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    Consistency Checks for Power-Law Calibration Functions

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    Recently, considerable numerical effort has been devoted to obtaining solutions to crack problems in incompressible J2 deformation theory materials of pure power-law type (εσn). Following Il'yushin's observation of the scalability of such solutions, many investigators have conducted broad parametric studies on crack length and material exponent, and have tabulated normalized J and deformation magnitudes. Due to numerical difficulties such as slow convergence, incompressibility, or inadequate finite-element mesh refinement, the solutions do not always agree.

    We outline the basis for a very stringent general test of the “quality” of proposed solutions by applying the well-known equivalence of J and energy difference rate with respect to crack length.

    The test is applied to data available in the literature, and conclusions are drawn as to their accuracy.


    J-integral, power-law calibration functions, J, -estimation procedures, consistency checks, elastic-plastic fracture

    Author Information:

    Parks, DM
    Associate professor of mechanical engineering, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass.

    Kumar, V
    Mechanical engineer, Corporate Research and Development, General Electric Co., Schenectady, N.Y.

    Shih, CF
    Associate professor, Division of Engineering, Brown University, Providence, R.I.

    Committee/Subcommittee: E08.08

    DOI: 10.1520/STP37304S