A Generalized, Three Dimensional Definition, Description, and Derived Limits of the Triaxial Failure of Metals

Metal failure in many applications, such as ballistic impact, containment, shielding, and crashworthiness, with the exception of thin shells, occurs while the metal is in a three dimensional state of stress. Many previous definitions of triaxiality use two invariants to define the relative stress state in a virtual element, leading to a characterization that can be better thought of as biaxial. An additional, second parameter, based upon the third stress invariant is defined, which extends the characterization of the state of stress to three dimensions and to true triaxiality. The relation of the two parameters is explored and limits are found in the failure surface which aid in defining critical failure regions. Standard tests are compared to these regions of interest and new tests are proposed which envelope the limits of the failure surface, and thus define this failure surface.