Hill Yield Criteria - Hill 1993 Yield Criterion

Hill 1993 Yield Criterion

In 1993, Hill proposed another yield criterion for plane stress problems with planar anisotropy. The Hill93 criterion has the form

\left(\cfrac{\sigma_1}{\sigma_0}\right)^2 + \left(\cfrac{\sigma_2}{\sigma_{90}}\right)^2 + \left\left(\cfrac{\sigma_1\sigma_2}{\sigma_0\sigma_{90}}\right) = 1

where is the uniaxial tensile yield stress in the rolling direction, is the uniaxial tensile yield stress in the direction normal to the rolling direction, is the yield stress under uniform biaxial tension, and are parameters defined as

\begin{align} c & = \cfrac{\sigma_0}{\sigma_{90}} + \cfrac{\sigma_{90}}{\sigma_0} - \cfrac{\sigma_0\sigma_{90}}{\sigma_b^2} \\ \left(\cfrac{1}{\sigma_0}+\cfrac{1}{\sigma_{90}}-\cfrac{1}{\sigma_b}\right)~p & = \cfrac{2 R_0 (\sigma_b-\sigma_{90})}{(1+R_0)\sigma_0^2} - \cfrac{2 R_{90} \sigma_b}{(1+R_{90})\sigma_{90}^2} + \cfrac{c}{\sigma_0} \\ \left(\cfrac{1}{\sigma_0}+\cfrac{1}{\sigma_{90}}-\cfrac{1}{\sigma_b}\right)~q & = \cfrac{2 R_{90} (\sigma_b-\sigma_{0})}{(1+R_{90})\sigma_{90}^2} - \cfrac{2 R_{0} \sigma_b}{(1+R_{0})\sigma_{0}^2} + \cfrac{c}{\sigma_{90}} \end{align}

and is the R-value for uniaxial tension in the rolling direction, and is the R-value for uniaxial tension in the in-plane direction perpendicular to the rolling direction.

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