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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 (ε ∞ σn). 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
Associate professor of mechanical engineering, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass.
Mechanical engineer, Corporate Research and Development, General Electric Co., Schenectady, N.Y.
Associate professor, Division of Engineering, Brown University, Providence, R.I.