Finite strain formulation of elasto-plasticity without yield surface: theory, parameter identification and applications

Abstract

In this study, a finite strain formulation of elasto-plasticity without the yield surface is analyzed. It is found that the presented model allows for a good description of the elasto-plastic response for many metallic materials. Furthermore, it is noted that the model involving a limited number of material parameters is able to capture such effects as indefinite elastic limit, strain hardening, strain softening and the Bauschinger effect. An algorithm for the evaluation of constants is described and the determined values are given for NC high carbon tool steel, copper, brass, Inconel alloy, tungsten heavy alloy and aluminum.

Phenomenological Model of Low-Carbon Steels Hardening during Multistage Drawing

“…, then the above theories will give significant errors [23][24][25], particularly, in the estimation of the acquired mechanical properties of the wire. Besides, obtaining of analytical expressions, based on such grounds, involves certain mathematical difficulties, especially if there is a task of obtaining practical engineering dependencies.…”

Numerical implementation of finite strain elasto-plasticity without yield surface

“…1. In parallel to the FE simulations, every considered process has been independently simulated in Scilab by direct integration of the one-dimensional process equations (cf Suchocki and Skoczylas, 2016). An excellent agreement has been found between ABAQUS and Scilab predictions which is depicted in Fig.…”

“…The basic concepts of the considered framework were first introduced as a part of a viscoplastic constitutive model for polymeric materials, cf Suchocki (2015). Further research proved applicability of the proposed theory to model the material response of metals (Suchocki and Skoczylas, 2016). However, in the case of metallic materials, correct numerical implementation of the considered class of constitutive equations requires a completely different approach from the one used in polymer modeling.…”

“…However, the concept of an intrinsic time adopted therein and defined as the arclength in the nine-dimensional strain space has been slightly modified for the purpose of present considerations (cf Suchocki, 2015;Suchocki and Skoczylas, 2016). The fictitious time is utilized to build a functional of the deformation history which determines the material stress response and is analogous to the history functional known from the viscoelasticity theory (e.g.…”