Plasticity in shaping

Overview

ABSTRACT

Rigid-plastic behavior is a mapping of the actual behavior of metallic alloys. This mapping serves as the basis for the construction of all the more realistic models of plastic behavior. The objective of this theory is to describe the behavior of rigid-plastic material in a state of stress and deformation broader than that observed in mono-load testing, such as traction, torsion and bending. For that, it is necessary to make various assumptions and initially disregard the finer phenomena that occur in actual materials.

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AUTHOR

Eric FELDER: Ingénieur civil des Mines de Paris, Doctor of Science - Senior Researcher at the Centre de mise en forme des matériaux (CEMEF) - École des Mines de Paris, CNRS Sophia-Antipolis

INTRODUCTION

As seen in § 4.1 of the [42] dossier, rigid-plastic behavior is a schematization of the actual behavior of metal alloys. It serves as the basis for the construction of all more realistic plastic behavior models. It is therefore particularly instructive to present it first.

The aim of this theory is to describe the behavior of RPP material in a more general state of stress and strain than that observed in single-load tests (tension, torsion, bending), and to specify the relationships between the quantities measured in these various tests. To achieve this, it is necessary to make various assumptions and initially neglect the finer phenomena encountered in real materials.

The fundamental notions of plasticity have a very simple but fundamental framework, namely the rigid-plastic body or RPP.

In this issue, we look at :

plasticity criterion ;
plastic flow law ;
description of friction ;
a statement of theorems for analyzing shaping operations;
at the end, a significant illustration through the example of rolling with traction of thin sheets.