“Hosford yield criterion”的意思、由来-开放百科全书

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Hosford yield criterion

释义

Hosford yield criterion for isotropic plasticity
Hosford yield criterion for plane stress
Logan-Hosford yield criterion for anisotropic plasticity
Logan-Hosford criterion in plane stress
References
See also

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^[1] is a generalization of the von Mises yield criterion. It has the form

where , i=1,2,3 are the principal stresses, is a material-dependent exponent and is the yield stress in uniaxial tension/compression.

Alternatively, the yield criterion may be written as

This expression has the form of an L^p norm which is defined as

When , the we get the L^∞ norm,

. Comparing this with the Hosford criterion

indicates that if n = ∞, we have

This is identical to the Tresca yield criterion.

Therefore, when n = 1 or n goes to infinity the Hosford criterion reduces to the Tresca yield criterion. When n = 2 the Hosford criterion reduces to the von Mises yield criterion.

Note that the exponent n does not need to be an integer.

Hosford yield criterion for plane stress

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 is shown in the adjacent figure.

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

where F,G,H are constants, are the principal stresses, and the exponent n depends on the type of crystal (bcc, fcc, hcp, etc.) and has a value much greater than 2.^[4] Accepted values of 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

where is the R-value and is the yield stress in uniaxial tension/compression. 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. For values of that are less than 2, the yield locus exhibits corners and such values are not recommended.^[4]

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.
4. ^¹Hosford, W. F., (2005), Mechanical Behavior of Materials, p. 92, Cambridge University Press.

Hosford yield criterion for isotropic plasticity

Hosford yield criterion for plane stress

Logan-Hosford yield criterion for anisotropic plasticity

Logan-Hosford criterion in plane stress

References

See also