A yield surface is a five-dimensional surface in the six-dimensional space of stresses. The yield surface is usually convex and the state of stress of inside the yield surface is elastic. When the stress state lies on the surface the material is said to have reached its yield point and the material is said to have become plastic. Further deformation of the material causes the stress state to remain on the yield surface, even though the shape and size the surface may change as the plastic deformation evolves. This is because stress states that lie outside the yield surface are non-permissible in rate-independent plasticity, though not in some models of viscoplasticity.
The yield surface is usually expressed in terms of (and visualized in) a three-dimensional principal stress space, a two- or three-dimensional space spanned by stress invariants or a version of the three-dimensional Haigh–Westergaard stress space. Thus we may write the equation of the yield surface (that is, the yield function) in the forms:
- where are the principal stresses.
- where is the first principal invariant of the Cauchy stress and are the second and third principal invariants of the deviatoric part of the Cauchy stress.
- where are scaled versions of and and is a function of .
- where are scaled versions of and, and is the Lode angle.
Famous quotes containing the words yield and/or surface:
“As yields no mercy to desert,
Nor grace to those that crave it.
Sweet sun, when thou lookest on,
Pray her regard my moan;
Sweet birds, when you sing to her,
To yield some pity, woo her;”
—Thomas Lodge (1558?1625)
“The surface of the ground in the Maine woods is everywhere spongy and saturated with moisture.”
—Henry David Thoreau (18171862)