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Mechanical testing of A285 carbon steel, a storage tank material, was performed to develop fracture properties based on the constraint theory of fracture mechanics. A series of single edge-notched bend (SENB) specimen designs with various levels of crack tip constraint were used. The variation of crack tip constraint was achieved by changing the ratio of the initial crack length to the specimen depth. The test data show that the J-R curves are specimen-design-dependent, which is known as the constraint effect. A twoparameter fracture methodology is adopted to construct a constraint-modified J-R curve, which is a function of the constraint parameter, A 2 , while J remains the loading parameter. This additional fracture parameter is derived from a closed form solution and can be extracted from the finite element analysis for a specific crack configuration. Using this set of SENB test data, a mathematical expression representing a family of the J-R curves for A285 carbon steel can be developed. It is shown that the predicted J-R curves match well with the SENB data over an extensive amount of crack growth. In addition, this expression is used to predict the J-R curve of a compact tension specimen (CT), and good agreement to the actual test data is achieved. To demonstrate its application in a flaw stability evaluation, a generic A285 storage tank with a postulated axial flaw is used. For a flaw length of 10% of the tank height, the predicted J-R curve is found to be similar to that for a SENB specimen with a short notch, which is in a state of low constraint. This implies that the use of a J-R curve from the ASTM (American Society for Testing and Materials) standard designs, which typically are high constraint specimens, may be overly conservative for analysis of fracture resistance of large structures.

Two-pion-exchange and other higher-order contributions to the pp → ppπ 0 reaction Y. Kim (a,b) , T. Sato (c) , F. Myhrer (a) and K. Kubodera AbstractMuch effort has been invested on effective-field-theoretical studies of the near-threshold N N→N N π reactions and, in order to deal with the somewhat large three-momentum transfers involved, the momentum counting scheme (MCS) was proposed as an alternative to the usual Weinberg counting scheme. Given the fact that a quantitative explanation of the existing high-precision N N → N N π data requires a careful examination of higher chiral order contributions to the transition operator, we make a detailed numerical investigation of the convergence property of MCS for a pilot case of the pp → ppπ 0 reaction. Our study indicates that MCS is superior to the Weinberg scheme in identifying dominant higher order contributions to the N N→N N π reactions.There exists a substantial accumulation of high-precision data on various observables for the near-threshold NN →NNπ reactions, e.g. [1], and providing a coherent understanding of these experimental results has been a prominent theoretical challenge, see e.g., [2,3,4,5,6,7,8,9]. Heavy-baryon chiral perturbation theory (HBχPT), which is a low-energy effective field theory of QCD, is expected to offer a systematic framework for describing these reactions. In HBχPT, the four-momentum Q characterizing a given physical process is assumed to be small compared to the chiral scale Λ χ ≃ 4πf π ≃ 1 GeV, and contributions to the transition amplitude are classified according to the power (chiral order) of the expansion parameter ǫ ≡ Q/Λ χ . 1The coefficients of possible terms in the HBχPT Lagrangian, called low-energy constants (LECs), can in principle be linked to the matrix elements of QCD operators but in practice they are determined from experimental observables. Once all the LEC are fixed up to a specified chiral order, HBχPT allows us to make predictions for a wide range of hadronic and electroweak processes.Although, as mentioned, HBχPT presupposes the smallness of its expansion parameter Q/Λ χ , the pion production reactions involve somewhat large momentum transfers, p ≃ √ m π m N , even at threshold. This implies that the application ofHBχPT to the NN → NNπ reactions may involve some delicate aspects, but this also means that these processes may serve as a good test case for probing the applicability (or the limit of applicability) of HBχPT. It is worth emphasizing that finding a valid EFT expansion scheme for the NN → NNπ reactions is of general importance (going beyond the specific context of the NN→NNπ reactions) because, once such a scheme is found, we expect to be able to develop similar frameworks for other nuclear processes which involve rather large energy-momentum transfers and hence may not be quite amenable to the straightforward application of the ordinary HBχPT approach. To account for the rather large momentum transfers involved in the NN →NNπ reactions, Cohen, Friar, Miller and van Kolck [5] proposed to r...