test performed on two unnotched specimens of monolithic silicon nitride and Hi-Nicalon/BN/silicon-nitride composite. The ultimate bending stress, (TV, and the longitudinal Young’s modulus, E, of these materials were calculated from the following relationships derived from the classical beam theory: ub = 3P112BW2 (2) and E = P13/4SBW’ (3) where P is the applied load and 6 the deflection. From these relationships, the ultimate bending stress is (rb=538 and 672 MPa for the matrix and the composite, respectively. Making the crude assumptions that (1) the ultimate tensile stress, (T,,, and the ultimate bending stress of the composite are equal and (2) up to the ultimate stress of the composite, all the fibers are still bearing the load, then the ultimate tensile stress of the fibers in the composite, rf, can be calculated by using eqn (4). The value so calculated can be viewed as an upper limit of the ultimate stress of the fiber tested under tensile mode: (Tf = U”/V, (4) With g’, = (To = 672 MPa, gf is 1400 MPa. This value is much lower than that measured by Nippon Carbon for virgin Hi-Nicalon fibers ((TV = 1940 MPa)“, and this point must be emphasized. Otherwise, from eqn (2), the longitudinal Young’s modulus is E =206 GPa and 164 GPa for the monolithic matrix and the composite, respectively. As noted, the modulus of the monolithic silicon nitride is higher than that of the composite. This surprising result would suggest that there is no enhancement in the stiffness of the monolithic matrix by the incorporation of these high-modulus fibers3 (Ef = 250 GPa). In fact, when inserting the values of the longitudinal Young’s modulus and the volume fraction of the matrix [E, = 193 GPa (see the next paragraph) 6oq HkNicalonlBNISi3N4 ---+-- S13N4(M) 00 0.1 0.2 0.3 0.4 deflection (mm) Fig. 5(a) Three-point flexure test of unnotched monolithic silicon nitride and Hi-Nicalon/BN/silicon-nitride composite, 0 FSF, a P>P, OF=0 h, Fig. 5(b) Three-point flexure test of unnotched monolithic silicon nitride and Hi-Nicalon/BN/silicon-nitride composite