Yield criterion

von Mises

Daniel Weschke

December 30, 2018

List of Symbols

\(\sigma\)

MPa

Stress

1 General remarks

All yield criterion transform the real triaxial stress state to a virtual uniaxial stress state. They differ in material mechanical related criteria.

2 von Misesyield criterion

Assumption: Linear elasticity.

Equivalent tensile stress or equivalent von Misesstress \(\sigma\ti{v}\) [1]

\[\sigma\ti{v} = \frac{1}{\sqrt{2}} \sqrt{(\sigma_1-\sigma_2)^2 + (\sigma_2-\sigma_3)^2 + (\sigma_3-\sigma_1)^2}\]

as a function of principle stresses, holds an under load a volumetric shape-changing-energy as a criterion. It is the mathematical formulation of the the yield point, the beginning of the plastic deformation. [1]

Aside: The shown equivalent tensile stress were already suggested by Huber [2] some years before von Misesused them. And half a century before considered by Maxwell [3] .

References

[1] (1,2)

von Mises, R. Mechanik der festen körper im plastisch- deformablen zustand. In Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse. Weidmannsche Buchhandlung, Berlin, 1913, Heft 4, pp. 582–592. [ http ]

[2]

Huber, M. T. Die spezifische formanderungsarbeit als maß der anstrengung eines materials. Czasapismo Techniczne 22 (1904), 38–40, 49–50, 61–62, 80–81.

[3]

Maxwell, J. C. Letter to William Thomson, 1856.