Reconcile the perfectly elastoplastic model to simulate the cyclic behavior and ratcheting

Abstract

Perfectly elastoplastic constitutive model is modified through a smoothing factor introduced by Liu [ Liu, C.-S., 2003. Smoothing elastoplastic stress-strain curves obtained by a critical modification of conventional models. Int. J. Solids Struct. 40, 2121Struct. 40, -2145]. The new model allows plasticity to happen in a non-zero-measure yield volume in stress space, rather than that of conventional zero-measure yield surface, and within the yield volume the plastic modulus is varying continuously. It endows a specific strain-hardening rule of flow stress and is able to describe the phenomena of strain hardening, cyclic hardening, the Bauschinger effect, mean-stress relaxation, strain ratcheting, out-of-phase hardening, as well as erasure-of-memory. In order to suppress the over prediction of ratcheting we consider a scalar function of smoothing factor, which can simulate the saturation behavior of uniaxial/multiaxial strain ratcheting. These effects are demonstrated through numerical examples. The existence of stress equilibrium point and limiting surface is a natural result without requiring an extra design. Moreover, the non-linear constitutive equations can be converted into a linear system for augmented stress in the Minkowski space, of which the symmetry group is a proper orthochronous Lorentz group SO o (5, 1). The augmented stress is a time-like vector, moving on hyperboloids inside the cone. When taking the Prager kinematic hardening rule into account we can simulate some cyclic behaviors of SAE 4340 and grade 60 steels within a certain accuracy through the use of only three material constants and a fixed smoothing factor. To simulate the ratcheting behaviors of SS304 stainless steel we allow the smoothing factor to be an exponential decaying function of k.

Two complementary trios material model and experimental simulations of SAE 4340 and RHA

“…An elastic/plastic model with a unique yield surface has severe limitations as pointed out by Liu [2006]: (a) a discontinuous stress rate and strain rate relation is predicted, which changes abruptly when stress reaches the yield surface, (b) upon loading, the consistent condition requires the subsequent stress points to remain on the yield surface, and (c) the hysteresis loop for a partial unloading-reloading cycle, the Masing effect and the strain ratcheting phenomenon cannot be described properly.…”

“…See, for example, [Chaboche 1991;1994;Voyiadjis and Sivakumar 1991;1994;Hassan and Kyriakides 1992a;1992b;Ohno and Wang 1993a;1993b;1994;Bari and Hassan 2001;Voyiadjis and Abu Al-Rub 2003;Chen and Jiao 2004;Vincent et al 2004;Dieng et al 2005;Chen et al 2005;Liu 2006]. This list reflects just some of the active research dealing with the cyclic behaviors of materials, and improvements are still in progress.…”

“…Liu and Chang [2005] have studied the material models endowed with the anisotropic quadratic yield criteria from a noncanonical Minkowski frame to enhance the computational accuracy. However, many higher-order nonquadratic yield criteria have been proposed to simulate the distortion of yield surfaces during plastic deformation, which is an important issue in plasticity theory; see, for example, [François 2001;Chiang et al 2002;Bron and Besson 2004;Cazacu and Barlat 2004;Kowalczyk and Gambin 2004;Vincent et al 2004;Liu and Chang 2004;Wu et al 2005;Yeh and Lin 2006;Christensen 2006].…”