An Upper Bound Solution for the Compression of an Orthotropic Cylinder.

Lihui Lang,Yun-Che Wang,Sergei Alexandrov

doi:10.3390/ma14185253

Abstract

The upper bound theorem is used in conjunction with Hill’s quadratic yield criterion for determining the force required to upset a solid cylinder. The kinematically admissible velocity field accounts for the singular behavior of the real velocity field in the vicinity of the friction surface if the maximum friction law is adopted. The regime of sticking is also taken into consideration. The effect of this regime on the upper bound limit load is revealed. In particular, the kinematically admissible velocity field that includes the regime of sticking may result in a lower upper bound than that with no sticking. The boundary value problem is classified by a great number of geometric and material parameters. Therefore, a systematic parametric analysis of the effect of these parameters on the compression force is practically impossible. An advantage of the solution found is that it provides a quick estimate of this force for any given set of parameters.

Highlights

The upsetting of solid cylinders is an important metal-forming operation [1]. This process is used as a test for evaluating flow stress and friction [2]
A typical disadvantage of upper bound solutions is that the regime of sticking friction is ignored
A circular solid cylinder is upset between two parallel rough plates (Figure 1)

Summary

Introduction

The upsetting of solid cylinders is an important metal-forming operation [1] This process is used as a test for evaluating flow stress and friction [2]. A typical disadvantage of upper bound solutions is that the regime of sticking friction is ignored (for example, [23,24,25,26,27]). An exception is the solution provided in [34] for the upsetting of a hollow cylinder This solution is based on Hill’s quadratic yield criterion [35]. The overall motivation of this research is to demonstrate, using a simple example, that plastic anisotropy, which is a very common property of metallic materials, should not be ignored in upper bound solutions for metal forming processes

Statement of the Problem

Kinematically Admissible Velocity Field

Numerical Examples

Conclusions