PLANE-STRESS YIELD CRITERION FOR HIGHLY-ANISOTROPIC SHEET METALS

The paper presents a plane-stress yield criterion in the form of a finite series that can be expanded to retain more or less terms, depending on the volume of experimental data. Due to its structure, the model is suitable for a variety of practical applications. An identification procedure consisting in the minimization of an error-function is used to evaluate the coefficients included in the yield criterion. The effectiveness of this strategy is proved for the particular situations when sets of 8 and 16 experimental values are available. In both cases, the input quantities (normalized yield stresses and r-coefficients) are obtained from uniaxial and biaxial tensile tests. The performances of the yield criterion are evaluated by comparing its predictions with the experimental data for an AA2090-T3 aluminium alloy. Another test is performed on a fictitious material exhibiting a distribution of the anisotropy parameters that would lead to the occurrence of 8 ears in a cylindrical deep-drawing process.

[1]  R. Hill.  The mathematical theory of plasticity , 1950 .

[2]  F. Barlat,et al.  Prediction of tricomponent plane stress yield surfaces and associated flow and failure behavior of strongly textured f.c.c. polycrystalline sheets , 1987 .

[3]  R. E. Dick,et al.  Plane stress yield functions for aluminum alloy sheets , 2002 .

[4]  F. Barlat,et al.  Plane stress yield function for aluminum alloy sheets—part 1: theory , 2003 .

[5]  Frédéric Barlat,et al.  Application of the theory of representation to describe yielding of anisotropic aluminum alloys , 2003 .

[6]  Frédéric Barlat,et al.  Linear transfomation-based anisotropic yield functions , 2005 .

[7]  Dorel Banabic,et al.  An improved analytical description of orthotropy in metallic sheets , 2005 .

[8]  A. H. van den Boogaard,et al.  A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states , 2006 .

[9]  Frédéric Barlat,et al.  Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function , 2006 .

[10]  P. Comba,et al.  Part I. Theory , 2007 .

[11]  F. Barlat,et al.  Anisotropy and Formability , 2007 .

[12]  Dorel Banabic,et al.  Influence of constitutive equations on the accuracy of prediction in sheet metal forming simulation , 2008 .

[13]  Jeong Whan Yoon,et al.  On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming , 2008 .

[14]  Frédéric Barlat,et al.  Advances in anisotropy and formability , 2010 .