Plastic forming processes of transverse non-homogeneous composite metallic sheets

Gal Davidi

doi:10.1515/eng-2021-0029

Abstract

Abstract In this work an analysis of the radial stress and velocity fields is performed according to the J 2 flow theory for a rigid/perfectly plastic material. The flow field is used to simulate the forming processes of sheets. The significant achievement of this paper is the generalization of the work by Nadai & Hill for homogenous material in the sense of its yield stress, to a material with general transverse non-homogeneity. In Addition, a special un-coupled form of the system of equations is obtained where the task of solving it reduces to the solution of a single non-linear algebraic differential equation for the shear stress. A semi-analytical solution is attained solving numerically this equation and the rest of the stresses term together with the velocity field is calculated analytically. As a case study a tri-layered symmetrical sheet is chosen for two configurations: soft inner core and hard coating, hard inner core and soft coating. The main practical outcome of this work is the derivation of the validity limit for radial solution by mapping the “state space” that encompasses all possible configurations of the forming process. This configuration mapping defines the “safe” range of configurations parameters in which flawless processes can be achieved. Several aspects are researched: the ratio of material's properties of two adjacent layers, the location of layers interface and friction coefficient with the walls of the dies.

Highlights

High importance exists for thin walled structures like sheets that play a pivotal role in the advanced modern industries
In Addition, a special un-coupled form of the system of equations is obtained where the task of solving it reduces to the solution of a single non-linear algebraic differential equation for the shear stress
The solution for equation (26) sometimes does not exist. This is due to the nature of it being an algebraic differential equation rather than a differential equation

Summary

Introduction

High importance exists for thin walled structures like sheets that play a pivotal role in the advanced modern industries. We shall mention bulging formation in sheets forming (Johnson & Rowe [21]), in certain configurations This phenomenon was first reported by Hill [18, 19] that set the criterions for its appearance and showed that it happens where the velocity field derived (from the analytical solutions) is not physical ( the stress field is physical). It can be said that the appearance of flaws indicates the non-homogeneous influence of the material on the radial solution validity limit It can be seen in Alexandrov et al [2, 9] in the case of radial two-dimensional tri-layered symmetric sheet flow pattern, the influence of this phenomenon by finding configurations where there is no solution for the equations. That is based on Davidi [10], we shall investigate the various forming processes in the case of continuous non-homogeneity of the material that will enable us to broaden the knowledge on these phenomena and find configurations to ensure their prevention

Mathematical model

Case study

Summary and conclusions