13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- The Elusive Temperature Dependence of the Master Curve Kim Wallin VTT Materials and Built Environment, P.O. Box 1000, FI-02044 VTT, Espoo, Finland Kim.Wallin@vtt.fi Abstract 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(K∞), 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(K∞) 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. Keywords Master Curve, Cleavage fracture, Temperature dependence 1. Introduction The Master Curve (MC) method is a statistical, theoretical, micromechanism based, analysis method for fracture toughness in the ductile to brittle transition region. The method, originally developed at VTT simultaneously account for the scatter, size effects and temperature dependence of fracture toughness. The method has been successfully applied to a very large number of different ferritic steels and it forms the basis of the ASTM testing standard for fracture toughness testing in the transition region (ASTM E1921-12). 1.1. The basic Master Curve The MC approach is based on a statistical brittle fracture model, which gives for the scatter of fracture toughness in the form of Eq. (1) [1]. [ ] 4 I min IC I 0 min K K P K K 1 exp K K ⎛ ⎞ ⎡ ⎤ − ⎜ ⎟ ≤ = − − ⎢ ⎥ ⎜ ⎟ ⎝ ⎣ − ⎦ ⎠ , (1) In Eq. (1), P[KIC ≤ KI] is the cumulative failure probability, KI is the stress intensity factor, Kmin is the theoretical lower bound of fracture toughness and K0 is a temperature and specimen size dependent normalization fracture toughness, that corresponds to a 63.2% cumulative failure probability being approximately 1.1· IC K (mean fracture toughness). The special form of Eq. 1 with (KI –Kmin) 4, instead of KI 4 –Kmin 4, comes from a conditional crack propagation criterion, which makes the MC to deviate from a simple weakest link model of the weakest link. The model predicts a statistical size effect of the form of Eq. (2) [1].
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