13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- distribution. The stress integral appearing in Eq. (2) defines the Weibull stress, wσ , a term coined by the Beremin group [3], in the form 0 , 1 1 1 1 0 ≥ Ω Ω = ∫ Ω σ σ σ m m w d (3) A central feature of this methodology involves the interpretation of wσ as a macroscopic crack driving force [4-5]. Consequently, it follows that unstable crack propagation (cleavage) occurs at a critical value of the Weibull stress; under increased remote loading (as measured by J), differences in evolution of the Weibull stress reflect the potentially strong variations of near-tip stress fields 2.2. Effects of Plastic Strain on the Probabilistic Crack Driving Force The previous approach can be further extended to include the strong effects of near-tip plastic strain on cleavage microcracking thereby altering the microcrack distribution entering into the local criterion for fracture. Based upon direct observations of cleavage microcracking by plastic strain made in ferritic steels at varying temperatures [6-8], a generalized form of the Weibull stress can be defined as 0 , 1 1 1 1 (1 ) 0 ≥ Ω Ω = ∫ Ω + σ σ ε σ β γ m m p w d (4) Here, ( ) f J p = ε is the near-tip effective plastic strain, and γ and β are parameters defining the contribution of the plastic strain on cleavage fracture probability; for example, setting 0=γ recovers the conventional description for the probability distribution of fracture stress. The above plastic term correction simply reflects the increase in cleavage fracture probability that results from the growth in microcrack density with increased levels of near-tip plastic strain. Ruggieri [5] provides further details on the character of the previous definition for the generalized Weibull stress. Early work of the Beremin group [3] also recognized the potential strong effects of plastic deformation on cleavage fracture. Based on experimental analyses of the failure strain for notched specimens made of an ASTM A508 steel, they proposed a modified form of previous Eq. (3) as 0 , 2 exp 1 1 1 1 0 ≥ Ω − Ω = ∫ Ω σ σ ε σ m p m w d m (5) which indicates that wσ increases approximately with 2) exp( pε . 3. Summary of the Master Curve Approach Wallin [9] has developed a relatively straightforward procedure to characterize fracture toughness data over the DBT region, widely known as the master curve approach, which relies on the concept of a normalized curve of median fracture toughness vs. temperature applicable to hold experimentally for a wide range of ferritic pressure vessel and structural steels. The approach begins by adopting a three-parameter Weibull distribution to describe the distribution of toughness values in the form
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