Materials Tutorial 1 - Properties of Materials

It is important for a material to have the right properties for the job in hand.  For example, glass is a stiff material (i.e. doesn't change shape easily), but it's very brittle.  Therefore it will not make a good structural material for a bridge.  Stone is very strong in compression (i.e. when squashed) but is quite weak in tension (when pulled).  Therefore stone bridges are built to withstand high compressive forces.  Old stone bridges were built to carry horses and carts (a mass of no more than 2500 kg), but today carry 40 tonne lorries.

 

 

Notice how that on this bridge, there are steel straps on the right hand side of the arch.  Clearly the arch has deformed under tensile loads (pulling forces) and has started to crack.  Steel is very strong when subjected to a tensile load, and is strengthening the bridge.  On the far left of the bridge, just behind the tree, you can see another steel frame that is holding the wing-walls together.  These measures, along with a weight limit, will ensure the bridge will remain safe for many years.

 

Photo by Chris Millar, Wikimedia Commons

 

Wood and iron can be used to make bridges. There is a myth that Sir Isaac Newton designed a bridge (the Mathematical Bridge) over the River Cam in Cambridge that required no bolts or nails, and built it himself.  Actually it was designed by William Etheridge and built by James Essex in 1749 (22 years after Newton's death).  Sorry to ruin a good story.

 

Cast iron was widely used in bridges, although it can be brittle, causing bridge failure. At 19.15 on Sunday 28th December 1879 a train crossed the Tay Bridge during a severe storm.  The bridge collapsed, plunging the train into the River Tay.  Everyone on board was killed.  Poor design work and slovenly construction contributed to the disaster.  A new and more substantial bridge was built alongside, and much of the old bridge was re-used in the new.  It was opened in 1887 and has been in use since.  So the girders were not that bad...

 

Some Definitions

Property

Definition

Strength

How much force is needed to break something.  Not always a fair comparison.  Something that is thick will be stronger than a thin section.  A fairer test is the breaking stress.

Breaking Stress

Breaking stress = breaking force area

Force is applied at 90 o to the area.

Stiffness

How difficult it is to change the shape of the object.  If we load wires of the same length and diameter with the same tension, the stiffest is the one that stretches the least.

Brittle

Stiff, but not strong

Elastic

Ability of a material to regain its original shape after it is distorted.

Plastic

A material that does NOT regain its original shape after it is distorted.

Flexible

Can bend easily without breaking or deforming.

Ductile

Can be drawn out into wires

Malleable

Can be hammered into shape.

Alloy

A mixture of metals

 

Question 1

Give one example of a material that is:

Stiff:

Brittle:

Plastic:

Elastic and strong:

Answer

 

 

Density

Density is defined as

mass per unit volume

 

Density, mass, and volume are linked by a simple relationship:

 

r = m

      V

 

The strange looking letter r is rho, a Greek letter 'r'.  It is the Physics code for density. 

 

SI Units for density are kg m-3.  In some texts, you will find some densities given in g cm-3.  It is important that you use the SI units otherwise formulae will not work.  To convert you will need the following conversion:

1 g cm-3 = 1000 kg m-3

 

Lengths must be in metres.

1 mm = 1 10-3 m
1 cm = 1 10-2 m
 

Mass must be in kilograms.

1 g = 1 10-3 kg
 

Watch out for these bear traps.

 

Also the physics code r has nothing to do with resistivity.

 

 

 

Question 2

 What are the following densities in kg m-3?                                              

 

1.29 g cm-3

 

 

7.6 g cm-3

 

 

19.6 g cm-3

 

Answer

Question 3

What is the volume of 100 g of Mercury of which the density is 13 600 kg m-3?

Answer

Question 4

When is a plastic not a plastic?

Answer

 

Measuring Density

We can measure density quite simply by weighing the sample on a top pan balance.  Most top-pan balances measure in grams.  We need to convert from grams to kilograms by dividing by 1000.

 

If the object is regular, the volume is easily worked out by measuring the dimensions and applying a formula, e.g.

 

Volume = length width height

 

The volume will be in cm3.  Again we need to convert cm3 to m3.  1 cm3 = 1 10-6 m3.

 

Here are some other regular objects:

You do remember how to work out these volumes, don't you?

 

An irregular object can be lowered into a eureka (or displacement) can.  The volume of displaced water can be measured.

 

 

 

Question 5

An empty paint tin has a diameter of 0.150 m and a height of 0.120 m, and a mass of 0.22 kg.  It is then filled with paint to a depth of 7mm from the top.  Now the paint tin has a total mass of 6.50 kg.  Calculate:

a. The mass of the paint;

b. The volume of the paint;

c. The density of the paint.

Give your answer to an appropriate number of significant figures.

Answer

 

The link to the Engineering Toolbox site will take you to some typical densities of metals and alloys.  Click HERE.

 

Alloys

Engineers and scientists need to evaluate the properties of the materials they intend to use.  Alloys are mixtures of elements, usually metals.  These may have physical properties that are quite different from the pure metals.  For example, pure iron is a rather weak metal.  If it contains a certain proportion of carbon, it makes steel, which is much stronger.  If there is more carbon, then the alloy is rather brittle, and can shatter.  However cast iron machines well, and is resistant to rust. 

 

Alloys can be tailored to special requirements.  Duralumin has been used for many years in the aviation industry.  It consists of:

 

If we know the proportions of each metal in the alloy we can work out the density.  We can find the densities of each metal in a data-book:

 

Metal

Density (kg m-3)

Aluminium

2712

Copper

8930

Magnesium

1738

Manganese

7210

 

 

Worked example

What is the density of duralumin?

Answer

Let us assume that the volume is going to be 1 m3.  These are the relative proportions.  Use mass = density volume:

 

  • 4.4% copper = 0.044 8930 kg = 393 kg.

  • 1.5% magnesium = 0.015 1738 kg = 26.1 kg

  • 0.6% manganese = 0.006 7210 kg = 42.3 kg

  • 93.5% aluminium = 0.935 2712 kg = 2536 kg

Total mass in 1 m3 = 393 kg + 26.1 kg + 42.3 kg + 2536 kg = 2997.4

 

Density = 3000 kg m-3.

 

As well as being very low density, duralumin is also very hard and durable.

 

Question 6

An alloy tube of volume 1.8 10-4 m3 consists of 60 % aluminium and 40 % magnesium by volume.  Calculate:

a. The mass of:

     i.      Aluminium

    ii.      Magnesium in the tube;

 

b. The density of the alloy.

 

Density of aluminium is 2700 kg m-3 and magnesium 1700 kg m-3.  

Back

 

 

Using materials

Aeroplanes are made out of materials that have very low density.  They have to have a low mass, and every effort is made to ensure that the machine does not carry anything that is not needed.  Therefore the machine can carry useful load that enables it to earn money.  They are made from aluminium (density 2700 kg m-3), or an alloy of aluminium and titanium (very expensive).  Some aircraft are made of carbon fibre, which is very strong, but has a very low density.

 

A large aircraft like a Jumbo jet (Boeing 747), if made of steel, would barely waddle about the aerodrome.  It could not take off.  Using low density materials, giant freight aircraft such as the Antonov 225 can be built.

 

Originally designed to take the Russian space shuttle on its back, this brute can take a 100 tonne railway locomotive easily in its hold.  Boeing are proposing to build something even bigger, the Pelican, with a mass of 1000 tonnes empty, with a payload of 800 tonnes, and an appetite for fuel to match.

 

Composite Materials

A typical composite material is shown below:

The core can be a honeycomb structure which is particularly strong.

 

Composite materials are not confined to the aerospace industry.  Composite materials such as plywood are made up in layers of wood in which the grains cross at 90 degrees to each other.  Plywood is often found in shelving, covered with a veneer of fine wood.  Plywood is stronger than shelves made of the equivalent thickness of normal wood.

 

 

The picture above shows a home-made thicknesser (an electric planer that can machine wood to a chosen thickness).  The planer machine is mounted in a plywood jig.  (Later it broke.)

 

Another composite material found in the furniture industry is chipboard.  Unlike plywood, it is very heavy and very feeble.  But it's cheap.

 

The composite materials above are rigid.  However flexible composites are widely available, for example Kevlar.  Police officers wear body protection made from Kevlar to prevent injuries from attempts to stab them.  Thicker Kevlar is used in bullet-proof jackets.  This dog is bullet and stab-proof in his Kevlar jacket.

 

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