Application of the Plasticity Models That Involve Three Stress Invariants

Abstract

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.

The role of stress-state on the deformation and fracture mechanism of hydrided and non-hydrided Zircaloy-4

“…(5). The potential for a negligibly small change in volume with plasticity is due to the I1 dependence (where I1 is the first invariant of the stress tensor or the hydrostatic component) observed for beta-treated Zircaloy-4 [33,34]. Hence, no volume correction is made in this work, as the magnitude is small.…”

“…Since ductile materials have been observed and theorized to not be susceptible to failure at a triaxiality value of À0.33 or less [65], the failure strain is assumed to increase to a value of 1.0 at the triaxiality value of À0. 33.…”

Adaptive Incremental Finite Element Procedure for Solving Elastoplastic Frictional Contact Problems Subjected to Normal and Tangential Loads

“…They concluded that the use of the Lagrange multiplier based strategy had an advantage in few critical situations, where the penalty method failed to produce convincing results due to excessive penetration. Zhang et al [2012] used the FE software ABAQUS adopting an updated Lagrangian formulation to solve large deformation elastoplasticity problems. They adopted a yield function, which was assumed to be a function of the first invariant of the stress tensor and the second and third invariants of the deviatoric stress tensor.…”