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http://dx.doi.org/10.5228/KSTP.2022.31.4.214

Yield Functions Based on the Stress Invariants J2 and J3 and its Application to Anisotropic Sheet Materials  

Kim, Y.S (School of Mechanical Engineering, Kyungpook National University)
Nguyen, P.V. (Bosch Vietnam Co.)
Kim, J.J. (Depart. Mech. Engng, Univ. New Hamphire(USA))
Publication Information
Transactions of Materials Processing / v.31, no.4, 2022 , pp. 214-228 More about this Journal
Abstract
The yield criterion, or called yield function, plays an important role in the study of plastic working of a sheet because it governs the plastic deformation properties of the sheet during plastic forming process. In this paper, we propose a novel anisotropic yield function useful for describing the plastic behavior of various anisotropic sheets. The proposed yield function includes the anisotropic version of the second stress invariant J2 and the third stress invariant J3. The anisotropic yield function newly proposed in this study is as follows. F(J2)+ αG(J3)+ βH (J2 × J3) = km The proposed yield function well explains the anisotropic plastic behavior of various sheets by introducing the parameters α and β, and also exhibits both symmetrical and asymmetrical yield surfaces. The parameters included in the proposed model are determined through an optimization algorithm from uniaxial and biaxial experimental data under proportional loading path. In this study, the validity of the proposed anisotropic yield function was verified by comparing the yield surface shape, normalized uniaxial yield stress value, and Lankford's anisotropic coefficient R-value derived with the experimental results. Application for the proposed anisotropic yield function to aluminum sheet shows symmetrical yielding behavior and to pure titanium sheet shows asymmetric yielding behavior, it was shown that the yield curve and yield behavior of various types of sheet materials can be predicted reasonably by using the proposed new yield anisotropic function.
Keywords
invariant $J_2$; invariant $J_3$; stress deviator; anisotropic yield function; symmetric yield function; asymmetric yield function;
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