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Research Papers: Materials and Fabrication

On the Modified Monotonic Loading Concept for the Calculation of the Cyclic J-Integral

[+] Author and Article Information
Ross Beesley

Department of Mechanical
and Aerospace Engineering,
University of Strathclyde,
Glasgow G1 1XJ, UK

Haofeng Chen

Department of Mechanical
and Aerospace Engineering,
University of Strathclyde,
Glasgow G1 1XJ, UK
e-mail: haofeng.chen@strath.ac.uk

Martin Hughes

Siemens Industrial Turbomachinery Ltd.,
Waterside South,
Lincoln LN5 7FD, UK

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received October 24, 2014; final manuscript received February 20, 2015; published online June 10, 2015. Assoc. Editor: Kunio Hasegawa.

J. Pressure Vessel Technol 137(5), 051406 (Oct 01, 2015) (11 pages) Paper No: PVT-14-1169; doi: 10.1115/1.4029959 History: Received October 24, 2014; Revised February 20, 2015; Online June 10, 2015

This paper investigates an approach for calculating the cyclic J-integral through a new industrial application. A previously proposed method is investigated further with the extension of this technique through a new application of a practical three-dimensional (3D) notched component containing a semi-elliptical surface crack. Current methods of calculating the cyclic J-integral are identified and their limitations discussed. A modified monotonic loading (MML) concept is adapted to calculate the cyclic J-integral of this 3D semi-elliptical surface crack under cyclic loading conditions. Both the finite element method (FEM) and the extended finite element method (XFEM) are discussed as possible methods of calculating the cyclic J-integral in this investigation. Different loading conditions including uniaxial tension and out-of-plane shear are applied, and the relationships between the applied loads and the cyclic J-integral are established. In addition, the variations of the cyclic J-integral along the crack front are investigated. This allows the determination of the critical load that can be applied before crack propagation occurs, as well as the identification of the critical crack direction once propagation does occur. These calculations display the applicability of the method to practical examples and illustrate an accurate method of estimating the cyclic J-integral.

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References

Irwin, G., 1957, “Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate,” ASME J. Appl. Mech., 24, pp. 361–364.
Griffith, A. A., 1921, “The Phenomena of Rupture and Flow in Solids,” Philos. Trans. R. Soc. London A, 221, pp. 163–198. [CrossRef]
Rice, J. R., 1968, “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,” ASME J. Appl. Mech., 35(2), pp. 379–386. [CrossRef]
Wells, A. A., 1963, “Application of Fracture Mechanics at and Beyond General Yielding,” Br. Weld. J., 10, pp. 563–570.
Broek, D., 1986, Elementary Engineering Fracture Mechanics, 3rd ed., Martinus Nijhoff, Springer, Dordrecht, The Netherlands. [CrossRef]
Anderson, T. L., 2005, Fracture Mechanics: Fundamentals and Applications, 2nd ed. CRC Press, Boca Raton, FL.
Ainsworth, R. A., 1999, R5: An Assessment Procedure for the High Temperature Response of Structures, Procedure R5: Issue 2, British Energy Generation Ltd, Gloucester.
Milne, I., Ainsworth, R. A., Dowling, A. R., and Stewart, A. T., 1988, “Assessment of the Integrity of Structures Containing Defects,” Int. J. Pressure Vessels Piping, 32, pp. 3–104. [CrossRef]
Begley, J. A., and Landes, J. D., 1972, “The J-Integral as a Fracture Criterion,” ASTM STP, 514, pp. 1–20.
Kishimoto, K., Aoki, S., and Sakata, M., 1980, “On the Path Independent Integral-J,” Eng. Fract. Mech., 13(4), pp. 841–850. [CrossRef]
Bucci, R. J., Paris, P. C., Landes, J. D., and Rice, J. R., 1972, “J Integral Estimation Procedures,” ASTM STP, 514, pp. 40–69.
Dowling, N. E., 1976, “Geometry Effects and the J-Integral Approach to Elastic–Plastic Fatigue Crack Growth,” ASTM STP, 601, pp. 19–32.
Zhu, X.-K., and Joyce, J. A., 2012, “Review of Fracture Toughness (G, K, J, CTOD, CTOA) Testing and Standardization,” Eng. Fract. Mech., 85, pp. 1–46. [CrossRef]
Dassault Systems Simulia Corporation, 2012, Version 6.12-3.
Paris, P., and Erdogan, F., 1963, “A Critical Analysis of Crack Propagation Laws,” ASME J. Fluids Eng., 85(4), pp. 528–534.
Sumpter, J. D. G., and Turner, C. E., 1976, “Method for Laboratory Determination of JC,” ASTM STP, 601, pp. 3–18.
Dowling, N. E., and Begley, J. A., 1976, “Fatigue Crack Growth During Gross Plasticity and the J-Integral,” ASTM-STP, 590, pp. 82–103.
Chattopadahyay, J., 2006, “Improved J and COD Estimation by GE/EPRI Method in Elastic to Fully Plastic Transition Zone,” Eng. Fract. Mech., 73(14), pp. 1959–1979. [CrossRef]
Miller, A. G., and Ainsworth, R. A., 1989, “Consistency of Numerical Results for Power Law Hardening Materials and the Accuracy of the Reference Stress Approximation,” Eng. Fract. Mech., 32(2), pp. 233–247. [CrossRef]
Moës, N., Dolbow, J., and Belytschko, T., 1999, “A Finite Element Method for Crack Growth Without Remeshing,” Int. J. Numer. Methods, 46(1), pp. 131–150. [CrossRef]
Chen, W., and Chen, H., 2013, “Cyclic J-Integral Using the Linear Matching Method,” Int. J. Pressure Vessels Piping, 108–109, pp. 72–80. [CrossRef]
Tanaka, K., 1983, “The Cyclic J-Integral as a Criterion for Fatigue Crack Growth,” Int. J. Fract., 22(2), pp. 91–104. [CrossRef]
Leidermark, D., Moverare, J., Simonsson, K., and Sjöström, S., 2011, “A Combined Critical Plane and Critical Distance Approach for Predicting Fatigue Crack Initiation in Notched Single-Crystal Superalloy Components,” Int. J. Fatigue, 33(10), pp. 1351–1359. [CrossRef]

Figures

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Fig. 1

The geometry of the investigated test specimens

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Fig. 2

FE mesh of structure showing (a) entire specimen and close-up view of notch (b) and (c)

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Fig. 3

Open crack surfaces

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Fig. 4

Location of applied loads under uniaxial tension conditions

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Fig. 5

Location of applied loads under out-of-plane shear conditions

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Fig. 6

Contour plots of: (a) stress from MML analysis and (b) stress range from cyclic loading analysis under uniaxial loading conditions

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Fig. 7

Enlarged view of contour plots of crack tip of: (a) stress from MML analysis and (b) stress range from cyclic loading analysis under uniaxial loading conditions

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Fig. 8

Contour plots of: (a) strain from MML analysis and (b) strain range from cyclic loading analysis under uniaxial loading conditions

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Fig. 9

Enlarged view of contour plots of crack tip of: (a) strain from MML analysis and (b) strain range from cyclic loading analysis under uniaxial loading conditions

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Fig. 10

Contour plots of: (a) stress from MML analysis and (b) stress range from cyclic loading analysis under out-of-plane shear loading conditions

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Fig. 11

Enlarged view of contour plots of crack front of: (a) stress from MML analysis and (b) stress range from cyclic loading analysis under out-of-plane shear loading conditions

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Fig. 12

Contour plots of: (a) strain from MML analysis and (b) strain range from cyclic loading analysis under out-of-plane shear loading conditions

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Fig. 13

Enlarged view of contour plots of crack front of: (a) strain from MML analysis and (b) strain range from cyclic loading analysis under out-of-plane shear loading conditions

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Fig. 14

Schematic diagram showing node numbering

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Fig. 15

Enlarged view of crack tip showing contour paths

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Fig. 16

ΔJ-integral variation with increasing uniaxial load

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Fig. 17

ΔJ-integral variation with increasing out-of-plane shear load

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Fig. 18

ΔJ variation along crack front under uniaxial tension loading conditions

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Fig. 19

ΔJ variation along crack front under out-of-plane shear loading conditions

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Fig. 20

Image of experimental setup showing (a) specimen in tensile test machine and (b) enlarged view of specimen positioned in machine with extensometers positioned on specimen edge

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