Table Of ContentYIELD POINT PHENOMENA IN
METALS AND ALLOYS
Yield Point Phenomena
•
In
Metals and Alloys
E. O. Hall
Plenum Press
NEW YORK
© E. O. Hall 1970
Softcover reprint of the hardcover 1s t edition 1970
US Edition published by PLENUM PRESS
a division of Plenum Publishing Corporation,
227 West 17th Street, New York, NY 10011
Library of Congress Catalog Card Number 75-120336
ISBN-13: 978-1-4684-1862-0 e-ISBN-13: 978-1-4684-1860-6
001: 10.1007/978-1-4684-1860-6
Preface
Exceptions to the rule are always interesting, and the anomalies in
the stress-strain curves of mild steel and in many other metals and
alloys have excited the curiosity of engineers and scientists for well
over a hundred years. Yet it is only during the last twenty years that
significant theoretical advances have been made, and the aim of this
book has been to examine these theories against the background of
the considerable volume of experimental results published over the
last few years, up to mid-1969.
Hence this review volume has a two-fold aim; the first chapter
attempts to review the general theories of yield point phenomena,
using sufficient examples only to illustrate the theories. This chapter
is intended to be complete in itself, and could be read by under
graduates who wish to appraise rapidly the general background to
the problem. The remaining chapters deal, in turn, with the various
alloys exhibiting yield point phenomena. Thus, chapter 2 on mild
steel, is a more extensive study of quench and strain ageing, while
Chapter 3 is on the refractory metals and discusses theories of the
low-temperature strength. The next concerns hydrogen in meta-Is.
Chapters 5 and 6 discuss the face-centred cubic alloys, particularly
the cases of the unloading yield point and intermetallic compounds.
Chapter 7 covers hexagonal and ionic structures. A brief final chapter
considers the areas where further research may be fruitful.
Some knowledge of dislocation theory and stereographic projection
must be assumed, but the aim is to make the book as self-contained
as possible, and of interest to a wide range of solid-state physicists,
metallurgists and engineers.
Acknowledgments
I started this book while on sabbatical leave at the University of
Cambridge in 1966 and therefore wish to thank both the University
of Newcastle, for granting the leave, and Professor R. W. K. Honey
combe, of Cambridge University, for the use of facilities in his
department. In addition, the help given by colleagues in supplying
either unpublished data, or data prior to publication, is acknowledged
in the text. Finally, I wish to thank Mrs. J. Saunders and Mrs. E.
Burns for their careful typing of the draft and final copy respectively.
Contents
Preface v
Acknowledgments VI
List of Plates viii
1 YIELD POINT PHENOMENA AND THEIR THEOR-
ETICAL BACKGROUND 1
Introduction - The effects of tensile machine and specimen
stiffness - Types of yield point effects - The upper yield
point-experimental-The upper yield point-theoretical -
The lower yield point - Strain ageing - Pseudo yield points
2 IRON AND ITS ALLOYS 65
Introduction - Effects of carbon, nitrogen and other
elements - Quench ageing - Yielding behaviour - Strain
ageing kinetics - Effects of radiation damage-Single
crystals - Steels
3 THE GROUP VA AND VIA METALS 127
Introduction - Vanadium - Chromium - Niobium - Molyb
denum - Tantalum - Tungsten - Alloys of these metals
Discussion
4 HYDROGEN IN METALS 157
Hydrogen embrittlement - Solubility of hydrogen in
metals - Mild steel-Group Va and VIa metals - Nickel
Palladium - Titanium and zirconium
5 ALUMINIUM AND ITS ALLOYS 171
Introduction - The unloading yield point effect - ' Com
mercially pure' aluminium - Aluminium-copper alloys
Aluminium-magnesium alloys - Other aluminium alloys
Theories ofy ield points in aluminium alloys
viii Contents
6 OTHER FACE-CENTRED CUBIC METALS AND
ALLOYS 201
Introduction - Copper and its dilute alloys - Brass - Silver
and its alloys - Nickel and its alloys - Thorium - Ordered
alloys
7 MISCELLANEOUS MATERIALS 233
Introduction - Whiskers - Ionic crystals - Semiconducting
materials - Hexagonal metals and alloys
8 DISCUSSION 256
APPENDIX 260
BIBLIOGRAPHY 262
INDEX 287
List of Plates
opposite
page
1.1 Luders bands in mild steel 24
1.2 Luders bands in pie dish 24
1.3 Shear at front of Luders band 25
1.4 Luders bands in mild steel 25
1.5 Luders bands 25
1.6 Dislocation loops 56
1.7 Dislocation cell structure 56
2.1 Dislocations in N-Fe alloy 57
2.2 Band markings in mild steel 57
2.3 Stacking faults in steel 57
3.1 Defects in chromium 152
3.2 Strain markings in tantalum 152
4.1 Luders bands in steel strip 153
4.2 Dislocation patterns in nickel 153
5.1 Band markings in AI-Cu alloy 184
5.2 Strains in AI-Mg alloy 184
7.1 Dislocations in Mg-Th alloy 185
1
Yield Point Phenomena and their
Theoretical Background
1.1 Introduction
When certain materials such as mild steel are deformed in tension, it
is found that the stress-strain curve is not smooth, but shows marked
irregularities, with negative slopes occurring at or near the initial
yield on the curve. The actual shape of the stress-strain curve is de
pendent, to some extent, on the type and characteristics of the tensile
testing machine used; nevertheless one may include all cases where
Sa/S€ is negative as examples of yield point effects deserving attention.
Again using mild steel as an example, the progress of deformation
may be divided into three stages, as shown in Fig. 1.1. The normal
elastic extension AB is terminated at a stress level known as the upper
yield stress au. Deformation then proceeds at a decreased stress level
known as the lower yield stress aL, but the deformation at this stage is
not homogeneous: the specimen is divided into regions, known as
Luders bands (after Luders (1860)t), where the strain has the value
shown in Fig. 1.1, and other regions which are not yet deformed
€L
with zero strain. These bands are also known as Hartmann lines, after
Hartmann (1896) or as 'stretcher strains'. Since this Luders strain
can in steel be as high as 5%, dependent on grain size, the deformed
regions on a test specimen may be clearly shown under conditions of
critical illumination. Plate 1.1(a) shows a Luders band in a steel strip
specimen, and Plate l.1(b) in a stiffer, heavier specimen. Although the
morphology differs in the two cases, in both specimens the upper
yield stress may be regarded as a nucleation stress, and the lower
yield stress as the growth stress, of the Luders bands themselves.
t In fact, these bands were first noted by Piobert (1842) - French publica
tions often refer to these bands as the Piobert-Luders phenomena.
1-
2 Yield Point Phenomena in Metal and Alloys
Thus, at the lower yield stress, deformation proceeds by the growth
of Luders bands, which spread along the specimen, until at the point
D (Fig. 1.1) the entire surface of the test specimen is covered, and all
areas of the test length have been strained by an amount Beyond
€L.
this point, from D to the ultimate tensile stress at E, deformation is
essentially homogeneous and thereafter necking develops, leading to
normal ductile fracture at F.
As will be seen, there are numerous variants of this stress-strain
curve, dependent on material, temperature, grain size and other
metallurgical variables; nevertheless these general principles may
apply. The technological importance of yield points is great; in
pressed mild steel components for example, the Luders bands may
Siress
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FIGURE 1.1. Diagrammatic stress-strain curve of mild steel
lead to markings resulting from the inhomogeneous deformation
these are commonly known as stretcher strains. Plate 1.2 shows a
typical example in a pressed steel pie dish, where in most cases cus
tomers are not concerned with irregularities on the underside of pies,
but in other examples of large pressed components, such as motor car
bodies, stretcher strains make it difficult to achieve the high degree of
surface finish required prior to painting. Elaborate procedures are
adopted, such as deforming the sheets by temper rolling, or roller
levelling by a total amount somewhat less than so that on subse
€L,
quent pressing, deformation will occur virtually homogeneously
from the numerous Luders band nuclei so produced (see, for example,
Butler and Wilson (1963) and Verduzco and Polakowski (1966».
Yield Point Phenomena and their Theoretical Background 3
Although in certain alloy systems the Luders strains may exceed
several hundred per cent, in others the value of may be exceedingly
€L
small. The variations involved and their dependence on the metal
lurgical variables is the core of this monograph.
1.2 The effects oft ensile machine and specimen stiffness
Before studying yield point phenomena any further, it is necessary to
dispose of two elementary, yet important, aspects of the measure
ment of yield points; the effects of the tensile machine and specimen
stiffness.
Tensile machines are divided into two types, the so-called 'soft'
and 'hard' machines. In the former, the load is considered con
nected to the specimen by a soft spring, so that if the specimen yields
suddenly the load is virtually unaffected. Deadweight loading, hy
draulic machines and pivoted beam type tensile machines come in this
category, although in the latter, some allowance can be made by not
ing the drop in the beam as the yield point is reached. But for follow
ing rapid changes in load, such as is found with mild steel at elevated
temperatures, these are of limited value. For accurate measurements,
and to follow rapid changes in load, hard machines are necessary.
Here the load is measured and transmitted to the specimen by a load
cell and stiff members, so that very small sudden elongations in the
specimen result in a large drop in load, and accurate and rapid record
ing of load is likewise essential. Tensile machines of the Instron type
or, for lighter loads, the inverted Polanyi type described by Adams
(l959), are convenient for this study. Load cells, with outputs recorded
on fast (1 s F.S.D.) recorders, are also essential.
The effects of machine rigidity may be simply illustrated by reference
to Fig. 1.2(a). Here, the tensile specimen shown is imagined to have a
Young's modulus E, while the machine and supporting members have
an effective spring constant K. Thus, under a load L, the extension of
the system is L/K + Ll/(AE) where 1 is the specimen length and A its
cross section.
If the specimen extends by an amount Sl the overall extension is
constant; the load measured changes by SL so that
SL(1/K + l/(AE)) + L Sl/(AE) = 0
SL/L = - Sl/(AE/K + /)
For a given value of Sl, it can easily be seen that as K 0 for very
---,)0-
o.
soft machines, SL/L
---,)0-
The spring constant K of the machine may be determined quite
Description:Exceptions to the rule are always interesting, and the anomalies in the stress-strain curves of mild steel and in many other metals and alloys have excited the curiosity of engineers and scientists for well over a hundred years. Yet it is only during the last twenty years that significant theoretica
