Hill Yield Criteria - Generalized Hill Yield Criterion

Generalized Hill Yield Criterion

The generalized Hill yield criterion has the form

$\begin{align} F|\sigma_{2}-\sigma_{3}|^m & + G|\sigma_{3}-\sigma_{1}|^m + H|\sigma_{1}-\sigma_{2}|^m + L|2\sigma_1 - \sigma_2 - \sigma_3|^m \\ & + M|2\sigma_2 - \sigma_3 - \sigma_1|^m + N|2\sigma_3 - \sigma_1 - \sigma_2|^m = \sigma_y^m ~. \end{align}$

where are the principal stresses (which are aligned with the directions of anisotropy), is the yield stress, and F, G, H, L, M, N are constants. The value of m is determined by the degree of anisotropy of the material and must be greater than 1 to ensure convexity of the yield surface.

Read more about this topic: Hill Yield Criteria

Famous quotes containing the words generalized, hill, yield and/or criterion:

“One is conscious of no brave and noble earnestness in it, of no generalized passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in manner—in brief, what is there is the feeble, uninspiring quality of German painting and English music.”
—H.L. (Henry Lewis)

“For now the moon with friendless light carouses
On hill and housetop, street and marketplace,
Men will plunge, mile after mile of men,
To crush this lucent madness of the face....”
—Allen Tate (1899–1979)

“While the white man keeps the impetus of his own proud, onward march, the dark races will yield and serve, perforce. But let the white man once have a misgiving about his own leadership, and the dark races will at once attack him, to pull him down into the old gulfs.”
—D.H. (David Herbert)

“If we are to take for the criterion of truth the majority of suffrages, they ought to be gotten from those philosophic and patriotic citizens who cultivate their reason.”
—James Madison (1751–1836)