Hosford Yield Criterion - Hosford Yield Criterion For Isotropic Plasticity

Hosford Yield Criterion For Isotropic Plasticity

The Hosford yield criterion for isotropic materials is a generalization of the von Mises yield criterion. It has the form

\tfrac{1}{2}|\sigma_2-\sigma_3|^n + \tfrac{1}{2}|\sigma_3-\sigma_1|^n + \tfrac{1}{2}|\sigma_1-\sigma_2|^n = \sigma_y^n \,

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

\sigma_y = \left(\tfrac{1}{2}|\sigma_2-\sigma_3|^n + \tfrac{1}{2}|\sigma_3-\sigma_1|^n + \tfrac{1}{2}|\sigma_1-\sigma_2|^n\right)^{1/n} \,.

This expression has the form of an Lp norm which is defined as

When, the we get the L∞ norm,

. Comparing this with the Hosford criterion

indicates that if n = ∞, we have

(\sigma_y)_{n\rightarrow\infty} = \max \left(|\sigma_2-\sigma_3|, |\sigma_3-\sigma_1|,|\sigma_1-\sigma_2|\right) \,.

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.

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