Mechanics of Sheet Metal Forming - ...

Mechanics of Sheet Metal Forming - Z. Marciniak, Obróbka blachy

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Mechanics of Sheet
Metal Forming
Mechanics of Sheet
Metal Forming
Z. Marciniak
The Technical University of Warsaw, Poland
J.L. Duncan
The University of Auckland, New Zealand
S.J. Hu
The University of Michigan, USA
OXFORD AMSTERDAM BOSTON LONDON NEW YORK PARIS
SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO
Butterworth-Heinemann
An imprint of Elsevier Science
Linacre House, Jordan Hill, Oxford OX2 8DP
225 Wildwood Avenue, Woburn, MA 01801-2041
First published by Edward Arnold, London, 1992
Second edition published by Butterworth-Heinemann 2002
Copyright
2002 S.J. Hu, Z. Marciniak, J.L. Duncan
All rights reserved
The right of S.J. Hu, Z. Marciniak and J.L. Duncan to be identified as the authors of this work has been
asserted in accordance with the Copyright, Designs and Patents Act 1988
All rights reserved. No part of this publication
may be reproduced in any material form (including
photocopying or storing in any medium by electronic
means and whether or not transiently or incidentally
to some other use of this publication) without the
written permission of the copyright holder except
in accordance with the provisions of the Copyright,
Designs and Patents Act 1988 or under the terms of a
licence issued by the Copyright Licensing Agency Ltd,
90 Tottenham Court Road, London, England W1T 4LP.
Applications for the copyright holder’s written permission
to reproduce any part of this publication should be addressed
to the publishers
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloguing in Publication Data
A catalogue record for this book is available from the Library of Congress
ISBN 0 7506 5300 0
For information on all Butterworth-Heinemann publications visit our website at www.bh.com
Typeset by Laserwords Private Limited, Chennai, India
Printed and bound in Great Britain
Contents
Preface to the second edition
ix
Preface to the first edition
xii
Introduction
xi
1 Material properties
1
1.1 Tensile test
1
1.2 Effect of properties on forming
10
1.3 Other mechanical tests
12
1.4 Exercises
13
2 Sheet deformation processes
14
2.1 Introduction
14
2.2 Uniaxial tension
14
16
2.4 Yielding in plane stress
17
2.5 The flow rule
22
2.6 Work of plastic deformation
24
2.7 Work hardening hypothesis
25
2.8 Effective stress and strain functions
26
2.9 Summary
27
2.10 Exercises
27
3 Deformation of sheet in plane stress
30
3.1 Uniform sheet deformation processes
30
3.2 Strain distributions
31
3.3 Strain diagram
31
3.4 Modes of deformation
33
3.5 Effective stress – strain laws
36
3.6 The stress diagram
39
3.7 Principal tensions or tractions
41
3.8 Summary
43
3.9 Exercises
43
v
Disclaimer
xi
4 Simplified stamping analysis
45
4.1 Introduction
45
4.2 Two-dimensional model of stamping
46
4.3 Stretch and draw ratios in a stamping
57
4.4 Three-dimensional stamping model
57
4.5 Exercises
59
5 Load instability and tearing
61
5.1 Introduction
61
5.2 Uniaxial tension of a perfect strip
62
5.3 Tension of an imperfect strip
64
5.4 Tensile instability in stretching continuous sheet
67
75
5.6 The forming window
79
5.7 Exercises
80
6 Bending of sheet
82
6.2 Variables in bending a continuous sheet
82
6.3 Equilibrium conditions
84
6.4 Choice of material model
85
6.5 Bending without tension
86
6.6 Elastic unloading and springback
92
6.7 Small radius bends
96
6.8 The bending line
100
6.9 Bending a sheet in a vee-die
104
6.10 Exercises
106
7 Simplified analysis of circular shells
108
7.1 Introduction
108
7.2 The shell element
108
7.3 Equilibrium equations
110
7.4 Approximate models of forming axisymmetric
shells
111
7.5 Applications of the simple theory
112
7.6 Summary
115
7.7 Exercises
116
8 Cylindrical deep drawing
117
8.1 Introduction
117
8.2 Drawing the flange
117
8.3 Cup height
123
8.4 Redrawing cylindrical cups
123
8.5 Wall ironing of deep-drawn cups
125
8.6 Exercises
127
vi
Contents
6.1 Introduction
82
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