13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- Grade C pressure vessel steel provides the cleavage fracture toughness data needed to estimate 0T . For the tested material, the Weibull stress methodology yields estimates for the reference temperature, 0T , from small fracture specimens which are in good agreement with the corresponding estimates derived from testing of much larger crack configurations. 2. Overview of the Weibull Stress Model for Cleavage Fracture 2.1. Weakest Link Modeling of Cleavage Fracture Extensive work on cleavage fracture in ferritic steels demonstrates that cracking of grain boundary carbides in the course of plastic deformation and subsequent extension of these cracks into the surrounding matrix governs failure. The inherent random nature of failure micromechanism causes large scatter in the measured values of cleavage fracture toughness for ferritic steels tested in the DBT region thereby complicating quantitative assessments of fracture behavior in terms of meaningful toughness values. A continuous probability function derived from weakest link statistics conveniently characterizes the distribution of toughness values, described by cJ -values, as [1] ( ) − − = − − α th c th c J J J J F J 0 1 exp (1) which is a three-parameter Weibull distribution with parameters , ) ( , 0 th J J α . Here, α denotes the Weibull modulus (shape parameter), 0J defines the characteristic toughness (scale parameter) and th J is the threshold fracture toughness. Often, the threshold fracture toughness is set equal to zero so that the Weibull function given by Eq. (1) assumes its more familiar two-parameter form. The above limiting distribution remains applicable for other measures of fracture toughness, such as Jc K or δ (CTOD). Under SSY conditions, the scatter in cleavage fracture toughness data is characterized by 2=α for cJ -distributions or 4=α for Jc K -distributions [2]. A number of micromechanics models to describe transgranular cleavage, most derived from the local approach philosophy, have focused on probabilistic methodologies which couple the micromechanical features of the fracture process with the inhomogeneous character of the near-tip stress fields. By adopting weakest link arguments to describe the failure event, the overall fracture resistance is assumed to be driven by the largest fracture-triggering particle that is sampled in the fracture process zone ahead of crack front. This approach enables defining a probability distribution for the fracture stress of a cracked solid with increased loading (represented by the J-integral) in terms of a two-parameter Weibull distribution [3-5] in the form ( ) 0 , 1 exp 1 1 exp 1 1 0 ≥ = − − Ω Ω = − − ∫ Ω σ σ σ σ σ σ m u w m u w d P (2) where Ω denotes the volume of the (near-tip) fracture process zone, 0Ω represents a (unit) reference volume and 1σ is the maximum principal stress acting on material points inside the fracture process zone. In the present work, the active fracture process zone is defined as the loci where ys λσ σ ≥ 1 , with 2 ~ 2.5 ≈λ and ys σ represents the material’s yield stress. Parameters m and uσ appearing in Eq. (2) denote the Weibull modulus and the scale parameter of the Weibull
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