Prediction of yield functions on BCC polycrystals

ABSTRACT nonlinear optimization theory, we predict the yield function of single BCC crystals in Hillʹs criterion form. Then we give a formula on the macroscopic yield function of a BCC polycrystal Ω under Sachsʹ model, where the volume average of the yield functions of all BCC crystallites in Ω is taken as the macroscopic yield function of the BCC polycrystal. In constructing the formula, we try to find the relationship among the macroscopic yield function, the orientation distribution function (ODF), and the single BCC crystalʹs plasticity. An expression for the yield stress of a uniaxial tensile problem is derived under Taylorʹs model in order to compare the expression with that of the macroscopic yield function.