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

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 two-parameter fracture methodology is adopted to construct a constraint-modified $J-R$ curve, which is a function of the constraint parameter, $A2,$ 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 reasonable agreement to the actual test data is achieved. To demonstrate its application in a flaw stability evaluation, the configuration of 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.