- 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 theyield 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 thevon 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)
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