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)

    ““Oh, let’s go up the hill and scare ourselves,
    As reckless as the best of them tonight,
    By setting fire to all the brush we piled
    With pitchy hands to wait for rain or snow....””
    —Robert Frost (1874–1963)

    “Alas, why would you heap this care on me?
    I am unfit for state and majesty.
    I do beseech you take it not amiss,
    I cannot nor I will not yield to you.”
    —William Shakespeare (1564–1616)

    “Faith in reason as a prime motor is no longer the criterion of the sound mind, any more than faith in the Bible is the criterion of righteous intention.”
    —George Bernard Shaw (1856–1950)