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.
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
^Hosford, W. F. (1972). A generalized isotropic yield criterion, Journal of Applied Mechanics, v. 39, n. 2, pp. 607-609.
^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.
^
abHosford, W. F., (2005), Mechanical Behavior of Materials, p. 92, Cambridge University Press.