Hosford yield criterion

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

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[edit] Hosford yield criterion for isotropic plasticity

The Hosford yield criterion for isotropic materials [1] 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 σi, i=1,2,3 are the principal stresses, n is a material-dependent exponent and σy 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.

[edit] Hosford yield criterion for plane stress

The plane stress, isotropic, Hosford yield surface for three values of n
The plane stress, isotropic, Hosford yield surface for three values of n

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\right) + \cfrac{1}{2}|\sigma_1-\sigma_2|^n = \sigma_y^n \,

[edit] Logan-Hosford yield criterion for anisotropic plasticity

The Logan-Hosford yield criterion for anisotropic plasticity [2] [3] 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, σi 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.

[edit] Logan-Hosford criterion in plane stress

The plane stress, anisotropic, Hosford yield surface for four values of n and R=2.0
The plane stress, anisotropic, Hosford yield surface for four values of n and R=2.0

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 σy is the yield stress in uniaxial tension/compression. For a derivation of this relation see Hill's yield criteria for plane stress.

[edit] References

  1. ^ Hosford, W. F. (1972). A generalized isotropic yield criterion, Journal of Applied Mechanics, v. 39, n. 2, pp. 607-609.
  2. ^ Hosford, W. F., (1979), On yield loci of anisotropic cubic metals, Proc. 7th North American Metalworking Conf., SME, Dearborn, MI.
  3. ^ 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.

[edit] See also