October 1997 Fibrous monolithic ceramics 247: matrix-fiber-reinforced composites. For example, we find that point bend test Charalambides et al. 21 This test is the elastic properties of fibrous monoliths can be predicted with specimen, and then loading it in tor pi the elastic behar four-point bend ination occurs. The steady-state einforced laminates. But the fra d necessary delamination crack and the of fibrous monoliths is quite different, because these materials specimen dimer used to compute the interfacial ontain neither strong fibers nor a weak matrix. The failure fracture resistar mechanisms and associated dissipative mechanisms that are important in fiber-reinforced composites, I9 do not occur r in (2) Elastic Properties fibrous monoliths; therefore, those theories are not applicable To predict the elastic response of fibrous monolithic ceram- Instead, we find that the fracture process that occurs in fibrous s with multiaxial architectures, it is necessary to first under monoliths can be described by existing theories for the fracture stand the elastic behavior of uniaxially aligned fibrous mono- count for the unique structure of fibrous monoliths on to ac- liths along principal directions. These predictions are made of two-dimensional layered materials after modificatio using appropriate micromechanical models and a knowledge of the elastic properties of the constituent materials. Once these () Experimental Procedure predictions are made, laminate theory is used to predict the Elastic properties of both the fibrous monolithic ceramics off-axis elastic properties for uniaxially aligned materials and and monolithic ceramics were measured using the impulse- the elastic moduli for fibrous monolithic ceramics with multi- excitation technique using a commercially available tester axial architectures. The predictions are verified by measuring Grindo-sonic Model MK4x, J. w. Lemmon, St Louis, MO) he elastic moduli in many test coupons ccording to ASTM E 494-92a 20 In this test, the specimen is We assume that uniaxial fibrous monolithic ceramics pos- excited using a small driver, and the resonant frequency is sess a plane of isotropy perpendicular to the axis of the fibrous measured using a piezoelectric transducer. The modulus is then texture. The additional assumption that out-of-plane stresses calculated from the resonant frequency, the specimen dimen- can be ignored reduces the number of required elastic constants sions, and the specimen density. Youngs modulus was deter to four and allows the use of classical laminate theory to predict mined using bars with dimensions 3 mm x 4 mm x 45 mm, and he properties at an arbitrary angle for materials with uniaxial shear modulus was determined on plates 3 mm x 20 mm x 45 architectures and the moduli for materials with biaxial archi- mm. Bars with a uniaxially aligned architecture were machined tectures 22 These four elastic constants are calculated in terms parallel or perpendicular to the fibrous texture to determine of the engineering properties E1, E2, G12, and v12.We express Young's modulus in the I and 2 directions(E and E2, respec these properties for each architecture in terms of the composi- of the BN (EBN) and sin angle(0) with respect to the I direction to determine E(0). The (EsN) constituent materials shear modulus was determined using plates machined with the (A) Elastic Properties along Principal Directions: Uni- ng axis parallel to the direction of interest. For biaxial archi- axial Architecture: All elastic property predictions for fibrous tectures, one layer was designated the 0o layer, and the axis of monolithic ceramics are made from the elastic moduli of the Strength measurements at room temperature and at elevated Si3N4 of 320 GPa is used. This value is obtained from mea- emperature were performed using a computer-controlled surements performed on bars of monolithic Si3 Na of the same screw-driven, testing machine(Model 4483, Instron Corp, composition as that of the fibrous monolithic cells and hot- Canton, MA)operated in displacement control. The crosshead pressed under the same conditions and onsistent with val displacement rate was 0.5 mm/min for all tests. Specimens cited in the literature. 23 It is difficult to measure the elastic were tested in four-point flexure with an inner span of 20 mm properties of bulk BN. Similar to fabricated graphite, 4 the and an outer span of 40 mm. For elevated-temperature tests, the elastic properties of bulk BN vary greatly with fabrication tech- and an outer strowds allowed to stabilize for 10 min prior nique. Furthermore, the high degree of internal damping makes to testing. The energy absorption capability of a specimen was measurement using the impulse-excitation technique difficult characterized by the work-of-fracture(WOF), which was com- Only a few examples of successful modulus measurements on outed by taking the total area under the load-displacement BN are known in the literature. Two of the more commonl ng by twice the cross-sectional area of the reported values are 19.6 GPa26 and 22 GPa.27 However, these specimen values should be used with caution because the microstructure Interfacial fracture resistance was determined using a four- of the BN present in hot-pressed fibrous monolithic ceramics is Panel B. Material Combinations Although this article focuses on fibrous monoliths made Table bl. Material Combinations that have been used om SiaN4 and BN, fibrous monoliths have been fabricated to Fabricate Fibrous monoliths using many different material combinations. Some ex- Cell boundary Reference amples of all-ceramic fibrous monoliths and metal-ceramic fibrous monoliths that have been successfully fabricated are All-ceramic fibrous monoliths presented below. The usual limitations to processing of composite materials also apply to fibrous monoliths: i.e. the Hb2 constituent materials must be phase compatible. In addition, the constituent materials must be compatible with the poly C(graphite) mer binders that are used in the extrusion process ALO -ZrO Ceramic-metal fibrous monoliths ALo Advanced Ceramic Research, Tucson, AZmatrix–fiber-reinforced composites. For example, we find that the elastic properties of fibrous monoliths can be predicted with existing theories used for predicting the elastic behavior of traditional fiber-reinforced laminates. But the fracture behavior of fibrous monoliths is quite different, because these materials contain neither strong fibers nor a weak matrix. The failure mechanisms and associated dissipative mechanisms that are important in fiber-reinforced composites18,19 do not occur in fibrous monoliths; therefore, those theories are not applicable. Instead, we find that the fracture process that occurs in fibrous monoliths can be described by existing theories for the fracture of two-dimensional layered materials after modification to ac￾count for the unique structure of fibrous monoliths. (1) Experimental Procedure Elastic properties of both the fibrous monolithic ceramics and monolithic ceramics were measured using the impulse￾excitation technique using a commercially available tester (Grindo-sonic Model MK4x, J. W. Lemmon, St. Louis, MO) according to ASTM E 494-92a.20 In this test, the specimen is excited using a small driver, and the resonant frequency is measured using a piezoelectric transducer. The modulus is then calculated from the resonant frequency, the specimen dimen￾sions, and the specimen density. Young’s modulus was deter￾mined using bars with dimensions 3 mm × 4 mm × 45 mm, and shear modulus was determined on plates 3 mm × 20 mm × 45 mm. Bars with a uniaxially aligned architecture were machined parallel or perpendicular to the fibrous texture to determine Young’s modulus in the 1 and 2 directions (E1 and E2, respec￾tively). Young’s modulus also was measured as a function of angle (u) with respect to the 1 direction to determine E(u). The shear modulus was determined using plates machined with the long axis parallel to the direction of interest. For biaxial archi￾tectures, one layer was designated the 0° layer, and the axis of the bar was machined parallel to this layer. Strength measurements at room temperature and at elevated temperature were performed using a computer-controlled, screw-driven, testing machine (Model 4483, Instron Corp., Canton, MA) operated in displacement control. The crosshead displacement rate was 0.5 mm/min for all tests. Specimens were tested in four-point flexure with an inner span of 20 mm and an outer span of 40 mm. For elevated-temperature tests, the furnace temperature was allowed to stabilize for 10 min prior to testing. The energy absorption capability of a specimen was characterized by the work-of-fracture (WOF), which was com￾puted by taking the total area under the load–displacement curve and dividing by twice the cross-sectional area of the specimen. Interfacial fracture resistance was determined using a four￾point bend test developed by Charalambides et al.21 This test is performed by first notching a specimen, and then loading it in four-point bending until delamination occurs. The steady-state load necessary to propagate the delamination crack and the specimen dimensions are then used to compute the interfacial fracture resistance. (2) Elastic Properties To predict the elastic response of fibrous monolithic ceram￾ics with multiaxial architectures, it is necessary to first under￾stand the elastic behavior of uniaxially aligned fibrous mono￾liths along principal directions. These predictions are made using appropriate micromechanical models and a knowledge of the elastic properties of the constituent materials. Once these predictions are made, laminate theory is used to predict the off-axis elastic properties for uniaxially aligned materials and the elastic moduli for fibrous monolithic ceramics with multi￾axial architectures. The predictions are verified by measuring the elastic moduli in many test coupons. We assume that uniaxial fibrous monolithic ceramics pos￾sess a plane of isotropy perpendicular to the axis of the fibrous texture. The additional assumption that out-of-plane stresses can be ignored reduces the number of required elastic constants to four and allows the use of classical laminate theory to predict the properties at an arbitrary angle for materials with uniaxial architectures and the moduli for materials with biaxial archi￾tectures.22 These four elastic constants are calculated in terms of the engineering properties E1, E2, G12, and n12. We express these properties for each architecture in terms of the composi￾tion (VBN) and the elastic properties of the BN (EBN) and Si3N4 (ESN) constituent materials. (A) Elastic Properties along Principal Directions: Uni￾axial Architecture: All elastic property predictions for fibrous monolithic ceramics are made from the elastic moduli of the constituent Si3N4 and BN. A value for the Young’s modulus of Si3N4 of 320 GPa is used. This value is obtained from mea￾surements performed on bars of monolithic Si3N4 of the same composition as that of the fibrous monolithic cells and hot￾pressed under the same conditions and is consistent with values cited in the literature.23 It is difficult to measure the elastic properties of bulk BN. Similar to fabricated graphite,24 the elastic properties of bulk BN vary greatly with fabrication tech￾nique. Furthermore, the high degree of internal damping makes measurement using the impulse-excitation technique difficult. Only a few examples of successful modulus measurements on BN are known in the literature.25 Two of the more commonly reported values are 19.6 GPa26 and 22 GPa.27 However, these values should be used with caution, because the microstructure of the BN present in hot-pressed fibrous monolithic ceramics is Panel B. Material Combinations Although this article focuses on fibrous monoliths made from Si3N4 and BN, fibrous monoliths have been fabricated using many different material combinations. Some ex￾amples of all-ceramic fibrous monoliths and metal–ceramic fibrous monoliths that have been successfully fabricated are presented below. The usual limitations to processing of composite materials also apply to fibrous monoliths; i.e., the constituent materials must be phase compatible. In addition, the constituent materials must be compatible with the poly￾mer binders that are used in the extrusion process. Table BI. Material Combinations that have been Used to Fabricate Fibrous Monoliths Cell Cell boundary Reference All-ceramic fibrous monoliths ZrB2 BN † HfB2 BN † SiC BN 8, 53 SiC C (graphite) 7, 53 Al2O3 C (graphite) 54 Al2O3 Al2TiO5 6 Al2O3 Al2O3–ZrO2 6 Ceramic–metal fibrous monoliths Al2O3 Fe–Ni 55 Al2O3 Fe 55 Al2O3 Ni 56 † Advanced Ceramic Research, Tucson, AZ. October 1997 Fibrous Monolithic Ceramics 2475