13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 5.4. Cleavage Fracture Predictions Using the Weibull Stress Model The procedure used here to predict the effects of constraint loss for the experimental cleavage fracture toughness data follows the toughness scaling model introduced by Ruggieri and Dodds [4]. Based upon micromechanics considerations, the scaling model requires the attainment of a specified value for the Weibull stress to trigger cleavage fracture in different specimens even though J-values may differ markedly. Here, we predict the distribution of cleavage fracture values for the deep crack SE(B) specimens ( = aW 0.5) using the distribution of measured fracture toughness for the precracked Charpy (PCVN) configuration. Figures 4(a-b) show the computed evolution of wσ with increased levels of loading, as characterized by J, for the deep crack SE(B) specimen and PCVN configuration using the calibrated m-values displayed previously in Table 1. Here, we direct attention to the evolution of wσ vs. J derived from using 0=γ (no plastic strain correction) and the plastic strain modified Beremin model (Eq. (5) previously described). In each plot, the correction / 0.5 / 0.5 ( ) 0 0 = = → a W a W SE B PCVN J J defines the predicted 0J -value for the deep crack SE(B) specimen at = T −80°C which then enables estimating the reference temperature, 0T , for the tested pressure vessel steel. Table 2 summarizes the predicted 0J -values and the estimated 0T for all different forms of wσ adopted in the present work. The sensitivity of 0J -predictions on the adopted formulation for wσ is evident in these results which also strongly impacts estimates of 0T . The standard definition of wσ described by previous Eq. (3), which is essentially the original Beremin model, provides a conservative estimate of 0T . In contrast, adoption of the linear plastic correction overpredicts the 0J -value for the deep crack SE(B) specimen and, consequently, the reference temperature. However, use of the plastic strain modified Beremin models yields a 0T estimate which is in very good agreement with the corresponding estimate derived from the master curve analysis based on toughness values for the 1-T, deep crack SE(B) specimen with = aW 0.5. 6. Concluding Remarks This study describes a probabilistic framework based on the Weibull stress model to predict the effects of constraint loss on macroscopic measures of cleavage fracture toughness in the ductile-to-brittle transition region. A central objective is to determine the indexing temperature 0T based on the Master Curve methodology from PCVN specimens. An additional feature of the proposed approach also includes the effect of near-tip plastic strain on cleavage microcracking which impacts directly the magnitude of the Weibull stress and, consequently, the toughness scaling curves. While the correction term included into the Weibull stress assumes an ad-hoc linear dependence of microcrack density on plastic strain, our exploratory analyses demonstrate the effectiveness of the Weibull stress model to provide 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.
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