Prediction of yield functions on BCC polycrystals
- 1 Downloads
By the nonlinear optimization theory, we predict the yield function of single BCC crystals in Hill’s criterion form. Then we give a formula on the macroscopic yield function of a BCC polycrystal Ω under Sachs’ 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 crystal’s plasticity. An expression for the yield stress of a uniaxial tensile problem is derived under Taylor’s model in order to compare the expression with that of the macroscopic yield function.
Key wordsyield function the ODF BCC polycrystal single BCC crystals anisotropy
Unable to display preview. Download preview PDF.
- Bunge, H.J., Texture Analysis in Material Science: Mathematical Methods, London: Butterworths, 1982.Google Scholar
- Sachs, G., Zur ableilung einer fleissbedingung, Z. Verein Deut. Ing., Vol.72, 1928, 734–736.Google Scholar
- Taylor, G.I., Plastic strain in metals, J. Inst. Met., Vol.62, 1938, 307–324.Google Scholar
- Hosford, W.F., The Mechanics of Crystals and Textured Polycrystals, Oxford University, New York, 1993.Google Scholar
- Hill, R., The Mathematical Theory of Plasticity, Clarendon press, Oxford, 1950.Google Scholar
- Huang, M. and Zheng, C., Green’s function and effective elastic stiffness tensor for arbitrary aggregates of cubic crystals, Acta Mechanica Solida Sinica, Vol.17, No.4, 2004, 337–346.Google Scholar