Hosford yield criterion

Alternatively, the yield criterion may be written as This expression has the form of an Lp norm which is defined as When

, the we get the L∞ norm, indicates that if n = ∞, we have This is identical to the Tresca yield criterion.

For the practically important situation of plane stress, the Hosford yield criterion takes the form A plot of the yield locus in plane stress for various values of the exponent

The Logan-Hosford yield criterion for anisotropic plasticity[2][3] is similar to Hill's generalized yield criterion and has the form where F,G,H are constants,

are the principal stresses, and the exponent n depends on the type of crystal (bcc, fcc, hcp, etc.)

Though the form is similar to Hill's generalized yield criterion, the exponent n is independent of the R-value unlike the Hill's criterion.

Under plane stress conditions, the Logan-Hosford criterion can be expressed as where

For a derivation of this relation see Hill's yield criteria for plane stress.

A plot of the yield locus for the anisotropic Hosford criterion is shown in the adjacent figure.

that are less than 2, the yield locus exhibits corners and such values are not recommended.