In Fig.1 A to
B is the Hooke's law
region. B is the proportional
limit . C is the elastic
limit , beyond which there is permanent set , and
if the stress is removed the graph returns as shown dotted.
D is the yield point, at
which the yield stress acts.
E is the point at which the main
plastic flow processes begins.
F is the breaking strain or
stress . G is the point at which
the sample will finally break, if being tested with a tensometer.
The area under the graph represents the energy per unit volume stored
in the stretched sample. The area between the solid line and the
dotted line is the energy converted from mechanical to heat if the
sample is stretched and then unstretched.
The graph only falls between F and
G because the stress is being worked
out relative to the original area of the wire - giving the
nominal stress . The fall is because in this region the
wire has reduced in cross-sectional area, forming the
neck at which it will eventually break. (Using the
reduced area of this neck, the calculated real stress would not fall,
and so the graph would be flat in this final section. This is not
particularly relevant to a practical engineer)
Max. elastic strain 0.5%; max. plastic strain 50%.
Materials are classified as:
(i) Strong/Weak , defined as its
breaking stress i.e. the stress needed to break it.
{For Engineers, the initial yield strength may be more important than
the maximum load strength; a metal pylon which has bent out of shape
could reasonably be described as having 'failed', even though it is
now broken}
(ii) Stiff/Flexible , defined as its
Young's Modulus E (the steepness of the
elastic straight initial section of the Stress/strain graph) i.e. how
difficult it is to stretch it.
(iii) Tough/Brittle , defined as the
total area under the graph to the breaking point. It is therefore,
for example, measurable by swinging a pendulum down to break the
sample, and finding how much energy the pendulum loses in the
process. For a given strength, toughness is therefore a measure of
how much the material stretches before it breaks.
(iv) Ductility , defined more loosely
as the breaking strain i.e. how much the material can be stretched
before it breaks; it applies to reshaping by drawing. A closely
linked quality is malleability ; which
is ability to be reshaped by hammering.
One material, for example, must be 'tougher' than another if it has
the same strength, but greater ductility.
Ductility is related to the extent of the plastic region, which
itself is an indication of resistance to crack growth {The
hardness of a material is separately defined, as
resistance to plastic indentation; it is measured by pressing a
standard indentor with standard force onto the material's surface,
and finding the diameter of the dent produced}
Glass, for example, is strong but brittle. Metals are strong, and
useful for construction because they are tough and therefore can be
moulded by, for example, cold pressing into new shapes. Epoxy resin
is strong and tough.
Alloys: Types of iron and
steel : Pure iron, like most pure
crystalline metals, is soft and ductile. Ferrite, with little Carbon,
is soft and ductile. As the impurity Carbon is added we obtain
Wrought Iron, which is about 0.04% Carbon. {This was discovered by
chance; in about 1400 BC the Hittites of Anatolia (now Turkey) found
that if iron was heated in charcoal, it became much stronger. The
adding of Sulphur to pure rubber is similar} Adding more Carbon gives
the Carbon Steels, which include between 0.04% Carbon (Mild
Steel is about 0.25%) and 2.25% Carbon (High Carbon
Steel covers about 0.6% to 2%). (Confusingly, the rather
brittle material with 2% to 4% Carbon is called Cast Iron) Mild
steel, which is strong and tough, is useful for construction
purposes, for sheet steel for the car industry, for wires, for pipes,
and for girders; it can be moulded by pressure, even when cold. By
contrast, High Carbon steel, which is even stronger, but more
brittle, is used for tools and cutters; it is very hard to mould, and
therefore instead tends to be cast.
Stainless Steel is iron combined with 18% Chromium, 8% Nickel, and
0.15% Carbon. It is used, for example, for cooking utensils.
Brass, similarly, is stronger than Copper. Silver becomes stronger as
it is combined with Copper (7.5%). Pure Gold is too weak and flexible
for many purposes, and therefore is combined with Silver to make it
stronger and stiffer for use in jewellery.
The graph on the left shows the effect of
combining two metals in an alloy. There is no yield point. Instead,
there is a quite smooth transition from the elastic to the plastic
region. The same shape is obtained for, say, pure Aluminium, Iron,
and Copper.
The graph on the right shows a material which is brittle. It extends
according to Hooke's law, and then suddenly breaks. There is no
plastic flow {This graph also describes the behaviour of glass}
Class prac with long copper wire, weights, pulley
(see Duncan). Look at the broken ends for the neck ,
using a low-power microscope.
Heat Treatments
Annealing is the heating of a
metal to just below its melting point, keeping it there for a while,
and then letting it cool slowly. The metal is found to be more
flexible, ductile, and tough, as a result (Demo or class
prac with paper clip, bent first, then heated to red heat in
a Bunsen for, say, 2 min; when cooled in air, it is much more
flexible).
Work hardening is the flexing, stretching, 'working', of
a metal, which makes it stiffer (it happens even on a single
stretching of a metal wire in an experiment). (Class
prac with soft iron sheets; if they are repeatedly flexed,
you can feel the region getting more difficult to bend - you can also
feel the heat generated as work is done on the metal). If a metal is
drawn through a die , to make a wire, then it is
strengthened, though made less tough, in the process. This is not
helpful if we are making copper wires, but it is if we are making
wire for steel-belted radial tyres.
Annealing is typically needed to undo the effects of work-hardening,
which occur while a metal is being shaped for some purpose, by
forging (pushing into a mould while warm), extruding, rolling, and
drawing (cold-working). The blacksmith, hammering a lump of metal
into the desired shape - say, a horse-shoe - would regularly anneal
the metal he was working on, in order to make it easier to continue
to reshape. If this is not done, then further working, as well as
being increasingly difficult, will tend to lead to cracking, since
the metal is becoming brittle. Hence a cold-working-annealing
cycle is used.
Quench hardening , of steel, is achieved by heating
to about 800 oC, and then cooling rapidly in water or oil.
{Severe stresses are created in direct quenching, because the outside
cools first. This is reduced by interrupted quenching,
in which the process of cooling is done in two rapid stages, with a
gap.}
Quenching gives strong, relatively brittle, steel.
Tempering of steel is toughening, achieved by
reheating. It often follows quenching, aiming to retain most of the
newly achieved strength of the steel, while reducing its
brittleness.
Creep . This is gradual increase in strain with no
increase in stress. It increases with temperature; it can be as much
as a few percent per hour, at high temperatures with high stresses.
It continues until the metal fractures. Creep is of extreme
importance in turbines and power stations.
Lead has such a low melting point that normal temperatures count as
relatively high for it, so it creeps, for example, on the roofs of
buildings such as churches.
Fatigue is a weakness in metal which develops when
it is subjected to varying stress, typically in periodic cycles - for
example, in aircraft, and in engine connecting rods. Even if the
maximum stress in these cycles is well below the safe limit, this
fluctuating stress causes a small crack to slowly spread, until the
part is so weakened that the remaining section fractures. (No
microscopic explanation is given below)
In Fig. 2, A is the point where the
mutual potential energy is minimum; this is therefore the equilibrium
distance for two atoms. It is also the point,
C , where the mutual force is zero. At
D the force becomes rapidly stronger
and repulsive, as the electron orbitals refuse to overlap because of
the Pauli exclusion principle (a quantum mechanical exchange force).
At E the force is attraction, though
becoming increasingly weak; this is the Van der Waals force, an
electrostatic force due to the electron orbitals not being
consistently centred on the nucleus, making every atom an electric
dipole (???) {The shape of the PE graph follows from that of the
Force graph - indeed the force graph is proportional to the slope of
the energy graph.}
In the elastic region, the atoms
are simply moving slightly away from each other - away from their
equilibrium positions. When the stress is removed, the attractive
force pulls them back to the position. Where the force graph crosses
the axis, the line is roughly straight, so that small increases in
force produce proportional increases in distance, thus explaining
Hooke's law.
If the substance is heated, the atoms gain vibrational kinetic
energy, and move, roughly with SHM, diagonally back and forth along
the force graph. On the PE graph this is represented by moving back
and forth across the potential well. Since the well is unsymmetrical
(the repulsive force increases more rapidly with distance than the
attractive force does), the atoms now spend more time each cycle
further away from each other. This explain the thermal expansion of
the sample.(Demo: Show the model shaped plastic tube with a
ball-bearing)
The energy needed to get from the bottom of the potential well to
zero, multiplied by Avogadro's number, should approximately give the
latent heat of vapourisation per gmol.
At the Yield point slipping of the crystal planes begins
to occur, quite suddenly.
X-ray diffraction as evidence of structure
(Demo use Microwave plus expanded polystyrene sheets,
and then the balls in the block (see Duncan pp.23-4)
In the plastic region, the
slipping of complete crystal planes cannot be the explanation of the
extent, and relative ease, of change of shape. (Demo
with a pack of cards, to show how extension is possible by the
sliding of crystal planes) The problem is that calculations, using
the interatomic force, of the stress needed to produce such slipping,
give results much larger than those actually needed. The proposed
easier mechanism for the slipping is the movement of
dislocations. These may pre-exist
in the metal, or be created by a shear force. The diagram shows a
point dislocation , which is one atom missing from a
regular crystal lattice; it could also be an edge-on view of a
line dislocation , which is a whole row of atoms
missing. (The third kind of dislocation is a three-dimensional twist
of layers of atoms, called a screw dislocation )
The dislocation is just below atom 1. If atom 4 shifts its
bond from 2 to 1, the effect is that the dislocation moves one step
to the right. If atom 5 now shifts its bond from 3 to 2,
the dislocation moves again. The effect is that the layer of four
atoms at the top has moved to the right, relative to the lower layer
of four atoms. The difference between moving one layer of atoms
passed another by this method, rather than by a complete slippage of
a layer, can be illustrated with two sheets of paper on top of each
other on a bench (Demo ). Suppose that a certain
amount of friction acts per unit area of paper, to prevent sideways
motion. If you now slide the top sheet over the bottom one, the
maximum amount of frictional force opposes the motion. Now suppose
that the upper sheet contains a dislocation, illustrated by a 'ruck',
as in a carpet - a section of the paper which is folded up in a loop
(like a line dislocation). This ruck can be moved along, at right
angles to the line, in such a way that no pieces of paper actually
slide past each other at all, although the net result, at the edge of
the paper, is that the top sheet has moved relative to the bottom
one. The frictional force is much reduced, but movement still
occurs.
In the region of a dislocation, some atoms are closer than normal,
others further away. Both lead to extra potential energy. For the
dislocation to move, only a few atoms at a time have to move from
their lowest energy position.
The absence of dislocations explains why a single-crystal whisker of
metal is so much stronger than a normal piece of metal of that
shape.
Alloys. If some Carbon atoms are
put into pure Iron, they lower the potential energy of the atoms near
a dislocation, making more difficult the moving of the dislocation.
The alloy is therefore stronger (by a factor of about 4), but less
tough. The same applies to putting zinc into copper (brass), and tin
into copper (bronze). The dental amalgam is a nice
example, where the liquid mercury becomes solid as a result of adding
silver and tin.
An alloy can be a solid solution , which is a random
mixture of atoms, or intermetallic , with regular
alternation of atoms throughout, or multiphase , with
different crystals mixed together in a grain structure
(see below).
Grain structure. When a metal
crystallises, it does not usually form into one continuous crystal
lattice, with a few lines of symmetry - monocrystalline
. Instead, different regions of the liquid form into individual
crystals, each with their own lines of symmetry -
polycrystalline . These regions are grains
; the interfaces between them are grain boundaries . The
grain is clearly visible under microscope, since the regions can be
etched.
Each grain has its own slip planes, but these will not align with
those of a neighbouring grain.
Therefore at normal, low temperatures, fine grain structure results
in greater strength and less ductility. However, at high
temperatures, creep (see below) occurs more with small
grains, with atomic diffusion across grain boundaries
Annealing and work hardening.
When the metal is originally formed as a liquid, and allowed to cool,
the crystals form with randomly positioned dislocations in the
lattice (of various kinds: point, edge, and screw dislocations). A
few line dislocations will increase the ductility of a crystalline
material by 1000 times. When the sample is first stretched to the
yield point , these dislocations rearrange, as the metal
is observed to yield, to extend with almost no extra force, until the
edge dislocations become pinned into position, in a kind of traffic
jam (dislocation entanglement ). We can imagine the
dislocations moving in various directions through the metal, and
reaching positions at which they cannot move because of other
dislocations blocking their path. At this stage the metal become
stronger, and stiffer, and its yield stress increases; it is also
more brittle.
Working cold also breaks up the grain into smaller
fragments. Since these fragments are now oriented in different
directions, there is less continuity for the slip planes; this
implies that moving dislocations must be redirected as they try to
enter a new grain. The result is like a traffic pile-up on a road, as
a sequence of dislocations travelling in one grain is blocked by a
grain boundary. There is therefore less ability to extend by plastic
flow.
Annealing , heating to below the melting point, followed
by cooling, relieves the stresses that have built up in the metal as
a result of working. The increased random thermal KE enables the
atoms to adjust their bonds (though without breaking free -
liquefying), {The exact effect depends on the temperature reached,
and the length of time taken for the heating and the cooling} so
that, on cooling, re-crystallisation occurs on new 'nuclei'. The
dislocation tangles are removed, and the grain reforms in larger
sections. The actual effect depends on the temperature and the time,
since it is a process of actual atomic diffusion; for example, 15 min
at 580 oC will produce small grain in brass, while 1 hr at
700 oC will produce much larger crystals, and hence a much
weaker, flexible, and ductile, metal.
Creep This occurs in polycrystalline
metals (those which have grains in them), occurring more
at higher temperatures. The smaller the grains, the less far the
atoms have to diffuse to transfer to new grain boundaries. {If the
metal is vertically stressed, the horizontal grain boundaries have an
increased amount of space, while the vertical ones are somewhat
compressed. As a result, atoms tend to migrate, if the temperature is
high enough for them to do so, from the vertical to the horizontal
boundaries, extending the material}
Quench hardening and tempering: The steel contains
grains of austenite (Pure iron, in a face-centred cubic structure,
which exists between - 912 oC and 1394 oC and
in which Carbon atoms can be incorporated to give a solid solution),
martensite, ferrite (pure iron, in a body-centred cubic structure, at
room temperature) and iron carbide (cementite ; a
crystal lattice with three Fe and one C in a repeating pattern;
strong but brittle). {A 'solid solution' means that there is no
special organisation of the iron and carbon atoms, because of the
high temperature}
Austensite will cool to ferrite plus iron carbide, if the carbon is
given time to diffuse from the regions which will become ferrite, and
into those that will become iron carbide. If we cool the austenite
very rapidly (quenching ), this process is avoided, and
instead a body-centred tetragonal form of iron is produced, with the
carbon atoms in the lattice as random impurities (i.e.. still in
solid solution)
Martensite is very strong, but brittle (because of its carbon content
- see above). Tempering , reheating the martensite, can
toughen it without reducing its strength significantly - it replaces
the martensite with a fine dispersion of rigid carbide particles,
within a tough ferrite matrix. The carbide blocks the movement of
dislocations in the ferrite, while the ferrite deforms locally at
points of stress concentration, blunting the tips of cracks when they
start to form.
(amorphous/glassy, like a snap photo of a
liquid)
(Note that plastic is an everyday word which is not used in this section, except in the sense of 'extending with permanent deformation'- in this sense metals show 'plastic' behaviour)
1. Natural eg. hair, silk, wool,
rubber, cellulose (leaves, stems, roots) Artificial ,
made by the polymerisation of normal chemicals such as ethylene eg.
polythene, nylon, glass, ebonite.
Typically polymers have density similar to that of water (1000
kgm-3); their stiffness is about 1/10 th of that of metal;
their strength is about 1/6 th of that of steel (less at higher
temperatures); they suffer more from creep.
2. Two rough types: Amorphous and Semi-crystalline.
More amorphous are soft and flexible (eg. rubber and other elastomers; perspex).
More semicrystalline are strong and
stiff (eg. polyethylene; nylon).
(When stretched, all materials tend to become more crystalline in behaviour i.e.. stiffer).
These are just rough classifications; polymers vary continuously in type from the most crystalline to the most amorphous.
More crystalline materials have an increasingly precise melting temperature tmat which they change from solid to liquid, as the crystals collapse.
The more amorphous a material - with some cross-links (see below) - the less there is a melting point, and the more clearly - instead - there is a temperature called the glass transition temperature tg (the glass point). It is 98 oC for polystyrene; -73 oC for pure rubber. Below 98 oC , polystyrene - in a mug, for example - is brittle and stiff. If it is heated above this value, it fairly suddenly softens, becoming rubbery. Further rise in temperature leads to further softening. The textbooks describe the series of stages as going from 'leathery', through 'viscous', to 'runny'. When the temperature falls below this value, the polystyrene returns to its stiff, brittle, behaviour - called 'glassy'.
Heating a more amorphous material above its tg sounds like melting, but it isn't the same. There is no organised crystal structure to start with, so it can't fall to bits in a dramatic change of state. The material cannot therefore change from a solid to a liquid; it just gets softer and softer. For these materials the melting temperature tm is not defined.
An example of a more semi-crystalline material is Polyethylene, at its densest, cold-drawn; it is about 50% crystalline. It therefore has a reasonably well-defined tg, given in data-books as "about 110 oC". It is getting close to a pure crystal like copper - which remains hard until it melts at a precise temperature. Although it still softens a little before it melts - what is left of the glass transition - there is no clear transition worth marking with a tg.
The diagram above shows how Polythene become rather less stiff, strong, and brittle, as it is heated. However, there is no tg, because there are not enough cross links for it to become rubbery. (Despite N & P 6th edn p.167) Instead, its crystals will fall apart - it will melt - at about 110 oC.
Elastomers are elastic substances which recover their original dimensions after being stretched; they include rubber (with some added sulphur), and synthetic rubbers like SBR (for car and lorry tyres). They can often sustain a strain of 10.
Also, if certain other atoms are introduced into polymers (eg. Sulphur into rubber) they become stiffer (vulcanised rubber), eventually to the extent of becoming very hard. This type, once set hard, does not soften as it is heated, until it is destroyed.
Also, if certain other atoms are introduced into
polymers (eg. sulphur into rubber) they become stiffer (vulcanised
rubber), to the extent of becoming very hard. This type, once set
hard, does not soften as it is heated (until it is destroyed).
The diagram shows the stress/strain graph for rubber, with some
sulphur added. The left-hand graph is the usual one; the top curve is
for extension, the bottom one for subsequent contraction. This
produces a hysteresis loop . Since the area beneath the
upper curve is the work done stretching, and the area under the lower
curve is the work done contracting, the shaded area is the energy
(per unit volume) which has 'gone missing' during the cycle. It has
appeared in the form of heat in the rubber (Class practical
1: A single sudden extension of a thick elastic band
produces a rise in temperature which can be felt on the lips). For
the rubber of, say, a car tyre, it is important that the hysteresis
loop should be as narrow as possible, otherwise the tyre will tend to
overheat - the rubber is said to have greater resilience
.
The left-hand graph also shows that after the long region of easy
extension, the rubber become harder to extend. (Class practical 2:
Stretch a rubber band to show (i) hysteresis loop (ii) remarkable
stiffness) beyond the elastic extension)
If the rubber is cooled below a certain temperature, for example by
plunging it into liquid nitrogen, then its behaviour radically
changes, and it becomes 'glassy'. All more amorphous polymers, such
as rubber, will display glassy behaviour below their g.t.p.
temperature.(Demonstration: If you can get hold of some liquid
nitrogen, a rubber ball or tube can be shattered after immersion in
it)
Polymers also display creep ; the
strain increases under constant stress.
1. A polymer, as its name suggests, is a big molecule made up of
'many mers'. Each big molecule is 1000 to 100 000 atoms, arranged in
repeating sections eg. a cellulose molecule is 1000 X
C6H12O6; Polyethylene
is made from C2H4 ethylene, becoming a
repeating chain of Carbons, with a Hydrogen atom on each side.
The basic repeating unit within the polymer is called a
mer . (The molecule from which the unit has been made,
before its rearrangement, is called the monomer . Thus,
in the case of polyethylene, the monomer is a normal ethylene
molecule, with its double bond)
The ethylene is a gas, a product of cracking petroleum. If it is
heated to about 200oC under a pressure of about 1000 atm,
the double bond between the carbon atoms becomes rearranged, so that
instead of remaining linking the two carbons in a single ethylene
molecule, one bond 'looks outwards', becoming available to bond with
other similarly affected ethylene molecules. This is called
polymerisation - it is usually aided by a catalyst. This
particular kind is called addition polymerisation. {An
alternative is condensation polymerisation, in which the reaction
produces a by-product, often water}
Similarly, nylon is a polyamide .
Two mers can be involved in one polymer, in which case the result is
called a copolymer . {Combining the mers called
butadiene and styrene, for example, gives a common type of artificial
rubber}
3. More semi-crystalline 'forms (eg. polythene, nylon) have chains running parallel to each other; only Van der Waals forces are acting, but they are strengthened by acting along long chains at close range. Evidence : X-ray photos show quite sharp dots (not as sharp as for real crystals of NaCl, though). They tend to be denser, because of the closer order of the molecules, and to have a sharper melting point, than amorphous forms, and less of a glass transition point.
The chance of the long molecules becoming
perfectly aligned along their length is very small; even the densest
polyethylene, in which the molecules are closest packed, shows
evidence of amorphous regions amongst the local regular crystalline
regions.
4. More amorphous forms
(eg. perspex, rubber) have less hint of a lattice structure, being
more of a mass of tangled molecules; the chains run in a coiled,
disordered, tangle (the chaotic tangle shows no sign of organisation
on an X-ray diffraction pattern). The typical length of a molecule,
tangled, will only be the square root of its length if straight. If
these forms are stretched, the molecules become less tangled and
coiled, therefore the material becomes more crystalline in behaviour
(signs of a crystalline organisation begin to appear in the X-ray
diffraction pattern). This occurs with cold-drawn polyethylene.
Pure natural rubber is an example of an amorphous polymer (its
monomer is isoprene - C5H8), as is perspex. It
is stiff and brittle (glassy) when cold (meaning 'below its glass
transition temperature'); it is very soft and sticky when 'hot'. The
chain movement, given the chaotic state they are in, is easier at
higher temperatures. Pure rubber is too soft for any uses, so the
behaviour of, for example, a rubber band, is already the result of
adding some sulphur to the rubber, to create some cross-links and
make the material stiffer.
When amorphous polymers are cooled down from their melting
temperatures, they do not form any kind of nice crystal patterns, and
thus are effectively supercooled liquids. As long as the temperature
remains high enough, molecular vibration occurs in the free space.
However, once temperature falls to the glass transition temperature,
the vibrations have reduced, the free space has reduced, and the
molecules can no longer rearrange into new patterns when stress is
applied. The polymer becomes more stiff and brittle, and is called a
glass . Polystyrene, for example, has a g.t.t. of around
98 oC, which is why it is brittle at room temperature
(Demo : pour boiling water into an expanded
polystyrene cup, in a beaker)
More thermoset polymers Polymers can be modified by introducing other atoms, often oxygen. For example, sulphur is added to pure rubber, by a process calledvulcanisation {Discovered by accident by Charles Goodyear in 1839} Carbon black, added to already vulcanised rubber, produces further strength and stiffness. These atoms make covalent cross-links between the molecular chains, resulting in increased stiffness and brittleness. The resulting material is called a thermoset , meaning that raising its temperature will not cause it to become plastic and malleable. Lightly cross-linked amorphous polymers such as rubber with a little sulphur, and other elastomers, with their wide spacing between cross-links - about 1 link every 100 atoms - have extraordinary elasticity - with breaking strain of up to 10.
Adding more alien atoms leads to highly
cross-linked thermosetting polymers, such as ebonite (which is rubber
with a lot of sulphur), bakelite, melamine, polyurethane, and epoxy
resin, after initial moulding on production, set solid like rubber,
but are much harder, and more brittle. {The molecular structure of
polyurethane paints and varnishes is completed by Oxygen atoms,
entering from the air when the paint is used, and forming
cross-links} They remain hard as their temperature is raised - only
changing as the cross-links break and chemical decomposition
occurs.(Demo: Make some araldite or resin filler. These are
advertised as having larger average molecular weight than their
rivals, presumably implying that these get more effectively tangled
together)
Wood, and wool, are natural thermoset polymers.
More thermoplastic polymers, including both ones
which are more semi-crystalline, and ones which are more amorphous,
have fewer cross links (side branches); the chain molecules are held
together primarily by Van der Waals forces. If they are heated
moderately - in the case of the more amorphous, above the glass
transition temperature - the vibration of the molecules weakens the
Van der Waals force, and the material becomes more plastic and can
be easily moulded. The material is effectively inclined to behave
as a liquid, in terms of the kinetic energy of its molecules, but is
restrained from entirely doing so by the links between the long
molecules. When it cools it retains its previous properties. (If
heated too much, as with thermosets, the covalent bonds between atoms
in the molecular chain break, decomposing the material -
Depolymerisation )
The molecular explanation of the appearance of the glass transition point with more amorphous polymers.
Rubbery behaviour, intermediate between solid and liquid, depends on the presence of a moderate number of cross-links between the long molecules. As long as the temperature remains high enough, molecular vibration occurs in the free space. However, once the temperature fall to the glass transition temperature, the vibrations have reduced, the free space has reduced, and the molecules can no longer rearrange into new patterns when stress is applied. The polymer becomes more stiff and brittle, and is called a 'glass'.
Polystyrene is fairly amorphous, with a fair number of cross links. It has a gtt. of 98 oC, so it is brittle at room temperature, but goes rubbery at 100 oC. (Demo: As already described: Squeeze a thin white polystyrene cup to show its brittleness. Now pour fresh boiling water into the cup - with the cup in a beaker! Watch it collapse.) It brittleness is the result of the cross links, which prevents the molecular rearrangement which would otherwise reduce stress at the sharp end of a crack.
A polymer with no cross links, whether more amorphous or more semicrystalline, behaves more like a pure crystal as the temperature rises; at a particular temperature it changes quite suddenly from solid to a liquid. This applies to pure rubber, and to pure polythene. Either the molecules are held in a structure, or, once they have enough kinetic energy, they become independent.
In other words, it is the presence of a moderate number of cross-links which enables a material, within a certain range of temperatures, to go into the soft, rubbery, state - intermediate between solid and a liquid - characteristic of a thermoplastic. Too many cross-links, and the material is permanently solid (thermoset). Too few cross-links, and it is either a liquid or a solid.
Examples of polymers: These polymers tend
to be destroyed by ultra-violet light - which is a problem if they
used outside. Polyethylene for outside use, for example, needs to be
combined with carbon black to produce a composite material (see
below) in which the carbon protects the polymer from the u.v.; this
is what outdoor piping and gutters are often made of.
Teflon, devised in 1938, is polyethylene with all the hydrogen atoms
replaced by fluorine atoms (polytetrafluoroethylene); it is heat
resistant to chemical degradation, and doesn't soften up to about 250
oC. It is also an electrical insulator, and has low
friction.
Styrene is a monomer like ethylene, but with one H replaced by a
benzene ring; polymerisation gives polystyrene, where the benzene
side group links the chains together, making the polymer
relatively stiff and brittle. When foamed, it is used for cups, for
insulation, and for flotation.
Acrylic has a more complex side group, preventing much
crystallisation. Again, it is strong, stiff, and brittle. Its two
special properties are transparency, and resistance to chemical
degradation by u.v. - properties which make it attractive both to
painters, and to designers of household display items.
Molecular explanation of brittleness:
Samples of material tend to have minute cracks, about a micrometer
long, in their sides. When the sample is stretched, this can produce
brittleness.
The diagram shows the mechanical effect of a small crack in
concentrating stress lines in the material close to the end of the
crack. The effect can be experimentally demonstrated using polarised
light in Photoelastic stress analysis (demo with two
polaroids and a plastic protractor) The result is that the crack
tends to spread across the material, leading to brittle failure. This
effect is very noticeable with glass. (demo
of glass cutting)
In the case of metals, the build-up of stress near the tip of the
crack, threatening to break the next bond, is released by plastic
flow; dislocations move into the region of the crack, blunting its
tip. In metals, the edge dislocations shift, blunt the crack tip, and
reduce the stress concentration.
Most crystalline (with no cross-links): Dense Polythene (especially if cold-drawn) (tm @ 110 oC).
Less crystalline (with some cross-links) thermoplastics: Low Density Polythene; Polystyrene (tg @ 98 oC; Nylon (tg @ 230 oC); PVC (tg @ 80 oC)
More amorphous (with some cross-links) elastomers: Rubber in rubber bands (tg @ -73 oC)
More amorphous (with many cross-links) thermosets: wood; bakelite; epoxy resin and natural resin (no tg and no tm)
Most amorphous (with no cross-links): Pure natural rubber (tg @ -50 oC)
The following graphs are mainly taken from past London Board examination questions, showing the kind of information that the pupil should know.
Concrete , which is cement with sand and gravel, is
a material which is strong under compression, but weak under
extension.
To improve its strength under extension, it is
reinforced. Typically the concrete is made around steel
bars, taking advantage of the strength of the metal under extension.
{Conveniently, the thermal expansivity of both materials is
almost exactly the same, so that temperature changes will not tend to
loosen the bars in the concrete}
A step beyond this is pre-stressed
reinforced concrete , in which the steel bars embedded in the
concrete have already been extended. This enables the concrete to be
in compression, even when it is used as a beam where the lower edge
would normally be in tension - the lower edge merely becomes less
compressed, and the difference between the compression of the upper
and lower edges provides the necessary force to counteract
gravity.
Fibre-reinforced plastic (FRP) A fishing rod can be
constructed of parallel glass fibres bonded together by polymeric
resin (or polyester). The glass gives the composite its stiffness,
while the resin is stronger; the glass has about 10 times the
stiffness of the resin, while the resin has about 20 times the
strength of the glass. The two materials need to deform together, to
preserve the object; a shear stress will occur at the interface
between the glass and the resin, so they need to be well bonded.
In fibreglass, the fibres can be arranged longitudinally (fishing
rod, pole for pole-vault), in a two-dimensional grid (boat hull
shell), and in all directions (safety helmet).
Foamed polystyrene is technically a composite of polymer and gas cells. If the cells are closer it is suitable for flotation. If they are open it is used for absorbing liquid.
Wood is a composite, consisting
of 50% cellulose, a polymer of C, H, and O, with no side branches -
therefore partially crystalline - and 25% lignin, which is a
three-dimensional, cross-linked, polymer. It has a Young's Modulus of
7 X 109 Pa, not many orders of magnitude less than
steel.
Plywood is a laminate, made from thin (about 1 mm) layers of wood
placed one on top of the other with the grain of each perpendicular
to its neighbour. It therefore does not have the strong and weak axis
that a single wood slice of equivalent thickness would have.
Epoxy resin can be combined with Aluminium powder, to give a
composite which is easier to machine.
Classifications therefore are:
Laminates (plywood); fibre composite (FRP);
particle composite (concrete).
Bridging a space with beams
The precise study of materials is valuable because the engineer wants
to be able to choose, or design, an appropriate material to satisfy a
human need. For example, people may want to build a bridge across a
river; they may want to build a support for a roof across the top of
a house.
The magnetisation is the sum of the magnetic moment of
the atoms of the material (per unit volume). Each atom behaves as a
tiny magnet. The relative permeability mr is the ratio
of the B in the material to the applied
Bo
Compare this with the absolute permeability of the
vacuum, mo.">(ie.
the field that would exist in a vacuum, in the region where the
material is - as a result of, say, the electric current in the coils
of a solenoid).
Ferromagnetism : Pure soft Iron, for example, at
temperatures below 768 oC, displays
ferromagnetic property, due to the tiny magnets (atoms'
magnetic dipole moments) being aligned into domains. If the random
thermal motion of the atoms is not too great, the local fields of
neighbouring atoms cause a spontaneous parallel alignment of the
magnetic moments - giving a lower energy ordered configuration.
Spontaneous alignment also occurs in Nickel below 358 oC,
Cobalt below 1 130 oC, and Gadolinium below 16
oC. (??? check) (Demo of Gadolinium in
hot water)
Each atom's magnetic dipole moment is due to the electron spin,
combined with the orbital magnetic effect, in incomplete shells. In a
magnetic field, the domains line up, increasing the strength of the
field in the region. Soft iron (pure) is attracted by a non-uniform
magnetic field, experiencing a force in towards the region of
stronger field.
Paramagnetism : (Para- meaning
'like') Above the Curie temperature , the domain
alignment in iron is temporarily destroyed by the increasing thermal
kinetic energy of the atoms; the iron now displays paramagnetic
properties. It is still attracted into a non-uniform field,
but much more weakly. This attraction is common to materials which
are not ferromagnetic at any temperature.
It is inversely proportional to the absolute temperature.
The microscopic explanation is that the magnetic dipoles are randomly
arranged, operating independently - unlike in ferromagnetism But when
the field is applied, the little magnets still tend to line up in the
field - though not as effectively as when they are already in
organised domains. The higher the temperature, the more the random
shifts of orientation of the atoms dominates the lining up.
Diamagnetism: In 1845 Michael
Faraday discovered that Bismuth and glass are repelled by a magnetic
field; other examples are copper, gold, silver, and lead. They have
negative magnetic susceptibility (the field is reversed in the
material ???, or is it just less than 1). This is an application of
Lenz' law; the orbiting electron experiences a changing magnetic
field as it orbits, and therefore alters its orbit in such a way as
to reduce the change.
Hysteresis curve
. In ferromagnetic materials, as
Bo
rises, B also rises,
but tends to level off (Saturation ). If
Bo
is now reduced to zero, the material remains (weakly)
magnetised (the remanence). To eliminate it, a coercive
field must be applied in the opposite direction.
Soft iron has a low coercivity, low retentivity, and large
m
. This gives at a long, narrow, hysteresis
loop. If the material is taken round a cycle, for example by an
alternating current in a nearby wire, the enclosed area is associated
with the amount of energy converted to other forms The need for this
energy loss - to heat - to be minimised in, for example, the core of
a transformer, combined with the demand for maximum magnetic linkage,
implies that soft iron is the suitable choice for the core.
Steel, and alloys such as Alnico (iron, nickel, cobalt, and
aluminium) have high coercivity, high retentivity, and lower
m
. They are suitable for making permanent
magnets.
Electrical insulators have very few free charge carriers. They are
therefore suitable for use as the material between the plates of a
parallel plate capacitor. One use of the material is simply to keep
the plates from touching, when they need to be close together to
achieve large capacitance (C =
e
oe
r/d). But some materials, as well
as insulating, will, for a given stored charge, also significantly
reduce the electric field between the plates, and hence the voltage
between them. They thus increase the capacitance
(C = Q
/V ). (Demo with reed
switch and demountable parallel plates, or with air capacitor and
paraffin)
A material which can be polarised by the action of an applied
electric field is called a dielectric ; all electrical
insulators are dielectric.
e
r is called the relative
permittivity of the material. It is often much more than 1.
Materials with atoms that are already electrically polarised - have
an electric dipole - have an advantage, since the
applied electric field, due to the charges on the surfaces of the
opposing plates, merely has to rotate the orientation of the electron
orbital (the orientation effect ). By considering, for
example, the charges that will then appear on the outer surfaces of
the insulator, opposite to those on the plates, we see that the
result is an electric field DE
within the material which is in the reverse
direction to the applied field E . The
resultant field in the region between the plates is reduced to
E - DE.
e
r is large for such
materials.e
r is about 80 for
water.
Atoms, in materials,
which are not already electrically polarised, will be
polarised by the applied field. The end result will be the same, but
the reduction in the resultant field is less, so
e
r is less.
Frequency Dependence Of e
r: If the electric field is
reversed, the polarised atoms will reverse to follow it. However, if
the field reverses increasing frequently, the atoms begin to display
an inertia in following the field, and the mean
DE
begins to reduce.
If, therefore, a capacitor is being used in an oscillatory circuit,
its value will reduce as the frequency of the oscillation is
increased. (Demo How??)
Dielectric Heating : If the electric field is rapidly
reversed, the flipping of the electric dipole generates heat in the
material (?electric hysteresis). In a microwave oven, the
electromagnetic microwave is tuned to a driving frequency such that
the electric field will make atoms of water resonate as their dipole
is reversed. The water thus gains heat energy.