The J-integral resistance curve is the most important material properties in fracture mechanics that is often used for structural integrity assessment. ASTM E1820 is a commonly accepted fracture toughness test standard for measuring the critical value of J-integral at the onset of ductile fracture and J-R curve during ductile crack tearing. The recommended test procedure is the elastic unloading compliance method. For a stationary crack, the J-integral is simply calculated from the area under the load-displacement record using the η-factor equation. For a growing crack, the J-integral is calculated using the incremental equation proposed by Ernst et al. (1981, “Estimations on J-integral and Tearing Modulus T From a Single Specimen Test Record,” Fracture Mechanics: Thirteenth Conference, ASTM STP 743, pp. 476–502) to consider the crack growth correction. For the purpose of obtaining accurate J-integral values, ASTM E1820 requires small and uniform crack growth increments in a J-R curve test. In order to allow larger crack growth increments in an unloading compliance test, an improved J-integral estimation is needed. Based on the numerical integration techniques of forward rectangular, backward rectangular, and trapezoidal rules, three incremental J-integral equations are developed. It demonstrates that the current ASTM E1820 procedure is similar to the forward rectangular result, and the existing Garwood equation is similar to the backward rectangular result. The trapezoidal result has a higher accuracy than the other two, and thus it is proposed as a new formula to increase the accuracy of a J-R curve when a larger crack growth increment is used in testing. An analytic approach is then developed and used to evaluate the accuracy of the proposed incremental equations using single-edge bending and compact tension specimens for different hardening materials. It is followed by an experimental evaluation using actual fracture test data for HY80 steel. The results show that the proposed incremental J-integral equations can obtain much improved results of J-R curves for larger crack growth increments and are more accurate than the present ASTM E1820 equation.
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October 2012
Materials And Fabrication
Improved Incremental J-Integral Equations for Determining Crack Growth Resistance Curves
Xian-Kui Zhu
Xian-Kui Zhu
Battelle Memorial Institute
, 505 King Avenue, Columbus, OH 43201
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Xian-Kui Zhu
Battelle Memorial Institute
, 505 King Avenue, Columbus, OH 43201J. Pressure Vessel Technol. Oct 2012, 134(5): 051404 (8 pages)
Published Online: September 10, 2012
Article history
Received:
August 8, 2011
Revised:
November 18, 2011
Online:
September 10, 2012
Published:
September 10, 2012
Citation
Zhu, X. (September 10, 2012). "Improved Incremental J-Integral Equations for Determining Crack Growth Resistance Curves." ASME. J. Pressure Vessel Technol. October 2012; 134(5): 051404. https://doi.org/10.1115/1.4005945
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