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)

    “I got my first clear view of Ktaadn, on this excursion, from a hill about two miles northwest of Bangor, whither I went for this purpose. After this I was ready to return to Massachusetts.”
    —Henry David Thoreau (1817–1862)

    “If others surpass you in knowledge, in charm, in strength, in fortune, you have other causes to blame for it; but if you yield to them in stoutness of heart you have only yourself to blame.”
    —Michel de Montaigne (1533–1592)

    “I divide all literary works into two categories: Those I like and those I don’t like. No other criterion exists for me.”
    —Anton Pavlovich Chekhov (1860–1904)