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)

    “What rein can hold licentious wickedness
    When down the hill he holds his fierce career?”
    —William Shakespeare (1564–1616)

    “It is the characteristic of great poems that they will yield of their sense in due proportion to the hasty and the deliberate reader. To the practical they will be common sense, and to the wise wisdom; as either the traveler may wet his lips, or an army may fill its water-casks at a full stream.”
    —Henry David Thoreau (1817–1862)

    “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)