page_title: Yield surface
section_title: Barlat's Yield Surface
hierarchical_section_title: Yield surface / Examples of yield surfaces / Barlat's Yield Surface
caption_attribution_description: English: The Barlat's Yld2000-2D yield loci
context_page_description: 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 of 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 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 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.
context_section_description: For the anisotropic materials, depending on the direction of the applied process (e.g., rolling) the mechanical properties vary and, therefore, using an anisotropic yield function is crucial. Since 1989 Frederic Barlat has developed a family of yield functions for constitutive modelling of plastic anisotropy. Among them, Yld2000-2D yield criteria has been applied for a wide range of sheet metals (e.g., aluminum alloys and advanced high-strength steels). The Yld2000-2D model is a non-quadratic type yield function based on two linear transformation of the stress tensor:
   :
  where  is the effective stress. and  and  are the transformed matrices (by linear transformation C or L):
  where s is the deviatoric stress tensor.
  for principal values of X’ and X”, the model could be expressed as: 
  and:
  where  are eight parameters of the Barlat's Yld2000-2D model to be identified with a set of experiments.
caption: The Yld2000-2D yield loci for a AA6022 T4 sheet.
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