**Published:** Jan 2011

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**Source: **STP1526-EB

Accurate estimate of the *J* integral is required in a valid experimental evaluation of *J*-based fracture resistance curves for ductile materials. The fracture toughness test standard ASTM E1820 allows a basic method and a resistance curve method to be used experimentally to evaluate the *J* values via standard specimens. The basic method obtains *J* estimates using the η factor method that was developed for a stationary crack. The resistance curve method obtains crack growth corrected *J* estimates using an incremental equation that was proposed by Ernst et al. (“Estimation on *J*-lntegral and Tearing Modulus *T* from a Single Specimen Test Record,” Fracture Mechanics: Thirteenth Conference, ASTM STP 743, 1981, pp. 476–502) for a growing crack and has been accepted as the most accurate equation available for about three decades. Recently, Neimitz (“The Jump-Like Crack Growth Model, the Estimation of Fracture Energy and *Eng. Fract. Mech.*, Vol. 75, 2008, pp. 236–252), and Kroon et al. (“A Probabilistic Model for Cleavage Fracture with a Length Scale-Parameter Estimation and Predictions of Growing Crack Experiments,” *Eng. Fract. Mech.*, Vol. 75, 2008, pp. 2398–2417) presented two different approximate equations for the *J*-integral, which they proposed as more accurate than the Ernst equation. Therefore, further investigation is needed to determine a truly accurate approximation for the *J*-integral equation. With this objective, the present paper proposes different mathematical and physical models to approximate the *J*-integral equation. The physical models are developed in terms of the deformation theory and the jump-like crack growth assumption. Relations between the proposed models and the existing equations are identified. Systematic evaluations of the proposed models are then made using a theoretical procedure of *J-R* curves for both low and high strain hardening materials, and using experimental data from an actual single edge-notched bend specimen made of HY80 steel. Accuracy of the proposed models is determined, and a more accurate approximation of *J*-integral equation is thus suggested for *J-R* curve testing.

**Keywords:**

J, -integral, J-R, curve, incremental , J, -integral equation, crack growth, fracture test

**Author Information:**

Zhu, Xian-Kui *Battelle Memorial Institute, Columbus, OH*

Joyce, James A.*U.S. Naval Academy, Annapolis, MD*

**Committee/Subcommittee:** E08.05

**DOI:** 10.1520/STP49282S