The basic principles and practical applications of indentation fracture are reviewed.

Indentation fracture: principles and applications

A general expression for the failure probability of a brittle material is developed by using the properties of flaw size distribution and the stress necessary to fracture an inclined crack. A comparison is made with Weibull analysis and an expression for the Weibull modulus, which is known to be an empirical material constant, is related to the properties of the flaw size distribution of a material. Limitations in the application of Weibull analysis are also discussed.

Statistical approach to brittle fracture

Measurement and statistics of single pellet mechanical strength of differently shaped catalysts

A new strength distribution function for brittle materials is developed, which applies to materials with an inhomogeneous distribution of flaws. The probability of failure is F=1− exp [−〈N c,s 〉] where 〈N c , s 〉 is the mean number of critical defects in the specimen of size S. The well-known Weibull statistics are a special case of the new statistics for a special flaw size distribution. Several aspects of the relationships between the Weibull statistics and material structure are analysed in the light of the new formalism. Examples are materials with several different flaw distributions or rising crack resistance. The conditions necessary to get a Weibull distribution as well as the reasons why Weibull distributions are observed so often in the daily material testing practice are discussed. Finally, the minimum number of test specimens necessary to guarantee a reliable prediction of the component's reliability using Weibull's theory is given. This number depends on the necessary reliability as well as on the loaded (effective) volumes of the test specimens and components, respectively.

A general strength distribution function for brittle materials

Full-length rat alpha and beta cardiac myosin heavy chain sequences: comparisons suggest a molecular basis for functional differences

A new analytical method for calculating crack density distributions from Hertzian fracture data is presented This is the first correct analysis to be reported within the limitations of the assumptions made and is also one which can be readily applied Results are presented for a piece of polished pure silica glass and their statistical significance is discussed

Determination of Surface Crack Size Densities in Glass

IT is almost instinctive to assess the strengths of solids by scratching their surfaces and observing the response. This so-called scratch test has been used by mineralogists for many centuries and an empirical scale of “scratch-hardness” was developed by the Austrian mineralogist Mohs in 1824 (ref. 1) which is still very useful today. Mohs selected ten minerals and proposed a scale such that each mineral will scratch the one on the scale below it, but will not scratch the one above it.

T. R. Wilshaw

Papers

Determination of Surface Crack Size Densities in Glass

Instrumented Scratch Test for measuring the Fracture Behaviour of Strong Solids