October 1997 Fibrous monolithic ceramics 2477 sin e Table l. Measured and Predicted values of young Modulus for Several Multilayer Fibrous Monoliths This expression is plotted in Fig. 8 with the experimentally measured values, showing that there is very good agreement ±6o][o45/ between experiment and prediction Measured modulus(GPa)198±2205±7202±3 (F Young's Modulus for Multiaxial Architectures: The 198 198 Young's modulus for multiaxial architectures is calculated terms of the engineering properties E1, E2, G12, and v12 using baut icat t ound ihestaquarid te xrs o lengtate th present Tare by an individual cell is related to the geometry of the specimen Il shows the measured and predicted Young's moduli for three 90]. The experimental values and the predictions from laminate earie d can be calculated using laminate theory as described architectures with simple stacking: [0/90), [0/460), and [0/45/ ary, and theory agree within 2.5% Unlike most monolithic ceramics or layered A(G) Summary of Elastic Properties: Because of the tex- strophic failure of the entire layer of cells on the tensile surface of the specimen. In other words, local failure of a single cell properties along the principal axes differ from the values pre- does not always cause global failure. If the stress that was have been presented that allow the elastic properties to be carried by the fractured cell can be transferred to neighboring accurately predicted. Principal moduli were determined from the elastic properties of the constituent materials and, with possible for the layer to remain intact after the failure of indi- vidual cells. Presumably, this behavior is favored when there to accurately predict modulus as a function of ply angle within are many cells in the specimen and the variability in the models can be extended to predict the elastic moduli for fibrous If loading is continued beyond the point where the fracture onolithic ceramics with multiaxial architectures of an individual cell occurs, eventually enough cells fracture so that the remaining cells on the tensile surface can no longer bear the applied stress, and an entire layer of cells fractures. In IV. Failure Mechanisms in Fibrous monoliths Two modes of failure have been observed during the flexural simple laminates, where fracture is controlled by weak-link atistics. Because the failure of fibrous monoliths is controlled of the beam because of tensile stress, or failure can initiate near by damage accumulation, the strength should be less sensitive the midsection of the beam because of shear stress. Either can to preexisting flaws than either monolithic ceramics or simple ditions. and on the fracture resistance of the cell and the cell laminates boundary. Tensile failure is favored when the cell boundaries load-bearing capacity of the bar is reduced, because the effec- are tough in comparison to that of the cells. Shear failure is tive cross section of the bar is smaller. In the case of uniaxially favored when the cell boundaries are weak compared to the aligned specimens with cells aligned at zero degrees(on-axis), cells. In a flexural test, the span-to-depth ratio of the bar de termines the relative magnitude of the normal stress to the the maximum applied load is typically achieved at the poi have a strength of -450 MPa. If the test is conducted in dis- tested as a short, thick beam. We consider each failure mecha- placement control, it is possible for the specimen to continue to nism separately bear a substantial load to large deflections even after the peak () Tensile Failure by Cell fracture load is achieved. An example of a typical stress-deflection for For an individual cell, the failure criterion is simply that a specimen in which failure initiated on the tensile surface is ailure occurs when the normal, tensile stress carried by that fa shown in Fig. 9(a). Each stress drop is associated with the cell exceeds the strength of the cell. Because the cells are made fracture of one or several layers of cells. The progressive nature from SiNa, the strength of an individual cell depends on the of the fracture process is shown in Fig. 9(b), the side surface of flaw size and fracture resistance of the cell. The stress carried this specimen after testing. The area under the stress-deflection curve is related to the energy dissipated by the sample during his noncatastrophic fracture. Typically, uniaxially aligned ecimens tested on-axis have a work-of-fracture of.5 Measure Predicted ( Tensile Failure by Cell-Boundary fracture In architectures where cells are misaligned with respect to the axis of the applied load, it is possible for the cells to remain intact, but for the specimen to fail when the surrounding cell boundary fractures. An SEM micrograph of the fracture surface of a BN cell boundary is shown in Fig 3, which shows that fracture in the interphase occurs by separation of the platelike grains between the weak, basal planes of the BN. It is likely that the preexisting Mrozowski microcracking in the Bn in terphases weakens the BN interphase by introducing large pre- existing defects that can propagate to failure Figure 10(a) shows examples of stress-deflection curves for specimens tested with cells oriented at 90 and at 30 with ersus orient hs Measu he Bn interphase on the tensile surface. Thus, the strength isn 4 sin u (5c) This expression is plotted in Fig. 8 with the experimentally measured values, showing that there is very good agreement between experiment and prediction. (F) Young’s Modulus for Multiaxial Architectures: The Young’s modulus for multiaxial architectures is calculated in terms of the engineering properties E1, E2, G12, and n12 using laminate theory. The equations are too lengthy to present here, but can be found in standard texts on laminate theory.22 Table II shows the measured and predicted Young’s moduli for three architectures with simple stacking: [0/90], [0/±60], and [0/±45/ 90]. The experimental values and the predictions from laminate theory agree within 2.5%. (G) Summary of Elastic Properties: Because of the tex￾ture associated with fibrous monolithic ceramics, the elastic properties along the principal axes differ from the values pre￾dicted using rule-of-mixture models. However, simple models have been presented that allow the elastic properties to be accurately predicted. Principal moduli were determined from the elastic properties of the constituent materials and, with experimentally measured shear modulus data, have been used to accurately predict modulus as a function of ply angle within the plane of hot pressing. It also has been shown that these models can be extended to predict the elastic moduli for fibrous monolithic ceramics with multiaxial architectures. IV. Failure Mechanisms in Fibrous Monoliths Two modes of failure have been observed during the flexural testing of fibrous monoliths. Failure can initiate on the surface of the beam because of tensile stress, or failure can initiate near the midsection of the beam because of shear stress. Either can occur depending on the specimen geometry and loading con￾ditions, and on the fracture resistance of the cell and the cell boundary. Tensile failure is favored when the cell boundaries are tough in comparison to that of the cells. Shear failure is favored when the cell boundaries are weak compared to the cells. In a flexural test, the span-to-depth ratio of the bar de￾termines the relative magnitude of the normal stress to the shear stress; therefore, the same material might fail because of tensile stress if tested as a long, slim beam, but fail in shear if tested as a short, thick beam. We consider each failure mecha￾nism separately. (1) Tensile Failure by Cell Fracture For an individual cell, the failure criterion is simply that failure occurs when the normal, tensile stress carried by that cell exceeds the strength of the cell. Because the cells are made from Si3N4, the strength of an individual cell depends on the flaw size and fracture resistance of the cell. The stress carried by an individual cell is related to the geometry of the specimen and the constituent elastic properties of the cell and cell bound￾ary, and can be calculated using laminate theory as described earlier. Unlike most monolithic ceramics or layered ceramics, the failure of an individual cell does not necessarily cause cata￾strophic failure of the entire layer of cells on the tensile surface of the specimen. In other words, local failure of a single cell does not always cause global failure. If the stress that was carried by the fractured cell can be transferred to neighboring cells that are strong enough to bear the increased stress, it is possible for the layer to remain intact after the failure of indi￾vidual cells. Presumably, this behavior is favored when there are many cells in the specimen and the variability in the strength of the cells is high.30 If loading is continued beyond the point where the fracture of an individual cell occurs, eventually enough cells fracture so that the remaining cells on the tensile surface can no longer bear the applied stress, and an entire layer of cells fractures. In this case, failure of the layer involves the accumulation of failure of a number of cells. Contrast this with monoliths or simple laminates, where fracture is controlled by weak-link statistics. Because the failure of fibrous monoliths is controlled by damage accumulation, the strength should be less sensitive to preexisting flaws than either monolithic ceramics or simple laminates. Once a layer of cells fractures during flexural loading, the load-bearing capacity of the bar is reduced, because the effec￾tive cross section of the bar is smaller. In the case of uniaxially aligned specimens with cells aligned at zero degrees (on-axis), the maximum applied load is typically achieved at the point just prior to failure in the layer of cells closest to the tensile surface. Uniaxially aligned specimens tested on-axis typically have a strength of ∼450 MPa. If the test is conducted in dis￾placement control, it is possible for the specimen to continue to bear a substantial load to large deflections even after the peak load is achieved. An example of a typical stress–deflection for a specimen in which failure initiated on the tensile surface is shown in Fig. 9(a). Each stress drop is associated with the fracture of one or several layers of cells. The progressive nature of the fracture process is shown in Fig. 9(b), the side surface of this specimen after testing. The area under the stress–deflection curve is related to the energy dissipated by the sample during this noncatastrophic fracture. Typically, uniaxially aligned specimens tested on-axis have a work-of-fracture of ∼7.5 kJ/m2 . (2) Tensile Failure by Cell-Boundary Fracture In architectures where cells are misaligned with respect to the axis of the applied load, it is possible for the cells to remain intact, but for the specimen to fail when the surrounding cell boundary fractures. An SEM micrograph of the fracture surface of a BN cell boundary is shown in Fig. 3, which shows that fracture in the interphase occurs by separation of the platelike grains between the weak, basal planes of the BN. It is likely that the preexisting Mrozowski microcracking13 in the BN in￾terphases weakens the BN interphase by introducing large pre￾existing defects that can propagate to failure. Figure 10(a) shows examples of stress–deflection curves for specimens tested with cells oriented at 90° and at 30° with respect to the applied load. The pattern of cracking is shown in Figs. 10(b) and (c), where the side surfaces of the specimens are shown after testing. Failure is catastrophic and initiates in the BN interphase on the tensile surface. Thus, the strength is Fig. 8. Young’s modulus versus orientation for uniaxially aligned fibrous monoliths. Measured values are indicated by points. Line is the predicted behavior using the brick model and laminate theory. Table II. Measured and Predicted Values of Young’s Modulus for Several Multilayer Fibrous Monoliths [0/90] [0/±60] [0/±45/90] Measured modulus (GPa) 198 ± 2 205 ± 7 202 ± 3 Predicted modulus (GPa) 201 198 198 October 1997 Fibrous Monolithic Ceramics 2477