Hosford yield criterion

The Hosford yield criterion is a function that is used to determine whether a material has undergone plastic yielding under the action of stress.

Hosford yield criterion for isotropic plasticity

The Hosford yield criterion for isotropic materials [ Hosford, W. F. (1972). "A generalized isotropic yield criterion", Journal of Applied Mechanics, v. 39, n. 2, pp. 607-609.] is a generalization of the von Mises yield criterion. It has the form:$cfrac\{1\}\{2\}|sigma\_2-sigma\_3|^n\; +\; cfrac\{1\}\{2\}|sigma\_3-sigma\_1|^n\; +\; cfrac\{1\}\{2\}|sigma\_1-sigma\_2|^n\; =\; sigma\_y^n\; ,$where $sigma\_i$, i=1,2,3 are the principal stresses, $n$ is a material-dependent exponent and $sigma\_y$ is the yield stress in uniaxial tension/compression.

The exponent "n" does not need to be an integer. When "n = 1" the criterion reduces to the Tresca yield criterion. When "n = 2" the Hosford criterion reduces to the von Mises yield criterion.

Hosford yield criterion for plane stress

For the practically important situation of plane stress, the Hosford yield criterion takes the form:$cfrac\{1\}\{2\}left(|sigma\_1|^n\; +\; |sigma\_2|^n\; ight)\; +\; cfrac\{1\}\{2\}|sigma\_1-sigma\_2|^n\; =\; sigma\_y^n\; ,$

Logan-Hosford yield criterion for anisotropic plasticity

The Logan-Hosford yield criterion for anisotropic plasticity [Hosford, W. F., (1979), "On yield loci of anisotropic cubic metals", Proc. 7th North American Metalworking Conf., SME, Dearborn, MI.] [Logan, R. W. and Hosford, W. F., (1980), " Upper-Bound Anisotropic Yield Locus Calculations Assuming< 111>-Pencil Glide", International Journal of Mechanical Sciences, v. 22, n. 7, pp. 419-430.] is similar to Hill's generalized yield criterion and has the form:$F|sigma\_2-sigma\_3|^n\; +\; G|sigma\_3-sigma\_1|^n\; +\; H|sigma\_1-sigma\_2|^n\; =\; 1\; ,$where "F,G,H" are constants, $sigma\_i$ are the principal stresses, and the exponent "n" depends on the type of crystal (bcc, fcc, hcp, etc.) Accepted values of $n$ are 6 for bcc materials and 8 for fcc materials.

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.

Logan-Hosford criterion in plane stress

Under plane stress conditions, the Logan-Hosford criterion can be expressed as:$cfrac\{1\}\{1+R\}\; (|sigma\_1|^n\; +\; |sigma\_2|^n)\; +\; cfrac\{R\}\{1+R\}\; |sigma\_1-sigma\_2|^n\; =\; sigma\_y^n$where $R$ is the R-value and $sigma\_y$ is the yield stress in uniaxial tension/compression. For a derivation of this relation see Hill's yield criteria for plane stress.

References

See also

*Yield surface
*Yield (engineering)
*Plasticity (physics)
*Stress (physics)