Determination of Constraint-Modified J-R Curves for Carbon Steel Storage Tanks

Abstract

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.

Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization

“…Garwood [225] was among the first and showed that an experimental J-R curve derived from the center-cracked panel was appreciably steeper than one obtained from a three-point bend specimen, but the initiation toughness values were essentially identical for these two geometries. Similar constraint effects on J-R curves for ductile materials under plane strain conditions were observed widely by many other investigators, including McCabe et al [226], Towers and Garwood [227], Eisele et al [228], Hancock et al [229], Joyce et al [230][231][232], Wardle [233], Lam et al [234], Neimitz et al [235], and Shen et al [236]. All experimental results showed that deeply cracked, bending loaded standard specimens result in lower J-R curves, and shallow cracked, predominantly tensile loaded nonstandard specimens lead to higher J-R curves, with the plane strain initiation toughness J Ic being nearly independent of these specimen geometry and loading mode effects.…”

“…Since the RKR model is not applicable to growing cracks, a new methodology has been developed to relate a constant value of Q or A 2 to each resistance curve. The first author and his coworkers [234,271,279,281,290,291] have proposed a unique technique for correcting constraint effect on J-R curves using the parameter Q or A 2 . By assuming an analytic power-law function, a family of constraint-dependent J-R curves can be constructed for ductile crack growth, in conjunction with use of at least three typical experimental J-R curve data and numerical results of the constraint parameter determined at the loading level of initiation toughness.…”

“…This suggests that Q cannot be used directly to describe the constraint effect on a J-R curve because its value varies on the resistance curve, as shown by Faleskog [264]. Accordingly, the J À A 2 three-term solution was used to characterize the elastic-plastic crack-tip fields for two-and three-dimensional geometries [274][275][276][277], and the parameter A 2 was used to quantify the constraint effect on the fracture toughness J c , J Ic and J-R curves for ductile materials [278,271,234,279].…”

Increasing Safety and Reducing Environmental Damage Risk from Aging High-Level Radioactive Waste Tanks

“…Crack growth criteria development -CTOD/CTOA The crack growth resistance (J-R) curves for A285 carbon steel (the material of construction for Type I and II waste tanks) were determined using bend specimens with various a/W (crack length to specimen width) ratios. These geometry dependent J-R curves can be expressed as a function of a crack tip constraint parameter [2]. In this subtask, the fracture testing in Ref.…”

“…This trend can be qualitatively demonstrated. Since the J-R curves are crack-tip-constraint dependent [2], the CTOD/CTOA fracture criteria must also be a function of constraint. Without the initially higher values of CTOD/CTOA, the fracture testing data will be underestimated [3].…”