The failure of ceramic materials is caused by the extension of small flaws. Therefore, linear-elastic fracture mechanics can be applied to describe the failure behaviour. The main problem in the application of the simple fracture mechanics relation is the existence of a rising crack growth resistance curve, which is caused by crack bridging forces behind the advancing crack tip or by transformations in front of the crack tip. The increasing crack growth resistance leads to problems in the transformation of results from specimens with macrocracks to components with natural cracks.

Fracture Mechanics of Ceramics

A review is presented of the experimental data on subcritical crack growth in geological materials. The main parameters describing subcritical crack growth are the critical stress intensity factor Kc, the subcritical crack growth limit Ko, and the stress intensity factor-crack velocity (K-v) relationship between Ko and Kc. The K-v data are presented in terms of an equation in which the crack velocity depends on stress intensity factor raised to a power n because this is common practice in experimental studies. These data are presented as tables and in synoptic diagrams. For silicates the value of n increases as the environment becomes depleted in hyroxyl species and with increase in the microstructural complexity of the solid. Values of n as low as 9.5 have been found for tensile cracking of quartz in basic environments and as high as 170 for tensile cracking of basalt in moist air. Insufficient experimental data are available to predict subcritical crack growth behavior at depth in the earth's crust without major extrapolations of the data base. Schematic outlines are presented, therefore, of the probable influence on subcritical crack growth of some key parameters in the crustal environment. These include stress intensity factor, temperature, pressure, activity of corrosive environmental agent, microstructure, and residual strains. In addition, a discussion is presented of the likely magnitude of the subcritical crack growth limit. For stress corrosion tensile crack growth of quartz a limit of approximately 0.2 of the critical stress intensity factor is inferred from theoretical calculations. Further problems discussed with regard to the extrapolation of experimental data to crustal conditions include the choice of a suitable equation to describe crack growth and the magnitude of parameters in these equations. A brief discussion of the double torsion testing method is presented in order to aid the interpretation of experimental results because it is almost the sole method used to study subcritical cracking in rocks.

Subcritical crack growth in geological materials

Handbook of SiC properties for fuel performance modeling

On discute des mecanismes de renforcement des ceramiques par pontage des fissures a l'aide de trichites et d'autres types de renforcants discontinus. On montre que le renforcement par pontage des fissures peut etre combine avec d'autres mecaniques de renforcement (par exemple par transformation de phase) et que l'on peut obtenir des effets de synergie. La conception des materiaux renforces repose fortement sur le controle des proprietes des materiaux et des constituants microstructuraux

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Microstructural design of toughened ceramics

Microcracks in rocks: a review

Evaluation of literature data combined with new experimental measurements shows that crystal structure is a basic factor in the grain-size dependence of the critical fracture energy of ceramics. Notch beam (NB), double cantilever beam (DCB), and work-of-fracture (WOF) tests of materials having a cubic crystal structure generally agree and show, at most, a limited variation of fracture energy with grain size. However, maxima of the order of 25% in γ at intermediate grain size and 25% decreases in γ at larger grain size may occur. Materials of noncubic crystal structure show broader variations in γ with G. Both DCB and WOF tests show γ passing through maxima that are typically 100 to >400% of values at fine or large grain size. Limited DT data are consistent with this trend but various results of NB tests are mixed. Some NB test data agree with the DCB and WOF trends, whereas others taken from the same materials show no change or only a limited continuous decrease of γ as G increases.

Grain‐Size Dependence of Fracture Energy in Ceramics: I, Experiment

Fracture strengths (δ), fracture-initiating flaw sizes, and mirror radii (r), as outlined by either the mist or the hackle boundary, were measured for silicate and nonsilicate glasses (e.g. As2S3 and glassy carbon). For all glasses, δr1/2= constant. The average ratios of inner and outer mirror radii to flaw size were ∼10:1 and ∼13:1, respectively, for most of the glasses. Critical fracture energies calculated from either flaw or mirror size agreed very well with those obtained by double-cantilever-beam measurements.

Prediction of Fracture Energy and Flaw Size in Glasses from Measurements of Mirror Size

An analysis was made of cantilever beam specimens used for crack propagation studies, Included in this analysis were the effects of a plastic zone at the crack tip, beam rotation, and the viscoelastic response of the material. This analysis showed that application of a constant bending moment to the specimen rather than a constant load provides a test in which the strain energy release rate,G, is independent of crack length. Other advantages of this test configuration are that corrections for shear or beam rotation effects are not necessary. Results of this test on both glass and ceramics are reported.

Crack Propagation Studies in Brittle Materials.

A mathematical model of the grain-size dependence of fracture energy of noncubic ceramics is developed and discussed. This model attributes the maxima in fracture energy of noncubic materials to countertrends of increasing numbers of microcracks and decreasing energy absorption per microcrack as grain size increases. The model predicts results similar to those experimentally observed. Agreement between calculated and measured fracture energy values is generally good, except for materials with extreme anisotropy. Sources of these differences and methods of improving calculations are discussed.

Grain‐Size Dependence of Fracture Energy in Ceramics: II, A Model for Noncubic Materials

Fracture mechanics is combined with fracture surface analysis to analyze brittle failure of glass bars which were tested relative to the direction of grinding. Grinding essentially produces two sets of flaws from which failure occurs. In the most severe set, formed basically parallel to the grinding direction, the ratio of the average depth (a) to the half-width (b) is 0.5. In the less severe set, formed perpendicular to the grinding direction, the average a/b ratio is 1.6. In both sets the most severe flaws are generally associated with a particularly deep grinding groove or gouge. The strength reduction resulting from testing perpendicular to the grinding direction results from the larger flaw size and slightly higher stress-intensity factor resulting from the greater ellipticity of the flaws formed parallel to the grinding grooves and perpendicular to the tensile axis. Detailed analysis of these 2 sets of flaws causing failure of appropriately oriented specimens shows that (1) the fracture mirror radius, r, occurs at a constant stress-intensity level independent of flaw geometry; (2) unsymmetric fracture mirrors result from unsymmetric, irregular flaws leading to unsymmetric stress-intensity distributions; (3) is constant for semielliptical flaws; and (4) fracture energy calculated from an expression including mirror constants, the flaw-to-mirror size ratio, and the flaw geometry agrees with measured values over a wide range of a/b values.

S. W. Freiman

Papers

Grain‐Size Dependence of Fracture Energy in Ceramics: I, Experiment

Prediction of Fracture Energy and Flaw Size in Glasses from Measurements of Mirror Size

Crack Propagation Studies in Brittle Materials.

Grain‐Size Dependence of Fracture Energy in Ceramics: II, A Model for Noncubic Materials

Effect of Grinding on Flaw Geometry and Fracture of Glass