MEC4119Z: MECHANICAL BEHAVIOUR OF MATERIALS

Chapter 1: Structure, Classification and Properties of Engineering Materials

Introduction

The mechanical behaviour, or performance, of an engineering component is intricately linked to the Process-
Structure-Property relationships where Performance forms the fourth apex of the tetrahedron as indicated in
Figure 1. Assuming that one has a component of fixed composition, then the performance of the component
will not only depend on its composition, but will be determined by the processing route for the material which
in turn will determine the material’s structure and ultimately its mechanical properties. Consequently, a single
material of fixed composition may give rise to a range of mechanical properties (and indeed chemical
properties) depending on its structure, which in turn is strongly influenced by the processing route. For
example, a medium carbon steel will have a particular combination of mechanical properties when it is in the
normalised condition (heat treatment process), but after being subjected to a joining process by fusion
welding, or to a forming process involving substantial plastic deformation, the mechanical properties will be
considerably modified. This is because processing will change the structure of the material.

Figure 1: Graphical description of the close relationships between performance of a component and
the Process – Structure – Property relations of engineering materials. (from Granta CES
Education slides).

Although mechanical properties are described in more detail later, it is pertinent to introduce some terms
now. The term stress refers to load or force per unit area. Strain refers to elongation or change in dimension
divided by original dimension. Application of stress on a material or component causes strain. If the strain
goes away after the applied stress (or load) is removed, then the strain is said to be elastic (small strains which
are fully recoverable). If the strain remains after the applied stress is removed then the strain is said to be
plastic (large strains that are irreversible – at least without further intervention). When the deformation is
elastic and stress and strain are linearly related, the slope of the stress-strain diagram is known as the elastic
or Young’s modulus. A level of stress needed to initiate plastic deformation is known as the yield strength.
The maximum percent deformation we can get is a measure of the ductility of a material. These concepts are
discussed further in a later chapter. Figure 2 shows the influence of heat treatment on the yield strength and
fracture toughness (both important mechanical properties for structural integrity) of a 0.35wt% carbon steel.
The heat treatments range from the normalised or annealed state to the extreme quench heat treated
condition. Notice the large increase in yield strength but very drastic reduction in fracture toughness in the

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quench (martensite) condition compared to the normalised or annealed condition. The mechanical properties
can be restored towards the normalised / annealed state by tempering the quenched (martensite) state at
progressively higher temperatures. Nowhere in this process chain has the composition of the steel been
changed; the mechanical properties have changed because the different process conditions (heat treatments
in this case) have altered the steel’s microstructure. This behaviour will be further explored in the chapter on
steels, their microstructure and properties.

Figure 2: Influence of heat treatment process on the mechanical properties of a 0.35wt.% carbon steel.
(from Granta CES Education slides).

So what is STRUCTURE of an engineering material?

The structure of an engineering material can be interrogated at a broad range of scales from the atomic state
to the macro-state where the latter generally represents features that you can see with the naked eye. Most
often we refer to the microstructure of an engineering material, which loosely defined means the structure of
the material that we can see with the aid of a microscope. Nowadays the latter definition can be somewhat
misleading because modern sophisticated electron microscopes can almost image at an atomic level.
Nevertheless, in most engineering situations the microstructure refers to features that range in size from
about 1 – 1000 microns which enables the polycrystalline structure of engineering materials to be captured.
Of course this does not mean that the features smaller than 1 micron are not important in controlling
mechanical properties, and observations at these higher magnification levels would be necessary to fully
understand the mechanical (and sometimes chemical) behaviour. A brief schematic comparison between the
atomic structure level and crystal structure (or microstructure) level is exhibited in Figure 3. Physical
properties, and the elastic modulus (generally referred to as a mechanical property) are controlled by the
atomic attributes whereas other mechanical properties such as strength, toughness and plastic elongation are
very sensitive to the material’s microstructure. But, as will be shown later, a major and fundamental aspect
of mechanical behaviour is directly influenced by the bonding character (it will be further illustrated that
bonding character is a key distinguishing feature relating to the many property differences between metallic
and non-metallic materials).

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Figure 3: Comparison of the material properties that are generally controlled at atomic level versus
microstructure level. (from Granta CES Education slides).

Notwithstanding the range in observation scales mentioned above, the fundamental differences in the
behaviour of the different classes of engineering materials starts at the atomic bonding level. In other words,
the way in which atoms are bound to one another to make up a *crystal lattice.

*crystal lattice: solid matter can exist in crystalline form or non-crystalline form where the latter is also
referred to as the amorphous or glassy state. Non-crystalline materials are either of the ceramic-type
(e.g. glass) or polymers. Most structural materials are crystalline, or more particularly, polycrystalline.

It goes without saying then that scientists and engineers are interested in the entire materials spectrum that
stretches from the atomic state (at length scales less than 10-10m) up to macro-length scales of greater than
10-3m. The diagram in Figure 4 displays this length scale spectrum and highlights the approach taken by
materials scientists versus materials and design engineers. In the former case, materials scientists generally
build on structure to develop materials that provide particular microstructure-property relationships and they
focus on understanding these relationships with a view to improving the properties. The eventual outcome is
that a “box” of engineering materials becomes available from which the design engineer can choose to meet
their requirements. In the engineering case, the development of materials is design driven. A design engineer
will develop a particular material property requirement to meet the design performance, and if a material
with these property attributes is not immediately available in the “box of engineering materials”, a material
may need to be tailored to meet the design requirement. This approach will work from the right to the left in
Figure 4 and will generally stop at the stage where the property requirement is met. In other words, the design
engineer may be less concerned as to why the particular property arises as long as they can achieve the desired
property, and thus one might say that the material is “engineered” to meet the design requirement – hence
the concept of engineered materials. This is all very well and it works most times, but properties can change
in service (as they often do in high temperature, high stress and chemically active environments) and the
engineering practitioner has to be able to deal with these problems to prevent failure. For example, it is the
engineer, and not the materials scientist, who has to ensure that a commercial aircraft is in a highly safe
condition to fly, or that power plant components will not unexpectedly fail and result in unplanned outages
which can sometimes rise to catastrophic levels.

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Figure 4: Illustration of different approaches to produce engineering materials (science-driven
approach) versus engineered materials (design-driven approach). (from Granta CES
Education slides).

Bonding in materials

Each atom is composed of a positively charged nucleus surrounded by a sufficient number of negatively
charged electrons so that the charges are balanced and the atom remains neutral in the equilibrium state.
The protons carry the positive charge and the neutrons, which approximately equal the number of protons,
contribute to the mass of the atom. The number of electrons in the neutral state identifies the atomic number
and the element of the atom. Many of the similarities and differences among the elements can be explained
by the respective atomic structures and Figure 5 demonstrates some examples of the structure of different
atoms by displaying the electron (or orbits) according to the Bohr model. There is a maximum number of
electrons that can be contained in a particular shell which is given by 2n2 where n is the shell (or orbit) number,
often labelled as K, L, M…where K has n=1 (Figure 5(a)). The number of electrons in the outermost shell,
relative to the maximum number of electrons allowed, determines to a large extent the atom’s chemical
affinity for other atoms. The outer shell electrons are called the valence electrons – atoms with full valence
shells are inert (e.g. helium) whereas atoms with incomplete valence shells are potentially chemically reactive.

(a)

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 (b)

Figure 5: (a) Atom structure as described by the Bohr model (e.g. K-shell, L-shell, etc.).
(https://www.thoughtco.com/basic-model-of-the-atom-603799). (b) Comparison of the Bohr
atom models for some atoms falling within the first 18 elements of the Periodic Table.

When atoms gain extra electrons or lose one or more of their electrons their charge will change to produce
negative ions (electronegative) or positive ions (electropositive) respectively. Clearly ions of opposite charge
can attract and form strongly bonded compounds. But this is not the only type of bonding that can occur in
materials. In fact the principal reason we have such a broad range in properties across the engineering
materials spectrum is due to the very different types of bonding that can occur between atoms.

Ionic bond:

In the ionic bond, the atoms of one element give up their outermost electron(s), which in turn are attracted
to the atoms of some other element to increase their electron count in the outer shell. In other words positive
ions and negative ions are formed which attract one another to form a strong ionic bond (see Figure 6(a)). An
example is the formation of table salt: Na = Na+ + 1e- (positive ion)
Cl + 1e- = Cl- (negative ion)
Na + Cl = Na+Cl-

This type of bonding is highly directional in that particular atoms attract to form adjacent positions in the
lattice structure, which in most cases is a regular crystalline lattice (see Figure 6 (b)). Any disruption of the
positions of the ions in the crystal lattice would cause an imbalance in the “like-unlike” charge attractions and
hence movement of the atoms in the lattice is not permitted. Since the outer shell electrons are strongly
associated with the particular ionic bond atom pair, this type of bond leads to low electrical conductivity (or
non-conductors in most cases). For the same reason of high bond directionality, ionically bonded materials
also have very low ductility which is a mechanical property that will be explained in more detail in the next
chapter.

(a) (b)

Figure 6: (a) Formation of ionic bond by transfer of valence electron (V) from one atom (positive ion)
to fill the valence shell of another atom (negative ion). (b) Arrangement of positive and
negative ions in a crystal lattice structure.

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Covalent bond:

Materials with covalent bonding are characterised by bonds that are formed by sharing valence electrons
among two or more atoms (see Figure 7(a)). For example, a silicon atom, which has a valence of four, obtains
eight electrons in its outer energy shell by sharing its electrons with four surrounding silicon atoms. Each
instance of sharing represents one covalent bond; thus, each silicon atom is bonded to four neighbouring
atoms by four covalent bonds (Figure 7(b)). In order for the covalent bonds to be formed, the silicon atoms
must be arranged so the bonds have a fixed directional relationship with each other. Covalent bonds are very
strong. As a result, covalently bonded materials are very strong and hard. For example, diamond (C), silicon
carbide (SiC), silicon nitride (Si3N4), and boron nitride (BN) all exhibit covalency. These materials exhibit very
high melting points, which means they could be useful for high-temperature applications. On the other hand,
the temperature resistance of these materials present challenges in their processing. In the same way as for
ionically bonded materials, covalently bonded materials have limited ductility because the bonds are highly
directional. The electrical conductivity of many covalently bonded materials is not high since the valence
electrons are locked in bonds between atoms and are not readily available for conduction.

(a) (b)

Figure 7: (a) Electron sharing to fill valence shell. (b) Si covalent bonds.

Metallic bond:

The metallic elements have more electropositive atoms that donate their valence electrons to form a “sea” of
electrons surrounding the atoms (see Figure 8(a)). Aluminium, for example, gives up its three valence
electrons, leaving behind a core consisting of the nucleus and inner electrons. Since three negatively charged
electrons are missing from this core, each aluminium atom has a positive charge of three. The valence
electrons move freely within the electron sea and become associated with several atom cores. If you contrast
this behaviour with that of ionic and covalent bonding it is easy to see that metallic bonds have very low
directionality (or non-directionality) compared to the high directionality associated with ionic and covalent
bonding. Nevertheless, metallic bonds are strong since the positively charged ion cores are held together by
mutual attraction to the electrons. Because their valence electrons are not fixed in any one position, most
pure metals are good electrical conductors. If a voltage is applied, the valence electrons move thereby causing
a current to flow when a circuit is completed.

Although metallic bonding has low directionality and valence electrons are free to roam randomly, metallic
materials are crystalline. In fact engineering metals and alloys are most often polycrystalline as a result of
multiple crystal nucleation during the liquid to solid transformation. The polycrystallinity nature of wrought
metals and metal alloys is further modified during the entire thermo-mechanical process as the macro-form
of the metal is changed from the cast state (usually a slab or ingot) to plate, sheet, rod, tube, etc forms. The
reader is referred back to the polygon in Figure 1 to highlight the relationship between process and structure
(and of course consequently properties and performance). The crystal forms of metals can be quite varied
(there are seven different crystal systems) but the most common are cubic and hexagonal. Examples of cubic

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crystal forms are indicated in Figure 8(b) and include the body-centred cubic form and the face-centred cubic
form. Both these cubic forms occur in iron and consequently account for the broad range of mechanical
properties that are obtainable in steels.

(a) (b)

Figure 8: (a) Sea of electrons surrounding positively charged atoms. (b) Examples of face-centre cubic
(FCC) and body-centred cubic (BCC) unit cells.

van der Waals bonding

van der Waals forces are secondary bonds which generally hold together molecules rather than represent the
bonding of the molecule itself. For example, with water (H2O) the hydrogen and oxygen are bonded together
very strongly by covalent bonding, but the individual H2O molecules are attracted to one another by the
secondary van der Waals forces (Figure 9(a)). When water is heated to its boiling point, the van der Waals
forces weaken completely and the H2O molecules separate from one another to become steam. But the H2O
molecule itself does not break up. In general, the simplified picture of van der Waals forces can be described
as follows:

If two electrical charges +q and -q are separated by a distance d, the dipole moment is defined as q x d. Atoms
on their own are electrically neutral (proton charge is balanced by electron charge). And the positive and
negative charges are centred such that there is no dipole moment. When a neutral atom is exposed to an
internal or external electric field the atom gets polarised (i.e. the centres of the negative and positive charges
are separated). This creates or induces a dipole moment (Figure 9(b)). In some molecules, the dipole moment
does not have to be induced – it exists by virtue of the direction bonds and the nature of atoms. These
molecules are known as polar molecules (e.g. as described for water above) and the attraction between the
oppositely charged dipoles is the van der Waals forces. As will be elaborated in the next section on
classification of materials, van der Waals forces play a very prominent role in distinguishing the properties of
polymeric materials, particularly with regard to bonding the long-chain molecules together.

(a) (b)

Figure 9: (a) Water molecules attracted as a result of dipole formation. (b) Attraction between atoms
(van der Waals forces) as a result of dipole formation.

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Classification of Materials

There are several different ways of classifying engineering materials but the traditional distinction of metals,
ceramics (including glasses and glass ceramics), polymers and composites remains the most practical
classification. Although this classification tends to exclude natural materials (e.g. the very important
traditional structural material wood), most engineering (or engineered) materials that follow the relationships
described in the tetragon in Figure 1 can be described as either metallic, ceramic, polymeric, or a combination
of these materials to form composite materials.

Metals and alloys

These include iron-based alloys (steels, cast irons), aluminium, titanium, nickel, copper, magnesium and zinc.
In most cases these metals are used in alloy form as a result of better structural strength, but pure forms of
copper, titanium, aluminium and zinc definitely play a strong role in a broad range of engineering applications.
In general metals have good electrical and thermal conductivity. Metals and alloys have relatively high
strength, high stiffness, ductility or formability, and shock resistance (toughness). They are particularly useful
for structural or load-bearing applications and are generally used in alloy form as mentioned above. The
spectrum of alloys for any particular metal type can be huge as in steels (iron-based) and aluminium alloys.
Furthermore, there are many metal alloys that can be heat treated to provide a broad range of mechanical
properties as indicated in the example of a medium carbon steel in Figure 2.

Ceramics and glasses

Ceramics can be defined as inorganic crystalline materials. Ceramics are probably the most natural materials
since most geological rocks and minerals can fit the ceramic material description (sedimentary rocks are a
special case that can probably be described as a ceramic composite material). Advanced ceramics are
materials made by refining naturally occurring ceramics and other special processes. Advanced ceramics are
used as tool bits, insulators (electrical and heat, e.g. heat shield tiles for space craft), computer chips, wear
resistance components in precision instruments, sensors amongst others. Some ceramics are used as barrier
coatings to protect metallic substrates in turbine engines from oxidation as well as wear resistant coatings in
the boiler environment in power plant. Ceramics are also used in consumer products such as paints (TiO2
pigment), fillers in plastics, and for industrial applications such as the catalyst support in exhaust converter
systems and the oxygen sensors used in motor cars. Traditional ceramics are used to make bricks, tableware,
sanitaryware, refractories (heat-resistant material), and abrasives. Generally, due to the presence of porosity
(small holes), ceramics do not conduct heat well and must be heated to very high temperatures before
melting. Ceramics are strong and hard, but also very brittle. The latter is their downfall from a structural point
of view and there is very little that can be done to change this situation. The brittleness of ceramics will be
contrasted with the ductile behaviour of metals in the chapter that deals with plastic deformation. Attempts
are made to limit the impact of the inherent brittle behaviour of ceramics by improving the processing route
for ceramics. Ceramic components are usually made by preparing fine powders which are converted into
different shapes by a process of pressing and sintering (high temperature diffusion bonding usually without
any melting or very limited melting). Modern processing techniques, which produce high purity very fine
powders, can make ceramics sufficiently resistant to fracture so that they can be used in some load-bearing
applications such as impellors in turbine engines and valves in internal combustion engines. The brittleness
of ceramic materials is mostly manifest in applications where components suffer tensile loading or high speed
impact damage. However, ceramics have exceptional strength under compression. This is why bricks and
concrete can support huge building structures. Consequently the challenge for civil and structural engineers
is to design such that the structures are in compression. In cases where there is a tensile stress component,
concrete is reinforced with steel to provide the tensile strength component that is necessary. However, it is
unlikely that anyone would fly in an aircraft that contains ceramic structural components!

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Glass is an amorphous (non-crystalline) material, which is often but not always, derived from molten silica. It
is included in the ceramic classification because it essentially fits the ceramic material description (inorganic,
non-metallic), but it is non-crystalline, and unlike ceramic materials in general, shapes are formed from the
molten (or non-solid) state. Glasses are used in houses, cars, computer, television and phone screens, and
many other applications. In fact nowadays glass is a major construction material as displayed by the facades
of many modern buildings. Glasses can also be thermally treated (tempered) to make them stronger and also
safer when they fracture (e.g. the side and rear windows on a motor car.

Polymers

Polymers are typically organic materials. They are produced using a process known as polymerisation.
Polymeric materials include rubber (special elastomers) and many types of adhesives. Many polymers have
very good electrical resistivity (good insulators). They also provide good thermal insulation. Although they
have low strength, their low density means that they have good strength-to-weight ratios. They are typically
not suitable for use at high temperatures but they generally have good resistance to corrosive chemicals (but
in many instances they can be readily degraded by sunlight unless sufficiently UV-stabilised). Polymers have
many applications ranging from bulletproof vests, data storage disks, ropes, and liquid crystal displays (LCDs)
to clothes and coffee cups. There are three principal types of polymers namely thermoplastics, thermosets
and elastomers. In all cases they are represented by long chain C-C atom arrangements where the carbon
atoms are covalently bonded, but the long chain molecules are bonded to one another in quite different ways.
In the case of thermoplastics, the long chain molecules are bonded to one another by the weaker van der
Waals forces (or hydrogen bonds). The strength of these cross-chain bonds are very temperature sensitive
and hence the thermoplastics can become very brittle at low temperatures, but are able to flow (soften
substantially) at higher temperatures. Thus the name thermoplastic. Thermosets, on the other hand, have
much stronger cross-link bonds (covalent bonds) between the long chain molecules which do not appreciably
weaken as temperature increases until the material degrades in totality (hence the name thermoset). The
more cross-link bonds that occur, the stronger and less ductile is the thermoset polymer. Consequently,
thermoset polymers are generally much stronger than thermoplastics and they cannot be moulded as easily
as the latter. Elastomers are somewhere between the two extremes of thermoplastics and thermosets. They
do contain a small number of strong cross-linked bonds (lightly cross-linked) but the van der Waals bond forces
between the chains are very low and hence the chains can easily slide past one another under stress, but not
permanently since, when the load is released, the few cross-link bonds restore the material to its original
shape. Consequently the deformation can be described as elastic – hence the name elastomer.

At a glance one can see in Figure 10(a) that the arrangement of atoms can be quite chaotic and hence polymers
are for most part non-crystalline. However, by controlling the alignment of long-chain molecules in the
polymer, some sense of order (and hence crystallinity) can be established. Figure 10(b) illustrates zones where
the chains are parallel-aligned (crystallite zone) and where they are randomly aligned in the same material.
Hence this polymer has both crystalline and non-crystalline regions which influences its properties. The more
crystalline a polymer is, the higher the strength. Crystallinity can be controlled by polymer processing and
hence once again the tetragon in Figure 1 can be used to describe the inter-relationships between structure-
process-properties-performance.

Although we readily identify the three generic classes of materials, namely metals, ceramics and polymers by
their appearance, and hence macro-features, they can also be readily distinguished by focusing only on the
type of bonding that makes up the materials, namely metallic bonding (metals), ionic or covalent bonding
(ceramics), and long C-C covalently bonded chain molecules (polymers). Consequently it is easy to understand
why the property range (mechanical, electrical, thermal and chemical) is so different for the different generic
classes of materials. This aspect will be reinforced further when the deformation behaviour of materials is
considered in more detail.

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 (a) (b)

Figure 10: (a) Successive bonding between carbon atoms (covalent) which make up the individual long-
chain molecules, and bonding between chains (either weak bonds or strong covalent bonds)
in polymers. (b) Schematic illustration of the arrangement of long-chain molecules in a
polymer that give rise to zones of crystallinity and amorphous regions.

Composite materials

The main idea in developing composites is to blend the properties of different materials. These are formed
from two or more materials, producing properties not found in any single material. Concrete, plywood, and
glass fibre reinforced polymer (or commonly known as fibreglass) are examples of composite materials.
Fibreglass is made by dispersing glass fibres in a polymer matrix. The glass fibres make the polymer stiffer,
without significantly increasing its density. With composites we can produce lightweight, strong, ductile, high
temperature-resistant materials or we can produce hard, yet shock-resistant, cutting tools that would
otherwise shatter. Advanced aircraft and aerospace vehicles rely on heavily on composites such as carbon-
fibre reinforced polymers. Sports equipment such as bicycles, golf clubs, tennis rackets, and the like also make
use of different kinds of composite materials that are light and stiff.

Properties of engineering materials

Metals have relatively high elastic moduli. They can be made strong by alloying and by mechanical and heat
treatment, but they remain ductile, allowing them to be formed by deformation processes. Certain high-
strength alloys (spring steel for instance) have ductilities as low as 2%, but even this is enough to ensure that
the material yields before it fractures and that fracture, when it occurs, is of a tough, ductile type. Partly
because of their ductility, metals are prey to fatigue; and of all the classes of material, they are the least
resistant to corrosion.

Ceramics and glasses, too, have high moduli, but, unlike metals, they are brittle. Their “strength” in tension
means the brittle fracture strength; in compression it is the brittle crushing strength, which is about fifteen
times larger. And because ceramics have no ductility, they have a low tolerance for stress concentrations (like
holes or cracks) or for high contact stresses (at clamping points, for instance). Ductile materials accommodate
stress concentrations by deforming in a way that redistributes the load more evenly; and because of this, they
can be used under static loads within a small margin of their yield strength. Ceramics and glasses cannot.
Brittle materials always have a wide scatter in strength and the strength itself depends on the volume of
material under load and the time for which it is applied. So ceramics are not as easy to design with as metals.
Despite this, they have attractive features. They are stiff, hard and abrasion-resistant (hence their use for

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bearings and cutting tools); they retain their strength to high temperature; and they are corrosion resistant.
They must be considered as an important class of engineering material.

Polymers and elastomers are at the other end of the spectrum. They have moduli that are low, roughly fifty
times less than those of metals, but they are strong – nearly as strong as metals. A consequence of this is that
elastic deflections can be large. They creep, even at room temperature, meaning that a polymer component
under load may, with time, acquire a permanent set. And their properties depend on temperature so that a
polymer, which is tough and flexible at 20ºC, may be brittle at the 4ºC of a household refrigerator, yet creep
rapidly at the 100ºC of boiling water. None have useful strength above 200ºC. If these aspects are allowed
for in design, the advantages of polymers can be exploited. And there are many. When combinations of
properties, such as strength per unit weight are important, polymers are as good as metals. They are easy to
shape: complicated parts performing several functions can be moulded from a polymer in a single operation.
The large elastic deflections allow the design of polymer components that snap together, making assembly
fast and cheap. And by actually sizing the mould and pre-colouring the polymer, no finishing operations are
needed. Polymers are corrosion resistant, and they have low coefficients of friction. Good design exploits
these properties.

Composites combine attractive properties of the other classes of materials while avoiding some of their
drawbacks. They are light, stiff and strong, and they can be tough. Most of the composites at present available
to the engineer have a polymer matrix – epoxy or polyester, usually – reinforced by fibres of glass, carbon or
Kevlar; we restrict ourselves to these. They cannot be used above 250ºC because the polymer matrix softens,
but at room temperature, their performance can be outstanding. Composite components are expensive and
they are relatively difficult to form and join. So despite their attractive properties, the designer will only use
them when the added performance justifies the added cost.

Definitions of Material Properties

Each material can be thought of as having a set of attributes: its properties. It is not a material, per se, that
the designer seeks; it is a specific combination of these attributes: a property profile. The material name is
the identifier for a particular property profile. The properties themselves are standard, and are divided into
several groups listed in Table 1. However, certain properties have different meanings depending on the type
of material that is being referenced. The word “strength” or symbol “σf”, for example, requires special
definition. For metals and polymers it is the yield strength, but since the range of materials includes those
which have been worked, the range spans initial yield to ultimate strength; for most practical purposes it is
the same in tension and compression. For brittle ceramics, it is the crushing strength in compression, not that
in tension which is about 15 times smaller. For elastomers, strength means the tear strength. For composites,
it is the tensile failure strength (the compressive strength can be less as a result of fibre buckling).

DENSITY

Density is the weight per unit volume (usual units: Mg/m3). We measure it today as Archimedes did: by
weighing in air and in a fluid of known density.

ELASTIC MODULUS

Defined as the “slope of the linear elastic part of the stress-strain curve” in Figure 11; the usual units are GPa
or GN/m2. Young’s modulus, E, describes tension or compression; the shear modulus, G, describes shear
loading; and the bulk modulus, K, describes the effect of hydrostatic pressure. Equations relating these various
parameters are listed below.

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 3G E E
E= ; G= ; K=
1 + G / 3K 2(1 + ν ) 3(1 − 2ν )

Poisson’s ratio, ν, is dimensionless: it is the negative of the ratio of the lateral strain to the axial strain during
axial loading. Typical values are ν ≈ 1/3; G ≈ 3/8E; K ≈ E.

Table 1: Design limiting material properties.

STRENGTH

For metals, we identify σf with 0.2% offset yield strength σy (Figure 11); that is, the stress at which the stress-
strain curve for axial loading deviates by a strain of 0.2% from the linear elastic line.

For polymers, σf is identified as the stress σy at which the stress-strain curve becomes markedly non-linear;
typically a strain of 1% (Figure 12). This may be caused by “shear-yielding”: the irreversible slipping of
molecular chains; or it may be caused by “crazing”: the formation of low density, crack-like volumes which
scatter light, making the polymer look white. Polymers are a little stronger (≈ 20%) in compression than in
tension.

Strength, for ceramics and glasses, depends strongly on the mode of loading (Figure 13). In tension,
“strength” means the fracture strength, σft. In compression it means the crushing strength σfc which
is much larger; typically

σfc ≈ 15 σft
We identify σf for a ceramic with the larger compressive strength σfc .

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The strength of a composite is best defined by a set deviation from linear elastic behaviour: 0.5% is
sometimes taken. Composites that contain fibres (and this includes natural composites like wood)
are a little weaker (up to 30%) in compression than tension because the fibres buckle. We will refer
to σf for composites as the tensile strength.

Figure 11: The stress-strain curve for a metal, showing the modulus E, the 0.2% yield strength, σy, and
the ultimate strength, σu.

Figure 12: Stress-strain curves for a polymer, below, at and above its glass transition temperature, Tg.

Figure 13: Stress-strain curves for a ceramic in tension and in compression. The compressive strength σc
is 10 to 15 times greater than the tensile strength σt. We identify σf with σc.

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SUMMARY: Strength depends on material class and on mode of loading.

MODULUS OF RUPTURE

When the material is difficult to grip (as is a ceramic), its strength can be measured in bending. The modulus
of rupture or MOR (usual units MPa or MN/m2) is the maximum surface stress in a bent beam at the instant of
failure (Figure 14). One might expect this to be exactly the same as the strength measured in tension, but for
ceramics it is larger (by a factor of about 1.3) because the volume subjected to this maximum stress is small
and the probability of a large flaw lying in it is also small; in simple tension all the flaws see the maximum
stress.

Figure 14: The modulus of rupture (MOR) is the surface stress at failure in bending. It is equal to, or
slightly larger than the failure stress in tension.

ULTIMATE STRENGTH

The ultimate (tensile) strength σu (usual units MPa) is the nominal stress at which a round bar of the material,
loaded in tension, separates (Figure 11). For brittle solids – ceramics, glasses and brittle polymers – it is the
same as the failure strength in tension. For metals, ductile polymers and most composites, it is larger than
the strength σf, by a factor of between 1.1 and 3 because of work hardening or (in the case of composites)
load transfer to the reinforcement.

HARDNESS

The hardness, H, of a material (usual units MPa) is a crude measure of its strength. It is measured by pressing
a pointed diamond or hardened steel ball into the surface of the material. The hardness is defined as the
indentor force divided by the projected area of the indent. It is related to the quantity we have defined as σf
by

H ≅ 3 σf

TOUGHNESS

The toughness, Gc (usual units kJ/m2), and the fracture toughness, Kc (usual units MPa.m1/2), measure the
resistance of the material to the propagation of a crack. The fracture toughness is measured by loading a
sample containing a deliberately introduced crack of length 2c (Figure 15), recording the tensile stress σc at
which the crack propagates. The quantity Kc is then calculated from

Kc = Y σc πc

14
and the toughness from

K c2
Gc =
E (1 + υ )

where Y is a geometric factor, near unity, which depends on details of the sample geometry, and E and υ are
Young’s modulus and Poisson’s ratio respectively. Measured in this way Kc and Gc have well defined values
for brittle materials (ceramics, glasses, and many polymers). In ductile materials a plastic zone develops at
the crack tip, introducing new features into the way in which cracks propagate which necessitate more
involved characterisation. Values for Kc and Gc are, nonetheless, cited, and are useful as a way of ranking
materials.

Figure 15: The fracture toughness, Kc, measures the resistance to the propagation of a crack. The failure
strength of a brittle solid containing a crack of length 2c is σf = YKc (πc)1/2.

FATIGUE

Cyclic loading not only dissipates energy; it can also cause a crack to nucleate and grow, culminating in fatigue
failure. For many materials there exists a fatigue limit: a stress amplitude below which fracture does not occur,
or occurs only after a very large number (>108) of cycles. This information is captured by the fatigue ratio, f (a
dimensionless quantity). It is the ratio of the fatigue limit to the yield strength, σf.

WEAR, OXIDATION, and CORROSION

Wear, oxidation and corrosion are harder to quantify, partly because they are surface, not bulk, phenomena,
and partly because they involve interactions between two materials, not just the properties of one. When
solids slide (Figure 16) the volume of material lost from one surface, per unit distance slid, is called the wear
rate, W. The wear resistance of the surface is characterised by the Archard wear constant, KA (units MPa-1)
defined by the equation

W
= KA P
A
where A is the area of the surface and P the normal pressure pressing them together. Data for KA are
available, but must be interpreted as the property of the sliding couple, not of just one member of it.

15
Figure 16: Wear is the loss of material from surfaces when they slide. The wear resistance is measured
by the Archard wear constant KA. S is the sliding distance.

Dry corrosion is the chemical reaction of a solid surface with dry gases. Typically, a metal, M, reacts with
oxygen to give a surface layer of the oxide MO2:

M + O2 → MO2

Wet corrosion – corrosion in water, brine, acids or alkalis – is much more complicated and cannot be captured
by rate equations with simple constants. It is more usual to catalogue corrosion resistance by a simple scale
such as A (very good) to E (very bad).

-oo0oo-

16
 MEC4119Z: MECHANICAL BEHAVIOUR OF MATERIALS
Chapter 2: Part A – Hardness Testing

Hardness has several connotations that include resistance to indentation, resistance to

scratching, resistance to cutting, brittleness, wear resistance, and so forth. In its most general
sense, hardness implies resistance to deformation. As applied to metals, hardness is a
measure of resistance to plastic, i.e., permanent deformation as would be determined in a
uniaxial tensile test. It is not surprising, therefore, that hardness can be correlated with both
yield strength and tensile strength. Hard materials exhibit high strengths, while soft materials
have low strengths.

For the most part, hardness testing involves static indentation, although the mineralogists
often employ qualitative scratch testing. The latter involves ranking hardness on a scale of 1-
10 as defined by the Mohs scale of hardness. For example, if an unknown mineral scratches
quartz, but cannot scratch topaz, then its hardness is between 7 and 8 on the Mohs scale. Bulk
hardness testing of engineering materials, on the other hand, is much more quantitative and
several static tests have been developed over the years and include the popular Brinell,
Rockwell and Vickers methods.

How does hardness relate to the Stress-Strain curve?

When a cylindrically shaped metal specimen is loaded uniaxially in tension, the resultant
stress-strain curve is initially linear. This represents the elastic property of the metal and the
slope of the stress-strain curve gives the elastic modulus. As the stress is increased, a point is
reached where the curve deviates from linearity. This point coincides with plastic
(permanent) deformation of the metal and is known as the yield point (σy). Increasing the
stress beyond this point leads to further plastic deformation (plastic strain), but the stress level
required to increase strain generally increases. Thus we say that the metal work-hardens, and
such deformation increases the strength and hardness of the material in the deformed region.

A material that can be plastically deformed in the uniaxial tension test will not deform
plastically under a hydrostatic pressure, even if the applied load significantly exceeds the
material’s yield strength. Plastic deformation requires either shear-stress or shear-strain
conditions. This has important consequences in indentation hardness because about two-
thirds of the mean contact pressure is hydrostatic pressure. Only about one-third of the
applied pressure produces plastic flow. Thus, the mean pressure P between the metal and the
indentor is three times the flow stress (σy):
P ≈ 3σy

The hydrostatic pressure condition developed at

the root of the indentation is easily understood
by observing what happens during the
indentation of modelling clay (Figure 1). The
flow pattern demonstrates that the material
under the indentation is constrained from
flowing by the material adjacent and much
below the indented region.
Figure 1: Deformed grid pattern on a
meridianal plane in a Brinell hardness 1
test – modelling clay.
When a material is loaded by a point indentor, the flow in the centre is downward and to the
left and right, as indicated by the slip-line field solution in Figure 2. Actual hardness
indentations demonstrate this effect in Figure 3. The indentations have been imaged by
interference microscopy, and the uniform fringes within the indentations indicate the depth of
the indents. The wavy fringes on the surface adjacent to the indents demonstrate the uneven
surface that is produced as a result of the lateral/upward flow of material from beneath the
indentor.

Figure 2: Slip-line filed solution for pointed indentor.

Flow in centre area is downward and to left and right, Figure 3: Wavy interference lines
as indicated by arrows in adjoining area. illustrate the flow of material on the
surface adjacent to the indentations.

Example 1: Approximation of tensile strength of martensitic stainless steel

The hardness (HV30) was measured for a martensitic stainless steel in the as-quenched
condition and the quench and temper condition:
As-quenched hardness: 444HV30 (4351 MPa)
Quench and temper: 295HV30 (2891 MPa)
According to the calculation of the HV number, the units of the hardness number are kg/mm2.
In order to convert these values to MPa (usual units of strength for metals), we multiply by
9.8 ms-2 (gravity). These values are given in parentheses above. From our relationship of
hardness (pressure) equal to three times tensile strength, the calculated tensile strengths are:
As-quenched strength: 1450 MPa
Quench and temper: 963 MPa
The actual measured tensile strengths from uniaxial tensile tests were determined as:
As-quenched:
Yield strength = 976 MPa Ultimate tensile strength = 1309 MPa
Quench and temper:
Yield strength = 861 MPa Ultimate tensile strength = 937 MPa
Comment:
Although we say that the mean pressure P between the metal and the indentor is three times
the flow stress, we know that the yield stress (or more appropriately, the initial flow stress)
continues to rise as the metal is progressively deformed. The maximum flow stress measured
in a uniaxial tensile test is the ultimate tensile strength (or UTS). It is therefore not surprising
that calculated strength form the hardness measurements is greater than the yield stress
measured during the tensile test. In fact, inspection of the results demonstrates that the
calculated strength value (from the HV measurement) more closely correlates with the
measured ultimate tensile strength.

2
Types of Static Hardness Tests

A ball, cone, or pyramid significantly harder than the specimen is pressed into the surface
under a known load. The load per unit of contact surface area or projected area is the measure
of hardness, as in the Brinell, Vickers or Knoop tests. Alternatively, the depth of the partly
recovered impression can be measured, as in the Rockwell test.

BRINELL TEST

In this test a ball of known diameter is pressed into the flat, smooth specimen surface under
set loading conditions (L in kilograms-force). The Brinell hardness number (HB) is
calculated on the average of two measurements of the impression diameter d made at right
angles to each other using the following formula in which D is the ball diameter:

2L
HB = 1
πD 2 {1 − [1 − (d / D) 2 ] 2 }
In practice, the HB value is determined by consulting
tables supplied with the machine that give the HB
values for various diameters for each possible load.
Depending on the type of test machine available, the
operator has to make a decision regarding the choice of
load and ball diameter. Because HBs vary noticeably
as the load is changed, ASTM Specification E10
recommends use of standard loads for a given ball
diameter for metals of different hardnesses. The most
common procedure for large testing machines uses a
10-mm diameter hardened steel ball with a load of
3000kgf applied for 10 to 15 s. The test load is chosen
so that the impression diameter is in the range of 2.5 to
6.0 mm, i.e., 25 to 60 percent of the diameter of the
10-mm ball.
The recommended standard loads according to ASTM
Specification E10, for use with the 10-mm diameter
ball, are listed in Table 1. The table illustrates that the
load is adjusted according to the hardness range of the
material when a fixed ball diameter is employed. If
the same sample is tested using the three standard
loads (3000, 1500, and 500 kgf), one observes that the
HB value increases as the applied load increases. To
circumvent this problem, it is recommended that the
L/D2 ratio be held constant for a given material.
Because of the variations in HB that can occur under
non-standard test conditions, it is recommended that
the nature of these conditions be stated when reporting
such data. For example, if a hardness of 70 HB was
obtained using a 10-mm diameter ball, a load of 1500
kgf, and a load duration of 60 s, the hardness results Figure 4: (a) Schematic of the principle
of the Brinell indentation process. (b)
would be expressed as 70 HB 10/1500/60. Brinell indentation with measuring scale
in millimetres.
3
Table 1: Standard test loads for the Brinell test

Ball diameter, mm Load, kgf Recommended range, HB

10 3000 96 - 600
10 1500 48 - 300
10 500 16 - 100

Example 2: Selection of measuring parameters for bench-top hardness tester

The choice of load and ball diameter to be used in a Brinell test is determined by two factors:
(i) the value of the L/D2 ratio
(ii) the size of indentation that will provide optimum accuracy.
The same value of L/D2 will, in principle, give the same hardness value for different loads and
the value to be used will depend on the nature and hardness of the material to be tested. Four
standard values of L/D2 have been adopted, i.e., 30, 10, 5 and 1.
The value of the L/D2 ratio to be used should be stated in the specification for the material.
For guidance, appropriate values for representative materials are given in Table A below.
Table A: Values of L/D2 ratios for representative materials

Representative materials Approximate L/D2 Ball diameter Load

Brinell hardness ratio (mm) (kgf)
Steels and cast iron Above 100 30 2.5 188
Copper and aluminium alloys 30 to 200 10 5 250
Aluminium 15 to 100 5 5 125
Lead, tin and their alloys 3 to 20 1 10 100

VICKERS TEST

The Brinell test is not recommended for materials above 630 HB. The use of a pyramidal-
shaped indentor made from diamond was introduced in order to test materials too hard for the
Brinell test. The Vickers test involves the use of a square-based pyramid with an angle of
136° between opposite faces in order to obtain hardness numbers similar in magnitude to
Brinell numbers.

An outstanding advantage of the Vickers diamond

pyramid hardness test is that one continuous scale
is used to test all materials regardless of their
hardness. Because a geometrically similar
impression is made, irrespective of the applied
load, the HV value is reasonably constant over the
load range normally applied (except for very low
loads in microhardness testing). The ability to use
a wide range of loads and still obtain the same
hardness number makes the test useful on materials
of different thicknesses. In the standard Vickers
test, loads from 1 to 120 kgf have been employed.
However, loads above 30 kgf are infrequently
used, and the most common load is 10 kgf.
Figure 5: Schematic illustrating the 4
Vickers diamond pyramid indentor and the
indentation produced.
In performing the test, the load must be applied smoothly without impact and held in contact
for 10 to 15 s. The load should be correct to better than 1 percent. After removal of the load,
both impression diagonals are measured, and the average value is used to calculate HV by the
following equation:

2 L. sin(α / 2) 1.8544 L
HV = =
d2 d2
where d = mean diagonal, mm
L = load, kgf
α = face angle (136°)

In nearly all cases, HV is determined by referring to tables of HV for each possible load and
diagonal measurement. There are samples in which the measured diagonal is smaller than the
data in the tables, and a calculation must be employed. Most equipment manufacturers supply
a set of tables with the instrument; these tables are also found in ASTM Specification E92.

ROCKWELL TEST

The Rockwell test is based on measurement of an incremental change in penetration depth,

under an incremental change in load. The depth measurement is automatically indicated on a
calibrated dial that has units of hardness rather than depth. Thus, the test is quite rapid, and
the impression measurement errors and tedium are eliminated. However, the hardness scales
are completely arbitrary and do not have the physical meaning of the hardness values from the
Brinell and Vickers tests.

In the Rockwell test, a 10-kgf minor load is used to press the indentor into the sample and
establish a zero point for the test. Then the major load, 60, 100, or 150 kgf, is applied and
removed. The hardness is indicated on the dial gauge with the minor load still applied. The
hardness is an inverse function of the penetration depth due to the major load.

Figure 6: Principle of the Rockwell test.

5
There are several different test scales employed in the Rockwell test, but by far the most
common scales are the Rockwell C and Rockwell B scales. The Rockwell C test makes use
of a 120° conical diamond indentor with an applied load of 150 kgf. This test is used for
materials with hardness above 100 HRB and is applicable for most steels, hard irons, case
hardened steels, and so forth. The Rockwell B test employs a 1/16 inch steel ball indentor
with an applied load of 100 kgf. This test is used for materials such as aluminium, copper,
soft steels, and malleable iron.

Figure 7: Schematic of Rockwell testing machine

Some considerations when performing hardness tests

1. Wherever possible, a smooth clean surface should be prepared prior to indentation.

This is usually accomplished by grinding with fine emery paper. In the case of Brinell
or Vickers testing, where it is necessary to measure diameters/diagonals, a highly
polished surface will improve the accuracy of the result.
2. The sample should be well supported and the surface should be flat. Inclined surfaces
will produce uneven indentation and lead to erroneous measurement (see Figure 8).
3. Like any form of testing, the average of multiple indentations will improve the
accuracy of the result. Usually a minimum of five indentations should be performed.
6
 Caution should be exercised to avoid overlap
of the deformed regions associated with an
indentation. A distance of at least three times
the diameter/diagonal dimension should
separate the indentations. If the deformed
regions do overlap, then the hardness will
appear larger than the real value.
Figure 8: Inclined surface produces
uneven indentations (Vickers hardness).

4. The indentation load should be carefully assessed in relation to the thickness of the
test specimen. A general rule of thumb is that the total specimen thickness below the
indentation should be 10 times the indentation depth. An appropriate load must be
selected to maintain this condition. Figure 9 illustrates this situation.

(a) (b)
Figure 9: Cross-section of actual Brinell hardness indentations. (a) Incorrect load applied in relation to
specimen thickness. The deformation zone has spread to the bottom edge of the specimen, and hence
plastic flow is further constrained. In this case the measured hardness will be greater than the actual
hardness. (b) Correct choice of load. The deformation zone is well within the thickness of the specimen.

MICROHARDNESS TESTING

The term microhardness has been widely employed in

the literature to describe the hardness testing of
materials with low applied loads. This process is
generally carried out when the volume of material that
is to be indented is microscopic in size. For example, it
may be necessary to establish the individual phase
hardness in a two-phase microstructure. This type of
work is mostly carried out at a research level, where it is
important to characterise the different components of a
microstructure. An example of the hardness
measurement of the individual grains in steel is shown

in Figure 10. However, there are other reasons why the Figure 10: Microhardness indentations
microhardness technique is very important. It may be in steel. The different sized indentations
necessary to determine the hardness of thin foil, and as indicate variable hardness of individual
has been shown in the aforementioned section, the load grains. The diagonals of the largest
indentation measure about 30 microns.
7
must be carefully selected according the thickness of the
test specimen. This may require loads less than 1 kgf.
Consequently, a very small indentation is produced,
which requires reasonably high magnification for
measurement (usually a 20x or 40x objective lens).
Another reason for performing microhardness
measurements relates to the measurement of hardness as
function of distance. For example, it may be necessary to
determine the depth of casehardening in steel. Since the
case depth may only be the order of 200 – 600 microns,
the indentations need to be small. An example in Figure
11 demonstrates the correlation of Knoop hardness
readings with indentations on the cross section of a Figure 11: Correlation of Knoop
carburised case. hardness readings with indentations on
a cross section of a carburised case.

Microhardness measurements are carried out using

mostly Vickers diamond indentors, but the Knoop
diamond indentor is also employed. The latter
indentor is presented in Figure 12. The indentor
has a long and a short axis and is very useful for
determining anisotropy in hardness, particularly
when the hardness values differ by very small
amounts.

Figure 12: Pyramidal Knoop

indentor and resulting indentation in
the workpiece.

Measurement of the hardness of Polymeric materials

The hardness of polymeric materials is most often determined by using a durometer. This is a
hand-held instrument where application pressure is applied manually (Figure 13). Hardness
tests on polymers are conducted according to Shore A and Shore D methods (DIN 53505 or
ASTM D2040). The difference between Shore A and D lies in the geometry of the test needle

Figure 13: Round- and

quadrant-style durometers.
Note the indentor protruding
from the underside, which is
manually pushed into the
polymer by applying pressure
on the knurled knob at the top.
The penetration is indicated on
the dial in arbitrary units from 0
to 100.

8
(probe), as shown in Figure 14. Shore A and Shore D
methods are used for soft and hard materials
respectively. The Shore hardness units range from 0
to 100 and are dimensionless. Another instrument is
the Shore scleroscope, which measures the degree of
rebound of a diamond-tipped hammer dropped onto
the surface of the component from a known height.
This technique is used for a wide range in materials
including soft polymers, and brittle metals and
ceramics that cannot be indented as in the static
indentation tests. The hardness of polymers can also
be determined by the conventional static indentation
methods, but obviously careful selection of load is
necessary. However, the latter approach is generally
not very accurate since most polymers undergo visco-
elastic deformation. Figure 14: Shore A and D needle geometry.

An important approach to the measurement of the hardness of polymers is the actual

quantification of scratch hardness. Several instruments are available, and the principle
involves moving an indentor across the surface of the polymer under a set load. The width of
the scratch is measured and the hardness value is related to the inverse square of the scratch
width.

Bibliography

GF vander Voort, 1984, Metallography: Principles and practice. McGraw Hill.

9
 HARDNESS CONVERSION TABLES

Hardness conversion chart for steels

10
11
 MEC4119Z: MECHANICAL BEHAVIOUR OF MATERIALS
Chapter 2: Part B – Impact Testing

Under an increasing tensile stress a material will, at first, deform in a recoverable way. Then
at some point it will either yield, that is it will undergo plastic flow, or it will fracture.
Fracture occurs by the rapid propagation of a crack through the material. Which occurs all
depends on what happens at stress concentrations such as crack tips. Impact test conditions
have been chosen to represent those most severe relative to the potential for fracture, namely,
(1) deformation at a relatively low temperature, (2) a high strain rate (i.e., rate of
deformation), and (3) a triaxial stress state that is introduced by the presence of a notch.

Impact Testing Techniques

Two standardised tests, the Charpy and Izod, were designed to measure impact energy,
sometimes also termed notch toughness. For both Charpy and Izod, the specimen is in the
shape of a bar of square cross section, into which a V-notch is machined (Figure 1). The Izod
test specimen can also be a round bar.

Figure 1: Specimen and loading configurations for (a) Charpy V-notch and (b) Izod tests (see
ASTM E23).

The load is applied as an impact blow from a weighted pendulum hammer that is released
from a cocked position at a fixed height h. The specimen is positioned at the base of the
instrument. Upon release, the hammer mounted on the pendulum strikes and fractures the
specimen at the notch, which acts as a point of stress concentration for this high velocity
impact blow. The pendulum continues its swing, rising to a maximum height h', which is
lower than h (Figure 2). The energy absorption, computed from the difference between h and
h', is a measure of the impact energy. The primary difference between the Charpy and Izod
techniques lies in the manner of specimen support. Universal impact testing machines are
constructed in such a way that they can be configured for both Charpy and Izod tests (Figure
3).

Figure 3: Universal impact testing

Figure 2: A schematic drawing of an impact machine that can be configured for
testing apparatus. (See text for explanation). Charpy and Izod testing.

Both plane strain fracture toughness and these impact tests determine the fracture properties
of materials. The former are quantitative in nature, in that a specific property of the material
is determined (i.e., KIC). The results of the impact tests, on the other hand, are more
qualitative and are of little use for design purposes. Impact energies are of interest mainly in
a relative sense and for making comparisons – absolute values are of little significance.
Impact tests may therefore be used as a quality control on a production plant, or by
manufacturers in order to test the “quality” of the supplied product. Steel producers will often
specify minimum impact energy for their product. Figure 4 illustrates the fracture appearance
for a grey cast iron, and for a 0.4 wt% carbon steel heat treated in two different conditions.
The appearance of the fracture surface alone can provide an indication of the fracture
behaviour of the metal. Flat, facetted fracture surfaces indicate low energy impact (brittle
failure), whereas fracture surfaces exhibiting shear lips indicate much higher impact energies
(ductile behaviour).

Figure 4: Broken Charpy specimens, left to right, of

grey cast iron, AISI 4140 steel tempered to σuts ≈
1550 MPa, and the same steel at σuts ≈ 950 MPa.
Since the fracture behaviour of materials, and especially steels, is generally affected by
temperature changes, one of the primary functions of Charpy and Izod tests is to determine
whether or not a material experiences a ductile-to-brittle transition with decreasing
temperature and, if so, the range of temperatures over which it occurs. The ductile-to-brittle
transition is related to the temperature dependence of the measured impact energy absorption.
Testing the same specimen over a range in temperatures performs the determination of the
DBTT. The impact energy is plotted against test temperature, and the transition temperature
is identified from the shape of the curve. Figure 5 demonstrates the variation in Charpy V-
notch impact energy with temperature for normalised plain carbon steels of various carbon
contents. The DBTT is clearly defined for the 0.11 wt% carbon steel as there is a distinct
shift from a lower shelf energy of about 5 J (joules), to an upper shelf energy of just more than
200 J. The DBTT is quoted as the temperature corresponding to an impact energy value
midway between the lower shelf and upper shelf energies. In this case it is approximately -
45°C. [ASIDE: The scale on the impact tester converts the force and distance travelled by
the impact head to energy values, either as kgf-m, or a joules. The impact energy value is
sometimes quoted as J/mm2, and this simply takes into account the cross sectional area of the
notched specimen. Presenting the energy in this form allows the comparison of standard size
specimens with sub-size specimens. However, caution should be exercised in this regard
since different specimen sizes imply different geometric configurations. The geometry will
affect the triaxial stress at the notch and therefore change the fracture behaviour of the
metal.]

Figure 5: Variation in Charpy V-notch impact energy with temperature for normalised plain carbon steels of
various carbon contents. It is interesting to note that the DBTT increases with increasing carbon level, and
correspondingly the upper shelf energy decreases.
The temperature-transition behaviour is of some engineering significance as it aids in
comparing materials for use at various temperatures. In general, a material should not be
severely loaded at temperatures where it has a low impact energy. However, some caution is
needed in attaching too much significance to the exact position of the temperature transition.
This is because the transition shifts even for different types of impact tests, and more
particularly, for different sub-size specimen tests. The situation in a particular engineering
application represents another set of circumstances and therefore another curve, the position
of which cannot be determined with any degree of assurance.

Specimen orientation

Most wrought metallic materials are anisotropic in mechanical behaviour as a consequence of

directionality in the microstructure. The most visible directionality in the microstructure is
the grain shape. During rolling, forging, extrusion, drawing, and so forth, the grains become
elongated in the microstructure. Elongated grain structures are also produced during
solidification in a casting. Additional anisotropy is introduced by crystallographic preferred
orientations (texture). Strong textures will promote strong anisotropy in plastic flow, and
consequently affect fracture mode. In view of anticipated directionality in mechanical
behaviour, it is important to report the
specimen orientation when quoting impact
energy values. An example of orientation
labelling for a rolled metal is presented in
Figure 6. Specimens notched in the through-
thickness direction (T-L or L-T) generally
have the lowest impact energy values.
Obviously impact testing is a good way of
determining the extent of anisotropy, and in
this case specimens would be tested in all
three orientations. An example of the
anisotropy exhibited by a 12 wt% chromium Figure 6: Specimen orientation according to
steel is shown in Figure 7. The fractured geometry of rolled plate.
specimen on the left represents the L-S orientation, whereas the specimen on the right
represents the L-T orientation. Examination of the fracture surface clearly distinguishes a
difference in fracture mode. The impact energy for the L-T orientation is 65 J, whereas the
impact energy for the L-S orientation is in excess of 220 J. In fact the impact hammer
bounced back in this case!

Figure 7: Fractured Charpy specimens of 12

wt% chromium steel. The specimen on the
left has an L-S orientation and the specimen
on the right has an L-T orientation.
Drop weight impact tester

Although polymers can be impact tested in the same way as metals, drop weight testing is
also employed. Essentially this is a low velocity impact test technique where the incident
impact energy can be controlled by varying the drop height. This type of testing generally
refers to un-notched test specimens. There are two basic procedures: either drop the product
(e.g. a barrel full of liquid or a crate full of bottles) onto a rigid surface, or drop a mass onto
the plastics product (e.g. a pipe). The latter instrument is shown schematically in Figure 8.
The energy or test speed (or both) can be varied between individual drops by adjusting the
mass or the drop height. Results are usually expressed as the impact energy needed to give
50% failures at a given test temperature. Drop testing examines the behaviour of a plastic
product, including design and processing; results are therefore specific, but can involve the
testing of many samples and much more material compared to a pendulum test.

Apart from simply measuring absorbed impact

energy, impact testers can also be instrumented
to perform much more sophisticated impact
analysis. The apparatus is instrumented in
order that the penetration resistance force
history and impact velocity can be measured by
a data acquisition system for further analysis.
The rapid monitoring of load and deflection
during the impact event allows the impact
behaviour to be more quantitatively analysed
from the load-deflection curve. An example of
a load-deflection curve is presented in Figure
9. In this case the total plastic deformation
(Xtotal) is accurately recorded and includes the
energy expended in causing the flat plate to
“dish” as well as the actual indentation (Figure
10).

Figure 8: Schematic of an instrumented drop

weight tower. The energy of the impacting
hammer can be varied by altering the weight of
the hammer (tup), or by varying the initial height
of the hammer. Typically a tower may be about 5
metres high.
 Figure 9: A load-deflection curve indicating the total plastic deformation as measured by an
instrumented impact testing apparatus.

Figure 10: A sectional profile of the dishing and indentation deformation due to a rebound
impact. The total deformation (Xtotal) is measured from the load-deflection curve presented
in Figure 9.

Example: The influence of impact velocity on commercial purity aluminium

To test the influence of impact velocity on the impact response of aluminium, a range of
velocities were employed, namely 3.9, 5.2, 6.1 and 6.9 m.s-1. The load-deflection and energy-
deflection curves for the different impact velocities are presented in Figure 11. The
corresponding sectional profile for each test is presented in Figure 12. In this case the load-
deflection curves are not unlike a tensile test stress-strain curve. For the aluminium, impact
velocity has no influence on the yield point that occurs at approximately 2000 N, and the
shape of the load-deflection curves is similar in all instances. This demonstrates the strain
rate insensitivity of aluminium [this is attributed to the close-packed face centred cubic
structure of aluminium]. It is interesting that the extent of “dishing” is quite similar in all
cases.

3.9m/s
5.2m/s
Force and Energy vs. Displacement 6.05m/s
6.85m/s
changing impact velocity
crosshead mass 4.6kg
9000 120

8000
100
7000

6000 80
Force

Energy
5000
(N)

60

(J)
4000

3000 40

2000
20
1000

0 0

0 0.005 0.01 0.015 0.02 0.025

Displacement (m)
Figure 11: The load-deflection and energy-deflection curves illustrating the effect of impact velocity
on the impact response of aluminium as measured by an instrumented impact tester.

Figure 12: Sectional profiles of the impacted plates for the changing impact velocity tests. From top to
bottom, the impact velocities are 6.9, 5.2 and 3.9 m.s-1.
 MEC4119Z: MECHANICAL BEHAVIOUR OF MATERIALS
Chapter 2: Part C – Tensile Testing

The engineering tension test is widely used to provide design information on the strength of
materials and as an acceptance test for the specification of materials. In this test procedure, a
specimen is subjected to a continually increasing uniaxial tensile load (force), while
simultaneous observations are made of the elongation of the specimen. In its most basic
form, the data is output to produce a load-extension curve.

Engineering stress-strain curve

In the conventional engineering tension test, an engineering stress-strain curve is constructed

from the load-extension measurements made on the test specimen (Figure 1). The word
“engineering” is emphasised here, as it will be shown later that further calculation is required
to convert the output to a true stress-true strain relationship. The engineering stress, σe (or
sometimes, s), used in this stress-strain curve is the average longitudinal stress in the tensile
specimen. It is obtained by dividing the load, L, by the original cross sectional area of the test
specimen, A0.:

L The units for load are generally Newtons or kilo-

σe = Newtons (N or kN). The units for stress are thus
A0
N/mm2 or kN/mm2. Units expressed in N/mm2 are
equivalent to mega-Pascals (MPa). The latter unit is
mostly used to express the strength of engineering
materials.

The strain, εe, used for the engineering stress-strain curve is the average linear strain, which is
obtained by dividing the elongation of the specimen gauge length, δ, by its original gauge
length, 0 :

δ ∆  −  0 Elongation is generally represented as a

εe = = = percentage length change of the original gauge
0 0 0 length. The units for strain, however, are
dimensionless since strain is derived by dividing
change in length by initial length.

Figure 1: Engineering stress-

strain curve.
 Created by RD Knutsen, Centre for Materials Engineering, UCT / Page 2

Assessment of mechanical properties from the engineering stress-strain curve

The most frequently specified mechanical properties include tensile strength (or ultimate
tensile strength, UTS), yield strength, maximum elongation, and elastic (or Young’s)
modulus. Other properties may also include percentage reduction in area and fracture stress.

Tensile strength

The ultimate tensile strength (UTS) is the maximum load divided by the original cross
sectional area of the specimen (Lmax/A0). The UTS is the value most frequently quoted from
the results of a tension test and is often used in specifications, although its value lacks
significance. Before the UTS is reached, a ductile material has already undergone extensive
plastic deformation. From the point of view of a component in service, it would have deemed
to fail long before it reaches the UTS, since it would have already undergone a substantial
shape change. The UTS is easily calculated from the data output and this may explain its
popular use.

Yield strength

The yield strength represents the stress required to initiate permanent plastic deformation in
the material. It represents the transition between linear elastic behaviour and non-linear
plastic behaviour, and is the point on the stress-strain curve where the initial part of the stress-
strain curve deviates from linearity. Depending on the nature of the material, this may or may
not represent a sharp transition. The yielding behaviour of a material can thus be described as
continuous (gentle or continuous change in slope) or discontinuous (abrupt change in slope of
stress-strain curve). When discontinuous yielding occurs, it is easy to determine the yield
point of the material. A good example of this is the yielding of a low-carbon steel, as shown
in Figure 2. The load increases steadily with elastic strain (linear curve), drops suddenly,
fluctuates about some approximately constant value of load, and then rises with further strain.
The load at which the sudden drop occurs is called the upper yield point. The constant load is
called the lower yield point, and the elongation that occurs at constant load is called the yield-
point elongation.

Figure 3: Lüders bands on the surface of

Figure 2: Typical yield point behaviour of a low- a low-carbon steel as a result of stretching
carbon steel. Yielding is discontinuous at the upper the sheet just beyond the yield point
yield point and the Lüders band phenomenon gives during forming.
rise to a plateau or lower yield point.
 Created by RD Knutsen, Centre for Materials Engineering, UCT / Page 3

The lower yield-point plateau is associated with the formation of slip bands on the surface of
the metal, which are often referred to as Lüders bands. The formation of these bands arises
from the onset of localised plastic deformation due to the “unlocking” of dislocations from the
interstitial carbon atoms. Although Lüders band formation does not affect the fracture
properties of the metal, it does seriously affect the surface finish of the deformed metal. This
is a particular problem during the forming of low-carbon steels, especially when the surface
requires a paint finish. For example, in the automotive industry, body panels could be formed
from low-carbon steel, and if Lüders bands form, the surface would require grinding and
polishing before completing the painting operation.

When continuous yielding occurs, as is the case in Figure 1, the determination of the yield
point can be quite subjective. It can be difficult to identify the precise transition between
elastic and plastic behaviour (the point sometimes referred to as the elastic limit). The
concept of proof stress or offset yield attempts to overcome this problem. In this case, the
flow stress at a fixed strain value is used to define the yield strength. This property is
determined by the stress corresponding to the intersection of the stress-strain curve and a line
parallel to the elastic part of the curve offset by a specified strain. The offset is usually
specified as a strain of 0.1, 0.2, or 0.5% (corresponding strain values of 0.001, 0.002, and
0.005). The yield strength obtained by an offset method is commonly used for design and
specification purposes, because it avoids the practical difficulties of measuring the elastic
limit.

Measurement of ductility

In general, measurements of ductility are of interest in three respects:

(i) To indicate the extent to which a metal can be deformed without fracture in
metalworking operations such as rolling, extrusion, and complex forming operations.
(ii) To indicate to the designer the ability of the metal to flow plastically before fracture.
A high ductility indicates that the material is “forgiving” and likely to deform locally
without fracture should the designer err in the stress calculations or in the prediction of
the service load.
(iii) To serve as an indicator of changes in impurity level or processing conditions.
Ductility measurements may be specified to assess material quality, even though no
direct relationship exists between the ductility measurement and performance in
service.

The conventional measures of ductility that are obtained from the tension test are the
engineering strain at fracture, εf (usually called the elongation), and the reduction in area at
fracture, q. Elongation and reduction in area usually are expressed as a percentage and
require measurement of the specimen length at fracture (f) and the cross sectional area at the
point of fracture (Af), respectively.

 f − 0
εf = The value for εf can be read directly from the engineering
0
stress-strain curve. However, the value for Af has to be
measured from the actual fractured specimen. Invariably
A0 − A f fracture will occur in the necked region and great care needs to
q= be exercised in measuring the area of the fracture surface.
A0
 Created by RD Knutsen, Centre for Materials Engineering, UCT / Page 4

Although specifications often report the total elongation (elongation at fracture, εf), a useful
measurement is the total uniform strain (εu ) of the material. This is the plastic strain up to the
point of necking, or similarly, the strain that coincides with the UTS value. This value is
important in forming operations as it indicates the extent to which the material can be
plastically deformed before localised deformation will take place. For example, if the
manufacturing process involves a deep drawing operation to produce domestic holloware
(pots and pans), it is important that the material has a very good εu value. If not, the material
will undergo localised deformation (necking) prematurely and cause fracture during the deep
drawing operation. This subject is discussed further later on.

Modulus of elasticity

The slope of the initial linear portion of the stress-strain curve is the modulus of elasticity, or
Young’s modulus, as shown in Figure 2. The modulus of elasticity, E, is a measure of the
stiffness of the material. The greater the modulus, the smaller the elastic strain resulting from
the application of a given stress. Because the modulus of elasticity is needed for computing
deflections of beams and other members, it is an important design value.

The modulus of elasticity is determined by the binding forces between atoms. Because these
forces cannot be changed without changing the basic nature of the material, the modulus
elasticity is one of the most structure-insensitive of the mechanical properties. Generally, it is
only slightly affected by alloying additions, heat treatment, or cold work.

The resilience is the ability of the material to absorb energy when deformed elastically and to
return it when unloaded. This property usually is measured by the modulus of resilience, UR,
which is defined as:

1 σy σy
2
1
U R = σ yε y = σ y =
2 2 E 2E

This equation indicates that the ideal material for resisting energy loads in applications where
the material must not undergo permanent distortion, such as mechanical springs, is one having
a high yield stress and a low modulus of elasticity. For various grades of the steel, the
modulus of resilience ranges from 100 to 4500 kJ/m3, with the higher values representing
steels with higher carbon or alloy contents. The crosshatched regions in Figure 4 indicate the
modulus of resilience for two steels. Because of its higher yield strength, the high-carbon
spring steel has the greater resilience.

Figure 4: Comparison of the stress-strain

curves for high- and medium-carbon steels.
Crosshatched regions in this curve represent
the modulus of resilience, UR, of the two
metals. The UR is determined by measuring
the area under the stress-strain curve up to the
elastic limit of the metal. Point A represents
the elastic limit of the spring steel; point B of
the structural steel.
 Created by RD Knutsen, Centre for Materials Engineering, UCT / Page 5

Example 1: Difficulties experienced in measuring the elastic modulus of a metal

It is very tempting to measure the elastic modulus directly from the slope of the linear portion
of the engineering stress-strain curve. The actual calculation is quite easily accomplished
from the relationship E = σ /ε, and the units are the same as those for stress (MPa, or in the
case of most metals and ceramics, GPa). However, metals generally have high elastic moduli
and undergo very small elastic strains before the onset of plastic deformation (yielding).
Steels, for example, have elastic moduli in the range of 190 – 210 GPa. In addition, the
compliance of the test machine is critical in the initial stages of the tensile test. The gripping
apparatus and the cross-head movement takes up slack during the initial stages of the tension
test. When this slack is superimposed on the load-extension data for the elastic region, the
strain is exaggerated. The result is that a much lower elastic modulus is computed from the
stress-strain curve than the actual value for the metal. For example, the calculated value for
a steel specimen can be as low as 10 GPa. This situation can be improved by using a high
quality extensometer attached to the specimen gauge length. In this case, the extension is
only measured over the length of the specimen gauge, and the compliance of the test machine
does not affect the load-extension data. Nevertheless, this method is still not very accurate,
and steel elastic moduli are calculated at about 140-160 GPa. It is thus recommended that
tensile testing is not employed as a technique for sensitive measurement of elastic moduli of
metals.

The extensometers shown in the figure above are essentially clip-gauges that make physical contact
with the specimen. Two types of gauges are shown and are positioned for measuring the dimensional
changes to a metal specimen during uniaxial tensile testing. One of the gauges is positioned to
measure the length change (extension or elongation), and the other gauge is positioned to measure the
change in specimen width during uniaxial extension. Since these gauges are attached directly to the
specimen, they avoid problems with machine compliance.
 Created by RD Knutsen, Centre for Materials Engineering, UCT / Page 6

The toughness of a material is its ability to absorb energy in the plastic range. The ability to
withstand occasional stresses above the yield stress without fracturing is particularly desirable
in parts such as freight-car couplings, gears, chains, and crane hooks. Toughness is a
commonly used concept that is difficult to precisely define. Toughness may be considered to
be the total area under the stress-strain curve. This area, which is referred to as the modulus
of toughness, UT, is an indication of the amount of work per unit volume that can be done on
the material without causing it to rupture.

Figure 4 shows the stress-strain curves for high- and low-toughness materials. The high-
carbon spring steel has a higher yield strength and tensile strength than the medium-carbon
structural steel. However, the structural steel is more ductile and has a greater total
elongation. The total area under the stress-strain curve is greater for the structural steel;
therefore, it is a tougher material. This illustrates that toughness is a parameter that comprises
both strength and ductility.

Specimen geometry

The geometry of a test specimen is often influenced by the product form from which it is
taken. For example, only flat specimens can be obtained from sheet products. Test
specimens taken from thick plate may be either flat or round; according to ASTM E8M, the
standard diameter of a round tensile specimen must be 12.5mm. However, most ASTM
tensile test methods specify small or sub-size specimens that are proportional to the standard
specimens. An acceptable small-size specimen can have a gauge length of only 11-mm. The
general rule of thumb is that the gauge length should be five times the diameter of a
cylindrical specimen. This ensures a uniaxial tensile condition and reduces the risk of the
proximity of the specimen should affecting the average plastic flow along the gauge length. It
is also important to quote the initial gauge length of the test specimen when reporting
elongation data. The measured elongation values may vary for the same material if the gauge
length is varied, despite maintaining a fixed initial diameter. The nomenclature for a typical
tension test specimen is presented in Figure 5.

Figure 5: Nomenclature for a typical tension test specimen. The ends of round specimens may be
plain, shouldered, or threaded. Plain ends should be long enough to accommodate some type of
wedge grip. Rectangular specimens are generally made with plain ends, but may be shouldered to
contain a hole for a pin bearing.
 Created by RD Knutsen, Centre for Materials Engineering, UCT / Page 7

Test speed and test temperature

The tensile strength of most engineering materials is sensitive to both test speed and test
temperature. Consequently, these parameters should be carefully selected and monitored
during the course of testing. Most often tests are performed at room temperature (usually
between 20 - 25°C), unless an attempt is made to more closely simulate the service conditions
of the material. Test speed is slightly more subjective, and even the ASTM E8M standard
does not provide clear guidance. In fact this standard states that “specifying suitable
numerical limits for speed and selection of the method are the responsibilities of the product
committees”.

Test speed is related to the specimen gauge length to give what is known as the strain rate.
The strain rate is calculated according to:
The units for crosshead speed are mm per
Crosshead _ speed
Strain _ rate = second and specimen gauge is in mm. Thus
Specimen _ gauge _ length the units for strain rate are per second (s-1).

In our laboratory at UCT, we tend to use strain rates between 10-3 s-1 and 10-2 s-1 for most
uniaxial tension tests. This typically represents a low strain rate test and results agree very
well with most specifications. [The crosshead speed is the speed at which the specimen grips
move apart and is generally referred to as test speed when entering test parameters into the
testing machine].

In most steels, test speed and test temperature influence the yield strength, tensile strength and
ductility of the metal. Increasing test speed will raise the yield point and UTS, and decrease
ductility. Increasing the temperature will generally have the opposite effect. This behaviour
is summarised in Figure 6. [ASIDE: Metals such as austenitic stainless steel and aluminium
are not particular influenced by strain rate. We thus refer to them as strain rate-insensitive
materials].

Highest strain rate or

lowest temperature

Medium strain rate or

medium temperature

Lowest strain rate or

highest temperature

Figure 6: Influence of strain rate and

test temperature on the tensile stress-
strain curve of a ductile metal.
 Created by RD Knutsen, Centre for Materials Engineering, UCT / Page 8

True stress – true strain curve

The engineering stress-strain curve does not give a true indication of the deformation
characteristics of a metal, because it is based entirely on original dimensions of the specimen,
and these dimensions change continuously during the test. Also, ductile metal that is pulled
in tension becomes unstable and necks down during the course of the test. Because the cross-
sectional area of the specimen is decreasing rapidly at this stage in the test, the load required
to continue deformation falls off. The average stress based on the original area likewise
decreases, and this produces the fall-off in the engineering stress-strain curve beyond the
point of maximum load. Actually, the metal continues to strain harden to fracture, so that the
stress required to produce further deformation should also increase. If the true stress, based
on the actual cross-sectional area of the specimen, is used, the stress-strain curve increases
continuously to fracture. If the strain measurement is also based on instantaneous
measurement, the curve that is obtained is known as the true stress – true strain curve. This
is also known as a flow curve, because it represents the basic plastic-flow characteristics of
the material.

Any point on the flow curve can be considered the yield stress for a metal strained in tension
by the amount shown on the curve. Thus, if the load is removed at this point and then
reapplied, the material will behave elastically throughout the entire range of reloading. The
true stress, σt, expressed in terms of engineering stress, σe, is given by:

L
σt = (ε e + 1) = σ e (ε e + 1)
A0

The derivation of the above equation assumes both constancy of volume and a homogeneous
distribution of strain along the gauge length of the test specimen. Thus, this equation should
be used only until the onset of necking. Beyond the maximum load, the true stress should be
determined from actual measurements of load and cross-sectional area.

The true strain, εt, may be determined from the engineering or conventional strain, εe by:


ε t = ln(ε e + 1) = ln
0
This equation is also only applicable until the onset of necking for the reasons discussed
above. Beyond maximum load, the true strain should be based on actual area or diameter
measurements.

Figure 7 compares the true stress – true strain curve

with its corresponding engineering stress – strain
curve. Note that, because of the relatively large
plastic strains, the elastic region has been compressed
into the y-axis. In agreement with the expressions for
true stress and true strain, the true stress – true strain
curve is always to the left of the engineering curve
until the maximum load is reached.

Figure 7: Comparison of engineering

and true stress/true strain curves.
 Created by RD Knutsen, Centre for Materials Engineering, UCT / Page 9

Why is the true stress – true strain curve important to us?

The flow curve of many metals in the region of uniform plastic deformation can be expressed
by the simple power curve relation:
The subscript t has been omitted for convenience, but all
σ = Kε n expressions involve true stress and true strain values.

where n is the strain-hardening exponent, and K is the strength coefficient. A log-log plot of
true stress and true strain up to maximum load will result in a straight line as shown in Figure
8. The slope of this line is the strain-hardening exponent, n, and may have values from n = 0
(perfectly plastic solid) to n = 1 (elastic solid). This is shown schematically in Figure 9. For
most metals, n has values between 0.1 and 0.5.

Figure 8: Log-log plot of true stress/true

strain curve. (n is the strain-hardening
exponent and K is the strength coefficient).
Figure 9: Various forms of power curve
ranging from perfect plastic (n = 0) to perfect
elastic (n = 1).

How does the strain-hardening exponent (n) influence tensile behaviour?

The useful interpretation of the strain-hardening exponent (n) must be seen in relation to the
occurrence of plastic instability (necking) during tensile deformation. Necking generally
begins at maximum load during tensile deformation of a ductile metal, where the increase in
stress due to the decrease in the cross-sectional area of the specimen becomes greater than the
increase in the load-carrying ability of the metal due to strain hardening. A simple
manipulation of expressions can demonstrate that the plastic strain at the onset of necking
(i.e., the total uniform strain) has a numerical value equal to the strain-hardening exponent, n
[see example below]. Thus, ductile metals with high n values will tend to have high uniform
ductility. This is very good for situations that require good formability (resistance to localised
deformation).

Example 2: Instability in tension

For many metals demonstrating “normal” work hardening behaviour, the tensile test data
can be represented by a single exponential curve of the form:

σ = K (ε ) n (1)

Where σ and ε are true stress and true strain respectively.

 Created by RD Knutsen, Centre for Materials Engineering, UCT / Page 10

K = strength coefficient
n = strain-hardening (or work-hardening) coefficient.

Work hardening or strain hardening occurs in most metals and is defined as the slope of the
σ - ε curve;
dσ
i.e. where WHR =
dε

dσ
From equation (1), = n K ( ε )n-1
dε

σ
[NB. = K ( ε ) n-1 ]
ε

dσ σ
∴ = n (3)
dε ε

where σ and ε refer to a particular point on a stress-strain curve.

Instability in Tension

Strain-hardening tends to increase the load-carrying capacity of the specimen as deformation

increases. This effect is opposed by the gradual decrease in cross-sectional area of the
specimen as it elongates. Necking or localised deformation begins at maximum load, where
the increase is stress due to decrease in cross-sectional area of the specimen becomes greater
than the increase in the load-carrying ability of the metal due to strain hardening. This
condition of instability leading to localised deformation is defined by the condition dL = O
[ie. when load (L) reaches a constant].

By definition of true stress:

L = σ A

dL dσ dA
thus = A + σ (4)
dε dε dε

= O at UTS

From the constancy-of-volume relationship,

l   Ao 
ε = log e   = log e  
 lo   A 

then A = Ao exp (− ε )
 Created by RD Knutsen, Centre for Materials Engineering, UCT / Page 11

dA
∴ = −A
dε

[Remember: derivative of exp (-x) is –exp (-x).]

By substitution in equation (4), NECKED

REGION
dL dσ
= O=A + σ (− A )
dε dε

dσ
O = - σ
dε

dσ
∴ = σ at Lmax (UTS) (5)
dε

Graphical interpretation of the necking criterion. The

point of necking can be obtained from the true stress/true
strain curve by superimposing a plot of dσ/dε versus ε
on the true stress/true strain curve. The intersection of
the two curves indicates the point of necking (i.e., where
dσ/dε = σ).

Equation (5) says that necking will occur in uniaxial tension at a strain at which the slope of
the true stress-true strain curve equals the true stress at that strain.

It follows from equation (3) and (5) that

ε = n at the UTS

Thus for metals where the true stress- true strain curve can be approximated by equation (1),
the plastic instability strain has a numerical value equal to the exponent n of equation (1); ie.
at strains equal to or greater than the exponent n, the rate of increase in tensile strength, due
to strain hardening, is less than the rate of stress increase due to the diminution of cross-
sectional area.

Plastic instability is often important in forming operations with sheet metal since the strain at
which the deformation becomes localised constitutes the forming limit of the material. The
exponent n may be determined from a graph of log σ vs log ε , since equation (1) can be
written:

log σ = log K + n log ε

(n is determined from the slope of the above plot).
 MEC4119Z: MECHANICAL BEHAVIOUR OF MATERIALS
Chapter 3: Plastic Behaviour of Ductile Metals
Plastic Deformation

Plastic deformation is permanent, and strength and hardness are measures of a material’s resistance to this
deformation. On a microscopic scale, plastic deformation corresponds to the net movement of large numbers
of atoms in response to an applied stress. During this process, interatomic bonds must be ruptured and then
reformed. In crystalline solids, like metals, plastic deformation most often involves the motion of dislocations,
which are linear defects within the crystal lattice. Although these dislocations can occur in different forms,
plastic deformation is most easily envisaged by the motion of an edge dislocation (Figure 1). The process by
which plastic deformation is produced by dislocation motion is termed slip; the crystallographic plane along
which the dislocation line traverses is the slip plane, as indicated in Figure 1. Macroscopic deformation simply
corresponds to permanent deformation that results from the movement of dislocations, or slip, in response
to an applied shear stress. The strength of a metal can thus be increased by increasing its resistance to
dislocation movement.

Figure 1: When a shear stress is applied to the

dislocation in (a), the atoms are displaced,
causing the dislocation to move one Burgers
vector in the slip direction (b). Continued
movement of the dislocation eventually
creates a step (c), and the crystal is deformed.
The motion of the caterpillar is analogous to
the motion of a dislocation (d).

Dislocation motion is analogous to the mode of a locomotion employed by a caterpillar (Figure 1). The
caterpillar forms a hump near its posterior end by pulling in its last pair of legs a unit leg distance. The hump
is propelled forward by repeated lifting and shifting of leg pairs. When the hump reaches the anterior end,
the entire caterpillar has moved forward by the leg separation distance. The caterpillar hump and its motion
correspond to the extra half-plane of atoms in the dislocation model of plastic deformation.

1
Strengthening Mechanisms in Metals and Alloys

In order for atoms to slide past each other by dislocation movement, a critical stress needs to be applied to
the lattice to overcome the resistance1 to dislocation movement. Up until the point that dislocation
movement starts, the metal behaves elastically and the deformation is restored when the load is removed.
Once dislocation movement starts, there is a transition between elastic and plastic deformation and we say
that the metal has yielded to the applied stress. This is the origin of the very important yield strength property
that is used to describe mechanical behaviour of metals. In pure metals, the inherent friction stress that needs
to be overcome to cause dislocation movement is related to the bonding of the atoms. This resistance can be
increased in a number of ways and allows us to modify the strength of metallic materials by careful
composition and microstructural control. Different strengthening mechanisms are explained in the following
sections and include grain size strengthening and influence of prior deformation (referred to as strain
hardening).
1
If there was no resistance to dislocation movement, then all metals would be extremely weak and they would
plastically flow similar to liquids. Much of the resistance to dislocation movement comes from the attraction of
atoms to their nearest neighbours (bond strength) and therefore different metals will have different inherent
strengths. We can talk about this as the friction stress necessary to overcome movement of the dislocation.

Grain Size Strengthening

The size of grains, or average grain diameter, in a polycrystalline metal influences the mechanical properties.
Adjacent grains normally have different crystallographic orientations and, of course, a common grain
boundary, as indicated in Figure 2. During plastic deformation, slip or dislocation motion must take place
across this common boundary – say, from grain A to grain B in Figure 2. The grain boundary acts as a barrier
to dislocation motion for two reasons:

• Since the two grains are of different orientations, a dislocation passing into grain B will have to change
its direction of motion; this becomes more difficult as the crystallographic misorientation increases.
• The atomic disorder within a grain boundary region will result in a discontinuity of slip planes from
grain into the other.
•

Figure 2: The motion of a dislocation as it encounters a grain boundary, illustrating how the boundary acts as a
barrier to continued slip. Slip planes are discontinuous and change directions across the boundary.

It should be mentioned that for high-angle grain boundaries, it may not be the case that dislocations traverse
grain boundaries during deformation; rather, a stress concentration ahead of a slip plane in one grain may
activate sources of new dislocations in an adjacent grain. A fine-grained metal (one that has small grains) is

2
harder and stronger than one that is coarse grained, since the former has a greater total grain boundary area
to impede dislocation motion. For many materials, the yield strength σy varies with grain size according to:

σy = σ0 + ky d-½
In this expression, termed the Hall-Petch equation, d is the average grain diameter, and σ0 and ky are
constants for a particular material. Figure 3 demonstrates the yield strength dependence on grain size for a
brass alloy. Grain size may be regulated by the rate of solidification from the liquid phase, and also by plastic
deformation followed by an appropriate heat treatment. It should also be mentioned that grain size reduction
improves not only strength, but also the toughness of many alloys.

Figure 3: The influence of grain size on the yield strength of a 70Cu-30Zn brass alloy. Note that the grain diameter
increases from right to left and is not linear (i.e. square root relationship).

Strain Hardening

If one considers the stress-strain behaviour of a ductile metal, then it can be seen that the metal strengthens
as it is plastically deformed. This is easily observed from the stress-strain curve that is generated during a
standard tensile test (Figure 4). At the point of plastic yielding, the strength of the metal is σy. This represents
the start of plastic deformation (say strain = ε). As the metal plastically deforms, the stress required to deform
the metal increases as shown by the rising stress-strain curve. If the strength of the metal is determined after
a certain strain level (say ε'), it can be seen that this σ'y value is much greater than σy. Hence the metal has
been strengthened by cold work (i.e. plastic deformation usually carried out at room temperature). This type
of situation arises when metals are rolled (Figure 5) or drawn by metal-working processes at room
temperature or thereabouts. Since the metal plastically deforms during the metal working operation, its flow
behaviour is replicated to a large extent by its performance during a standard tensile test.

3
How does strain hardening (or work hardening) arise?

When we apply a stress greater than the yield strength, dislocations begin to slip. Eventually, a dislocation
moving on its slip plane encounters obstacles that pin the end of the dislocation line and the movement of the
dislocation is inhibited. At the same time, dislocations multiply as plastic deformation proceeds and these
dislocations interfere with their own motions. An analogy for this is when we have too many people in a room
it is difficult for them to move around. The result is an increased strength, but reduced ductility, for metallic
materials that have undergone cold working or work hardening as shown in Figure 6. Of course not all metals
strain-harden at the same rate and hence we find that some metals are more difficult than others to form into
shape. For example, some stainless steels require much higher forces than mild steel in order to form the
metals into equivalent shapes. The process of strain hardening can be reversed by performing an annealing
treatment that promotes the process of recrystallisation.

Figure 4: Increase in plastic flow strength as function of strain due to work hardening process in a ductile metal.

Figure 5: Reduction of metal thickness during rolling – strain hardening occurs as a consequence of the
accumulated plastic deformation.

4
Figure 6: The effect of cold work (i.e. strain hardening or work hardening) on the mechanical properties of

5
 MEC4119Z: MECHANICAL BEHAVIOUR OF MATERIALS
Chapter 4: Recrystallisation and Grain Growth
There are a number of advantages and limitations to strengthening a metallic material by cold working or
strain hardening:

• We can simultaneously strengthen the metal and produce the final shape.
• We can obtain excellent dimensional tolerances and surface finishes by the cold working process.
• The cold working process is an inexpensive method for producing large numbers of small parts, since
high forces and expensive forming equipment are not needed. Also, no alloying elements are needed,
which means lower cost raw materials can be used.
• Not all metals can be cold worked since they do not all have the same levels of ductility (e.g.
magnesium is rather brittle at room temperature).
• Ductility, electrical conductivity, and corrosion resistance are impaired by cold working. However,
since the extent to which electrical conductivity is reduced by cold working is less than that for other
strengthening processes, such as introducing alloying elements, cold working is a satisfactory way to
strengthen conductor materials, such as copper wires used for transmission of electrical power.
• Properly controlled residual stresses and anisotropic behaviour1 may be beneficial. However, if
residual stresses are not properly controlled, the materials properties are greatly impaired.
• Since the effect of cold working is decreased or eliminated at higher temperatures, we cannot use cold
working as a strengthening mechanism for components that will be subjected to high temperatures
during application or service.

1
During deformation, the grains rotate as well as
elongate, causing certain crystallographic directions
and planes to become aligned with the direction in
which stress is applied. Consequently, preferred
orientations, or textures, develop and cause
anisotropic behaviour. In processes such as rolling,
grains become oriented in a preferred crystallographic
direction and plane, giving a sheet texture. The
properties of a rolled sheet or plate depend on the
direction in which the property is measured. The
tensile properties of a cold rolled aluminium alloy are
indicated in the figure below. For this alloy, strength
is highest parallel to the rolling direction. The
strengthening that occurs by the development of
anisotropy or of a texture, is known as texture
strengthening.

As already explained, cold working is a useful strengthening mechanism, particularly when it occurs
concurrently with shaping operations. However, cold working leads to some effects that are sometimes
undesirable. For example, the loss of ductility or development of residual stresses may not be desirable for
certain applications. Since cold working or strain hardening results from increased dislocation density we can
assume that any treatment to rearrange or annihilate dislocations would begin to undo the effects of cold

1
working. The method by which cold working is reversed is called annealing and leads to processes of recovery
and recrystallisation in the metal. Annealing is a heat treatment used to eliminate some or all of the effects
of cold working.

Deformed State

The microstructure of a metal changes in several ways during deformation. First and most obvious, the grains
change their shape and there is a surprisingly large increase in the total grain boundary area. For rolling
deformation, the grain shape change is not axisymmetric since plastic flow is constrained in the transverse
direction. Thus the material suffers a plane strain condition where the deformation plane is defined by the
rolling direction and the normal direction. The new grain boundary area has to be created during deformation
and this is done by the incorporation of some of the dislocations that are continuously created during the
deformation process. A second obvious feature, particularly at the electron microscope level, is the
appearance of an internal structure within the grains. This too, results from the accumulation of dislocations.
The stored energy of deformation, which influences the recovery and recrystallisation processes, is generally
the sum of the energy of all of the dislocations and new interfaces that evolve during the deformation event.
Thirdly, the orientations of the individual grains of a polycrystalline metal change relative to the direction of
applied stress. These changes are not random and involve rotations that are directly related to the
crystallography of the deformation.
Annealing Response of Deformed Metals
Plastic deformation and the concomitant dislocation multiplication that occurs, leads to an increase in stored
energy in the microstructure. Consequently, there is a driving force to reduce this stored energy, which is
equivalent to the stored energy itself. Naturally, removing the dislocations reduces the stored energy, but
arranging the dislocations into low energy configurations can also reduce the energy. This latter process is
known as recovery, whereas the almost complete annihilation of dislocations occurs during the process of
recrystallisation.
The consequence of recovery is the division of the deformed grains into several subgrains whose relative
misorientation is by definition less than 15°, and more generally in the region of 1° to 10°. Dislocations,
arranging themselves into low energy configurations in such a way that a dislocation wall is formed, form the
subgrain boundaries. The accommodation of the dislocation wall leads to a curvature in the lattice, which in
turn produces the lattice misorientation of a few degrees. A schematic representation of a subgrain structure
is shown in Figure 1. The process of recrystallisation involves the migration of high angle grain boundaries,
which by definition represent misorientations greater than 15°. New grains form in the deformed
microstructure and grow in order to reduce the stored energy manifest by the high dislocation density (Figure
1c). The old grains are consumed, resulting in a new grain structure with a low dislocation density (Figure 1d).
Since the new grain will consume the deformed grain into which it grows, the orientation of the new grain will
be different to the old deformed grain. This situation implies that the nucleation of a new grain must precede
its growth, but what in fact happens is that these new grains grow from small regions, recovered subgrains or
cells, which are already present in the deformed microstructure. One of the many important consequences
of this idea is that the orientation of each new grain arises from the orientation present in the deformed state.
A more generalised view of the recovery and recrystallisation process is shown in Figure2. The elongated grain
structure that could have resulted from cold rolling is highly dislocated (a). When we first heat the meta, the
additional thermal energy permits the dislocations to move and form the boundaries of a polygonised subgrain
structure. The dislocation density, however, is virtually unchanged. This low-temperature treatment removes
the residual stresses due to cold working without causing a substantial change in dislocation density and is
called recovery. The mechanical properties of the metal are relatively unchanged during the recovery process
because the number of dislocations is not substantially reduced. However, since residual stresses are reduced

2
or even eliminated when the dislocations are rearranged, recovery is often called a stress relief anneal. In
addition, recovery restores high electrical conductivity to the metal, permitting us to manufacture copper or
aluminium wire for transmission of electrical power that is strong yet still has high conductivity. Finally,
recovery often improves the corrosion resistance of the metal.

Figure 1: Schematic illustration of microstructure evolution during recovery and recrystallisation. (a) Deformed
structure illustrating dislocation density, (b) arrangement of dislocations into cells to form subgrains, (c)
nucleation and growth of new grains during recrystallisation, (d) fully recrystallised state after
annihilation of high dislocation density.

Figure 2: Processes that occur during annealing of the cold worked state (a): after recovery (b), after
recrystallisation (c), and after grain growth (d).

When a cold worked metal is heated above a certain temperature, rapid recovery eliminates residual stresses
and produces the subgrain structure (polygonised dislocation structure). New small grains then grow out of
some of the subgrains and this leads into the process of recrystallisation. Because the growth of a new grain
involves grain boundary migration, the dislocations are annihilated as the new grain boundary sweeps through
the highly dislocated subgrain structure. Since many such new grains form and grow, the grain structure of
the recrystallised metal is much finer than the parent deformed structure. Consequently, the process of
recrystallisation is a means of grain refinement that can lead to grain size strengthening as discussed in Part
3. Although the strength increase due to grain size refinement is not as great as the strength increase due to
work hardening, the ductility and toughness is much greater for metals strengthened by grain size refinement.
This aspect of grain size refinement is clearly seen in Figure 2(c), where the recrystallised grain size is much
finer than the parent grain structure in 2(a).

Although the process of recrystallisation leads to grain size refinement, this advantage can be reversed if the
recrystallisation process is performed at a temperature that is too high and/or the metal is annealed for too
long. Although the recrystallisation process results in a decrease in the internal energy of the metal due to
dislocation annihilation, the greater grain boundary area per unit volume due to the finer grain size (as in

3
Figure 2(c)) increases the surface energy within the metal microstructure. Thus there is a driving force for
grain growth after the recrystallisation process is completed in order to continue lowering the internal energy
of the metal. If sufficient temperature and time (diffusion kinetics) is allowed after recrystallisation is
complete, then grain growth will occur. Of course, the process of grain growth also requires boundary
migration and therefore diffusion, and the extent of grain growth will depend on the temperature and time
parameters. An example of grain growth after recrystallisation is shown in Figure 2(d). An example of the
influence of annealing temperature on the grain growth in brass after recrystallisation is shown in Figure 3.

Figure 3: Grain growth in brass after annealing at (a) 400°C, (b) 650°C and (c) 800°C.

The evolution of mechanical properties of brass during recovery and recrystallisation is illustrated in Figure 4.
The left-hand side of the graph in Figure 4 demonstrates the influence cold work on mechanical property
development, whereas the right-hand side shows the influence of annealing temperature on the change in
mechanical property and electrical conductivity. Notice that not much happens, except for a slight change in
electrical conductivity up to about 250°C.

Figure 4: The effect of cold work on the properties of a Cu-35% Zn alloy and the effect of annealing temperature
on the properties of the same alloy that is cold worked by 75%.

4
Annealing and Materials Processing

The effects of recovery, recrystallisation, and grain growth are important in the processing and eventual use
of a metal or an alloy.

Deformation Processing: By taking advantage of the annealing heat treatment, we can increase the total
amount of deformation we can accomplish. If we are required to reduce a 15mm thick plate to say a sheet
thickness of 0.5mm, we can do the maximum permissible cold work, anneal to restore the metal to its soft,
ductile condition, then cold work again until we finally achieve the desired sheet thickness. The final cold-
working step can be designed to produce the final dimensions and properties required.

High Temperature Service: Neither strain hardening nor grain size strengthening are appropriate for an alloy
that is to be used at elevated temperatures, as in creep-resistant applications. When the cold-worked metal
is placed into service at a high temperature, recrystallisation immediately causes a catastrophic decrease in
strength. In addition, if the temperature is high enough, the strength continues to decrease because of growth
of the newly recrystallised grains.

Joining Processes: Metallic materials can be joined using processes such as welding. When we join a cold-
worked metal using a welding process, the metal adjacent to the weld heats up above the recrystallisation and
grain growth temperatures and subsequently cools slowly. This region is called the heat-affected zone (HAZ).
The structure and properties in the HAZ are shown in Figure 5. The mechanical properties are reduced
catastrophically by the heat of the welding process.

Figure 5: The structure and properties surrounding a fusion weld in a cold-worked metal. Note: Only the right-
hand side of the HAZ is marked on the diagram. There is a considerable loss in strength caused by
recrystallisation and grain growth in the HAZ.

5
 MEC4119Z: MECHANICAL BEHAVIOUR OF MATERIALS
Chapter 5: Strengthening in metals and alloys
The most convenient way of measuring the basic mechanical performance of a metallic material is by
conducting a tensile test on a specially machined or cast specimen. The tensile test measures the
resistance of a material to a static or slowly applied force. The strain rates in a tensile test are very low
(typically 10-4s-1 – 10-2s-1) and resemble a so-called quasi-static test condition. A test setup is shown in
Figure 1.

Figure 1: A unidirectional force is applied to a specimen in the tensile test by means of the moveable
crosshead. The crosshead movement can be performed using screws or a hydraulic mechanism.

During the tensile test, the specimen is extended by moving the grips apart. As the specimen is extension,
the resistance to deformation (or extension) is recorded by a loadcell attached to the crosshead. In this
way a load-extension curve is measured, which can then be converted to a an engineering stress – strain
curve. An example for a normal ductile metal is illustrated in Figure 2.

Figure 2: The stress-strain curve for an aluminium alloy.

The tensile curve in Figure 2 can be divided into two distinct regions, namely a linear (elastic) region and
a non-linear (plastic) region. The elastic property is determined by the underlying atomic bond strengths
in the metal and is largely controlled by the composition of the metal. The plastic behaviour is dependent
on the alloy composition and the microstructure condition of the metal. Consequently, the plastic
behaviour can be quite variable for a particular alloy composition if the microstructure is varied during
heat treatment and/or deformation and annealing. For the purposes of the present course, we will
concentrate on the plastic behaviour of the metal; in particular, we will concern ourselves with yield
strength, tensile strength and plastic elongation. But, before we can investigate strengthening
mechanisms in metals, we need to understand the nature of plastic deformation.

Plastic Deformation

Plastic deformation is permanent, and strength and hardness are measures of a material’s resistance to
this deformation. On a microscopic scale, plastic deformation corresponds to the net movement of large
numbers of atoms in response to an applied stress. During this process, interatomic bonds must be
ruptured and then reformed. In crystalline solids, like metals, plastic deformation most often involves
the motion of dislocations, which are linear defects within the crystal lattice. Although these dislocations
can occur in different forms, plastic deformation is most easily envisaged by the motion of an edge
dislocation (Figure 3). The process by which plastic deformation is produced by dislocation motion is
termed slip; the crystallographic plane along which the dislocation line traverses is the slip plane, as
indicated in Figure 3. Macroscopic deformation simply corresponds to permanent deformation that
results from the movement of dislocations, or slip, in response to an applied shear stress. The strength
of a metal can thus be increased by increasing its resistance to dislocation movement.

Figure 3: When a shear stress is applied to the

dislocation in (a), the atoms are displaced,
causing the dislocation to move one Burgers
vector in the slip direction (b). Continued
movement of the dislocation eventually
creates a step (c), and the crystal is deformed.
The motion of the caterpillar is analogous to
the motion of a dislocation (d).
Dislocation motion is analogous to the mode of a locomotion employed by a caterpillar (Figure 3). The
caterpillar forms a hump near its posterior end by pulling in its last pair of legs a unit leg distance. The
hump is propelled forward by repeated lifting and shifting of leg pairs. When the hump reaches the
anterior end, the entire caterpillar has moved forward by the leg separation distance. The caterpillar
hump and its motion correspond to the extra half-plane of atoms in the dislocation model of plastic
deformation.

Strengthening Mechanisms in Metals and Alloys

In order for atoms to slide past each other by dislocation movement, a critical stress needs to be applied
to the lattice to overcome the resistance1 to dislocation movement. Up until the point that dislocation
movement starts, the metal behaves elastically and the deformation is restored when the load is
removed. Once dislocation movement starts, there is a transition between elastic and plastic deformation
and we say that the metal has yielded to the applied stress. This is the origin of the very important yield
strength property that is used to describe mechanical behaviour of metals. In pure metals, the inherent
friction stress that needs to be overcome to cause dislocation movement is related to the bonding of the
atoms. This resistance can be increased in a number of ways and allows us to modify the strength of
metallic materials by careful composition and microstructural control. Different strengthening
mechanisms are explained in the following sections and include grain size strengthening, solid solution
effects, dispersion effects, and influence of prior deformation (referred to as strain hardening).
1
If there was no resistance to dislocation movement, then all metals would be extremely weak and they
would plastically flow similar to liquids. Much of the resistance to dislocation movement comes from the
attraction of atoms to their nearest neighbours (bond strength) and therefore different metals will have
different inherent strengths. We can talk about this as the friction stress necessary to overcome movement
of the dislocation.

Grain Size Strengthening

The size of grains, or average grain diameter, in a polycrystalline metal influences the mechanical
properties. Adjacent grains normally have different crystallographic orientations and, of course, a
common grain boundary, as indicated in Figure 4 (fig 7.12 on p.175 in Callister). During plastic
deformation, slip or dislocation motion must take place across this common boundary – say, from grain
A to grain B in Figure 4. The grain boundary acts as a barrier to dislocation motion for two reasons:

 Since the two grains are of different orientations, a dislocation passing into grain B will have to
change its direction of motion; this becomes more difficult as the crystallographic misorientation
increases.
 The atomic disorder within a grain boundary region will result in a discontinuity of slip planes
from grain into the other.

Figure 4: The motion of a dislocation as it encounters a grain boundary, illustrating how the boundary acts
as a barrier to continued slip. Slip planes are discontinuous and change directions across the
boundary.
It should be mentioned that for high-angle grain boundaries, it may not be the case that dislocations
traverse grain boundaries during deformation; rather, a stress concentration ahead of a slip plane in one
grain may activate sources of new dislocations in an adjacent grain. A fine-grained metal (one that has
small grains) is harder and stronger than one that is coarse grained, since the former has a greater total
grain boundary area to impede dislocation motion. For many materials, the yield strength y varies with
grain size according to:

y = 0 + ky d-½
In this expression, termed the Hall-Petch equation, d is the average grain diameter, and 0 and ky are
constants for a particular material. Figure 5 demonstrates the yield strength dependence on grain size
for a brass alloy. Grain size may be regulated by the rate of solidification from the liquid phase, and also
by plastic deformation followed by an appropriate heat treatment. It should also be mentioned that grain
size reduction improves not only strength, but also the toughness of many alloys.

Figure 5: The influence of grain size on the yield strength of a 70Cu-30Zn brass alloy. Note that the grain
diameter increases from right to left and is not linear (i.e. square root relationship).

Solid-Solution Strengthening

In metallic materials, one of the important effects of solid-solution formation is the resultant solid-
solution strengthening. This strengthening, via solid-solution formation, is caused by increased
resistance to dislocation motion and is one of the important reasons why brass (Cu-Zn alloy) is stronger
than pure copper. Jewellery could be made out of pure gold or silver. However, pure gold and silver are
extremely soft and malleable and the manufactured jewellery pieces will not retain their shape. This is
also why jewellers add copper to gold or silver. Two different types of solute situations are depicted in
Figure 6 below. In Figure 6(a), the solute atom is much smaller than the host atom, whereas in Figure
6(b), the solute atom is much bigger than the host atom. In both cases, the relative size misfit of the host
atoms and the solute atoms results in quite severe distortion of the crystal lattice. Given that dislocation
motion (i.e. plastic deformation in metals) occurs by the “sliding of atoms past each other”, the regions
of distorted lattice will interfere with this dislocation motion. Any mechanism that leads to inhibition of
dislocation movement will result in strengthening of the metal alloy. Consequently, the degree of relative
atomic size mismatch, as well as the amount of solute, will determine the change in strength due to solid-
solution strengthening.

(a) (b)

Figure 6: Distortion of host crystal lattice due to misfit of (a) smaller solute atom and (b) larger solute atom.
In both cases the misfit leads to increased strength.

In the copper-nickel (Cu-Ni) system, we intentionally introduce a solid substitutional atom (Ni) in the
original crystal structure (Cu). The Cu-Ni alloy is stronger than the pure copper. Similarly, if less than 30%
Zn is added to Cu, the Zn behaves as a substitutional atom that strengthens the Cu-Zn alloy, as compared
with pure Cu. The effects of solute size misfit and amount of solute on the strength of copper-based
alloys is summarised in Figure 7.

Strain Hardening

If one considers the stress-strain behaviour of a ductile metal, then it can be seen that the metal
strengthens as it is plastically deformed. This is easily observed from the stress-strain curve that is
generated during a standard tensile test (Figure 8). At the point of plastic yielding, the strength of the
metal is y. This represents the start of plastic deformation (say strain = ). As the metal plastically
deforms, the stress required to deform the metal increases as shown by the rising stress-strain curve. If
the strength of the metal is determined after a certain strain level (say '), it can be seen that this 'y value
is much greater than y. Hence the metal has been strengthened by cold work (i.e. plastic deformation
usually carried out at room temperature). This type of situation arises when metals are rolled (Figure 9)
or drawn by metal-working processes at room temperature or thereabouts. Since the metal plastically
deforms during the metal working operation, its flow behaviour is replicated to a large extent by its
performance during a standard tensile test.

How does strain hardening (or work hardening) arise?

When we apply a stress greater than the yield strength, dislocations begin to slip. Eventually, a dislocation
moving on its slip plane encounters obstacles that pin the end of the dislocation line and the movement
of the dislocation is inhibited. At the same time, dislocations multiply as plastic deformation proceeds
and these dislocations interfere with their own motions. An analogy for this is when we have too many
people in a room it is difficult for them to move around. The result is an increased strength, but reduced
ductility, for metallic materials that have undergone cold working or work hardening as shown in Figure
10. Of course not all metals strain-harden at the same rate and hence we find that some metals are more
difficult than others to form into shape. For example, some stainless steels require much higher forces
than mild steel in order to form the metals into equivalent shapes. The process of strain hardening can
be reversed by performing an annealing treatment that promotes the process of recrystallisation. This is
process is considered in more detail in Part 4.
Figure 7: The effects of several alloying elements on the yield strength of copper. Nickel and zinc atoms are
about the same size as copper atoms, but beryllium and tin atoms are much different from copper
atoms. Increasing both atomic size difference and amount of alloying element increases solid-
solution strengthening. (After Askeland and Phule, “The Science and Engineering of Materials”,
4th edition, 2003, Thomson/Brooks/Cole).

Figure 8: Increase in plastic flow strength as function of strain due to work hardening process in a ductile
metal.
Figure 9: Reduction of metal thickness during rolling – strain hardening occurs as a consequence of the
accumulated plastic deformation.

Figure 10: The effect of cold work (i.e. strain hardening or work hardening) on the mechanical properties of
copper.

Dispersion Strengthening

In the same way that dislocation motion is made more difficult by providing obstacles to dislocation
motion in the form of increased dislocation density (strain hardening), so too can the motion of
dislocations be impeded by the presence of harder second phases. For example, the presence of iron
carbide in the microstructure of plain carbon steel will increase the strength of the steel quite
considerable. This is due to the fact that dislocations glide through ferrite fairly easily, but cannot glide
through the carbide phase since it is non-metallic. Thus the more carbide phase present, the stronger the
steel will be (the strength of steels generally increases with increasing carbon level). Furthermore, the
distribution of the carbide phase is important and the particular lamellar plate morphology that develops
during the eutectoid reaction provides a very small path length between the ferrite and carbide phase.
Thus the dislocations have only a relatively short distance to glide through the ferrite phase before they
reach the carbide obstacle. In this way, the finer the pearlite morphology for a particular carbon steel,
the stronger the steel.
A special form of dispersion hardening is what is known as age or precipitation hardening. In this case,
very fine phases (of the order of nanometres) are precipitated in the metal matrix after performing an
extended isothermal heat treatment. Since these particles are very finely distributed, they provide many
obstacles to dislocation movement, and the strength can be increased by up to an order of magnitude
(e.g. aluminium alloys used in aircraft construction). An example of such a microstructure is presented in
Figure 11 and will be discussed in more detail in Module 3 of this course.

Figure 11: A transmission electron micrograph showing the microstructure of a AA7150 aluminium alloy that
has been precipitation hardened. The light matrix phase in the micrograph is an aluminium solid
solution. The strength is provided by the fine distribution of the plate-shaped near-equilibrium
MgZn2 phase. The scale marker is 1 micron long.
 MEC4119Z: MECHANICAL BEHAVIOUR OF MATERIALS
Chapter 6: Steel Microstructure, Heat Treatment and Properties

Ferrous alloys, which are based on iron-carbon alloys, include plain-carbon steels, alloy and
tools steels, stainless steels and cast irons. These are the most widely used materials in the
world. All of the strengthening mechanisms discussed in Chapter 5 apply to at least some of
the ferrous alloys. In this chapter we will further explore the microstructure development in
plain carbon steels and develop a greater understanding of the heat treatment / property
evolution in carbon steels. We will extend this discussion to include the influence of relatively
small additions of alloying elements on the broad range of microstructures and properties that
are achievable in steels.

Classification of Steels

The dividing point between “steels” and “cast irons” is 2.11 wt% carbon, where the eutectic
reaction becomes possible. For steels, we concentrate on the eutectoid portion of the phase
diagram in which the solubility lines and the eutectoid isotherm are specially identified. The
A3 shows the temperature at which ferrite starts to form; the Acm shows the temperature at which
cementite starts to form; and the A1 is the eutectoid temperature. These phase boundaries are
shown in Figure 1.

Almost all of the heat treatments of steel are directed toward producing the mixture of ferrite
and cementite that gives the proper combination of properties. Figure 2 shows the important
micro-constituents, or arrangements of ferrite and cementite that are usually sought. Pearlite is
a micro-constituent consisting of a lamellar mixture of very fine ferrite and cementite, where
these two phases have a distinctive plate-like morphology. In bainite, which is obtained by
transformation of austenite at a large undercooling, the cementite is more rounded than in
pearlite. Tempered martensite, a mixture of very fine and nearly rounded cementite in ferrite,
forms when martensite is reheated following its formation.

Before we explore the details regarding the microstructure evolution referred to in the preceding
paragraph, it is worthwhile considering example of certain steel designations and their
compositions. Table 1 demonstrates the range in steels based on different carbon levels, but
also introduces the notion of low alloy steels where elements other than carbon and manganese
become important as well. There are several different schemes used worldwide to designate a
steel type and these include the AISI (American Iron and Steel Institute) numbers, BS (British
Standard) numbers, EN (European Norm) numbers, DIN (Deutsche …) numbers, among others.
Of course this complicates matters and it is always useful to have a table of equivalent
designations in order to identify different steel types. Steels are more generally classified on
the basis of their carbon content and level of additional alloying elements. For example, plain
carbon steels contain, in addition to a certain carbon level, silicon levels up to 0.6 wt% and
manganese up to 1.65 wt%. Both these elements are added to assist in the steel making process
by way of acting as de-oxidisers1, but they also themselves dissolve in the steel to some extent
to contribute towards solid solution strengthening. Ultra-low carbon steels contain a maximum
of 0.03 wt% C. Low-carbon steels contain 0.04 to 0.15 wt% C. These low-carbon steels are
used for making car bodies and hundreds of other applications. Mild steel contains 0.15 to 0.30
wt% C. This steel is used in buildings, bridges, piping, etc. Medium-carbon steels contain 0.3
to 0.6 wt% C. These steels are used in making machinery, tractors, mining equipment, etc.

___________________________________________________________________________
-1-
High-carbon steels contain above 0.6 wt% C. These are used in making springs, railroad car
wheels, and the like. Note that cast irons are Fe-C alloys containing 2 to 4 wt% carbon.
1
Silicon and manganese tie up with oxygen to reduce the level of dissolved oxygen in the liquid metal and
form a solid component (slag) that floats on the surface of the liquid metal. This slag is usually skimmed
off the surface before the melt is allowed to solidify to produce the steel.

Figure 1: (a) The Fe-C phase diagram including carbon level up to 6.67 wt%, which is the carbon level in
cementite (Fe3C). (b) An expanded version of the Fe-C diagram around the eutectoid reaction.

___________________________________________________________________________
-2-
 5 microns

Figure 2: Scanning electron micrographs of (a) pearlite, (b) bainite, and (c) tempered martensite,
illustrating the differences in cementite size and shape among these three micro-constituents.

Table 1: Compositions of selected plain carbon steels and low alloy carbon steels.

General Heat Treatment Practice

Four simple heat treatments, namely, process annealing, annealing, normalising, and
spheroidising, are commonly used for steels (Figure 3). These heat treatments are used to
accomplish one of three purposes: (1) eliminating the effects of cold work, (2) controlling grain
size and dispersion strengthening, or (3) improving machinability.

Process annealing: The recrystallisation heat treatment used to eliminate the effect of cold
working in steels with less than about 0.25 wt% C is called a process anneal. The process
anneal is done 80C to 170C below the A1 temperature. The intent of the process anneal
treatment is to significantly reduce or eliminate residual stresses and to restore ductility.

___________________________________________________________________________
-3-
Figure 3: Schematic summary of the simple heat treatments for (a) hypoeutectoid steels and (b)
hypereutectoid steels.

Annealing and normalising: Steels can be dispersion

strengthened by controlling the fineness of pearlite (i.e.
by reducing the spacing between alternating ferrite and
cementite platelets). The steel is initially heated to
produce homogeneous austenite (usually referred to as the
austenitising heat treatment). In the case of annealing,
the steel is allowed to cool slowly in the furnace, thereby
producing coarse pearlite. Normalising allows the steel to
cool more rapidly, in air, producing fine pearlite.
Annealing generally results in about a 20-25% reduction
in strength compared to the normalised condition, but at
the same time increases the ductility by about the same
amount. Apart from increasing strength due to improved
dispersion strengthening, the normalising treatment also
promotes grain refinement. Grain refinement occurs as a
result of the cycle of solid-state phase transformations that
occurs on heating into the austenite region and then
cooling again to allow the decomposition of austenite to
form ferrite and cementite. This process is shown
schematically in Figure 4. Upon heating, the multiple
nucleation of austenite at the grain boundary sites results
in a much finer austenite polycrystalline microstructure
than the starting ferrite and pearlite structure. On
condition that the austenite temperature is not too high
and/or the soak time at temperature is not too long, the
austenite structure will

Figure 4: Refinement of grain structure

during normalizing heat
treatment.

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-4-
not grow appreciably at temperature. When cooled again, and since the cooling rate is relatively
fast (but not too fast so as to form martensite), multiple nucleation of proeutectoid ferrite and
then eutectoid ferrite and cementite will occur at the pre-existing austenite grain boundaries.
Since these products are being nucleated from a finer parent, the resultant low temperature
microstructure of ferrite and pearlite is much finer than the microstructure prior to the
normalisation process. If this process is repeated again, then the microstructure will refine
further. There is of course a limit to the level of grain refinement since the increase in surface
energy that derives from the grain size reduction will eventually drive grain growth at a certain
rate to reduce the extent to which the austenite can be refined at temperature.

Spheroidising: Steels, which contain a large concentration of Fe3C, have poor machining
characteristics. It is possible to transform the morphology of Fe3C using spheroidising. The
particular plate-like morphology of the alternating ferrite and Fe3C grains in pearlite lead to
relatively high grain boundary surface area per unit volume, and consequently high surface
energy per unit volume. During the spheroidising treatment, which takes several hours at about
30C below the A1 temperature, the Fe3C phase morphology changes into large, spherical
particles in order to reduce grain boundary area. The microstructure, known as spheroidite, has
a continuous matrix of soft, machinable ferrite (Figure 5). A similar microstructure occurs
when martensite is tempered just below the A1 for long periods of time, but this is discussed in
more detail later.

Figure 5: The microstructure of spheroidite, with Fe3C particles dispersed in the ferrite matrix. The Fe3C
particles range in size up to about 10 microns.

Controlled Heat Treatments of Plain Carbon Steels

So far we have considered the decomposition of austenite to form the equilibrium products of
ferrite and cementite on the one hand, and the formation of the highly metastable non-
equilibrium martensite as an alternative product. However, the decomposition of austenite can
be controlled to produce a greater variety of microstructures with corresponding variation in
mechanical properties. As the isothermal transformation temperature decreases, pearlite
becomes progressively finer before bainite begins to form. At very low temperatures,
martensite forms.

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Before we look at the Time-Temperature-Transformation (TTT) diagrams that illustrate the
formation of the different transformation products, it is necessary to first describe the formation
of bainite and martensite.
Bainite: The microstructure of bainite consists of ferrite and cementite phases, and thus
diffusional processes are involved in its formation. Pearlite is a diffusional transformation that
occurs between about 550C and 720C, whereas martensite forms at much lower temperatures
when diffusion is not possible. Hence there is a temperature band below 550C when neither
of these phases forms. This is the region in which lath-shaped fine aggregates of ferrite and
cementite are formed that possess some of the properties of the high temperature reactions
involving ferrite and pearlite as well as some of the characteristics of the martensite reaction.
Bainite forms as needles or plates, depending on the temperature of the transformation; the
microstructural details of bainite are so fine that their resolution is possible only using electron
microscopy. Between about 400C and 550C the morphology is described as upper bainite
and consists of stringers of Fe3C in ferrite laths. At lower temperatures, fine platelets of Fe3C
are precipitated within the ferrite and are usually aligned along specific crystallographic planes
in the ferrite (referred to as lower bainite). The morphologies of upper and lower bainite are
represented schematically in Figure 6 and can be compared with the formation of pearlite.

Figure 6: Schematic representation of the formation of pearlite, upper bainite and lower bainite.

Unlike martensite described below, bainite does involve diffusion of carbon. However, the
diffusion rate, and hence diffusion distance, is much more limited than that which occurs during
the higher temperature diffusion-controlled eutectoid transformation that leads to the pearlite

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morphology. Consequently, Fe3C forms at the ferrite grain boundaries to alleviate the high
carbon content that gathers ahead of the nucleated ferrite grain boundary as shown for the
formation of upper bainite in Figure 7. There is insufficient time for the diffusion-controlled
nucleation and growth of Fe3C adjacent to the ferrite grain (as in the eutectoid reaction), which
would lead to lower grain boundary (surface) energy and hence would be preferred at higher
transformation temperatures. Instead, multiple Fe3C precipitates form at the ferrite grain
boundary, which although produces higher grain boundary energy, the multiple nucleation
speeds up the transformation which is driven by the high undercooling (T) and hence high
thermodynamic driving force. The precipitation of the Fe3C reduces the local carbon
concentration and hence the ferrite grain can grow until the carbon concentration again becomes
sufficiently high to result in another wave of Fe3C precipitation at the new position of the ferrite
grain boundaries. Consequently, the end result is that the Fe3C precipitates appear within the
ferrite grain and at the grain boundary, and they are at much shorter distances apart than would
be the case when the eutectoid reaction occurs (see later discussion on mechanical properties).
The process has so far been described for a single ferrite grain (as in the first two illustrations
for upper bainite formation in Figure 7), but of course it is possible for multiple ferrite grains
to nucleate as seen in the remaining two illustrations for upper bainite formation. Again, it is
possible to support the argument for repeated ferrite nucleation in order to speed up the reaction
under the high thermodynamic driving force.

Figure 7: Closer look at the comparison of upper bainite and lower bainite formation.

There is no distinct cut-off between the formation of upper bainite and lower bainite and hence
the distinction between the two morphologies becomes less obvious at some point during the
cooling industry. The broad temperature range over which bainite can form is approximately
described in Figure 11. However, it is possible to identify the lower bainite morphology at
transformation temperatures above the martensite-start (Ms) temperature. In this case there is

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even less time for carbon diffusion, and instead of Fe3C precipitation occurring at the ferrite
grain boundaries, Fe3C precipitation occurs within the small ferrite grains in order to reduce the
level of carbon saturation in the ferrite. Of course this leads to even higher additional grain
boundary (surface) energy because the Fe3C precipitation is not able to take advantage of a pre-
existing (ferrite) grain boundary; but, again the much increased thermodynamic driving force
allows this to happen and the result is an even finer distribution of Fe3C precipitates in the
ferrite. The multiple nucleation of ferrite leads to the progressive formation of lower bainite as
displayed in the illustrations in Figure 7.

Martensite: Martensite is a phase that forms as the result of a diffusionless solid-state

transformation. In this transformation there is no diffusion and, hence, it does not follow the
Avrami transformation kinetics. The growth rate in martensitic transformations is so high that
nucleation becomes the controlling step. In steels, the FCC austenite transforms to body-
centred structure, but in view of the carbon that is locked in the lattice, the body-centred lattice
becomes distorted and results in a body-centred tetragonal (BCT) lattice rather than a BCC
lattice. The relationship between the FCC austenite and the BCT martensite (Figure 8(a)) shows
that the carbon atoms in the interstitial positions in the FCC lattice can be trapped during the
transformation to the body-centred structure, causing the tetragonal structure to be produced.
As the carbon content of the steel increases, a greater number of carbon atoms are trapped in
these sites, thereby increasing the difference between the a- and c-axes of the martensite (Figure
8(b)).

Figure 8: (a) The unit cell of BCT martensite is related to the FCC austenite unit cell. (b) As the percentage
of carbon increases, more interstitial sites are filled by the carbon atoms and the tetragonal
structure of the martensite becomes more pronounced.

In addition to the non-equilibrium BCT crystal structure that forms as a result of the c-axis
distortion caused by the locked-in interstitial carbon atoms, the shear transformation that occurs
to enable the body-centred crystal structure to form results in the development of very high
dislocation density. The dislocations develop due to the multiple slip that is necessary on
alternating crystal planes in order to maintain shape continuity within the parent austenite grain.
___________________________________________________________________________
-8-
Thus the formation of martensite in steels leads to high dislocation densities comparable to that
of very highly cold-worked metal (see later discussion on mechanical properties). The process
of slip (and hence dislocation formation) is illustrated in Figure 9. Figure 9(a) shows the shear
that is necessary to form the BCT crystal structure. However, this shear leads to a shape
discontinuity and hence cannot be accommodated within the austenite parent crystal (grain). In
order to allow the shear to occur (and hence formation of the BCT martensite crystal), and still
maintain shape continuity, multiple slip must occur on adjacent planes as shown in Figure 9(b).
In this way the shape continuity is still maintained, although the local residual stress will be
very high due to the high dislocation density that is produced in order to accommodate the slip
and the shape change.

Figure 9: (a) Shear is necessary to form the

BCT crytal structure from the FCC
crystal without diffusion. But the
shape change cannot be
accommodated in the parent austenite
grain. (b) Crystallographic slip
occurs on adjacent planes by
dislocation formation and movement
in order to accommodate the shape
change.

The plain carbon steel must be quenched, or rapidly cooled, from the stable austenite region to
prevent the formation of pearlite, bainite or primary micro-constituents. The martensite
reaction begins in a eutectoid steel when austenite cools below 220C, and is referred to as the
martensite start (Ms) temperature (Figure 11). The amount of martensite increases as the
temperature decreases. When the temperature passes below the martensite finish temperature
(Mf), the steel should contain 100% martensite. At any intermediate temperature, the amount
of martensite does not change as the time at that temperature increases (referred to as an
athermal reaction). Owing to conservation of mass, the composition of martensite must be the
same as that of the austenite from which it forms. There is no long-range diffusion during the
transformation that can change the composition. Thus, in iron-carbon alloys, the initial
austenite composition and final martensite composition are the same.

Time – Temperature – Transformation (TTT) curves

The equilibrium phase diagrams presented in Figure 1 do not consider the kinetics of the
transformation. The equilibrium diagram assumes that sufficient time is available for the
diffusion-controlled transformations to occur to completion. In reality, heat treatments are
generally performed under non-equilibrium conditions and therefore the cooling rate during the
heat treatment will determine the eventual microstructure at room temperature. A carefully
constructed TT curve for a particular steel composition will provide guidance as to what
microstructures will evolve during various cooling histories. Although the TTT curves are
constructed by performing isothermal heat treatments, the situation will not be too different
during continuous cooling (or combined continuous cooling and isothermal holding periods)
and reasonable approximations can be deduced for the final room temperature microstructures.
Figure 10 indicates the approach to constructing a TTT curve for a eutectoid (0.8wt% carbon)
steel. The steel is rapidly cooled from above the eutectoid temperature (727C) to a range of

___________________________________________________________________________
-9-
holding temperatures (isothermal) followed by rapid cooling to room temperature after set
periods (Figure 10(a)). The resulting microstructures are examined and the time is detected at
which 50% of the microstructure has transformed to pearlite during the relevant isothermal
holding period (Figure 10(b)). Of course the start and finish temperatures can also be detected
as indicated by points C and D respectively in Figure 10(b). The full spectrum of isothermal
intervals and wide range in holding periods will yield many microstructure combinations at
room temperature, which when examined for phase type and volume fraction will yield a
complete diagram as shown in Figure 11(a-c) for hypo-eutectoid, hyper-eutectoid and eutectoid
steel compositions.

Figure 10(a): Construction of the time-temperature-transformation (TTT) diagram for a eutectoid steel.

Figure 10(b): Indication of the transformation progress as austenite transforms to pearlite and the transfer of
this data to the TTT diagram for a eutectoid steel.

___________________________________________________________________________
- 10 -
___________________________________________________________________________
- 11 -
(c)
Figure 11: The time-temperature-transformation (TTT) diagram for a (a) hypo-eutectoid, (b) hyper-
eutectoid and (c) eutectoid steel. Ps, Bs and Ms are the pearlite start, bainite start and martensite
start points respectively. It can be seen from this diagram that pearlite and bainite are isothermal
reactions, whereas martensite is not.
Martensite in steels is very hard and brittle, just like ceramics. The BCT crystal structure has
no close-packed slip planes in which dislocations can easily move. The martensite is highly
supersaturated with carbon, since iron normally contains less than 0.022 % carbon at room
temperature, and of course martensite contains the amount of carbon present in the steel.
Finally, martensite has a fine grain size and an even finer substructure within the grains due to
the high dislocation density that arises from the accommodation of multiple shear that
accompanies the crystallographic transformation from FCC to BCT crystal structure. The
structure and properties of steel martensites depend on the carbon content of the alloy (Figure
12). When the carbon content is low, the martensite grows in a lath shape, composed of bundles
of flat, narrow plates that grow side by side (Figure 13(a)). This martensite is not very hard.
At higher carbon content, plate martensite grows, in which flat, narrow plates grow individually
rather than as bundles (Figure 13(b)). The hardness is much greater in the higher carbon, plate
martensite structure, partly due to the greater distortion, or large c/a ratio, of the crystal
structure.

Figure 12: The effect of carbon

content on the
hardness of
martensite in steels.

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- 12 -
Figure 13: (a) Lath martensite in low-carbon steel (X80). (b) Plate martensite in high-carbon steel (X400).

Mechanical Properties
The tensile yield strength is determined by the onset of dislocation movement. Consequently
the yield strength is increased as the density of obstacles to dislocation movement increases
(see strengthening mechanisms in Chapter 1). Taking this into account, the yield strength as
function of cooling rate for a plain carbon steel will increase as the microstructures change from
coarse pearlite, fine pearlite, upper bainite, lower bainite to martensite. This is schematically
illustrated in Figure 14(a). Since dislocation movement can be accommodated in ferrite but not
in Fe3C nor in highly dislocated and distorted martensite, it is easy to argue why the yield
strength should increase according to Figure 14(b). As the fineness of pearlite increases the
mean free path for dislocation movement in ferrite decreases and hence there is more grain
boundary restriction to dislocation movement. In the case of bainite the fine distribution of
Fe3C precipitates in ferrite decreases the mean free path for dislocation movement in ferrite
even further and hence there is a further increase in yield strength. Martensite, on the other
hand, produces an entirely new crystal structure (BCT), which combined with high dislocation
density, makes dislocation movement very difficult. Consequently the yield strength rises even
further. Since carbon is key to the microstructural features that occur in the steel during cooling
at variable rates, it is obvious that the level of strengthening will increase as the carbon content
in the steel increases. In the case of pearlite and bainite, the volume fraction of Fe3C will
increase according to the carbon level, and the tetragonality of the BCT martensite phase will
also increase as the increased carbon locked in solid solution leads to enhanced distortion of the
crystal structure. The latter effect is shown in Figure 8(b) and Figure 12.

___________________________________________________________________________
- 13 -
Figure 14: (a) Different cooling rates superimposed on TTT diagram for a eutectoid (0.8wt%) carbon steel:
 = coarse pearlite;  = fine pearlite + lower bainite;  = fine pearlite + lower bainite +
martensite;  = martensite.

Figure 14: (b) Tensile properties

as function of cooling
rates indicated in (a).
The red curves indicate
the nominal effect if a
higher carbon steel is
cooled in a similar
sequence.

Tempering of Martensite: – martensite is not an equilibrium phase. This is why it does not
appear on the Fe-Fe3C phase diagram. When martensite in steel is heated below the A1
temperature, the thermodynamically stable ferrite and Fe3C phases precipitate. This process is
called tempering. The decomposition of martensite in steels causes the strength and hardness
of the steel to decrease while the ductility and impact properties are improved (Figure 15). At
low tempering temperatures the martensite may form two transition phases- a lower carbon
martensite and a very fine non-equilibrium carbide. The steel is still strong, brittle, and perhaps
even harder than before tempering. At higher temperatures, the stable ferrite and Fe3C forms
and the steel becomes softer and more ductile. If the steel is tempered just below the A1
temperature, the Fe3C becomes very coarse and the dispersion-strengthening effect is greatly
reduced. By selecting the appropriate tempering temperature, a wide range of properties can

___________________________________________________________________________
- 14 -
be obtained. The product of the tempering process is a micro-constituent called tempered
martensite (Figure 16).

Figure 15: Effect of tempering temperature on

the mechanical property trend of a
eutectoid steel.

[Image width = 200 microns]

Figure 16: Tempered martensite as indicated in a light micrograph. The actual precipitated
carbides are not distinct due to their very small size but the darkened etched
effect indicates their presence.

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- 15 -
Role of alloying elements in carbon steels

If one critically examines the equilibrium Fe-C phase diagram, it is clear that carbon expands
the temperature range over which the FCC crystal form of iron is stable. For example, pure
iron will not exist in the FCC crystal form below 910C, whereas for a plain carbon steel the
FCC austenite phase (containing carbon in solid solution) can be stable down to the eutectoid
temperature at 727C. Thus we say that carbon in steel is an austenite stabilising element.
There are many other austenite stabilising elements, and indeed there are also ferrite stabilising
elements. The addition of alloying elements to plain carbon steels can influence the equilibrium
diagram in two ways:

(a) By expanding and opening the -field, even increasing the stability of austenite below
room temperature, and encouraging the formation of austenite over wider compositional
limits (Figure 17(b)). These elements are called -stabilisers or austenite
stabilisers/formers.
(b) By contracting and/or closing the -field, even to the point where the ferrite phase is
continuous from post-solidification all the way down to room temperature, and
encouraging the formation of ferrite over wider compositional limits (Figure 17(a)).
These elements are called -stabilisers of ferrite stabilisers/formers.
Austenite stabilisers:
Important elements that fall into this category are carbon, nitrogen (both interstitial elements)
and the substitutional elements nickel, manganese, zinc, cobalt and copper. Carbon and
nitrogen have by far the strongest potency for stabilising austenite, but there are many good
reasons why the level of these elements should be minimised in steels to avoid embrittlement
and deleterious effects on corrosion resistance (see later chapter on stainless steels). Nickel
and manganese are added to stainless steels in amounts in excess of 5wt% to stabilise
austenite at room temperature to form the important austenitic stainless steel family.
Ferrite stabilisers:
Substitutional alloying elements in this category include titanium, vanadium, molybdenum
and chromium (all are also strong carbide forming elements*), as well as silicon, aluminium,
beryllium and phosphorous. The ferrite stabilisers restrict the formation of -iron, causing
the -area of the diagram to contract to a small area referred to as the -loop. This means
that the relevant elements are encouraging the formation of bcc iron (ferrite), and one result
is that the - and -phase fields become continuous (Figure 17(a)). Alloys in which this has
taken place are, therefore, not amenable to the normal heat treatments involving cooling
through the /-phase transformation.
* when a substitutional alloying element combines with carbon to form a stable carbide, the
carbon that is removed from the austenite solid solution will tend towards destabilising the
austenite phase. In this way the formation of the carbide (or indeed a nitride) will have an
indirect effect of stabilising the ferrite phase.

___________________________________________________________________________
- 16 -
Figure 17: Influence of (a) ferrite-stabilisers and (b) austenite-stabilisers respectively on the phase field
stability for steels.

Hardenability
Alloying elements, on the whole, retard both the pro-eutectoid reactions and the pearlite
reaction so that TTT curves for alloy steels are moved increasingly to longer times as the alloy
content is increased. Additionally, those elements which expand the -field depress the
eutectoid temperature, with the result that they also depress the position of the TTT curves
relative to the temperature axes. This behaviour is shown by steels containing Mn or Ni. See
for example Figure 18 where the addition of Mn not only depresses the eutectoid temperature,
but also moves it to lower carbon levels. For example, in a 13Mn-0.8wt%C steel, pearlite can
form at temperatures as low as 400C. Of course this means that diffusion is much slower at
this low temperature and hence the time required for the transformation to start and finish is
increased substantially. In contrast, elements which favour the ferrite phase raise the eutectoid
temperature and the TTT curves move correspondingly to higher temperatures. See Figure 19
where the addition of Ti raises the eutectoid temperature and moves the eutectoid composition
to lower carbon levels. The additional requirement for Ti partitioning during the transformation
means that longer transformation times are required (TTT curve moves to the right). Despite
the increase in transformation temperature, the diffusion required by the alloying elements in
order to partition between the ferrite and austenite, and in particular since they are mostly
substitutional alloying elements, slows the transformation progress substantially. Again, the
influence of the additional alloying elements will move the TTT curves to the right (i.e. longer
times). There are a few elements that tend to move the TTT curves to the left, namely Si, Al,
Co and P, but their effect is mostly over-shadowed by other alloying elements and hence the
net effect is a move towards longer transformation times. See Figure 20 for summary.

___________________________________________________________________________
- 17 -
Figure 18: Influence of manganese (which is a -stabiliser) on the size and shape of the -field for a 0.35wt%
carbon steel.

Figure 19: Influence of titanium (which is a -stabiliser) on the size and shape of the -field for a carbon
steel.

___________________________________________________________________________
- 18 -
The slowing down of the ferrite and pearlite reactions by alloying elements enables these
reactions to be more readily avoided during heat treatment, so that much stronger low-
temperature phases such as bainite and martensite can be obtained in the microstructure. The
hard martensitic structure is only obtained in plain carbon steels by water quenching from the
austenitic condition whereas, by the addition of alloying elements, a lower critical cooling rate
is needed to achieve this condition. Consequently, alloy steels allow hardening to occur during
oil quenching, or even on air cooling, if the TTT curve has been sufficiently displaced to longer
times. We thus say that the hardenability of the steel has increased (note: this does not
necessarily mean that the peak hardness of the steel has increased, but rather that the ability to
harden the steel at a lower critical cooling rate has increased). Increased hardenability provides
particular benefit when thick section components are required to be strengthened by quench
and temper heat treatment processes, and/or thermal shock is to be avoided during cooling so
as to minimise the risk of cracking and distortion occurring. However, increased hardenability
does mean that the propensity for martensite formation in the heat affected zone (HAZ) during
fusion welding operations increases and hence post-weld heat treatments (PWHT) are required
to temper the HAZ after the welding operation is completed.

Figure 20: Indication of the influence of alloying elements on the position of the transformation start curves
on a TTT diagram.

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- 19 -
AC = air-cooled after heat treatment

FC = furnace-cooled after heat treatment

Materials = EN1, EN3, EN8 and SS

Mag = magnesium

Figure 1: EN1 – AC
Figure 2: EN1 – FC

Figure 3: EN3 – AC
Figure 4: EN3 – FC
Figure 5: EN8 – AC

Figure 6: EN 8 – FC
Figure 7: SS - AC High Mag

Figure 8: SS - AC Low Mag

Figure 9: SS - FC High Mag
Figure 10: SS - FC Low Mag