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The Theory of Materials Failure$
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Richard M. Christensen

Print publication date: 2013

Print ISBN-13: 9780199662111

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199662111.001.0001

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Isotropic Materials Failure Behavior

Isotropic Materials Failure Behavior

(p.50) 5 Isotropic Materials Failure Behavior
The Theory of Materials Failure

Richard M. Christensen

Oxford University Press

The failure theory for isotropic materials was derived in the previous chapter, with the end result being the mathematical forms of the failure criteria. Now it is important to visualize the failure surfaces or envelopes in three-dimensional principal stress space. A gallery of different failure envelopes is presented across the full range of T/C values, from the Mises cylinder at T/C = 1 to the brittle limit form at T/C = 0. The fracture cut-offs from the basic paraboloidal form commence at T/C = 1/2 with only an infinitesimal effect there, but becoming progressively larger as T/C diminishes, and becoming totally dominant at T/C = 0. The division of these failure envelopes into ductile and brittle regions is introduced as a preview to the full treatment in Chapter 8. Because the entire theory is calibrated by only the two properties, T and C, a related question concerns why these two properties are unique in this application. Why cannot any two strength properties suffice for formulating the basic theory? This question is taken up by considering the possible use of the shear strength and a dilatational strength. The particular example of a cracked solid as analyzed by Budiansky and O’Connell is used to reveal the necessity of using the T and C properties.

Keywords:   principal stress, Mises, fracture, paraboloid, ductile, brittle, uniaxial strengths

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