Table Of ContentTHE MECHANICAL
BEHAVIOUR OF
ENGINEERING MATERIALS
by
W. D. BIGGS, A.Met., B.Sc, M.A., Ph.D.
Engineering Dept., University of Cambridge
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AUTHOR'S PREFACE
MODERN engineering practice makes continual demands upon the
material and many of the time-honoured approximations made
by designers cease to be valid as operating conditions extend
beyond those hitherto encountered. Since the properties of interest
depend, in the last analysis, upon the structure (both at the
atomic and microscopic levels), the object of the present volume
is twofold. Firstly, to relate properties and structure, secondly
(and possibly more important), to provide a theoretical basis
upon which to extrapolate when conditions or materials outside
previous experience arise.
The three sections covered here include constitution, properties,
and significance of test data. In general the suggestions for
further reading are textbooks which are more readily available than
original papers, and because of this, individual acknowledgement
has not been possible. It is hoped that this general acknowledge-
ment will be both accepted (and forgiven) by the authors con-
cerned. Specific acknowledgements are, however, possible in three
cases, the Syndics of the University Press for permission to
publish certain problems, Professor B. G. Neal for helpful advice
and criticism, and my wife for her help in typing and checking the
manuscript.
Cambridge,
December 1963 W. D. B.
ix
CHAPTER 1
INTRODUCTION
WHEN an engineer specifies the use of a particular material for a
given application, he does so from a consideration of the proper-
ties of the substance. This statement must be examined further.
Firstly, the term "properties" is a very wide one and may have a
particular meaning to a particular group of people. Thus a
mechanical or structural engineer is primarily interested in the
load carrying capacity and in such characteristics as machine-
ability, weldability. On the other hand, an electrical engineer
requires some knowledge of conductivity, magnetic permeability,
dielectric constants—and while strength is still significant it is
often of secondary importance.
It is, perhaps, traditional that a classification of the different
states of matter is based, generally, upon a comparison of the
mechanical properties. This implies some consideration of the
resistance to an applied load so that most people would accept, in
principle, a classification of the type given below:
Solids: Possess some degree of elasticity or rigidity so that they
are capable of sustaining some degree of applied load without
undergoing permanent change of shape.
Liquids and gases: Have no intrinsic shape, furthermore, the
application of a shearing load sets up a continual motion
which can only be stopped by removing the load and applying
it in the opposite direction. When a gas or liquid is suitably
confined, it offers a measurable resistance to the application
of a load.
Much of the engineering analysis of the behaviour of materials
1
2 MECHANICAL BEHAVIOUR OF ENGINEERING MATERIALS
is based upon three generalisations which follow from the
classification above—these generalisations refer to materials which
possess certain simple characteristics :
(a) The ideal solid (linear elastic or Hookean solid), where the
deformation varies directly with the applied load and is
fully recovered when the load is removed.
(b) The ideal viscous (Newtonian) liquid, where the rate of
shear flow is directly proportional to the applied shear
load.
(c) The perfect gas, where pressure and volume vary according
to the relationship pv = constant (at constant temperature).
To a large extent engineering is a phenomenological science and
such generalisations are adequate for many practical purposes,
especially as the simple expedient of combining these types of
elementary behaviour enables us to obtain mechanical models
which approximate closely to the behaviour of many real materials.
This expedient is particularly useful in the field of rheology, which
attempts to establish a phenomenological theory of the general
behaviour of matter on the assumption that every material
possesses all the basic deformational properties in varying
proportions.
For many purposes an engineer's requirements can be met by a
purely phenomenological description of the behaviour but the
widening range of properties demanded by designers has resulted
in an extension of the use of materials into those regions which
were formerly regarded as impractical. Such extensions of use
demand a less empirical approach and have largely served to
indicate the limitations of, say, the classical theories of strength
of materials. At the same time they have emphasised the need for
a re-examination and a broadening of the assumptions which were
originally made. Thus a phenomenological classification of matter
is not, in itself, sufficient. Similarity of behaviour under one chosen
set of conditions does not, necessarily, indicate similarity of
structure at either the microscopic or the atomic level, nor does
it indicate similarity of the mechanisms which are responsible for
INTRODUCTION 3
the observed phenomena. A change in operating conditions can
(and frequently does) produce a totally dissimilar mode of be-
haviour which can only be understood or expected if the funda-
mental processes are sufficiently well comprehended. Furthermore,
it is difficult to classify many materials merely by inspection of
their observed properties. For instance, glass would be considered
a solid by most people appraised of its "normal" mechanical
properties, but its structure and mechanical behaviour under
appropriate conditions lead to the more generally acceptable view
that it is, in fact, a highly viscous liquid. Similarly, it is difficult to
distinguish gases under very high pressures from liquids—it is
probable that the liquid and gaseous phases are indistinguishable
for all materials if sufficiently high pressures are applied.
It appears, then, that both a classification of the various states
of matter and an evaluation of the properties of materials requires
examination at levels other than the purely phenomenological
one and necessitates some reference to the basic elements of which
matter is composed. In order to achieve this it will be necessary to
study the properties at two levels :
(a) The "microscopic" level, at which the material is considered
to be continuous but non-homogeneous, being formed of
elements of different properties and of finite dimensions.
This involves a study of the individual grains or crystals and
the effects of interaction of these grains with each other.
(b) The submicroscopic level where the material is considered
to be discontinuous and consists of particles of atomic or
molecular size. In the limit, all phenomena which are
sensitive to time and temperature originate at this level,
though, in many cases, the theoretical analysis is not yet
sufficiently complete to explain all the experimental data.
For many purposes, the mechanical properties of solids may be
satisfactorily explained by reference to the microscopic structure
only. In recent years, however, it has become clear that many of
the properties of engineering interest depend more upon the
presence of defects than upon the perfection of the structure at the
4 MECHANICAL BEHAVIOUR OF ENGINEERING MATERIALS
atomic level. This is particularly true of crystalline solids in which
metals form by far the largest and most important subdivision.
The present text, therefore, refers primarily to metals and alloys,
other (non-crystalline) solids are treated rather less fully. This is
largely dictated by the state of knowledge at the present time, for
although there is a large mass of data concerning the properties of
non-metallic materials, much of this is empirical and a full
explanation is made difficult by the complexities of an irregular
initial structure.
The last section of the book deals, broadly, with the interpre-
tation of tests and the selection of engineering materials. Its
position in the book is dictated largely by convenience, but
although some of the factors discussed there are best understood
after reading the earlier chapters, this section may be read first in
those cases where there is not already some familiarity with the
concepts of stress and strain or where testing facilities are such
that it may not be immediately possible to ensure that the reader
has been acquainted with, e.g. the shape of the stress-strain curve.
Throughout the text the author has endeavoured to confine the
discussion to those aspects of materials science which appear to be
reasonably well understood at the present time. The suggestions
for further reading include works which treat the more uncertain
areas of the subject in some detail. The author has, however,
permitted himself one short chapter (Chapter 10) for the ex-
pression of his own opinions. Not everyone will agree with these,
but it is hoped that they may provide a basis for further discussion
and thinking on the part of the reader.
CHAPTER 2
CONSTITUTION
2.1. INTRODUCTION
The idea of an atomic constitution of matter was arrived at
by the ancients but the ability to distinguish between an observed
property and the quantities which are responsible for it, is fairly
recent. Dalton's atomic theory was largely intuitive but the
attempt to explain certain quantitative laws of chemistry led to the
idea that matter was an «-fold repetition of indivisible units of
characteristic mass.
More recently, the internal structure of the atom itself has been
the subject of intensive study and it is no longer regarded as the
indivisible, ultimate unit. For our present purpose, a detailed study
of the structure of the atom is unnecessary but, since the mechani-
cal properties of solids are associated with the forces between the
atoms, we shall first consider the atomic structure briefly.
2.2. THE ATOM
The generally accepted model of the atom is that of a central
nucleus surrounded by systems of planetary electrons. The
greatest part of the mass is concentrated in the nucleus which
carries a positive electrostatic charge in the form of elementary
particles known as protons, this charge being balanced by the
negatively charged electrons. The proton mass is about 1835
times that of the electron, the total atomic mass being of the order
of 10-24 g with an effective "diameter" of about 10 -8 cm. The
nucleus may also contain neutrons; these have a similar mass to
that of the proton but carry no charge.
Each nucleus is characterised by the magnitude of the nuclear
5
6 MECHANICAL BEHAVIOUR OF ENGINEERING MATERIALS
charge (i.e. by the number of protons) so that a nucleus may be
defined in terms of Ze where Ζ (the atomic number) is an integer
and e is the unit of charge. Because of the large difference in mass
between proton (or neutron) and electron, the atomic weight M
is nearly proportional to the total weight of protons and neutrons
in the nucleus; this weight is normally measured relative to the
oxygen atom whose atomic weight is normally taken as 16.
While the nuclei are composite structures the electrons are
identical elementary particles each carrying a negative charge e
(1-6 χ 10~19 amp sec = 480 χ IO -10 e.s.u.) and since the atom
is normally electrically neutral it follows that, for a nuclear charge
+Ze there must be Ζ electrons. It is, however, possible for an
atom to exist with a few electrons more or less than Z; this causes
an excess negative or positive charge and the atom is said to be
ionised, the resultant particle being an ion.
The electrons are grouped in specific and distinct energy levels
around the nucleus; these are referred to as shells. The electrons
in the outermost shell (the valence electons) are particularly
important in determining the chemical behaviour of the atom and
the type of bond which it forms with other atoms. A relatively
stable structure is produced when there are eight electrons in the
valence shell; this structure is obtained in the inert gases neon,
argon, etc. An element such as chlorine (7 valence electrons) will
readily "accept" one more to become a negative ion, the reverse is
true of metals such as sodium which readily loses its single
valence electron to become a positive ion.
2.3. INTERATOMIC FORCES
It seems reasonable to assume that any deformation process
involves some relative movement of the atoms or ions, so that any
resistance which the material offers to an applied force must
derive from the forces which hold the atoms together. We may
classify these forces into two principal groups
(a) Primary bonds which act between atoms or ions
CONSTITUTION 7
(b) Secondary bonds between molecules which are themselves
composed of atoms or ions bonded as in (a).
The difference between these types may be expressed in terms of
the energy content of the bond,| the energy of the primary bond
being about a hundred times greater than that of the secondary
bonds.
The simplest primary bond is the ionic (or electrovaleni) bond
in which an atom such as sodium gives up its single valence
electron to, say, chlorine, the resultant compound (sodium
chloride) being bound by electrostatic forces between the oppositely
charged ions. Another type of primary bond, covalent bonding,
involves a sharing of the valence electrons, diatomic gases such as
O2, H2, etc., are bonded in this way as are many organic com-
pounds. It will be apparent that, while ionic bonding is limited to
dissimilar atoms, no such restriction exists in the case of covalent
bonding.
The model for metallic bonding is not so easy to develop. A
simplified concept is that of a "super molecule" in which the
valence electrons are statistically shared by all the atoms and
move like a "cloud" or "gas" between the positive ions, the
bonding being due to the attractive force between the ions and the
electron cloudj (Fig. 2.1).
Secondary bonds involve several different mechanisms but may
generally be described as weak forces (van der Waals' forces)
which act between molecules whose primary bonding requirements
are already satisfied. In many cases the secondary bonds may be
ignored but there are some substances (e.g. the inert gases) in
t One way in which bond energies may be gauged is by measuring the heat
of sublimation since this involves a direct escape of atoms as a solid transforms
into a gas.
+ Although greatly simplified this model is adequate for considering the
mechanical properties of metals and it also helps in the understanding of other
typically metallic properties. Thus the high electrical and thermal conduc-
tivity of metals is associated with the mobility of the electrons which are free
to move in an electric field or when thermally activated. For a more complete
review of the "free electron theory" and of the more quantitatively satisfying
"band theory" see Ref. 6.
