Prediction of Anisotropic Elastoplastic Instability with Rice’s Criterion in Plane Compression

Khalid Zhani,Ahmed Chenaoui,Michel Darrieulat

doi:10.17485/ijst/v14i18.117

Abstract

Objectives: The main objective of this work is the development of a mechanically coherent framework for the implementation of numerical simulation tools for sheet metal forming processes. The work at hand is part of a study of the mechanical behaviour of metallic materials subjected to large elastoplastic deformations during channel-die testing and a study of the mechanisms that limit their formability and cause their instability. We analyse the effect of induced rotation on the appearance of plastic instability predicted by Rice’s criterion. Methods: At the beginning, an adequate modelling of the mechanical behaviour of metals in large elasto-plastic deformations using the formalism in rotational referential is made. Then, a prediction of plastic instabilities is developed using Rice’s bifurcation criterion. Indeed, the integration of the law of anisotropic elastoplastic behaviour is presented in a three-dimensional kinematics framework in order to write the deformation tensor as a superior triangular matrix, with Hill’s anisotropic yielding function, using Runge Kutta’s method to integrate the obtained equations. Findings: we were able to show that Rice’s criterion can be used for any kind of material and that this criterion is effective in predicting what happens in metals. It predicts shear-band bifurcation in a continuous plastic medium. Hill’s criterion is suitable for what is weakly anisotropic. The model described above represents a good mathematical framework for analysing the behaviour of materials and plastic instability. Novelty: This study allows to apply Rice’s criterion in the case of a channel-die compression test, so as to locate plastic instability and see the appearance of shear bands for all types of materials; it demonstrates that the initial rotation of the material influences the appearance of shear-bands during a test simulating rolling. Keywords: Elastoplastic; Large deformations; Anisotropy; Plastic instability; Localisation

Highlights

The simulation of large deformations for elasto-plastic materials remains indispensable for forming and the calculation of structures
The present paper shows how an orthotropic material submitted to channel-die compression can be modelled in the framework of large strains and how it is affected by shear banding
Large strain formulation involves the use of numerous tensors but the calculations are greatly simplified by the introduction of a material rotation frame in which the deformation tensor takes the form of an upper triangular matrix

Summary

Introduction

The simulation of large deformations for elasto-plastic materials remains indispensable for forming and the calculation of structures. This is a problem that is always on the agenda due to its importance in applications, where industrial operations are limited by the appearance of deformation localization phenomena and plastic instabilities [1] [2] [3] [4]. Especially transverse anisotropic fiberreinforced polymers [7], are sensitive to that form of instability Even materials such as oxide layers that grow from a foam of iron in batteries offer analogous phenomena [8]

Objectives

Results

Conclusion