ISSN: 1546-962X
Published Online: 22 October 2009
Page Count: 20

More Accurate Approximation of J-Integral Equation for Evaluating Fracture Resistance Curves

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

Joyce, James A.
Mechanical Engineering Dept., U.S. Naval Academy, Annapolis,MD

(Received 12 May 2009; accepted 17 September 2009)

Abstract

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 (“Estimation on J-Integral 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 J_R Curve,” Eng. Fract. Mech., Vol. 75, 2008, pp. 236–252), and Kroon (“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

Paper ID: JAI102505
DOI: 10.1520/JAI102505
ASTM International is a member of CrossRef.