A Comparative Evaluation of Three Isotropic, Two Property Failure Theories

[+] Author and Article Information
Richard M. Christensen

 Lawrence Livermore National Laboratory, Livermore, CA 94551 and Stanford University, Stanford, CA 94305

J. Appl. Mech 73(5), 852-859 (Dec 02, 2005) (8 pages) doi:10.1115/1.2173007 History: Received May 21, 2004; Revised December 02, 2005

Three fundamentally different failure theories for homogeneous and isotropic materials are examined in both the ductile and brittle ranges of behavior. All three theories are calibrated by just two independent failure properties. These three are the Coulomb-Mohr form, the Drucker-Prager form, and a recently derived theory involving a quadratic representation along with a fracture restriction. The three theories are given a detailed comparison and evaluation. The Coulomb-Mohr form and the Drucker-Prager form are found to predict physically unrealistic behavior in some important cases. The present form meets the consistency requirements.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 5

Stress states σ11 vs σ22=σ33 and σ11=σ33 vs σ22, C-M theory

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Figure 1

Coulomb-Mohr failure form

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Figure 2

Biaxial stress state failure, T∕C=1∕3

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Figure 3

Stress states σ11 vs σ22=σ33 and σ11=σ33 vs σ22, D-P theory

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Figure 4

Stress states σ11 vs σ22=σ33 and σ11=σ33 vs σ22, present theory



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