Research Papers

The Theoretical Measure of the Ductility of Failure for All Isotropic Materials in All States of Stress1

[+] Author and Article Information
Richard M. Christensen

Professor Research Emeritus
Aeronautics and Astronautics Department,
Stanford University,
Stanford, CA 94305
e-mail: christensen@stanford.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 27, 2016; final manuscript received March 30, 2016; published online May 4, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(6), 061001 (May 04, 2016) (9 pages) Paper No: JAM-16-1157; doi: 10.1115/1.4033279 History: Received March 27, 2016; Revised March 30, 2016

The ductile/brittle failure theory for homogeneous and isotropic materials is extended to give a rational and mathematically rigorous measure for the ductility of failure. This new failure number methodology is completely developed and proved to be valid and general. It applies to all isotropic materials as subjected to any and all states of stress. Not only does the failure theory predict the safety or failure for any given stress state, it then projects the quantitative ductility level for the failure stress state. Many important examples are given with detailed interpretations of the results and with guides for general usage.

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Grahic Jump Location
Fig. 1

Ductility D in uniaxial tension as a function of T/C, Eq.(14)

Grahic Jump Location
Fig. 2

Biaxial failure stresses for the ductile limit material, T/C = 1

Grahic Jump Location
Fig. 3

Failure number Fn for equitriaxial tension and all materials types (26)

Grahic Jump Location
Fig. 4

Ductility D as a function of the failure number Fn, Eqs. (27) and (16)(18) for all states of stress and all materials



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