Conical extrusion of a work-hardening material: An asymptotic analysis
type: Item
instance of: scholarly article
title: Conical extrusion of a work-hardening material: An asymptotic analysis
zbMATH Open document ID: 0633.73050
DOI: 10.1007/BF00132681
published in: Journal of Engineering Mathematics
publication date: 1987-01-01T00:00:00Z
review text: We study steady-state conical extrusion of an isotropic, power-law hardening material with a Coulomb friction condition present at the die faces. An asymptotic theory is developed based on an axial velocity field which is nearly ``slug-like'', i.e., a deformation field for which the transverse variations of the axial velocity are modest in size. However, although the velocity is ``slug-like'', within the asymptotic limit considered the shear stresses are not negligible compared to the longitudinal deviatoric stresses. For this reason the theory accounts for the first manifestations of inhomogeneous deformation. In practical terms the validity of the asymptotic theory generally requires either the friction coefficient \(\mu\) to be small or the die slope \(\Delta\) h/L to be small (where \(\Delta\) h is the radius reduction and L the die length). The primary result of the work is a set of three coupled equations. In addition, the present formulation enables for the first time the development of a model of inhomogeneous deformation in conical extrusion which is analogous to the very popular inhomogeneous deformation theory developed for plane-strain sheet rolling. Results are presented for a number of examples illustrating the depature from a state of homogeneous compression which is typically found.
Mathematics Subject Classification ID: 74C15
Mathematics Subject Classification ID: 74C20
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74C99
zbMATH DE Number: 4031138
zbMATH Keywords: steady-state conical extrusion
zbMATH Keywords: isotropic, power-law hardening material
zbMATH Keywords: Coulomb friction
zbMATH Keywords: asymptotic theory
zbMATH Keywords: axial velocity field
zbMATH Keywords: slug-like
zbMATH Keywords: shear stresses
zbMATH Keywords: inhomogeneous deformation
author: R. E. Johnson
MaRDI profile type: Publication
cites work: Application of a Perturbation Technique Based on the Method of Characteristics to Axisymmetric Plasticity
cites work: On the theory of rolling
description: scientific article; zbMATH DE number 4031138