An unusual new material is hypothesized to fail when the absolute value of the hydrostatic stress exceeds a critical value. That is,

However, there is also a possibility that this material obeys either the maximum normal stress failure criterion or the maximum shear stress failure criterion. (a) Does the equation given constitute a possible failure theory? Why or why not? (b) Consider a uniaxial test, and on this basis define a convenient effective stress. (c) In three-dimensional principal normal stress space, describe the failure surface corresponding to the equation given. Also describe the failure locus for the special case of plane stress. (d) Describe a critical experiment, consisting of one or a few mechanical tests, and a minimum of experimentation, that provides a definitive choice among the aforementioned three criteria. Note that some of the mechanical tests that are feasible are uniaxial tension and compression, torsion of tubes and rods, internal and external pressure of closed-end tubes, biaxial tension in pressurized diaphragms, and hydrostatic compression.