Materials and Fabrication

Improved Incremental J-Integral Equations for Determining Crack Growth Resistance Curves

[+] Author and Article Information
Xian-Kui Zhu

 Battelle Memorial Institute, 505 King Avenue, Columbus, OH 43201

J. Pressure Vessel Technol 134(5), 051404 (Sep 10, 2012) (8 pages) doi:10.1115/1.4005945 History: Received August 08, 2011; Revised November 18, 2011; Published September 10, 2012; Online September 10, 2012

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 (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.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Schematic load-plastic displacement curves for three stationary cracks and a growing crack. (a) Upper step line approximation, (b) lower step line approximation, and (c) median step line approximation.

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Figure 2

Two given J-R curves in power-law functions

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Figure 3

Analytical data of load, displacement, and crack extension for two material models: (a) load-displacement curves, (b) load-crack extension curves

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Figure 4

J-R curves calculated by the three models for SE(B) specimen with a0 /W = 0.5 in the moderate hardening material (n = 0.1) and crack growth steps: (a) equal step da = 0.01b0 , (b) equal step da = 0.02b0 , and (c) unequal step da = 0.005–0.06b0

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Figure 5

J-R curves calculated by the three models for SE(B) specimen with a0 /W = 0.5 in the high hardening material (n = 0.2) and crack growth steps: (a) equal step da = 0.01b0 , (b) equal step da = 0.02b0 , and (c) unequal step da = 0.005–0.06b0

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Figure 6

Error comparisons for three estimation models at the maximum crack extension of 3 mm

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Figure 7

J-R curves calculated by the three models for C(T) specimen with a0 /W = 0.5, equal crack step of da = 0.02b0 , and the two hardening materials: (a) n = 0.1 and (b) n = 0.2

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Figure 8

Experimental J-R curves calculated by the three models for HY80 steel and unloading cycles of: (a) 33, (b) 23, and (c) 33 and 23



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