Comments on W.S. Lei’s discussion of “An engineering methodology for constraint corrections of elastic–plastic fracture toughness – Part II: Effects of specimen geometry and plastic strain on cleavage fracture predictions” by C. Ruggieri, R.G. Savioli and R.H. Dodds
Introduction
In recent communication to this journal, Lei [1] raised several questions on our previous work [2] which extended a modified Weibull stress model incorporating the influence of plastic strain on cleavage fracture to correct effects of constraint loss in fracture specimens with a diverse range of specimen geometry. Using experimentally measured -values derived from fracture toughness testing conducted on an A515 Gr 65 pressure vessel steel in the ductile-to-brittle transition (DBT) temperature, we demonstrated convincingly that the modified Weibull stress methodology effectively removes the geometry dependence on -values and yields estimates for the reference temperature, , from small fracture specimens in good agreement with the corresponding estimates derived from testing of larger crack configurations. We welcome any contribution and discussion on our extension of the Beremin model [3], [2]. Nevertheless, Lei’s discussion should not be uncritically endorsed. In this brief note, we address the key points of interest raised in Lei’s discussion in the approximate order they appear.
Section snippets
Estimation and significance of
The Weibull distribution is perhaps the most widely used distribution in reliability and lifetime analysis, including the statistical description of fracture strength related to the weakest link model [4], [5]. The general three-parameter Weibull distribution of the random variable has cumulative distribution function (CDF) in the formwhere and represent the shape, scale and location (threshold) parameters, respectively. When the threshold
Validity of the Weibull stress model
Lei questions the validity of Weibull stress-type models, including the original Beremin model and our proposed modified Weibull stress presented in [2]. This is addressed briefly here. We begin by recalling the distribution of the Weibull stress in the generalized formin which the Weibull modulus, m, and parameter define the shape and location of the distribution.
Now, limiting attention to the standard Beremin model [18] and the modified Weibull stress model
Conclusions
This brief note provides further arguments in support of the modified Weibull stress model and the associated approach adopted in Ruggieri et al. [2]. While application of the modified Weibull stress methodology predicted accurately the fracture toughness distribution for an A515 Gr 65 pressure vessel steel tested in the ductile-to-brittle transition region, it is clear from the work conducted by Ruggieri et al. [2] that additional studies are needed to further assess the robustness of the
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