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Fracture resistance of ductile materials is often characterized by a J-R curve, and measured using the fracture toughness testing standard ASTM E1820 (Standard Test Method for Measurement of Fracture Toughness). The recommended elastic unloading compliance method or resistance curve test method requires simultaneous measurements of applied load (P), load-line displacement (LLD), and crack-mouth opening displacement (CMOD) from a single test for the single-edge notched bend [SE(B)] specimen. The P-CMOD record is used to determine crack extension, and the P-LLD record in conjunction with the crack extension is used to calculate the J-integral. However, it is well known that while highly accurate CMOD measurements can be made, the measurement of LLD is less accurate and more difficult because of transducer mounting difficulties, specimen load point indentions and load train deflections, or a combination thereof. Extensive finite element analyses showed that the LLD-based J equation may give inaccurate results for a shallow-cracked SE(B) specimen because its geometry factor η may depend on the strain hardening exponent. In contrast for the same geometry, the CMOD-based η factor is insensitive to the hardening exponent, and thus a CMOD-based J equation could be more accurate to be used in the determination of J-R curves. Based on the energy principle, this paper proposes a CMOD-based J equation for a growing crack using an incremental function similar to the present ASTM E1820-06 formulation that is applicable to the J calculations for a J-R curve testing. The proposed CMOD-based J formulation contains two geometry factors, i.e., CMOD-based η and γ, and can consider the crack growth correction. The solutions of four geometry factors are presented for the SE(B) specimens with a wide range of crack length. The proposed formulation is then applied to determine J-R curves for HY80 steel using the load-CMOD record for SE(B) specimens, and the results are compared with those using the traditional LLD-based formulation. The comparison shows close agreement between these two formulations. It is recommended that the proposed formulation be used in ASTM E1820 to determine more accurate J-R curves and reduce test costs as well.

The consequences of a dynamic fracture in a gas-transmission pipeline require that pipelines be designed to avoid such incidents at a high level of certainty. For this reason, the related phenomonology has been studied since the early 1970s when the possibility of a dynamic ductile fracture was recognized. Full-scale experiments were done to characterize the fracture and gas dynamics associated with this process and empirical models were developed as a means to represent these experiments in a design or analysis setting. Such experiments focused on pure methane gas, and in the early days used steels with toughnesses less than 100 J, consistent with the steel making capabilities of the 1970s. Subsequently, interest shifted to larger diameter, higher pressure, higher BTU “rich” gases requiring higher toughness steels. The full-scale tests conducted to validate the arrest toughness levels determined that these empirical models were non-conservative. This paper presents a relationship between the dynamic crack propagation resistance and the apparent crack propagation resistance as measured by Charpy vee-notch (CVN) test specimens. This relationship is used in conjunction with the existing Battelle empirical criterion for dynamic-fracture arrest to determine the apparent toughness required to arrest a propagating ductile fracture in gas-transmission pipelines. The validity of this relationship is illustrated by successful predictions of arrest toughness in pipelines under a range of conditions including rich gases and high-toughness steels, including those showing a rising upper-shelf behavior.

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It is well known that the J-Q theory can characterize the crack-tip fields and quantify constraint levels for various geometry and loading configurations in elastic-plastic materials, but it fails at bending-dominant large deformation. This drawback seriously restricts its applications to fracture constraint analysis. A modification of J-Q theory is developed as a three-term solution with an additional term to address the global bending stress to offset this restriction. The nonlinear bending stress is approximately linearized in the region of interest under large-scale yielding (LSY), with the linearization factor determined using a two-point matching method at each loading for a specific cracked geometry in bending. To validate the proposed solution, detailed elastic-plastic finite element analysis (FEA) is conducted under plane strain conditions for three conventional bending specimens with different crack lengths for X80 pipeline steel. These include single edge notched bend (SENB), single edge notched tension (SENT) and compact tension (CT) specimens from smallscale yielding (SSY) to LSY. Results show that the bending modified J-Q solution can well match FEA results of crack-tip stress fields for all bending specimens at all deformation levels from SSY to LSY, with the modified Q being a load-and distance-independent constraint parameter under LSY. Therefore, the modified parameter Q can be effectively used to quantify crack-tip constraint for bending geometries. Its application to fracture constraint analysis is demonstrated by determining constraint corrected J-R curves.