October 1997 Fibrous monolithic ceramics 点200 50 0.1 Crosshead Displacement, d (mm) Fig. 11.(a) Side surface of a [0/45/90] fibrous monolith is shown after testing.(b) Stress-deflection response for [0/45/90) fibrous monolith distances between the 90 plies are generally only as long as shear Initiation the cell width. However, in many of the plies, multiple cracl ing of the off-axis cells are observed For specimens containing multiaxial architectures, it is pos- sible for the peak load to be achieved after the failure of an entire layer of cells. If cells on the tensile surface are not aligned in the direction of applied stress, failure of the cell boundary on the tensile surface can occur at a relatively low oad, but cells with 0 orientations that are just beneath the tensile surface can continue to bear substantially more load This leads to stress-deflection curves with pronounced nonlin- earities prior to the peak load. An example is shown for a h noticeable nonlinearity is observed when failure of a 45.layer occurs at -200 MPa but the load continues to increase until the failure of the first on-axis layer occurs at a nominal stress of rosshead Deflection, d(mm) 85 MPa. Using laminate theory, appropriate failure criteria can be established to predict when the nonlinearity in the Fig 12. Stress-deflection response is shown for a specimen tested at elevated temperature in which failure initiated in shear. (4) Shear failure Shear failure also has been observed in some specimens that V. Influence of Material Properties have a very low interfacial fracture resistance and/or a high As demonstrated by the stress-defection curves, fibrous pan-to-depth ratio. For a specimen loaded in four-point bend ing. there is a significant shear stress between the inner ar outer loading pins that can cause shear failure if it exceeds the original load-bearing capacity. Usually, a substantial amount of shear strength of the interphase before the tensile strength of energy is absorbed by the specimen, leading to a high work- the outermost layer is reached. When a shear crack propagates of- fracture in flexure and a large Charpy impact energy, 32 This through a weak interphase at the midplane of the specimen, the occurs as a consequence of delamination of BN cell bound- stiffness of the specimen is reduced. This reduction in stiffness anes leads to a large load drop when the test is conducted in dis- allowing the material to split apart gradually rather than fracturing catastrophically. We find that graceful failure re- placement control. When loading is continued beyond the first lres crack deflection at the bn cell boundaries as well as load drop, the stress again builds in each of the halves of the significant delamination cracking and sliding. The following specimen until cracking occurs in one of two places: sufficient shear stresses develop in each of the halves, causing them to sections discuss the conditions for delamination cracking, and split again along a weak interphase or tensile stresses devel the energy absorption mechanisms leading to high work-of- fracture Because the load-bearing capacity of the beam is greatly re- (Crack Deflection duced each time a shear crack propagates, it is usually the case When a crack initiates on the tensile surface of a fibrous that the peak load that the n can bear is achieved just monolithic ceramic, the stress-deflection behavior is dictated ior to propagation of the first shear crack. by crack deflection and subsequent delamination cracking. The Figure 12 is an example of a stress-deflection plot for a conditions that cause a crack to deflect at an interface between specimen that failed in shear when the was tested at two isotropic solids have been treated theoretically by several elevated temperatures. Using elastic-beam equations, the shea groups,33,34 These models suggest that crack deflection is stress on the midplane of this specimen when the shear crack governed by the ratio of the fracture resistance of the interface initiated was 23 MPa, while the tensile stress on the surface of to that of the cell, the elastic mismatch between the cell and the the beam was -300 MPa. The transition from tensile failure to cell boundary, and the location of interface at which fracture shear failure can be predicted if the shear strength of the cell occurs. Crack deflection is predicted when the fracture resis- boundary is known. Experimental measurements indicate that tance of the interface is low and when the elastic mismatch the shear strength of the BN cell boundary is-30 MPa at ro between the cell and the cell boundary is high temperature, but it decreases at elevated temperatures. To examine the influence of interfacial fracture resistance ondistances between the 90° plies are generally only as long as the cell width. However, in many of the plies, multiple crack￾ing of the off-axis cells are observed. For specimens containing multiaxial architectures, it is pos￾sible for the peak load to be achieved after the failure of an entire layer of cells. If cells on the tensile surface are not aligned in the direction of applied stress, failure of the cell boundary on the tensile surface can occur at a relatively low load, but cells with 0° orientations that are just beneath the tensile surface can continue to bear substantially more load. This leads to stress–deflection curves with pronounced nonlin￾earities prior to the peak load. An example is shown for a specimen with a [0/±45/90] architecture in Fig. 11(b). Here a noticeable nonlinearity is observed when failure of a 45° layer occurs at ∼200 MPa, but the load continues to increase until the failure of the first on-axis layer occurs at a nominal stress of 285 MPa. Using laminate theory, appropriate failure criteria can be established to predict when the nonlinearity in the stress–deflection curve will occur. (4) Shear Failure Shear failure also has been observed in some specimens that have a very low interfacial fracture resistance and/or a high span-to-depth ratio. For a specimen loaded in four-point bend￾ing, there is a significant shear stress between the inner and outer loading pins that can cause shear failure if it exceeds the shear strength of the interphase before the tensile strength of the outermost layer is reached. When a shear crack propagates through a weak interphase at the midplane of the specimen, the stiffness of the specimen is reduced. This reduction in stiffness leads to a large load drop when the test is conducted in dis￾placement control. When loading is continued beyond the first load drop, the stress again builds in each of the halves of the specimen until cracking occurs in one of two places: sufficient shear stresses develop in each of the halves, causing them to split again along a weak interphase or tensile stresses develop in each of the halves of the specimen, causing them to fail. Because the load-bearing capacity of the beam is greatly re￾duced each time a shear crack propagates, it is usually the case that the peak load that the specimen can bear is achieved just prior to propagation of the first shear crack. Figure 12 is an example of a stress–deflection plot for a specimen that failed in shear when the specimen was tested at elevated temperatures. Using elastic-beam equations, the shear stress on the midplane of this specimen when the shear crack initiated was 23 MPa, while the tensile stress on the surface of the beam was ∼300 MPa. The transition from tensile failure to shear failure can be predicted if the shear strength of the cell boundary is known. Experimental measurements indicate that the shear strength of the BN cell boundary is ∼30 MPa at room temperature,31 but it decreases at elevated temperatures. V. Influence of Material Properties As demonstrated by the stress–defection curves, fibrous monoliths can undergo noncatastrophic or ‘‘graceful failure,’’ during which the material retains a significant fraction of its original load-bearing capacity. Usually, a substantial amount of energy is absorbed by the specimen, leading to a high work￾of-fracture in flexure and a large Charpy impact energy.32 This occurs as a consequence of delamination of BN cell bound￾aries, allowing the material to split apart gradually rather than fracturing catastrophically. We find that graceful failure re￾quires crack deflection at the BN cell boundaries as well as significant delamination cracking and sliding. The following sections discuss the conditions for delamination cracking, and the energy absorption mechanisms leading to high work-of￾fracture. (1) Crack Deflection When a crack initiates on the tensile surface of a fibrous monolithic ceramic, the stress–deflection behavior is dictated by crack deflection and subsequent delamination cracking. The conditions that cause a crack to deflect at an interface between two isotropic solids have been treated theoretically by several groups.1,33,34 These models suggest that crack deflection is governed by the ratio of the fracture resistance of the interface to that of the cell, the elastic mismatch between the cell and the cell boundary, and the location of interface at which fracture occurs. Crack deflection is predicted when the fracture resis￾tance of the interface is low and when the elastic mismatch between the cell and the cell boundary is high. To examine the influence of interfacial fracture resistance on Fig. 11. (a) Side surface of a [0/±45/90] fibrous monolith is shown after testing. (b) Stress–deflection response for [0/±45/90] fibrous monolith. Fig. 12. Stress–deflection response is shown for a specimen tested at elevated temperature in which failure initiated in shear. October 1997 Fibrous Monolithic Ceramics 2479