How to Choose the Right
Material
1E10 Lecture
by
David Taylor
Mechanical Engineering Dept
What’s It About?
• This lecture is about the mechanical
properties of materials…
• …how to measure them and use them.
• It’s important for any material which is
going to be subjected to mechanical forces
in use.
• These forces cause the material to deform
(i.e. change shape) and may cause it to
fail (i.e. break).
Mechanical Properties in Design
• Designers need to know about mechanical
properties…
• …to choose the right material for a given
component (e.g. a car’s crankshaft) or
structure (e.g. a dam).
• They need to make sure that there won’t
be too much deflection under load, and
that the forces won’t be high enough to
cause failure.
Examples of Failures
A 737 engine; one of the turbine blades broke away and
exited through the engine casing, nearly taking someone’s
head off!
Examples of Failures
X-ray showing an artificial
hip joint, made of metal,
which broke in two whilst
inside someone’s leg.
As an engineer, you don’t
want to be famous for
designing a component that
failed.
Defining and Measuring
Mechanical Properties
• There are lots of mechanical properties; in
this lecture we are just going to look at the
simplest (and most important) ones, which
we call the “static” properties.
• These can be measured using very simple
tests, conducted on samples of the
material.
• The most important test is the tensile
test…
The Tensile Test
FORCE F
• Take a sample of
material
• Pull on the ends to
stretch it
Original
• Measure the force
Length Lo
needed
• You can also apply
other types of loads,
such as compression
or torsion, but we’ll
stick to tension here.
Stretch
to new
length L
Some Practicalities
• You can use any size and
shape of sample provided it has
parallel sides…
• …so the cross section is the
same throughout.
• The shape of the cross section
doesn’t matter, it can be
rectangular (as here), square,
circular, etc. Its area is A.
• Normally we make the ends of
the specimen bigger so it’s easy
to grip in the testing machine
Cross
Section of
Sample,
area A
The Stress/Strain Curve
• We want to see how much the sample stretches
for a given applied force.
• So we could plot the force, F, against the stretch
(L-Lo).
• But it’s better to normalise these quantities, so
that the overall size of the sample doesn’t
matter.
• We do this by calculating the STRESS, s, which
is F/A and the STRAIN, e, which is (L-Lo)/Lo.
Typical Results
(units N/m2 = Pa)
Stress s
• The stress/strain curve has different shapes in different materials;
below are some examples.
• As strain increases, stress can go up or down
• X indicates the point at which the sample breaks
X
X
X
X
Strain e (no units)
The stress/strain curve in more
detail…
• First Stage: Elastic Deformation
Stress s
In this part of the
curve, the material
behaves like a
spring.
X
If you remove the
stress, the strain
goes back to zero.
Stress is (usually)
proportional to
strain.
Strain e
Stiffness
• The material’s “stiffness” is the slope of the
stress/strain curve in the elastic region.
• Called Young’s modulus (or the elastic
modulus), symbol E.
• If the line is straight then E = stress/strain
at any point on the line.
Using Stiffness
• You can use E to calculate the strain for a
given stress, and therefore work out how
much the structure will deflect under
load…
• …e.g. how much a car’s suspension will
move when six people get in.
• Also used to find the stress in the material
for a given amount of deformation…
• …if this stress is too high it may fail.
Using Stiffness
• Also used to prevent buckling.
• Buckling is what happens when you have a long,
thin, structure loaded in compression…
• …like a straw or a drinks can when you push on
the ends.
• It suddenly “gives” – this is buckling.
• The analysis of buckling is complex – the
important thing is that the only material property
it depends on is E.
Elastic Energy
Stress s
• If you load up a material in its elastic region, to some
stress s…
• …then the area under the line is a measure of the energy
you used to do it. This area is actually the energy per unit
volume of material in the sample
• This energy is
stored in the
material and will
X
be released if you
unload it.
• This is very
useful in a
mangonel, for
example!
Strain e
Non-Linear Elasticity,Hysteresis
• In some materials
(e.g. some
polymers) the
stress/strain line is
curved in the elastic
region…
• …and sometimes
the loading and
unloading lines are
different.
Loading
Unloading
Non-Linear Elasticity,Hysteresis
• In that case E is
not constant…
• …and some
energy is lost,
(given by the area
between the
lines). This is
called hysteresis.
Loading
Unloading
Plastic Deformation, Damage and
Failure
• Above a certain stress, sy, the stress/strain line becomes
flatter and curved, and unloading gives you a permanent
deformation.
A
sy
Stress s
X
e.g. if you load up from
O to point A and then
unload, you get back to
B, not O.
The distance OB is the
plastic strain left in the
material
O
B
Strain e
Plastic Deformation, Damage and
Failure
• Why does this happen?
• It depends on the material.
• In metals, plastic strain occurs because the atoms in the
material can flow over each other.
• In other materials, such as concrete and wood, it’s due
to damage in the material; small cracks and splits which
weaken it.
• The important thing is that we can’t use the material at a
stress greater than sy, so for engineering purposes it’s
the maximum allowable stress.
Plastic Deformation, Damage and
Failure
• Two other points from the stress/strain curve:
• The maximum point in the curve is called the Ultimate
Tensile Strength (UTS). We used to use this as a
measure of the strength of a material but these days we
normally use sy.
• The strain and stress at the failure point X (ef, sf) are also
useful to know. ef is called the “ductility”; it tells you how
much deformation the material can take without failing,
which is useful for manufacturing operations like forging
and wire-drawing.
• The area under the
whole stress/strain curve
is the energy (per unit
volume) needed to make
it fail.
• But you get some
energy back in elastic
recoil (the black
triangle).
• The remaining area is
the energy absorbed by
the material in failing.
This is one measure of
the “toughness” of the
material.
Stress s
Energy Again, Toughness
X
O
Strain e
More About Toughness
• Toughness is a property which is difficult to
define.
• One definition is the energy to failure (as
above)…
• …but these days we normally use the so-called
“fracture toughness” which is a measure of how
easily the material cracks.
• You’ll learn more about toughness (and other
mechanical properties) in the materials course
next year.
Summary
• We’ve seen that the simple tensile test can
tell you a lot about how a material
performs under load…
• …how much it deforms, both temporarily
(elasticity) and permanently (plasticity)…
• …how much energy it can store and
release…
• …and how much stress and energy are
needed to break it.
What’s the stress?
• This material information is useful only if you know what
stress (or strain) is going to arise in the component or
structure that you’re designing.
• In the tensile test the stress is simply found by F/A, but
that’s not the case for a real structure, where the stress
will depend on the shape and forces it sees, and will vary
from place to place in the structure.
• Stresses can be calculated for any structure; these days
we mostly use computer models (such as finite element
analysis) but you can use analytical equations for simple
structures like beams and arches, and to get a rough
estimate in more complex cases.
• You will learn more about stress analysis in other
lectures and other courses.
More Information
• If you want to learn more, try…
• Textbooks by Ashby & Jones: Engineering
Materials books 1 and 2. We use these books in
courses in 2nd and 3rd year.
• Materials by Ashby, Shercliff and Cebon
• Lots of information on line, in Wikipedia,
company databases, etc