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Failure Theory Applications
A new section on applications has been added to the website on failure criteria. Six examples of failure applications are given which span the range from very ductile to very brittle isotropic and homogeneous materials. Summarizing two of the examples, first a very ductile polymer is examined wherein its tensile, compressive, and shear strengths are determined as influenced by a state of superimposed hydrostatic pressure. An interesting fallout from the example shows just how seriously in error the Mises criterion can be, even when applied to a ductile material.
The second example concerns the Hertz contact problem for a brittle glass. This is the problem of a rigid spherical indenter acting upon a half space of the brittle material. The load on the indenter at failure is found to vary as the third power of the uniaxial tensile strength of the glass.
All six examples are illustrative of the importance and utility of specific failure applications. Also, the examples are used to show the deficiency of predictions from the Coulomb-Mohr (Mohr-Coulomb) failure theory.
Usually failure criteria for particular materials types are treated on a case by case basis. The resulting empirical forms have totally unknown ranges or limits of validity as regards possible applications to other types of materials. The enabling and unifying approach of the present failure theory is that of the completely and all determining dependence upon the strength ratio, T/C, formed from the two uniaxial strengths. It is found that this nondimensional variable permits a continuous scan across all standard materials types, going from the ductile limit to the brittle limit.
The entire failure theory is based upon the T/C ratio, and this ratio along with the type of stress state can be used to determine the ductile versus brittle nature of the failure mechanism(s). These matters will be further amplified in the website in the near future.
This new section on applications is at: