Correlation of Fracture Toughness and Strength

An extensive collection of data on the fracture toughness ( K I c ) and strength (sigma f ) of brittle materials has been used to examine the relationship between the mean measured values of K I c and sigma f . Within this collection of data, it has been observed empirically that K I c frequently is linearly related to sigma f 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 K I c , sigma f , and the critical flaw size ( c 0 ) has been used to derive a general expression for (partial lowercase K I c /partial lowercase sigma f ) x in which the subscript x indicates a condition of constant grain size ( x = g ) or constant density ( x = rho). In general, (partial lowercase K I c /partial lowercase sigma f ) g is not the same as (partial lowercase K I c /partial lowercase sigma f ) rho . Imposing the empirical condition (partial lowercase K I c /partial lowercase sigma f ) x = lambda x , where lambda x is a constant, a relationship between sigma f 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.