Sheldon M. Wiederhorn

Subcritical Crack Growth in Ceramics

Subcritical crack growth that causes delayed failure is discussed in terms of fracture mechanics concepts. Techniques of characterizing subcritical crack growth are presented and the available crack growth data are discussed with particular emphasis on fracture mechanisms. Finally a design technique is presented to predict useful component lifetime from crack growth data after proof testing.

Effect of material parameters on the erosion resistance of brittle materials

Erosion data are compared with two theories that have been suggested to explain the erosive behaviour of solids. A dimensional analysis is applied to the variables that are important to erosion, and a multivariate, linear regression analysis is used to fit the data to the dimensional analysis. The results of the linear regression analyses are compared with the two theories in order to evaluate the applicability of these theories to erosion. Although semi-quantitative agreement of the data with the theories is obtained, some discrepancies are apparent. In particular, the dependence of erosion rate on hardness and critical stress intensity factor is greater than predicted by either of the two theories. These discrepancies are attributed primarily to microstructural aspects of erosion that are not modelled by either of the theories.

Effects of water and other dielectrics on crack growth

Effects of water and a variety of organic liquids on crack-growth rates in soda-lime-silica glass was investigated. When water is present in organic liquids, it is usually the principal agent that promotes subcritical crack growth in glass. In region I, subcritical crack growth is controlled primarily by the chemical potential of the water in the liquid; whereas in region II, crack growth is controlled by the concentration of water and the viscosity of the solution formed by the water and the organic liquid. In region III, where water does not affect crack growth, the slope of the crack-growth curves can be correlated with the dielectric constant of the liquid. It is suggested that these latter results can be explained by electrostatic interactions between the environment and charges that form during the rupture of Si-O bonds.

Atomically sharp cracks in brittle solids: an electron microscopy study

The issue of bond rupture versus microplasticity as an essential mechanism of crack propagation in brittle solids is addressed. A detailed survey of existing theoretical and experimental evidence relating to this issue highlights the need for direct observations of events within the crack-tip “process zone”, at a level approaching 10 nm. Transmission electron microscopy is accordingly used to study arrested cracks about sharp-contact (Vickers indentation and particle impact) sites in Si, Ge, SiC and Al2O3. The nature of the deformation which accommodates the irreversible contact impression is first investigated, in the light of Marshs proposal of an “equivalence” between indentation and crack-tip zone processes. Interfacial and tip regions of the surrounding cracks are then examined for any trace of a plasticity-controlled fracture process. Dislocation-like images are indeed evident at the crack planes, but these are shown to be totally inconsistent with any conventional slip mechanism. The close connection between the dislocation patterns and moiré fringe systems along the cracks points to “lattice mismatch” contrast in association with a partial closure and healing operation at the interface. Analysis of all other details in the crack patterns, e.g. the presence of a crack-front contrast band indicative of a residual strain field and the disposition of interfacial fracture steps relative to the dislocation/moiré system, reinforces this interpretation. It is concluded that the concept of an atomically sharp crack provides a sound basis for the theory of fracture of brittle solids.

Crack propagation and failure prediction in silicon nitride at elevated temperatures

A technique for studying high temperature crack propagation in ceramic materials is developed. The technique is used to obtain relationships between the crack propagation rate and the stress intensity factor for hot-pressed silicon nitride up to 1400° C. The data are then used to develop proof test diagrams which give values for the safe working stress levels for this material after proof testing (or any other flaw detection procedure).

Critical Analysis of the Theory of the Double Cantilever Method of Measuring Fracture‐Surface Energies

This paper presents a critical discussion of the double cantilever method of measuring fracture‐surface energies. It was found that the equation developed by Gillis and Gilman is valid for crack lengths greater than 1.5 times the crack arm height. The constants in this equation were evaluated and were found to be practically independent of the elastic constants of the material for which they were evaluated, suggesting that the equation could be used on any material. The Gilman and Gillis approach to the double cantilever problem was found to be consistent with the approach used by Gross and Srawley.

Effect of temperature on the fracture of sapphire

Abstract At low temperatures, metastable crack growth dictates the environment free strength of sapphire. Plastic deformation by dislocation motion or twin formation and growth plays no role in the fracture process at temperatures below 400° C. These conclusions are supported both by crack growth studies and critical stress intensity factor measurements on sapphire crystals, and by transmission electron microscopy studies of arrested cracks in sapphire and alumina.

Transient creep behaviour of hot isostatically pressed silicon nitride

Transient creep is shown to dominate the high-temperature behaviour of a grade of hot isostatically pressed silicon nitride containing only 4 wt% Y2O3 as a sintering aid. Contributing factors to transient creep are discussed and it is concluded that the most likely cause of longterm transient creep in the present study is intergranular sliding and interlocking of silicon nitride grains. In early stages of creep, devitrification of the intergranular phase, and intergranular flow of that phase may also contribute to the transient creep process. The occurrence of transient creep precluded the determination of an activation energy on the as-received material. However, after creep in the temperature range 1330–1430°C for times exceeding approximately 1100 h, an apparent activation energy of ≈ 1260 kJ mol−1 was measured. It is suggested that the apparent activation energy for creep is determined by the mobility and concentration of diffusing species in the intergranular glassy phase. The time-to-rupture was found to be a power function of the minimum strain rate, independent of applied stress or temperature. Hence, creep-rupture behaviour followed a Monkman-Grant relation. A strain rate exponent of − 1.12 was determined.

Tensile creep of whisker-reinforced silicon nitride

This paper presents a study of the creep and creep rupture behaviour of hot-pressed silicon nitride reinforced with 30 vol% SiC whiskers. The material was tested in both tension and compression at temperatures ranging from 1100 to 1250°C for periods as long as 1000 h. A comparison was made between the creep behaviour of whisker-reinforced and whisker-free silicon nitride. Principal findings were: (i) transient creep due to devitrification of the intergranular phase dominates high-temperature creep behaviour; (ii) at high temperatures and stresses, cavitation at the whisker-silicon nitride interface enhances the creep rate and reduces the lifetime of the silicon nitride composite; (iii) resistance to creep deformation is greater in compression than in tension; (iv) the time to rupture is a power function of the creep rate, so that the temperature and stress dependence of the failure time is determined solely by the temperature and stress dependence of the creep rate; (v) as a consequence of differences in grain morphology and glass composition between whisker-free and whisker-reinforced material, little effect of whisker additions on the creep rate was observed.

Creep and fracture of a vitreous-bonded aluminium oxide

Creep and creep-rupture behaviour of a commercial grade of glass-bonded, 96% aluminum oxide was characterized as a function of temperature and applied stress. The creep data were fitted to the classical empirical relation usually used to describe this phenomenon. The apparent activation enthalpy, ΔH = 926 kJ mol−1, and the stress exponent,n = 4.8, lie at the high end of the range reported for two-phase materials, primarily as a result of structural modifications that occur during creep. A stress-modified Monkman-Grant relationship was fitted to the creep-rupture data to give a stress exponent of −4.2. None of the available theories of creep rupture provided a satisfactory description of the present set of data. Analytical electron microscopy was used to characterize the composition and structure of this material. In the as-received material the intergranular phase was a glass of nearly uniform composition. During high-temperature exposure, devitrification of the glass resulted in the formation of various crystalline phases within the intergranular region of the material. Devitrification depended on both the proximity to the surface, where it was most pronounced, and on the state of stress. In this regard, flexural creep samples exhibited extensive crystallization within the tensile region of the flexural specimens, but little crystallization within the compressive cross-section. From the composition of the retained glass, estimates of the viscosity of the glass at the grain boundaries were made and used, in combination with microstructural information, to compare the creep behaviour with available theories of creep. The results of this paper are consistent with percolation and solution precipitation mechanisms of creep deformation. By contrast, cavitation did not seem to play a major role in the creep deformation process.