The Elusive temperature dependence on the Master Curve

The Master Curve methodology for describing cleavage fracture toughness, scatter, size-effects and temperature dependence has been standardized in ASTM E1921. The scatter and size-effects predicted by the method are based on theory, whereas the temperature dependence is the result of empirical observations. The reason for the seemingly nearly invariant temperature dependence of the cleavage fracture toughness of different steels has until now eluded theoretical explanations. The standard fracture toughness temperature dependence is expressed in terms of the normalization fracture toughness K0. However, K0 is really the product of three separate parameters, Kmin, K0i and P(K8), all of which are temperature dependent. Kmin is related to the steepness of the stress distribution in front of the crack, K0i is connected to the likelihood of initiation and P(K8) describes the likelihood of cleavage crack propagation in a unified stress field. This presentation gives some more insight into the factors that lead to the experimentally observed temperature dependence. Finally, a new more material specific temperature dependence usable instead of the standard expression is given