Correlation of Fracture Toughness and Strength

An extensive collection of data on the fracture toughness (KIc) and strength (sigmaf) of brittle materials has been used to examine the relationship between the mean measured values of KIc and sigmaf. Within this collection of data, it has been observed empirically that KIc frequently is linearly related to sigmaf when values are compared under conditions of either constant grain size (g) or constant density (rho). Assuming that the most-significant material parameters are g and rho, the general fracture-mechanics relationship among KIc, sigmaf, and the critical flaw size (c0) has been used to derive a general expression for (partial lowercaseKIc/partial lowercase sigmaf)x in which the subscript x indicates a condition of constant grain size (x=g) or constant density (x= rho). In general, (partial lowercaseKIc/partial lowercase sigmaf)g is not the same as (partial lowercaseKIc/partial lowercase sigmaf)rho. Imposing the empirical condition (partial lowercaseKIc/partial lowercase sigmaf)x= lambdax, where lambdax is a constant, a relationship between sigmaf and flaw size has been derived. For the observed conditions, the analysis indicates that the square root of the flaw size should vary as the reciprocal of the observed fracture strength.

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