Envelopes of shear and normal stresses for multiaxial stress state

Designing machines and equipment requires the ability to determine fatigue life. An engineer can make fatigue life predictions using mathematical fatigue life models. The usage of these tools requires knowledge of the parameters describing the state of stress. Since numerical calculations can be extremely time-consuming, two analytical relationships are proposed in the article. These formulas describe the envelopes of normal and shear stresses in the plane tangent to the surface of the test specimen. Dependencies can be applied for tension with phase shift torsion of the stress loading components. The correctness of the obtained relationships was verified by comparing their results with numerical solutions.