Ceramie composites reinforeed by continuous fibers Cox and Zok 667 is a commensurate increase in the number of material under most stress is small (as it is ahead of a notch) parameters to be determined by calibrating experiments. If so, the strength should follow weakest-link scaling Applications to circumferentially reinforced rotors have Comparisons of strengths in tension and bending (taking been presented, but proof of the predictive power of into account the nonlinear stress distributions) support localization models is not yet convincing [11] this hypothesis(MeNulty JC, Zok FW, unpublished data) Issues related to strength variability are addressed in more ling with more complex fiber architectures is also detail elsewhere in this journal [22] ch more challenging. The response of a 0/90"lamina prior to localization under loads aligned with the 0'fibers The degree of notch sensitivity is influenced by the nature the easiest case, since the cracking evolution is of the inelastic deformation occurring ahead of the notches best understood(5]. Damage in textile CMCs involves ( Fig. 1). In some materials (e. g. Nicalon TM/calcium much more complicated cracking patterns, for aluminosilicate), a damage zone of multiple matrix cracks micromechanical models are relatively crude (and not forms ahead of the notch, which has an analogous effec certain to improve, because of the difficulties of dealing to the plastic zone in metals(designated Class II behavior with the tortuous heterogeneity of textiles). Continuum by Evans [231). In others(e. g. C/C), nonlinearity arises damage approaches are necessarily more empirical from shear bands oriented parallel to the tensile direction (Class IIi behavior [23]). In more brittle CMCs, fracture Likewise, highly empirical approaches arc most credible occurs by the propagation of a dominant mode I crack, for multiaxial or off-axis loading, even in unidirectional with fiber failure and pullout in the crack wake, but with CMCs. A general method for developing multiaxial minimal inelastic deformation elsewhere(Class I behavior constitutive laws up to localization has been demonstrated [(23.1). Models of strength for Classes I and In have been for plane stress cases, using a combination of standard developed, based on line-spring representations of the tension, compression, and shear test data [12 ]. when the inelastic processes (24, 25 ]. Models that take into account constitutive laws are embedded in finite element calcula- large scale sliding [26] indicate that the maximum fber encouraging agreement is obtained with measured strain predicted from the line-spring models; the latter are ficlds. Stiffness changes under off-axis loading have been thus expected to provide conservative predictions for the measured ultrasonically [13]. stresses at the onset of fiber failure This area of work represents the culmination of efforts Some censure is due to several authors over loose claims to qualify CMCs as structural materials. Current activity that a given material has been found to be notch focuses on dealing with rate dependent behaviour at hi insensitive. This generally fallacious conclusion has been temperature, fatigue effects, and weakest link fract based on tests performed with relatively small notches statistics(volume effects) typically 1-5 mm. Moreover, there has been almost discussion of the effects of notch shape (circular holes versus sharp slits). In the presence of sufficiently large, Fracture and notch sensitivity sharp notches, the strength must follow the Griffith Tensile tests performed on specimens containing holes relation and the material must be notch-sensitive (as is or notches have demonstrated that many CMCs are even the most ductile metal). Researchers should identify relatively notch-insensitive [14-16, 17,18, 19, 20, 21). The the net-section stress at fracture is typically 80-100% of the i head scales associated with the bridging processes the notch sizes and shapes for which notch unnotched strength: considerably higher than the value sensitivity will occur calculated on the basis of the elastic stress concentration factor. Indeed, in some instances, there appears to be evidence of notch strengthening [14]. Measurements of Compressive failure in-plane strains (using moire interferometry (18)and Compressive failure of CMcs has remained largely unex stresses(using SPATE (14-16, 17.))have shown that plored. Some evidence exists that com strain concentrations are essentially unchanged by the [27]fall below tensile strengths [28 ] In CMCs with weak inelastic deformation but stress concentrations are reduced or porous matrices, observations to date [27]show that dramatically. However, even in the most notch-insensitive compressive failure involves kink band formation within materials, stress concentrations are not eliminated alto- fiber bundles(plies or tows), similar to the prevalent fail gether, yet the net section strength is essentially equal ure mechanisms in polymer matrix composites(laminates to the unnotched strength. Similar conclusions have been and textiles). In this case, compressive strength will be reached from finite clement simulations which incorporate governed by the initial misalignment of segments of fiber the inelastic deformation [12] bundles and the shear strength of the matrix. Compressive failure also involves interply and intraply delamination, These results suggest that the failure stress should exhibit which will probably be the principal mechanisms of failure volume dependence, being highest when the volume in CMCs with nonporous, relatively strong matrices.Ceramic composites reinforced by continuous fibers Cox and Zok 667 is a commensurate increase in the number of material parameters to be determined by calibrating experiments. Applications to circumferentially reinforced rotors have been presented, but proof of the predictive power of localization models is not yet convincing [ll]. Dealing with more complex fiber architectures is also much more challenging. The response of a 0/9O’laminate prior to localization under loads aligned with the O’fibers is the easiest case, since the cracking evolution is best understood [S]. Damage in textile CMCs involves much more complicated cracking patterns, for which micromechanical models are relatively crude (and not certain to improve, because of the difficulties of dealing with the tortuous heterogeneity of textiles). Continuum damage approaches are necessarily more empirical. Likewise, highly empirical approaches are most credible for multiaxial or off-axis loading, even in unidirectional CMCs. A general method for developing multiaxial constitutive laws up to localization has been demonstrated for plane stress cases, using a combination of standard tension, compression, and shear test data [l?]. When the constitutive laws are embedded in finite element calcula￾tions of strain distributions around a stress concentrator, encouraging agreement is obtained with measured strain fields. Stiffness changes under off-axis loading have been measured ultrasonically [13]. This area of work represents the culmination of efforts to qualify CMCs as structural materials. Current activity focuses on dealing with rate dependent behaviour at high temperature, fatigue effects, and weakest link fracture statistics (volume effects). Fracture and notch sensitivity Tensile tests performed on specimens containing holes or notches have demonstrated that many CMCs arc relatively notch-insensitive [14-16,17*,18*,19,20,21’]. The net-section stress at fracture is typically 80-100% of the unnotched strength: considerably higher than the value calculated on the basis of the elastic stress concentration factor. Indeed, in some instances, there appears to be evidence of notch strengthening [14]. Measurements of in-plane strains (using moire interferometry [18*]) and stresses (using SPATE [14-16,17*]) have shown that strain concentrations are essentially unchanged by the inelastic deformation but stress concentrations are reduced dramatically. However, even in the most notch-insensitive materials, stress concentrations are not eliminated alto￾gether, yet the net section strength is essentially equal to the unnotched strength. Similar conclusions have been reached from finite element simulations which incorporate the inelastic deformation [12*]. These results suggest that the failure stress should exhibit volume dependence, being highest when the volume under most stress is small (as it is ahead of a notch). If so, the strength should follow weakest-link scaling. Comparisons of strengths in tension and bending (taking into account the nonlinear stress distributions) support this hypothesis (MeNulty JC, Zok FW, unpublished data). Issues related to strength variability are addressed in more detail elsewhere in this journal [22]. The degree of notch sensitivity is influenced by the nature of the inelastic deformation occurring ahead of the notches (Fig. 1). In some materials (e.g. NicalonTVcalcium aluminosilicate), a damage zone of multiple matrix cracks forms ahead of the notch, which has an analogous effect to the plastic zone in metals (designated Class II behavior by Evans [23’]). In others (e.g. C/C), nonlinearity arises from shear bands oriented parallel to the tensile direction (Class III behavior [23-l). In more brittle CMCs, fracture occurs by the propagation of a dominant mode I crack, with fiber failure and pullout in the crack wake, but with minimal inelastic deformation elsewhere (Class I behavior [23*]). Models of strength for Classes I and III have been developed, based on line-spring representations of the inelastic processes [24*.,25]. Models that take into account large scale sliding [26”] indicate that the maximum fiber stress in the bridging zone is somewhat lower than that predicted from the line-spring models; the latter are thus expected to provide conservative predictions for the stresses at the onset of fiber failure. Some censure is due to several authors over loose claims that a given material has been found to be notch insensitive. This generally fallacious conclusion has been based on tests performed with relatively small notches: typically 1-5 mm. Moreover, there has been almost no discussion of the effects of notch shape (circular holes versus sharp slits). In the presence of sufficiently large, sharp notches, the strength must follow the Griffith relation and the material must be notch-sensitive (as is even the most ductile metal). Researchers should identify the length scales associated with the bridging processes and hence the notch sizes and shapes for which notch sensitivity will occur. Compressive failure Compressive failure of CMCs has remained largely unex￾plored. Some evidence exists that compressive strengths [27’] fall below tensile strengths [28-l. In CMCs with weak or porous matrices, observations to date [27*] show that compressive failure involves kink band formation within fiber bundles (plies or tows), similar to the prevalent fail￾ure mechanisms in polymer matrix composites (laminates and textiles). In this case, compressive strength will be governed by the initial misalignment of segments of fiber bundles and the shear strength of the matrix. Compressive failure also involves interply and intraply delamination, which will probably be the principal mechanisms of failure in CMCs with nonporous, relatively strong matrices