Yield Criteria for the Elastic-Plastic Design of Tubesheets With Triangular Penetration Pattern

To perform an elastic-plastic finite element analysis of a tubesheet, the anisotropic stiffness and yield properties of the perforated region are represented by an equivalent solid plate. Traditional anisotropic yield criteria (like Hill’s criterion) do not give accurate predictions under general biaxial loading because they neglect the plastic compressibility of the perforated material. A compressible-anisotropic second-order yield criterion is derived which can model both the actual out-of-plane and in-plane behavior. Using an equivalent stress vector, the in-plane symmetry properties of the second-order compressible model are examined for a triangular penetration pattern. Generally, the tubesheet symmetry is not precisely reflected by this model. Additional planes of symmetry can be introduced with a higher-order yield function. A fourth-order yield function with the required symmetry properties is presented which is in excellent agreement with the response of a finite element, elastic-plastic model of a tubesheet ligament under in-plane biaxial loading.