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

Abstract

Metal failure in many applications, such as ballistic impact, containment, shielding, metal forming, and crashworthiness, occurs while the material 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. In this paper, an additional 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 is used in defining the critical failure regions. Standard tests are examined to determine if they can provide enough data to construct these regions of interest and new tests are proposed, which envelope the limits and thus define this failure surface.