SEDL / STP / STP803V1-EB / STP37304S

Consistency Checks for Power-Law Calibration Functions

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.

Pages: 14    Published: Jan 1983

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Abstract

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.