THE THEORY OF MATERIALS FAILURE
Richard M. Christensen
|Publisher||Oxford University Press|
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A complete and comprehensive theory of failure for homogeneous materials is developed. The resulting general failure theory for isotropic materials and its related failure criteria are calibrated by two properties: the uniaxial tensile and compressive strengths, T and С. From such readily available data for most materials, the entire family of failure envelopes can be generated for any and all states of stress in any isotropic material. It is not just a coincidence that the number of independent failure properties being at two is the same as the number of independent elastic properties for isotropy. This relationship will be of considerable consequence. It will require a long and involved derivation to establish the operational capability and results mentioned briefly above. First, however, a historical survey and evaluation must be conducted. Insofar as general applications are concerned, the complete and absolute unsuitabilities are detailed for the Mises, Tresca, Drucker-Prager, and Coulomb-Mohr failure criteria. Only the Mises form is satisfactory for a specific class of materials—that being only for ductile metals. A general failure theory must cover not only ductile metals but also brittle metals, glassy and crystalline polymers, ceramics, glasses, and a variety of other isotropic materials types, just as does elasticity theory. Treating failure criteria with the appropriate and necessary generality has always remained an unsolved and historically formidable problem, and significant progress has been greatly impeded—even blocked.
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