Analytical determination of anisotropic parameters for Poly6 yield function

Abstract

The present work mainly focuses on the analytical determination of anisotropic parameters for Poly6 yield criterion, which is mathematically equivalent to Yoshida2013 yield function. The parameters of Poly6 yield criterion are expressed with the r-values and yield stresses without any optimization method, which has been successfully applied for highly anisotropic materials. The Poly6 yield criterion is analytically calibrated using two different methods under associated flow rule; i.e, 1) the shear flow stress and r(b) value and 2) the stresses under sigma(xx) = 2 sigma(yy) and 2 sigma(xx) = sigma(yy). The first type of analytical calibration from shear stress and r(b) value is compared with the Yoshida2013 yield criterion whose parameters are obtained from an optimization process, which shows that they are equivalent for describing stress and strain distributions. The yield loci of FCC materials predicted from the second method is similar to Yld2000-2d. Both methods of calibrating the analytical Poly6 yield criterion are shown to describe the r-value and uniaxial yield stress directionalities. The accuracy and effectiveness of the proposed analytical methods are verified through the selected FCC and BCC materials. The ability to describe the evolutions of materials' anisotropic behaviors with the proposed analytical Poly6 has been verified by applying it to AA5182-O.