Advances in ceramic composites reinforced by continuous fibers Brian N Cox* and Frank W Zokt Ceramic matrix composites reinforced with continuous fibers loads. The serious difficulties of ensuring durability are on the verge of insertion into hot engineering structures cratures are being confronted; oxidation Yet current research is only beginning to attack some of pesting of SiC fibers at intermediate temperatures, fiber the most critical problems. Key developments in the last eep at higher temperatures, and the chemical stability 24 months include the formulation of constitutive laws for of interfaces arc all hot topics. Textile reinforcement, continuum mechanics analyses: the discovery of stable weak especially with 3D architecture, has appeared as the xide-oxide interface systems: the analysis of how fiber creep solution to the unavoidable vulnerability of brittle matrix s life at high temperatures; confrontation of the problem composites to delamination. And even the central axiom of oxidation pesting at intermediate temperatures in Sic that CMCs cannot be tough unless the fiber/matrix based systems: re-examination of the maxim that interfaces interfaces are weak is now being challenged must be weak; and the advent of textile reinforcement as the olution to delaminat Modeling the inelastic regime Major progress has been made in the last year or two in devcloping design and reliability codes suitable for Addresses Rockwell Science Center, 1049 Camino Dos Rios PO Box 1085 field use from the wealth of micromechanical models in Thousand Oaks, CA 91358, USA the CMC literature. Effort has focused on generating Materials Department,University of California at Santa Barbara, CA constitutive laws for insertion into finite element models, ith the goal of reducing Current Opinion in Solid State Materials Science 1996 CMCs to standard continuum mechanics Current Chemistry Ltd ISSN 1359-0286 Nonlinearity in CMCs at room temperature involves matrix cracking, stochastic fiber fracture, damage local Abbreviation CMCs ceramic matrix composites ization, and fiber pullout. Two groups have presented exhaustive studies for unidirectional composites of the relation between micromechanical properties (including the interfacial friction stress, residual stresses, constituent Introduction elastic moduli. fiber radius, and fiber volume fraction) The period covered by this review (1995 and the and the macroscopic stress-strain response under aligned beginning of 1996, with selected inclusion of papers from loads prior to damage localization and ultimate failur 1994)marks a major epoch in the history of research [3-9]. Prior and well established models of matrix cracks into continuous fiber reinforced ceramic matrix composites bridged by sliding fibers are used as the physical basis (CMCs). From the carly 1980s, when CMC research for modeling. Micromechanical properties are deduced first enjoyed large scale funding and the attention of directly from experimental hysteresis loops, obviating any significant groups all over the world, effort has been detailed tests of interface conditions, for cxample fibcr concentrated on a simple paradigm of the ideal CMC. It pullout or pushout tests. One group has couched its work must have a weak fiber/matrix interface to allow energy in the language of micromechanics more familiar ro the absorption during fracture by the deflection of cracks, in CMC community [3, 451; the other in the language of the complete absence of any dislocation based toughening. continuum damage mechanics, but with a thermodynat Freed of stress concentration when the matrix cracked, potential function derived from the same micromechanics strong fibers would continue to bear high loads. This 16, 7, 8, 9]. They offer equivalent treatments of nonlinear approach to protecting CMCs from intrinsic faws, notches, ity up to localization, with some variations in the poi and damage was pursued almost entirely in the context of of view and in the level of micromechanical detail used unidirectionally reinforced CMCs, with aligned loads; and in fitting data. Both sets of work are essential readi mostly in terms of room temperature phenomena. It is now More empirical (probably unnecessarily so)treatments of very well understood. (See [1, 2] for recent articles covering nonlinearity in unidirectional CMCs have also appeared many aspects of work up to 1995.) Structural applications almost never involve uniaxial Recent extensions of the continuum damage approach stresses; and the long sought pay-off for CMCs will also deal with predicting the onset of damage localization, certainly come at high temperatures. Now we see at which is required to model ultimate failure and the notch ast the reduction of micromechanical models and our sensitivity of strength [11]. Localization and subsequent dctailcd understanding of matrix cracking and statistical fiber pullout involve distributions of Aaw strengths and fiber failure to constitutive laws suitable for use in stress redistribution effects which are complex and not finite element calculations of structures under complex generally well known in a particular material.There
666 Advances in ceramic by continuous fibers Brian N Cox* and Frank W Zokt Ceramic matrix composites reinforced with continuous fibers are on the verge of insertion into hot engineering structures. Yet current research is only beginning to attack some of the most critical problems. Key developments in the last 24 months include the formulation of constitutive laws for continuum mechanics analyses; the discovery of stable weak oxide-oxide interface systems; the analysis of how fiber creep limits life at high temperatures; confrontation of the problem of oxidation pesting at intermediate temperatures in Sic based systems; re-examination of the maxim that interfaces must be weak; and the advent of textile reinforcement as the solution to delamination problems. Addresses *Rockwell Science Center, 1049 Camino DOS Rios, PO Box 1065, Thousand Oaks, CA 91356, USA +Materials Department, University of California at Santa Barbara, CA 93106, USA Current Opinion in Solid State & Materials Science 1996, 1:666-673 0 Current Chemistry Ltd ISSN 1359-0266 Abbreviation CMCs ceramic matrix composites Introduction The period covered by this review (1995 and the beginning of 1996, with selected inclusion of papers from 1994) marks a major epoch in the history of research into continuous fiber reinforced ceramic matrix composites (ChlCs). From the early 198Os, when CMC research first enjoyed large scale funding and the attention of significant groups all over the world, effort has been concentrated on a simple paradigm of the ideal ChlC. It must have a weak fiber/matrix interface to allow energy absorption during fracture by the deflection of cracks, in the complete absence of any dislocation based toughening. Freed of stress concentration when the matrix cracked, strong fibers would continue to bear high loads. This approach to protecting CMCs from intrinsic flaws, notches, and damage was pursued almost entirely in the context of unidirectionally reinforced ChlCs, with aligned loads; and mostly in terms of room temperature phenomena. It is now very well understood. (See [1,‘2] for recent articles covering many aspects of work up to 1995.) Structural applications almost never involve uniaxial stresses; and the long sought pay-off for ChlCs will certainly come at high temperatures. Now we see at last the reduction of micromechanical models and our detailed understanding of matrix cracking and statistical fiber failure to constitutive laws suitable for use in finite element calculations of structures under complex loads. The serious difficulties of ensuring durability at high temperatures are being confronted; oxidation pesting of SIC fibers at intermediate temperatures, fiber creep at higher temperatures, and the chemical stability of interfaces are all hot topics. Textile reinforcement, especially with 3D architecture, has appeared as the solution to the unavoidable vulnerability of brittle matrix composites to delamination. And even the central axiom that CMCs cannot be tough unless the fiber/matrix interfaces are weak is now being challenged. Modeling the inelastic regime Major progress has been made in the last year or two in developing design and reliability codes suitable for field use from the wealth of micromechanical models in the Ch,iC literature. Effort has focused on generating constitutive laws for insertion into finite element models, with the goal of reducing the treatment of nonlinearity in CIVICS to standard continuum mechanics. Nonlinearity in CMCs at room temperature involves matrix cracking, stochastic fiber fracture, damage localization, and fiber pullout. Two groups have presented exhaustive studies for unidirectional composites of the relation between micromechanical properties (including the interfacial friction stress, residual stresses, constituent elastic moduli, fiber radius, and fiber volume fraction) and the macroscopic stress-strain response under aligned loads prior to damage localization and ultimate failure [3-91. Prior and well established models of matrix cracks bridged by sliding fibers are used as the physical basis for modeling. Micromechanical properties are deduced directly from experimental hysteresis loops, obviating any detailed tests of interface conditions, for example fiber pullout or pushout tests. One group has couched its work in the language of micromechanics more familiar to the ChlC community [3*,4’,5]; the other in the language of continuum damage mechanics, but with a thermodynamic potential function derived from the same micromechanics [6,7,8”,9]. They offer equivalent treatments of nonlinearity up to localization, with some variations in the point of view and in the level of micromechanical detail used in fitting data. Both sets of work are essential reading. hlore empirical (probably unnecessarily so) treatments of nonlinearity in unidirectional CMCs have also appeared 1101. Recent extensions of the continuum damage approach also deal with predicting the onset of damage localization, which is required to model ultimate failure and the notch sensitivity of strength [ 111. Localization and subsequent fiber pullout involve distributions of flaw strengths and stress redistribution effects which are complex and not generally well known in a particular material. There
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 calculations 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 altogether, 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 unexplored. 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 failure 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
668 Ceramics, composites and intergrowths Figure 1 While fatigue effects in CMCs with SiC or oxide fibers appear to be mainly related to interfacial degradation, with minimal fiber damage, carbon fibers can be entirely worn away by fatigue. Thus generally severe fatigue effects are found in CMCs based on carbon fibers [32 Delamination Whether toughness is achieved in a CMC by incorporating weak fiber matrix interfaces or a porous or otherwise weak matrix around fiber bundles, strength under loads acting normal to the fiber direction will be seriously impaired Thus while laminated CMCs exhibit encouraging in-plane toughness, they remain vulnerable to delamination. De lamination can be resisted to some degree by in-plane hbers crossing the fracture plane obliquely, but the work of fracture remains well below 1 k]m-2[33, 34]. Laminates of 2D fabrics (e. g, plain or satin weave)arc equally vulnerable The delani CMCs are not yet preferred for load bearing components in high performance applications such as turbine engines Schematics of three classes of cracking found in unidirectional or Current designs require them to sustain mainly thermal cross-plied CMCs (a)Class 1, matrix cracking plus fiber failure: (b) loads. Even then, thermal gradients present severe delani Class l, matrix cracking, no fiber failure: (e) Class l, shear damage. nation risks. Hutchinson and Lu(35)have explored how in textile CMCs, because of the strong role played by heterogene lamination crack interrupts hcat flow, producing theimal on the scale of fiber tows or bundles. Their identification is a topic of stresses and crack tip stress intensities. The design limit current research. implied for thermal gradients is quite stringent for realisti parameter values The obvious way to suppress delamination is by in corporating through-thickness reinforcement, for exam ple, by stitching, 3D weaving, or inserting short rods. tigue Very encouraging precedents exist in polymer compos Fatigue failure occurs in most CMCs. The dominant ites [36, 37]. While the processing challenges remain echanism at room temperature in CMCs based on largely unaddressed by the ceramics community, data oxide or SiC fibers involves matrix cracking on the first for other composite systems and theory lead the way loading cycle, followed by debonding and cyclic sliding Through-thickness reinforcement bridges delamination along the fiber-matrix interfaces. Repeated sliding causes cracks, often creating an analogue of the steady state wear of the fiber coatings, leading to a reduction in the matrix crack familiar from Mode I aligned loading of interface sliding stress and a corresponding reduction in CMCs [38]. A lower bound therefore exists for the critical e fiber bundle strength [29, 30]. It can also lead to load, regardless of delamination crack length. This allows higher permanent inelastic strains and a reduction in the simple design rules to be formulated. The minimum hysteresis modulus. The latter effects may be important volume fraction of through-thickness reinforcement re for dimensional stability The wear process is also likely quired to suppress delamination is usually only a few to produce flaws in the fibers, further reducing thc bundle percent or less [39]. For the thermal gradicnt problem in trength. Such effects have been seen in fiber-reinforced particular, through-thickness reinforcement also transports fibers extracted from composites before and after fatigue), thermal stresses 35 ion crack. reducing crack-induced titanium matrix composites(by comparing the strengths of heat across a delamin but not in CMCs, partly because of the diffculty of extracting fibers from ceramic matrices. Typically, the Thermal properties fatigue thresholds are 275% of the ultimate tensile To minimize thermal stress, CMCs must have high strength (UTS)and the retained strengths following thermal conductivity along with low thermal expansion fatigue loading are almost equal to the UTS. However, and stiffness. Despite their importance determining limited data suggest that the fatigue threshold is reduced the performance of CMC structures, thermal piopeitics by notches(relative to the notched tensile strength)and have received relatively little attention, with a few notable negative stress ratios [31] theoretical studies. Models have been developed to
666 Ceramics, composites and intergrowths Figure 1 r- (a) (b) Schematics of three classes of cracking found in unidirectional or cross-plied CMCs. (a) Class I, matrix cracking plus fiber failure; (b) Class II, matrix cracking, no fiber failure; (c) Class III, shear damage by matrix cracking. (Additional stress redistribution mechanisms exist in textile CMCs, because of the strong role played by heterogeneity on the scale of fiber tows or bundles. Their identification is a topic of current research.) Fatigue Fatigue failure occurs in most CMCs. The dominant mechanism at room temperature in CMCs based on oxide or SIC fibers involves matrix cracking on the first loading cycle, followed by debonding and cyclic sliding along the fiber-matrix interfaces. Repeated sliding causes wear of the fiber coatings, leading to a reduction in the interface sliding stress and a corresponding reduction in the fiber bundle strength [29,30*]. It can also lead to higher permanent inelastic strains and a reduction in the hysteresis modulus. The latter effects may be important for dimensional stability. The wear process is also likely to produce flaws in the fibers, further reducing the bundle strength. Such effects have been seen in fiber-reinforced titanium matrix composites (by comparing the strengths of fibers extracted from composites before and after fatigue), but not in CMCs, partly because of the difficulty of extracting fibers from ceramic matrices. Typically, the fatigue thresholds are 275% of the ultimate tensile strength (UTS) and the retained strengths following fatigue loading are almost equal to the UTS. However, limited data suggest that the fatigue threshold is reduced by notches (relative to the notched tensile strength) and negative stress ratios [31]. While fatigue effects in CMCs with Sic or oxide fibers appear to be mainly related to interfacial degradation, with minimal fiber damage, carbon fibers can be entirely worn away by fatigue. Thus generally severe fatigue effects are found in CMCs based on carbon fibers [32]. Delamination Whether toughness is achieved in a CMC by incorporating weak fiber/matrix interfaces or a porous or otherwise weak matrix around fiber bundles, strength under loads acting normal to the fiber direction will be seriously impaired. Thus while laminated CMCs exhibit encouraging in-plane toughness, they remain vulnerable to delamination. Delamination can be resisted to some degree by in-plane fibers crossing the fracture plane obliquely, but the work of fracture remains well below 1 kJm-2 [33,34]. Laminates of 2D fabrics (e.g., plain or satin weave) are equally vulnerable. The delamination problem is one of the main reasons CMCs are not yet preferred for load bearing components in high performance applications such as turbine engines. Current designs require them to sustain mainly thermal loads. Even then, thermal gradients present severe delamination risks. Hutchinson and Lu [35*] have explored how a delamination crack interrupts heat flow, producing thermal stresses and crack tip stress intensities. The design limit implied for thermal gradients is quite stringent for realistic parameter values. The obvious way to suppress delamination is by incorporating through-thickness reinforcement, for example, by stitching, 3D weaving, or inserting short rods. Very encouraging precedents exist in polymer composites [36,37*]. While the processing challenges remain largely unaddressed by the ceramics community, data for other composite systems and theory lead the way. Through-thickness reinforcement bridges delamination cracks, often creating an analogue of the steady state matrix crack familiar from Mode I aligned loading of ChlCs [38*]. A lower bound therefore exists for the critical load, regardless of delamination crack length. This allows simple design rules to be formulated. The minimum volume fraction of through-thickness reinforcement required to suppress delamination is usually only a few percent or less [39]. For the thermal gradient problem in particular, through-thickness reinforcement also transports heat across a delamination crack, reducing crack-induced thermal stresses [35*]. Thermal properties To minimize thermal stress, CMCs must have high thermal conductivity along with low thermal expansion and stiffness. Despite their importance in determining the performance of CMC structures, thermal properties have received relatively little attention, with a few notable theoretical studies. Models have been developed to
Ceramic composites reinforced by continuous fibers Cox and Zok 669 account for degradation in the thermal expansion and structural applications under aligned loads and whe conductivity of cross-ply laminates in the presence of environmental degradation has been controlled. Current periodic matrix cracks [40, 41]. The models highlight the research focuses on notch sensitivity, where the combi 2.portance of the Biot numbers associated with fiber nation of matrix cracking and the stress concentration of trix interfaces, bridged matrix cracks in longitudinal the notch accelerate creep rupture of fibers [46, 55]. Fiber plies, and unbridged cracks in transverse plies, along with creep encourages the dominance of a single matrix crack, the corresponding crack densities. The through-thickness since it tends to relieve stresses on parallel matrix cracks conductivity can also be impaired by the presence of which have initiated upon the first loading. This contrasts orosiry. The effects of porosity and fiber waviness with cracking at room temperature, where many cracks are have been incorporated into a cell model for plain usually found, even next to very sharp notches [ 14] the through-thickness thermal properties is particularly The creep properties of the fibers are obviously critical important in design because of the low delamination in setting design limits and for determining lifetime resistance of CMCs. Much is yet understood. For example, early experiments have shown challengingly complex A review of the models and the experimental work relationships between morphological changes and creep covering the past decade can be found in [43]. Despite rates in NicalonTM fibers [56, 57]; and both creep rates and progress in the development of models for the thermal strength are likely to be affected by interactions berween properties of composites, a critical assessment of the fibers and either interphases or the matrix (Morscher models has been hampered by the lack of experimental GN, unpublished data). Developing creep resistant fibers data on the thermal properties of the constituents and establishing confidence in their performance remain (especially the fibers)and the conductance of fiber-matrix central problems in the CMc field A peripheral field is developing in the potential (distant Creep future! )application of SiC-bascd CMCs in fusion reactors Environment and phase stability aside, the design bounds SiC is favoured for its low nuclear activation rate. Creep f CMCs under aligned loads are set by creep failure remains central, but is now coupled with radiation In glass matrix composites, creep occurs predominant in the matrix. In unidirectional glass matrix composites, Oxidation embrittlement high creep rates in the matrix under transverse loads The problem of oxidation embrittlement continues to cause considerable creep anisotropy. In asymmetrically plague SiC-based CMCs. The embrittlement involves laid-up laminates or in the presence of stress gradients, oxygen ingress through matrix cracks and the subsequent creep anisotropy within plies will compromise dimensional reaction of oxygen with both the fiber coatings and the stability [44]. In CMCs designed for higher temperatures, fibers [60,61]. It occurs as a so-called pest phenomenon, hich have nonglass matrices, the situation is reversed. being worst at temperatures lower than those of intended Polycrystalline fibers are fabricated with fine grains for service. At higher temperatures, oxidation products near trength, which are usually smaller than the grains in the the external surfaces tend to seal cracks and inhibit matrix. It is therefore the fibers that creep first. Consider- further oxygen ingress. (Yet high temperature interfacial able progress has now been made towards understanding degradation is still a potential problem [62]. )The pest the important consequences of this. Under sustained temperature can be determined by mechanical testing loads, matrix cracks, which would be arrested and remain of tensile specimens subject to a temperature gradient stable at room temperature, exhibit stable, time dependent along the specimen length: the gradient being produced growth as fiber creep degrades the shielding effects by (localized)induction heating near the gauge center of bridging fibers [45-47, 48]. The steady state matrix [61]. Typically, the pest temperatures are in the range cracking stress is no longer a lower bound for nonlinearity 600-800.C. These temperatures are considerably lower and ultimate failure [49]. Constitutive laws have been than those usually used for high temperature testing of derived for bridging fibers that creep [50, 51](as well CMCs. Consequently, the embrittlement phenomenon as for creeping interfaces [521). the incubation of crack can be readily overlooked growth from prior matrix faws has been modeled [51] and crack growth trends have been detailed [53]. Global Additional complications arise because of the inherent is now well understood [47, 50]. Possible failure modes currently used in CMCs). Experiments on SiC/Nicalon TMI for 0/90laminates with creeping fibers have been mapped minicomposites (single tow composites) confirm that in terms of fundamental material parameters [49, 54]. failure at elevated temperatures dominated by the strength degradation of the fibers alone Matrix cracking moderated by creeping fibers appears to (Morscher Gn, unpublished data) Composites containing be the critical failure path for CMCs in high temperature Hi-Nicalon TaI fibers with bn coatings appear to be more
Cemmic composites reinforced by continuous fibers Cox and Zok 669 account for degradation in the thermal expansion and conductivity of cross-ply laminates in the presence of periodic matrix cracks [40,41’]. The models highlight the importance of the Biot numbers associated with fiber matrix interfaces, bridged matrix cracks in longitudinal plies, and unbridged cracks in transverse plies, along with the corresponding crack densities. The through-thickness conductivity can also be impaired by the presence of porosity. The effects of porosity and fiber waviness have been incorporated into a cell model for plain weave architectures [42]. As noted earlier, knowledge of the through-thickness thermal properties is particularly important in design because of the low delamination resistance of CMCs. A review of the models and the experimental work covering the past decade can be found in [43]. Despite progress in the development of models for the thermal properties of composites, a critical assessment of the models has been hampered by the lack of experimental data on the thermal properties of the constituents (especially the fibers) and the conductance of fiber-matrix interfaces. Creep Environment and phase stability aside, the design bounds of CMCs under aligned loads are set by creep. In glass matrix composites, creep occurs predominantly in the matrix. In unidirectional glass matrix composites, high creep rates in the matrix under transverse loads cause considerable creep anisotropy. In asymmetrically laid-up laminates or in the presence of stress gradients, creep anisotropy within plies will compromise dimensional stability [44]. In CMCs designed for higher temperatures, which have nonglass matrices, the situation is reversed. Polycrystalline fibers are fabricated with fine grains for strength, which are usually smaller than the grains in the matrix. It is therefore the fibers that creep first. Considerable progress has now been made towards understanding the important consequences of this. Under sustained loads, matrix cracks, which would be arrested and remain stable at room temperature, exhibit stable, time dependent growth as fiber creep degrades the shielding effects of bridging fibers [45*117*,48]. The steady state matrix cracking stress is no longer a lower bound for nonlinearity and ultimate failure [49]. Constitutive laws have been derived for bridging fibers that creep [50*,51] (as well as for creeping interfaces [52]), the incubation of crack growth from prior matrix flaws has been modeled [51], and crack growth trends have been detailed [53]. Global creep plasticity in the presence of multiple matrix cracks is now well understood [47*,50*]. Possible failure modes for 0/90’laminates with creeping fibers have been mapped in terms of fundamental material parameters [49,54]. Matrix cracking moderated by creeping fibers appears to be the critical failure path for CMCs in high temperature structural applications under aligned loads and when environmental degradation has been controlled. Current research focuses on notch sensitivity, where the combination of matrix cracking and the stress concentration of the notch accelerate creep rupture of fibers [46’,55]. Fiber creep encourages the dominance of a single matrix crack, since it tends to relieve stresses on parallel matrix cracks which have initiated upon the first loading. This contrasts with cracking at room temperature, where many cracks are usually found, even next to very sharp notches [14]. The creep properties of the fibers are obviously critical in setting design limits and for determining lifetime. Much is yet to be understood. For example, some early experiments have shown challengingly complex relationships between morphological changes and creep rates in NicalonTbl fibers (56,571; and both creep rates and strength are likely to be affected by interactions between fibers and either interphases or the matrix (Morscher GN, unpublished data). Developing creep resistant fibers and establishing confidence in their performance remain central problems in the CMC field. A peripheral field is developing in the potential (distant future!) application of Sic-based CMCs in fusion reactors. SIC is favoured for its low nuclear activation rate. Creep failure remains central, but is now coupled with radiation damage [58,59]. Oxidation embrittlement The problem of oxidation embrictlement continues to plague Sic-based CMCs. The embrittlement involves oxygen ingress through matrix cracks and the subsequent reaction of oxygen with both the fiber coatings and the fibers [60,61’]. It occurs as a so-called pest phenomenon, being worst at temperatures lower than those of intended service. At higher temperatures, oxidation products near the external surfaces tend to seal cracks and inhibit further oxygen ingress. (Yet high temperature interfacial degradation is still a potential problem [62].) The pest temperature can be determined by mechanical testing of tensile specimens subject to a temperature gradient along the specimen length: the gradient being produced by (localized) induction heating near the gauge center (61.1. Typically, the pest temperatures are in the range 600-SOO’C. These temperatures are considerably lower than those usually used for high temperature testing of CMCs. Consequently, the embrittlemenc phenomenon can be readily overlooked. Additional complications arise because of the inherent instability of NicalonThl fibers (the most common fiber currently used in CMCs). Experiments on SiC/NicalonThl minicomposites (single tow composites) confirm that failure at elevated temperatures is, in some instances, dominated by the strength degradation of the fibers alone (Morscher GN, unpublished data). Composites containing Hi-NicalonThl fibers with BN coatings appear co be more
670 Ceramics, composites and intergrowths stable, although a critical assessment of their performance porous matrix that offers easy splitting paths [67,68] under conditions that accentuate the embrittlement has (Other wood-like ceramics presented recently are really be performed porous monoliths [69). )The propensity for splitting in CMCs can be enhanced by compressive residual stresses A rudimentary model has been developed to predict in the matrix [70]. Weak matrices and fiber entanglement the rupture time under static loading [60]. More refined within fiber bundles must also favour splitting [28] odcls are nceded to take into account in a more Precedents in polymer and carbon-carbon composites realistic way the nature of the oxidation processes and suggest that especially effective toughening mechanisms the mechanisms responsible for fiber strength degradation. for strong interface CMCs exist in textile composites Some thermodynamic calculations have been performed [71]: fiber bundles fail as units, but neighboring bundles to identify the dominant reaction products formed when are protected from stress concentration by easy splitting Bn and Sic are present with oxygen [63]. These have between bundles; and 3D architectures bind failed fiber been limited to a temperature of 1100"C, considerably bundles together to large strains, giving exceptional values higher than the pest temperature. The kinetics and of work of fracture Model brittle/brittle composites have thermodynamics of these reactions and their effects been devised to demonstrate the benefits of interlocking on strength degradation in the pest Icginc are poorly 3D architectures [72] understood The growing recognition of the prevalence of the em- Figure 2 brittlement phenomenon in virtually all SiC-based CMC has led to the development of all-oxide CMCs. These are described in a subsequent section of this review. Barring where SiC-based systems must endure long term exposure, the design stress will have to be limited to the matrix cracking stress,as this represents the threshold below which embrittlement is suppressed. Tw o strategie fully dense matrices, produced, for example, by melt infiltration, rather than chemical vapor infiltration(which usually results in large pores at which cracks initiate); or the use of hybrid laminates comprising alternating layers of fiber reinforced CMCs and fully dense ceramic sheets The latter approach has been demonstrated [64], although 2 it is expected to be limited in its use to components with those which can be using a tile construction Bending fracture in an oxide-oxide CN with no fiber coating (strong interface crack pal Materials development BD Dalgleish, U Ramamurty, and CG Levi. The most eye-catching advance of the last two years in chemistry has been the advent of monazites and closely related structures, for example, xenotimes, as terface coatings and matrices in all-oxide composites. Wood-like fracture has now also been observed in When prototypical LaPO4 is deposited on Al2O3 fibers weak-interface systems, including fibrous Si3N4-BN [73] (with care to maintain accurate 1: 1 La: P stoichiometry), and monazite composites a weak interface is formed which is extremely stable up to at least 1600C [65, 66]. The processing required While the progress with all-oxide CMCs is exciting, thei appears to be simple and reproducible enough and the inherent disadvantages persist. Oxides generally exhibit base materials sufficiently low in cost that monazites may higher thermal expansion and lower thermal conductivity well eliminate degradation by interphase reactions as a life than SiC-based CMCs and will therefore have to sustain imiting process in all-oxide composites. If so, this is a higher stresses and temperatures in thermal applications major breakthrough. There is substantial new activity in Moreover, the creep resistance of currently available oxide monazite processing and applications fibers is markedly inferior to that of SiC fibers (e.g Tough oxide-oxide CMCs with strong fber/matrix inter- ccs have now also bccn dcmonstratcd. Crack defection Problcms remain with chemical stability in carbon fiber characteristics like those seen in wood have been achieved CMCs [74-76 and oxide-oxide Cmcs with bn interface without fiber/matrix debonding by bundling fibers in a coatings [77]
670 Ceramics, composites and intergrowths stable, although a critical assessment of their performance under conditions that accentuate the embrittlement has yet to be performed. A rudimentary model has been developed to predict the rupture time under static loading (60). More refined models are needed to take into account in a more realistic way the nature of the oxidation processes and the mechanisms responsible for fiber strength degradation. Some thermodynamic calculations have been performed to identify the dominant reaction products formed when BN and SIC are present with oxygen [63]. These have been limited to a temperature of llOo”C, considerably higher than the pest temperature. The kinetics and thermodynamics of these reactions and their effects on strength degradation in the pest regime are poorly understood. The growing recognition of the prevalence of the embrittlement phenomenon in virtually all Sic-based CMCs has led to the development of all-oxide CMCs. These are described in a subsequent section of this review. Barring a significant materials breakthrough, in cases where Sic-based systems must endure long term exposure, the design stress will have to be limited to the matrix cracking stress, as this represents the threshold below which embrittlement is suppressed. Two strategies for improving upon the cracking stress could be adopted: stronger, fully dense matrices, produced, for example, by melt infiltration, rather than chemical vapor infiltration (which usually results in large pores at which cracks initiate); or the use of hybrid laminates comprising alternating layers of fiber reinforced CMCs and fully dense ceramic sheets. The latter approach has been demonstrated [64], although it is expected to be limited in its use to components with relatively simple geometry or those which can be produced using a tile construction. Materials development The most eye-catching advance of the last two years in chemistry has been the advent of monazites and closely related structures, for example, xenotimes, as interface coatings and matrices in all-oxide composites. When prototypical Lap04 is deposited on A1203 fibers (with care to maintain accurate 1:l La:P stoichiometry), a weak interface is formed which is extremely stable up to at least 16OO’C [65**,66*]. The processing required appears to be simple and reproducible enough and the base materials sufficiently low in cost that monazites may well eliminate degradation by interphase reactions as a life limiting process in all-oxide composites. If so, this is a major breakthrough. There is substantial new activity in monazite processing and applications. Tough oxide-oxide CMCs with strong fiber/matrix interfaces have now also been demonstrated. Crack deflection characteristics like those seen in wood have been achieved without fiber/matrix debonding by bundling fibers in a porous matrix that offers easy splitting paths [67”,68]. (Other wood-like ceramics presented recently are really porous monoliths [69].) The propensity for splitting in CMCs can be enhanced by compressive residual stresses in the matrix [70]. Weak matrices and fiber entanglement within fiber bundles must also favour splitting [ZS]. Precedents in polymer and carbon-carbon composites suggest that especially effective toughening mechanisms for strong interface CMCs exist in textile composites [71]: fiber bundles fail as units, but neighboring bundles are protected from stress concentration by easy splitting between bundles: and 3D architectures bind failed fiber bundles together to large strains, giving exceptional values of work of fracture. Model brittle/brittle composites have been devised to demonstrate the benefits of interlocking 3D architectures [72*]. Figure 2 Bending fracture in an oxide-oxide CMC made from woven fiber tows with no fiber coating (strong interfaces). Note the irregular crack path and the extent of fiber bundle pullout, reminiscent of wood. (Courtesy BD Dalgleish, U Ramamurty, and CG Levi.) Wood-like fracture has now also been observed in weak-interface systems, including fibrous SixNh-BN [73] and monazite composites. While the progress with all-oxide CMCs is exciting, their inherent disadvantages persist. Oxides generally exhibit higher thermal expansion and lower thermal conductivity than Sic-based CMCs and will therefore have to sustain higher stresses and temperatures in thermal applications. Moreover, the creep resistance of currently available oxide fibers is markedly inferior to that of Sic fibers (e.g., Hi-NicalonThr). Problems remain with chemical stability in carbon fiber CMCs [74-761 and oxide-oxide CMCs with BN interface coatings [77]
Ceramic composites reinforced by continuous fibers Cox and Zok 671 Interfaces ceramic matrix composites: L, theory. J Am Ceram Soc 1995, The mechanics of fiber/matrix interfaces and their relation 78:2709-2720. to bridged cracks and thence the constitutive properties of This and the following paper provide an excellent demonstration of the de- elopment of constitutive laws from micromechanical arguments. Restricted CMCs are mature areas of research (e.g. [781). One sub- to uniaxial loads stantial and still fairly original recent effort has addressed 4, Domergue measurements and the constituent p the role of interface roughness. Roughness has been exp measured on several typical systems [79] and its effect on rials, J Am Ceram Soc 1995. 78: 2721-2731 ber pullout relations has been measured and modeled [80, 81, 82]. Quantitative predictions of roughness effects dia FE, Evans AG: Hysteresis remain difficult because the roughness is geometrically eram soc 1996 complex. In some cases, roughness appears to cancel the 6. Hild F, Larsson P-L, Leckie FA: Uncoupled and coupled effect of Poissons contraction of a loaded fiber [80.1 validating the assumption of uniform interfacial friction caramic matrix composites. Comp Struct 1994, 29: 365-377 stresses, which has been popular because of its simplicit damage mechanics. Arch Appl Mech 1995. 65: 437-456. But generally, determining the relation between interfacial 8. Burr A, Hild F, Leckie FA: Continu calibrating fracture experiments[83]. It has been proposed Ap prese nic -matrix composites,Eur J Mach p" ofd s 1996. in onditions and fracture behaviour probably always require g constitutive laws for multiaxial loads. that roughness effects can be controlled by incorporating a compliant fiber coating to accommodate mismatch strains siderations, with the crack density inferred from modulus measurements. sed by unseated asperities [84-86 9. Hild F BurT A, Leckie FA: Matrix atrix composlte, Int J Solids Struct 1996 33:1209-1220 Substantial rate effects in stress-strain curves have been 10. Baste S, EI Bouazzaoui: An experimental investigation of measured in SiC/glass composites [87]. The material is stiffness reduction and cracks geometry in a ur stronger and exhibits lower cracking densities at higher brite matrix composite. J Comp Mater 1996, 30: 282-308 strain rates. These effects have been assigned tentatively 11 d6 d c bis composite s EruM时 to environmentally assisted matrix cracking(effective at Sods1995,13:731-749 low strain rates) and an increase in the interfacial friction 12. Genin GM, Hutchinson JW: Composite laminates in plan stress with strain rate(see also the section on Fatigue) Since weak interfaces are favoured in CMCs. the interfa- rty of the model in calculating stress and strain distributions around notches cial debond energy is usually ignored in analyzing matrix or holes. racking in CMCs. Including the interfacial debond energy 13. Baste S, EI Bouazzaoui R: Cracking orientation and induced in a model of fiber bridging has been shown to increase the of a caramic matrix composite under off-ax steady state matrix cracking stress, but the effect is small loading. J Mater Sci 1996, 31: 1575-1584 for material parameters representative of current CMCs 14. Cady CM, Mackin T, Evans AG: Slicon carbide/calcium J Am Ceram Soc 1995. 78: 77-82 la FE, Spearing SM, Mackin T), He MY, Evans AG: Notch The protection by interfacial debonding of a fiber inside 曲 in carbon matrIx composites. J Am a cracked coating has been modeled [89]. Experimental 16. Mall S, Bullock DE, Pemot J]: Tensile fracture behaviour of fibre work continues on interfacial characterization [90-92 eramic-matrix composite with hole Composites 1994,25:237-242. Acknowledgements 17. Mackin T, Purcell TE, He MY, Evans AG: Notch sensitivity and ARPA URI dON CR cI No No0l492-31808. AG EVans t Stress redistribution around notches in 2e eral Leckie. DB and Pd Morgan kindly reviewed sections of the manuscript. centration References and recommended reading sile test. Although the authors do not point it out, this implies that Papers of particular interest, published within the annual penod of review ess must be volumedependent and should follow weakest link have been highlighted of special interest 18. Mackin T, Perry KE, Epstein JS, Cady C, Evans AG: Strain fields outstanding interest s in ceramic-matrix composites. J The strain fields ahead of sharp notches have been measured in several 1. Nair SV, Jakus K(Eds): High Temperature Mechanical Behaviour 2. Lehman RL, El-Rahaiby SK, Wachtman JB Jr(Eds): Handbook Westerville, Ohio: American Ceram Society: 1995. d validating cor 9. Shercliff HR. Beaumont PwR, Vekinis G: Direct observation of 3. Vagaggini E, Domergue J-M, Evans AG: Relationships between tension J Mater Sci 1994. 29: 4184-4190
Ceramic composites rainforcad by continuous fibers Cox and Zok 671 Interfaces The mechanics of fiber/matrix interfaces and their relation to bridged cracks and thence the constitutive properties of CMCs are mature areas of research (e.g. [78]). One substantial and still fairly original recent effort has addressed the role of interface roughness. Roughness has been measured on several typical systems [79] and its effect on fiber pullout relations has been measured and modeled [80*,81,82]. Quantitative predictions of roughness effects remain difficult, because the roughness is geometrically complex. In some cases, roughness appears to cancel the effect of Poisson’s contraction of a loaded fiber [SO”], validating the assumption of uniform interfacial friction stresses, which has been popular because of its simplicity. But generally, determining the relation between interfacial conditions and fracture behaviour probably always requires calibrating fracture experiments [83]. It has been proposed that roughness effects can be controlled by incorporating a compliant fiber coating to accommodate mismatch strains caused by unseated asperities [84-86]. Substantial rate effects in stress-strain curves have been measured in Sic/glass composites (87.1. The material is stronger and exhibits lower cracking densities at higher strain rates. These effects have been assigned tentatively to environmentally assisted matrix cracking (effective at low strain rates) and an increase in the interfacial friction stress with strain rate (see also the section on Fatigue). Since weak interfaces are favoured in CMCs, the interfacial debond energy is usually ignored in analyzing matrix cracking in CMCs. Including the interfacial debond energy in a model of fiber bridging has been shown to increase the steady state matrix cracking stress, but the effect is small for material parameters representative of current CMCs [881. The protection by interfacial debonding of a fiber inside a cracked coating has been modeled (891. Experimental work continues on interfacial characterization (90-94. Acknowledgements BNC was supported by AFOSR contract No. F49620-94-C. F\VZ by the ARPA URI program, ONR contract No. NOO14-92-J-1808. AG Evans. F Leckie, DB Marshall, and PD Morgan kindly reviewed sections of the manuscript. References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted ss: . of special interest l * of outstanding interest 1. Nsir SV, Jskus K (Eds): High Temperature Mechanical Behaviour of Ceramic Composites. Boston: Butterworth-Heinemsnn; 1995. 2. Lehman RL, El-Rshaiby SK, Wachtmsn JB Jr (Eds): Handbook on Continuous Fiber-reinforced Ceramic Matrix Composites. Westorville, Ohio: American Cersm Society; 1995. 3. Vagaggini E, Domergue J-M, Evans AG: Relationships between . hystemrir measurements and the constituent properties of cenmic matrix composites: I, theory. I Am Ceram Sot 1995, 78:2709-2720. This and the following paper provide an excellent demonstration of the development of constitutive laws from micromechanical arguments. Restricted to uniaxial loads. 4. Domergue J-M, Vagaggini E, Evans, AG: Reiatfonships between . hysteresis measummenta and the constituent properties of cemmic matrix composites: II. experimental studies on unidirectional materials. J Am Ceram Sot 1995, 76:2721-2731. See the above comment in [3-l. Domergue J-M, Heredia FE, Evans AG: Hystarasis loops and the inelastic deformation of O/90 ceramic matrix composites. I Am Cemm Sot 1996,79:161-170. Hild F, Lsrsson P-L, Leckie FA: Uncouplad and coupled approaches to predict macrocrack initiation in fibar rainforced ceramic matrix composites. Comp Struct 1994,29:365-377. Burr A, Hild F, Leckie FA: Micro-mechanics and continuum damage mechanics. Arch Appl Mach 1995,65:437-456. Burr A, Hild F, Leckie FA: Continuum description of damage in cemmic-matrix composites Eur J Mach A - So/ids 1996, in press. A powerful approach to formulating constitutive laws for multiaxial loads. Includes relation to the micromechanics of multiple cracking via energy considerations, with the crack density inferred from modulus measurements. 9. Hild F, Burr A, Leckie FA: Matrix cracking and debonding of cemmic-matrix composite% lnt J So/ids Struct 1996, 33:1209-l 220. 10. Baste S, El Bouszzeoui: An experimental investigation of stiffness mduction and cracks gaometry in a unidirectional brittle matrix composlta J Comp Mater 1996, 30:262-306. 11. Hild F, BIIIT 4 Leckie FA: Ffber breakage and fiber pull-out of flbar-relnforcad ceramic-matrix composites. Eur J Mech A - Solids 1 gg5, 13~731-749. 12. Genin GM. Hutchinson JW: Composite laminates in plane . stress: constltutive modeling and stress redistribution due to matrix cracking. J Amer Cemm Sot 1996, in press. Plane stress constitutive relations for CMCs are developed and implemented in a finite element code. A compelling demonstration is presented of the utility of the model in calculating stress and strain distributions around notches or holes. 13. Baste S, El Bouazzaoui R: Cracking orient&ion and induced anisotropy of a ceramic matrfx composite under off-axis loading. J Mater Sci 1996, 31 :1575-l 504. 14. Cady CM, Ma&in TJ, Evans AG: Silicon carbide/calcium aluminosilicata: a notch-insensitive cernmic-matrix composite. J Am Ceram Sot 1995,70:77-62. 15. Heredia FE, Spearing SM, Mackin TJ, He MY, Evans AG: Notch effects in wrbon matrix composites. J Am Ceram Sot 1995, 76:2617-2627. 16. Mall S. Bullock DE, Pemot JJ: Tensile fracture bahaviour of fibrereinforcad caramic-matrix composite with hola Composites 1994, 25~237-242. 1Z Mackin TJ, Purcell TE, He MY, Evans AG: Notch sensitivity and . stress redistribution in three ceramic-matrix composites. J Am Ceram Sac 1995,76:1719-l 726. Stress redistribution around notches in several CMCs has been monitored using stress pattern analysis from thermo-elastic emission (SPATE). The maximum stress concentration diminishes with increasing applied stress, but remains significant at the point of fracture. The terminal level of stress concentration coupled with the notched strength indicates that the local tensile strength must be greater than the value measured in a standard uniaxial tensile test. Although the authors do not point it out, this implies that the failure stress must be volume-dependent and should follow weakest link scaling laws. 16. Ma&in TJ, Perry KE, Epstein JS, Cady C, Evans AG: Strain fields . and damage around notches in ceramic-matrix composites. J Am Ceram Sot 1996,79:65-73. The strain fields ahead of sharp notches have been measured in several CMCs using moirb interferometry. The strain concentrations at the notch tips are unaffected by the nonlinearity in the stress-strain response, but because of the nonlinear material response, the stress concentration must be reduced. Such measurements are crucial for understanding notch sensitivity and validating constitutive laws for CMCs. 19. Sherclii HR, Beaumont PWR, Vekinis G: Dimct observation of the fractum of CA!+glass/SIC composites: part II notched tension. J Mater Sci 1994,29:4164-4 190
872 Ceramics, composites and intergrowths 20. Droillard C, Voisard P Heibst C, Lamon J: Determination of 36. Dransfield K, Baillie C. Mai Y-w: Improving the ughness in 2-D woven SiC matrix composites sistance of CFRP by stitching.a review by chemical vapor infiltration. J Am Ceram Soc 1994 994.50:305-317 78:1201-1211 37. Cox BN, Flanagan G: Handbook of analytical methods for textile roillard C. Lamon J: Fracture toughness of 2-D woven SiC/sic calitewsites. Contractor Report to NASA Langley. Thousand Oaks, Soc1996,79:849-858 interfaces can yield sites, but largely applicable to CMCs 38. LU T and Hutchinson Jw: Role of fiber stitching in eliminating cross-ply ceramic com ites. J Am 22. Curtin WA: Stochastics and their role in structural erformance. Curr Opin Solid State Mater Sci 1996,1: 674-671 23. Evans AG, Zok FW: Review: the physics and mechanics of cracks lead the way to understanding the control of delamination by textile reinforcement 39. Cox BN, Massabo R, Kedward KT: The su This review compiles knowledge about the mechanical perf of laminations in curved structures by stitching Composites 1996, in press. esponse in tension and shear, the uhimate tensile strength, notch sensitivity, 40. Lu, Hutchinson Jw: Effect of matrix cracking and interface fatigue, stress corrosion, and creep. Many references are cited composites Composites 1995, 26: 403-414 ittle matrix composites. Acta Metall Mater 1994, crossply composites with matrix cracks. J Mech Phys Solids cracks are analyzed, with numerical results extended by analytical solutions of woven fabric composites. J umrer am samradions confrnn the easier timing that lent hed streng w Is 43. Hasselman DPH, Donaldson KY: Thermal conductivity of atively insensitive to the details of bridging la in 5. Gu P: Notch sensitivity of fiber-reinforced ceramics. int J Lehman RL, EI-Rahaiby SK, Wachtman JB Fracture1995,70253-266 fayette, Indiana: Ceramics Information Analysis Center ZC, Hutchinson JW, Evans AG, Budiansky B 1995:547-583 44. Weber CH, Lofvander JPA, Evans AG: Creep anisotropy 42:1139-1158 of a continuousfiber-reinforced silicon carbide/calcium silicate composite. J Am Ceram Soc 1994 fluenced but the stress notches which are therefore conservative estimators of strength. Wang M, Laird C: Damage and fracture of a cross woven tive set of papers reporting observations on matrix cracking in CMCs with creeping fibers 46. Jones CR, Henager CH Jr, Jo A thorough and useful account of failure mechanisms fibers during slow crack growth and the resu 28. Wang M, Laird C: Characterization of microstructure and ness of SiC/SIC composites. Scripta Metall Mate ensile behavior of a cross-woven C-SiC composite Acta Mater Key observations of ntral failure mechanism in an important class of Complements the preceding paper([27.) ans AG, Zok FW, McMeeking RM: Fatigue of ceramic matrix Lamouroux f Valles JL, Steen M: Intluence of damage Meta∥ Mater1995,43:859-875 30. Holmes JW, Sorensen BF: Fatigue behaviour of continuous Further evidence that fiber creep alloes subcritical matrix crack growth iber-reinforced ceramic matrix composites. In High Temperature 48. Henager CH Jr, Jones RK ch CF Jr, Stackpoole MM Bordia R: Time-dependent, environmentally assisted crack evated temperatures. Metall Mater Trans A 1996 27A:839-849 observations 49. Cox BN, Marshall DB, McMeeking RM, Begley MR: Matri 31. of fiofdgsies 1995, 2a/pie matrix composite with circular hole. s WA. savic cture. Edited by Willis JR. Dordrecht, The Netherlands Morris WL, Cox BN, Marshall DB, Inman RV, James MR: Fatigue temperature. J Am Ceram Soc 1994, 77: 792-800. 50 ley MR Evans AG. McMeeking R: Creep rupture in ceramic J Mater Sci1994,29:3643-365 ute DAW, Shercliff HR, Ashby MF: Modelling of fiber brid ured steady state cracking condition which is then used for analyzing crack er1995.320 mic matrix composites. Scripta Meta 055-1060. 51. ElAzab a, Ghoniem NM: Investigation of incubation time for 5. Hutchinson JW. Ly T: Lam lamination due to thermal ater1995.219:1 in fiber reinfore The essential mechanics of a critical technological I problem are I laid out ing-role of a
672 Ceramics, composites and intergrowths 20. Droillard C, Voisard P, Heibst C, Lamon J: Determination of fracture toughness in 2-D woven Sic matrix composites made by chemical vapor infiltration. J Am Ceram Sot 1994, 76:1201-l 211. 21. Droillard C, Lamon J: Fracture toughness of 2-D woven Sic/Sic . CVI-composites with multilayered interphases. J Am Ceram Sot 1996,79:649-656. This is a thought provoking demonstration that stronger interfaces can yield tougher composites, depending on the details of microcracking in the interphase region. 22. Curtin WA: Stochastics and their role in structural performance. Curr Opin Solid State Mater Sci 1996, 1:674-676. 23. Evans AG, Zok FW: Review: the physics and mechanics of . fibre-reinforced briffle matrix composites. J Mater Sci 1994, 29:3657-3696. This review compiles knowledge about the mechanical performance of CMCs. The most comprehensive models available and the status of experimental assessments are presented. Emphasis is placed on the stress-strain response in tension and shear, the uhimate tensile strength, notch sensitivity, fatigue, stress corrosion, and creep. Many references are cited. 24. . . He MY, Wu B, Suo 2: Notch-sensitivity and shear bands in brittle matrix composites. Acta Metal/ Mater 1994, 42:3065-3070. Notch sensitivity of class II CMCs is modeled using line springs to describe material nonlinearity within both shear bands and mode 1 damage zones ahead of the crack tip. A simple relation to describe the trends in notched strength with notch size is proposed: u/a, = (1 + xgEr) -1’2 where a,, is the initial notch strength, aand a, are the notched and unnotched strengths, E is Young’s modulus measured in the loading direction and Tis the fracture energy (measured on a large, notched specimen). Excellent correlation with numerical simulations confirms the earlier finding that notched strength is relatively insensitive to the details of bridging laws. 25. Gu P: Notch sensitivity of fiber-reinforced ceramics. Int J Fracture 1995, 70:253-266. 26. . . Xia ZC, Hutchinson JW, Evans AG, Budiansky B: On large scale sliding in fiber-reinforced composites. J Mech Phys So/ids 1994, 42:1139-l 156. Models of matrix cracking in which large scale sliding (fiber/matrix/slip zones large relative to the crack length) is taken into account compared with traditional line spring models. Crack tip stress intensity factors are not strongly influenced, but the stress concentration in bridging fibers at notches is found to be substantially overestimated by line spring models, which are therefore conservative estimators of strength. 27. Wang M, Laird C: Damage and fracture of a cross woven . C/SIC composite subject to compression loading. J Mater Sci 1996,31:2065-2069. A thorough and useful account of failure mechanisms. 26. Wang M, Laird C: Characterization of microstructure and . tensile behavior of a cross-woven C-SIC composite. Acts Mater 1996, 44:1371-1367’. Complements the preceding paper (127.1). 29. Evans AG, Zok FW, McMeeking RM: Fatigue of ceramic matrix composites. Acta Metall Mater 1995, 43:659-675. 30. Holmes JW, Serensen BF: Fatigue behaviour of continuous . fiber-reinforced ceramic matrix composites. In High Temperature Mechanical flehaviour of Ceramic Composites. Edited by Nair SV, Jakus K. Boston, Massachusetts: Buttemorth-Heinemann; 1995. This review provides a general overview of fatigue degradation and failure. The discussion is based predominantly on experimental measurements and observations. 31. Mall S, Weidenaar WA: Tension-compression fatigue behaviour of fibre-reinforced ceramic matrix composite with circular hole. Composites 1995, 26:631-636. 32. Morris WL, Cox BN, Marshall DB, lnman RV, James MR: Fatigue mechanisms in graphite/Sic composites at room and high temperature. J Am Ceram Sot 1994, 77:792-600. 33. Shercliff HR, Vekinis G, Beaumont PWR: Direct observation of the fracture of CAS-glass/Sic composites: part 1 delamination. J Mater Sci 1994, 29:3643-3652. 34. Kaute DAW, Sherclifl HR, Ashby MF: Modelling of fiber bridging and toughness of ceramic matrix composites. Scrip& Metal/ Mater 1995, 32:1055-l 060. 35. Hutchinson JW, Lu TJ: Laminate delamination due to thermal . gradients. Cambridge, Massachusetts: Harvard University: 1995. [Report No. MECH-2531. The essential mechanics of a critical technological problem are laid out. IndIspensable for designing thermal barriers. 36. Dransfield K, Baillie C, Mai Y-W: Improving the delamination resistance of CFRP by stitching - a review. Comp Sci Tech 1994, S&305-31 7. 37. Cox BN, Flanagan G: Handbook of analytical methods for textile . composites. Contractor Report to NASA Langley. Thousand Oaks, California: Rockwell Science Center; 1996, in press. A review of mechanisms and models for textile composites, developed for polymer composites, but largely applicable to CMCs. 36. Lu TJ and Hutchinson JW: Role of fiber stitching in eliminating . transverse fracture in cross-ply ceramic composites. J Am Ceram Sot 1995, 76:251-253. A valuable demonstration of how concepts from the mechanics of bridged cracks lead the way to understanding the control of delamination by textile reinforcement. 39. Cox BN, Massab6 R, Kedward KT: The suppression of delaminations in curved structures by stitching. Composites 1996, in press. 40. Lu TJ. Hutchinson JW: Effect of matrix cracking and interface sliding on the thermal expansion of fibre-reinforced composites. Composires 1995, 26:403-414. 41. Lu TJ, Hutchinson JW: Thermal conductivity and expansion of . cross-ply composites with matrix cracks. J Mech Phys Solids 1995,43:1175-l 196. The thermal expansion and conductivity of CMCs containing periodic matrix cracks are analyzed, with numerical results extended by analytical solutions. 42. Ning Q-G, Chou T-W: A closed-form solution of the transverse effective thermal conductivity of woven fabric composites. J Comp Mafer 1995, 29:2260-2315. 43. Hasselman DPH, Donaldson KY: Thermal conductivity of continuous fiber-reinforced ceramic-matrix composites. In Handbook on Continuous Fiber-Reinforced Ceramic Matri* Composites. Edited by Lehman RL, El-Rahaiby SK, Wachtman JB Jr. West Lafayette, Indiana: Ceramics Information Analysis Center; 1995:547-563. 44. Weber CH, LGfvander JPA, Evans AG: Creep anisotropy of a continuous-fiber-reinforced silicon carbide/calcium aluminosilicate composite. J Am Ceram Sot 1994, 77:1745-l 752. 45. Henager CH Jr, Jones RH: Subcritical crack growth in CVI . silicon carbide reinforced with NiccllonTM fibers: experiment and model. J Am Ceram Sot 1994,77:2361-2394. An early member of a definitive set of papers reporting observations on matrix cracking in CMCs with creeping fibers. 46. Jones CR, Henager CH Jr, Jones RH: Crack bridging by Sic . fibers during slow crack growth and the resultant fracture toughness of SiC/SiCt composites. Scripipta Metal/ Mater 1995, 3312067-2072. Key observations of the central failure mechanism in an important class of CMCs under static loads at high temperature. 47. Lamouroux F, VallLs JL, Steen M: Influence of damage on the . creep behaviour of ceramic matrix composites. Camp Engng 1995,5:1379-l 386. Further evidence that fiber creep alloes subcritical matrix crack growth. 4%. Henager CH Jr, Jones RH, Windisch CF Jr, Stackpoole MM, Bordia R: Time-dependent, environmentally assisted crack growth in NicalonTM-fiber-reinforced SIC composites at elevated temperatures. Metal/ Mater Trans A 1996, 27A:639-649. 49. Cox BN, Marshall DB, McMeeking RM, Begley MR: Matrix cracking in ceramic matrix composites with creeping fibers. Proceedings of the IUTAM Symposium on Nonlinear Analysis of Fracture. Edited by Willis JR. Dordrecht, The Netherlands: Kluwer; 1996, in press. 50. Begley MR, Evans AG, McMeeking RM: Creep rupture in ceramic . matrix composites with creeping fibers. J Mech Phys Solids 1995, 43~727-740. Very useful constitutive laws are defined for the bridging effect of creep ing fibers, but the reader should check [53] for remarks on the conjectured steady state cracking condition which is then used for analyzing crack growth. 51. El-Azab A, Ghoniem NM: Investigation of incubation time for sub-critical crack propagation in Sic-SIC composites. J Nucf Mater 1995, 219:101-109. 52. Gwo T-J, Nair SV: Creep crack growth in fiber reinforced composites with rate dependent bridging - role of a viscous fiber matrix interface. Mech Mater 1996, in press
Ceramic composites reinforced by cotinuous fibers Cox and Zok 673 eking RM: Time material classes. A model system of steel chains in an epoxy matrix provides 54. Cox BN, Marshall DB: Crack initiation in fiber-reinforced brittle 73. G, Halloran上 Fibro laminates. J Am Ceram Soc 1996, 79: 1181-1188. powderprocessed 55. Mumm DR, Morris WL, Dadkhah Ms, Cox BN: High temperature Mechanical akano K, Kamiya A, Nishino Y, Imura T, Chou T-W: Fabrication Composites, ASTM STP 1309. Philadelphia: ASTM; 1996. forced sillcon nitride composites. J Am eber CH, Kim KT, Heredia FE, Evans Ceram Soc 78:2811-2814 rupture in SiC-C composites. Mater Sci Eng A 75. Zhien L Jianjun Y, Zhiyun, x rface, microstructure and As glass-ceramic composites, J Bodet R, Bourret X, Lamon J, Naslain R: Tensile creep behaviour carbide-based fibre with a low oxygen content. J 76. Kawai C, Wakamatsu S: Fabrication of CsIC composites Mater Sci1995,30:661-667 58.日 Azab A Ghoniem properties. J Mater Sci 1996, 31: 2165-2170. la KK xu ZR, Ha J-S: 212845-848 59. Jones RH, Henager CH Jr: Fusion reactor application issues Ceram soc i9gu ts ar /mullite matrix composites./Eur on SIC/sIC composites, J Nuc Mater 199 78. shin D-W, Auh KH, Knowles KM: SiC tbre/borosilicate glass 219:55-6 60. Evans AG, Zok FW, McMeeking Models of high properties, J Ceram Soc Japan 1995, 103: 409-417. ceramic matrix composites. J Am Ceram Soc 1996, in press. t robe for ce配 FW Evans AG: Oxidation of a model composite. J Am Ceram Soc 80. Parthasarathy Ta, Marshall DB, Korans R: Analysis of the The prevalenc effect of interfacial roughness on fiber deb ing in bride matrlx composites. Acta Metall Mater 1994 BN/SiC, or C/B coatings. 42:3773-3784 ength or rupture time, along with diminished fiber pullout lengths on the An attractively simple micromechanical model of inteface e8s Is sup- acture ported by test data in the material studie 62. Jones RH, Henager CH Jr, Windisch CF Jr: High temperature 81. Huang CM, Zhu D, Xu Y, Mackin T, Kriven WM partal pressures. Mater Sci Eng A 1995, 198: 103-1 composites. Mater Sc Eng A 1995, 201: 159-168 Sun EY, Nutt SF e.0°672 lip and frictional 64. Cutler WA, Zok FW, Lange FF: Mechanical behavior of severa 1996,79:1825-1833. Philadelphia: ASTM: 1996. control of fit of monazite to be viewed as a major breakthrough. rties in caramic composites. Scripta Meta/l Mater 1994. 31:1079-1084 Eng A 85. Kerans R, Jero PD, Parthasarathy TA: Issues in the control of 95,195:215-222 rfaces in ceramic composites. Comp Sci Tech Monazite is chemically stable in alumina between 1400C and 1800C over long periods provided it is free of alkali metals and divalent elements. 88. Korans R: The role of coating compliance and fiber/matrix 67. Tu w-C, Lange FF, Evans AG: Concept for a 1895, 79: 41 0424.with"strong"interfaces./ Soc Scripta Metall Mater 1995, 32: 505-509 87. Sorensen BF Holmes J: Effect of loading rate on the The attainment of tough CMCs by surrounding fiber bundles(as in a textile) by a weak matrix is de mic matrix composite. J Am Ceram Soc 1096 68. Lange FF Tu WC, Evans AG: Processing of damage-tolerant, 79:313-32 stafac udiansky B, Evans AG, He on JW: Fiber-matrix dabone 195:145-150. ing in aligned fiber ceramic composites. Int J 69. Ota T, Takahashi M, Hibi T, Ozawa M, Suzuki S, HikichiY: or producing SIC"wood, J Am Ceram Soc1995,78:3409-3411 70.凵uT: Crack branching in』l。 xide ceramic comp。 sites. JAm scale intertacial debonding. J Mater Sci 1996, 31: 2027-2034 6,79:266-274 71. Cox BN: Modeling three-dimensional composites. in ad characterization of Niealon and H Advanced by atomic force microscopy. Mater Charact 1995, 35: 189- 91. Lamon J, Rebillat F: Microcomposite test procedure for G. Amsterdam: Kluwer: 1995: 49-62. mic matrix Soe1995,78:401-405. 92. Morscher GN, Martinez-Fermandez J, Purdy M: Determination of nterfacial properties using a single-fiber microcomposite test temal defects and lock-up mechanisms is explored, with reference to several Am Ceram So1996,79:1083-109
Cemmic composites reinforced by continuous fibers Cox and Zok 673 53. 54. 55. 56. 57. 58. 59. 60. 61. . Evans AG, Zok FW, McMeeking RM, Du ZZ: Models of hightempemture, environmentelly-assisted embrtttlement in cemmic matrix composites. J Am Cemm Sot 1996, in press. Heredia FE, McNulty JC, Zok FW, Evans AG: Oxidation embrifflement probe for ceramic-m&ix composites. J Am Cqmm So! 1995,7?!2097-2100. . The prevalence of stress oxidation at lntermeoiate temperatures 18 oemonstrated on several CMC systems containing NicalonTM fibers with either C, EN/SIC, or C/B coatings. The phenomenon is manifested in a reduction in strength or rupture time, along with diminished fiber pullout lengths on the fracture surface. 62. 63. Jones RH, Henager CH Jr, Windisch CF Jr: High tempamture corrosion end crack growth of SIC-SIC at wrleble oxygen partial pressures. Mater Sci Eng A 1996, 19&l 03-l 12. Sheldon SW, Sun EY, Nutt SR, Brennan JJ: Oxidation of BNcosted SK: fibers in cemmic m&ix composites. I Am Ceram sot 1996,7#:539-543. 64. Cutler WA, Zok FW, Lange R: Mechanical behavior of sowral hybrid cemmic matrix composite Iaminetes. J Am Ceram Sot 1996,79:1625-l 833. 65. Morgan PED, Marshall DB: Cemmic composites of monsrite and alumina J Am Ceram Sot 1995, 76:1553-l 563. Ge revelation of monazites as interface coatings. This discovery will come to be viewed as a major breakthrough. 66. Morgan PED, Marshall DB, Hourly RM: High-tempemtum . stability of monaxite-alumins composites. Mater Sci Eng A 19#5,1S6:215-222. Mona&e is chemically stable in alumina between 1400’ C and 1600’ C over long periods, provided it is free of alkali metals and d&lent elements. 67. Tu W-C, Lange FF, Evans AG: Concept for a damage-tolemnt . . cemmlc composite with “strong” interfeces. J Am Ceram Sot Begley MR, Cox BN, M&&eking RM: Time dependent crack growth in ceramic matrix composites with creeping flbsrs. Acta Metall Mater 1995, 43~3927-3936. Cox BN, Marshall DB: Crack initietion in fiber-reinforced brittle Iaminstes. J Am Cemm Sot 1996, 79:1161-l 168. Mumm DR, Morris WL, Dadkhah MS, Cox BN: High tempemture cmck growth in ceramic composites. In Thermal and Mechanical Test Methods and Behaviour of Continuous-Fiber Cemmic Composites, ASTM STP 1309. Philadelphia: ASTM; 1996. Weber CH, Kim Kl, Heredia FE, Evans AG: High tempemtum deformation and rupture in SIC-C composites. Mater Sci Eng A 1995, 1#6:25-31. Bodet R, Bourrat X, Lamon J, Naalain R: Tensile creep behaviour of a silicon carbide-based fibre with a low oxygen content. J Mater Sci 1995, 30:661-667. El Azab A, Ghoniem NM: Postirradiation fiber debonding and pull-out in Sic-SIC composites. J Nucl Mater 1994, 212~045-040. Jones RH, Henager CH Jr: Fusion reactor rpplicatlon issues for low activation SIC/SIC composites. J NW/ Mater 1995, 21#:55-62. 1995, 7#:417-424. 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J Mater Sci 1995, 30:399-404. Kawai C, Wakamatsu S: Fobricatlon of C/SIC composites by en alectrodeposltion/slntering method and the control of the properties. J Mater Sci 1996, 31:2165-2170. Chawla KK, Xu ZR, Ha J-S: Processing, structure, and properties of mullii fiber/mullii m&lx composites. J Eur Cemm Sot 1996,16:293-299. Shin D-W, Auh KH, Knowles KM: Sic fibre/borosillcste glass composite (pert 2) - fectors controlling the mechanical properties. J Cemm Sot Japan 1995,103:409-417. Parthaaarathy TA, B&age DR, Jero PD, Kerans RI: Effect of interfaclsl roughness penmeters on the fiber pushout behevior of a model composite. I Am Cemm Sot 1995, 76:3232-3236. Ptihasarathy TA, Marshall DB, Kerans RJ: An&is of the effect of interfaclsl rouahness on fiber debondinm end sliding ln brittle mstrlx &posites. Acta Metal/ Miter 1994, 4213773-3704. An attmctiwly simple micromechanical model of inteface rough nest is sup ported by test data in the material studied. 81. 82. 83. 84. 85. 66. 07. . 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