Stress-strain relations for uniform monotonic deformation under triaxial loading

Summary

A simple theory is given for the relationship between the stresses and the strains for monotonic straining under uniform triaxial loading. It is suggested that a principal strain may be composed of two partial strains, each of which is exclusively a function of the corresponding principal shear stress. It then follows that the relation between the shear stress and the partial strain is equal to the relation between the stress and transverse strain in uniform uniaxial tension (partial stress strain curve). The theory, which consequently agrees with the Mohr-Quest-criterion of yielding in a generalized form and which is also applicable to anisotropic metals, makes a purely graphical construction of the stress-strain curves for straining at arbitrary constant stress ratios easily possible. Though the theory cannot be fully exact especially at very small strains, it yields results which agree on the whole just as well or better with the available experimental results than does the more complicated octahedral theory based on the Huber- v. Mises-Hencky-criterion. On the basis of mathematical expressions for the stress-strain relation in simple tension and uniform straining in uniaxial loading expressions for the stress-strain relations at arbitrary constant stress-ratios are given. It is emphasized, however, that the graphical construction is simpler and probably yields more correct results.