Roy W. Rice

Comparison of stress concentration versus minimum solid area based mechanical property-porosity relations

Stress concentrations due to pore shape are questioned as a fundamental determinant of mechanical property-porosity relations, especially elastic property porosity relations. On the other hand, actual solid load-bearing areas, especially minimum solid areas of porous bodies, clearly are a determinant of mechanical property-porosity effects. The correlation of pore shape-stress concentration effects with elastic properties of ceramics can be explained by the correlation of pore shapes with minimum solid areas.

Evaluation and extension of physical property-porosity models based on minimum solid area

Physical property-porosity models based on minimum solid areas of idealized stackings of either: (1) spherical particles partially bonded (e.g. sintered), or (2) spherical pores in a solid matrix are shown to agree with appropriate physical property data for bodies whose porosity is reasonably represented by such stackings. Appropriate physical properties are those determined mainly by local stress or flux, e.g. elastic properties, strengths, and electrical and thermal conductivity. The minimum solid areas are, respectively, the: (1) bond (e.g. neck) area between particles defining pores smaller than the particles, or (2) minimum web thickness between adjacent pores being more than or equal to the surrounding particles (e.g. bubbles in a foam). Combinations of the models for mixtures of basic porosity types and changes in basic model parameters (e.g. stacking) over the significant porosity range covered, are shown to agree with the literature (mainly mechanical) property data for bodies of appropriate porosity combinations. Areas of further development and testing are noted.

Fracture surface analysis of ceramics

Flaw size, c, fracture mirror boundaries, r, fracture stress, σ, and critical fracture energy were measured for glasses, glass ceramics, and single and polycrystalline ceramics. The relationship σr1/2 = constant was verified for all these materials. The mirror constants, A, in these materials were shown to be directly proportional to the average critical stress intensity factor for crack propagation, KIC. Based on the A — KIC relationship, the outer mirror to flaw size ratio is shown to scatter about a value of 13∶1. Thus, the mirror constants were used to predict critical flaw sizes in these materials. The observed flaw sizes in most cases correlated well with those calculated. The cases in which poorer correlation was obtained are those in which flaw sizes were smaller than the grain size, flaws were pores or surrounded by porous regions, or where severe microcracking existed. It is shown that the elastic modulus is proportional to the mirror constant and probably to the critical fracture energy, but that the latter is highly dependent on local microstructure. The smaller inner to outer mirror ratios for polycrystalline ceramics over glasses is attributed to the difference in available paths for crack propagation.

Microstructural aspects of crack propagation in ceramics

X-ray microradiographic examination supported by optical and SEM observations was used to study crack propagation in various ceramics, including glasses and cubic and noncubic polycrystalline bodies of different grain sizes. The nature of crack propagation in ceramics was often extremely complex. While cracks in glassy materials were generally simple, as would be expected, in cubic and non-cubic polycrystalline specimens both wandering and branching of cracks was observed. In cubic materials, wandering and branching occurred on the scale of the grain size, while in fine grain, non-cubic materials these were on a multi-grain scale. Results are consistent with the grain size dependence of fracture energy. Elastic anisotropy and thermal expansion anisotropy were suggested as major factors in crack wandering and branching.

Pores as fracture origins in ceramics

Experimental studies and analysis of literature data show that while refinements are needed in fracture mechanics models of pores as flaws in glasses, such models are in reasonable overall agreement with observed strength behaviour. Thus, in glasses, single pores are generally “blunter” flaws than machining or other cracks. However, in polycrystalline materials single pores generally act as sharp cracks. Reasons for this glass-polycrystalline difference in terms of mechanisms and their relation to the models are discussed, along with differences in predicted and observed fracture paths. Quite variable and complex behaviour is indicated for origins from two or more pores in glass and polycrystalline bodies.

Fracture energy of Si3N4

The fracture energy of Si3N4 made by hot pressing, reaction sintering, and chemical vapour deposition (CVD) was studied. Extrapolation of fracture energies to zero additive or porosity levels, as well as analysis of CVD Si3N4 all indicate an intrinsic fracture energy of 20–30J m−2. Higher fracture energies in dense bodies with increasing additive content, or in some more porous bodies (relative to expected porosity dependence) are associated with crack branching. In dense bodies such branching may arise due to micro-cracking from combined effects of crack tip stresses and mismatch stresses due to differences in properties, especially thermal expansion, between Si3N4 and the additive or its reaction products. In porous bodies such branching appears to be due to spatial distribution of pores.

The effect of grinding direction on flaw character and strength of single crystal and polycrystalline ceramics

The effect upon the room-temperature strengths and fractures of flexure bars caused by grinding them either parallel or perpendicular to their tensile axis was investigated for selected single- and polycrystalline ceramics. Particular attention was given to the character of the flaws from which failure initiated. It was shown that grinding introduces two basic sets of flaws: one set forms at an average angle of ∼ 0°, and the other at an average angle of ∼ 90°, to the grinding direction. The angles of these flaws varied somewhat due to their formation on preferred fracture planes in single-crystal or larger-grain polycrystalline bodies as well as due to statistical effects. However, overall, the difference in these two sets of flaws was a major factor in the effect of grinding direction on strength. Flaws that formed approximately parallel with the grinding direction were typically more severe, and hence lead to lower strengths for grinding perpendicular to the bar axis, i.e. when the stress was perpendicular, or nearly so, to them.

Microstructural aspects of fabricating bodies by self-propagating synthesis

Existing data on effects of reactant compact microstructure on self-propagating synthesis, SPS type reactions is reviewed. Propagation rates generally decrease with increased compact density at higher densities, and reactions are no longer ignitable at high densities. At lower densities the trends may vary depending on the reactions. Propagation rates and ignitability also generally decrease with increasing particle size, and can be affected by particle shape. More exothermic reactions lead to greater expansion, hence porosity, in unconstrained samples, while resultant pore sizes are effected mainly by outgassing. Final grain sizes are not a significant function of the initial particle size (but can be effected by finer residual porosity).

Ceramic Fabrication Technology

Background and OverviewPreparation of Ceramic PowdersUse of Additives in Powder Preparation and Other Raw Materials and Nondensification UsesForming and Pressureless Sintering of Powder-Derived BodiesUse of Additives to Aid DensificationOther General Densification and Fabrication MethodsSpecial Fabrication MethodsCrosscutting, Manufacturing Factors, and FabricationIndex

Fracture processes in ferroic materials

Abstract This paper analyzes recent studies on the fracture behavior of BaTiO3 and Pb(ZrTi)O3. The analysis shows that the measured fracture parameters (strength, fracture energy, flaw size) in the ferroic state can be described by standard fracture mechanics equations which are modified to take into account internal stresses. Thus, the analysis suggests that the effects of ferroic mechanisms (ferroelastic twinning, phase transformations) on fracture are important only prior to catastrophic crack propagation.