Mechanical Engineering Faculty Research


Application of the Plasticity Models That Involve Three Stress Invariants

Document Type


Publication Date

Summer 6-30-2012


Increasing experimental evidence shows that the classical J2 plasticity theory may not fully describe the plastic response of many materials, including some metallic alloys. In this paper, the effect of stress state on plasticity and the general forms of the yield function and flow potential for isotropic materials are assumed to be functions of the first invariant of the stress tensor (I1) and the second and third invariants of the deviatoric stress tensor (J2 and J3). A 5083 aluminum alloy, Nitronic 40 (a stainless steel), and Zircaloy-4 (a zirconium alloy) were tested under tension, compression, torsion, combined torsion–tension and combined torsion–compression at room temperature to demonstrate the applicability of a proposed I1-J2-J3 dependent model. The I1-J2-J3 dependent plasticity model was implemented in ABAQUS via a user defined subroutine. The model parameters were determined and validated by comparing the numerically predicted and experimentally measured load versus displacement and/or torque versus twist angle curves. The results showed that the proposed model incorporating the I1-J2-J3 dependence produced output that matched experimental data more closely than the classical J2 plasticity theory for the loading conditions and materials tested. Read More:

Publication Title

International Journal of Applied Mechanics