# A-level Applied Science/Choosing and Using Materials/Properties

## Properties of materials

### Stiffness

Stiffness is the resistance of an elastic body to deflection by an applied force.* It is a crude measure because it does not account for the cross-section area, or the length, of the sample. A cuboid rubber will have different stiffness depending on which face you try to compress. The formula for stiffness is the force divided by the change in length.

### Stress

Stress is a measure of the force per unit area within a body*. (This is the definition of "Engineering stress" which does not take into account the change in cross-sectional area as the material deforms. "True stress" is force per unit area taking into account the change in area.) This is a better measure than the force alone, because it corrects for the area across which the force applies. Shear stress is stress along the main axis of the material (e.g. pulling on a rope) and normal stress is across the main axis (e.g. flexing a rope). Tensile stress is shear stress which is pulling on an object. Compressive stress is shear stress which is pushing on an object.

### Ultimate tensile strength

The tensile strength of a material is the maximum amount of tensile stress that it can be subjected to before failure.* The definition of failure can vary according to material type and design methodology. Ultimate Tensile Strength is the maximum stress a material can withstand without complete fracture.*

### Strain

Strain is the deformation caused by the action of stress on a physical body. Strain is measured by calculating the change in length (termed the stretch or absolute strain) and comparing the stretch to the original length.* Strain is positive if the material has gained length (in tension), and negative if it has reduced length (in compression). Strain has no units of measure but sometimes is given as a percentage.* By calculating strain as a percentage we correct for the length of the object.

### Young modulus

A better measure than stiffness is the Young modulus. This is the relationship between stress and strain:

Because stress accounts for the cross-section area of the sample, and strain for its length, the Young modulus depends only on the material being studied, not its shape.

#### Young modulus calculations

Complete the following table by using the formula above:

 Young modulus (N m-2) Stress (N m-2) Strain Lead 1.38 x 108 0.00862 Aluminium 4.67 x 108 0.00658 Iron 3.18 x 108 0.00151 Copper 1.30 x 1011 1.24 x 108 Nickel 2.19 x 1011 8.77 x 108 Aluminium alloy 7.10 x 1010 6.19 x 108 Stainless steel 2.15 x 1011 0.00963 Mild steel 2.12 x 1011 0.00770 Nickel alloy 2.19 x 1011 0.945 % Piano wire 5.00 x 109 0.805 %

### Elasticity and Plasticity

Elasticity is a property of an object: it undergoes elastic (as opposed to plastic) deformation in response to stress.*

Plasticity is a property of a material to undergo a non-reversible change of shape in response to stress. Plastic deformation occurs under shear stress, as opposed to brittle fractures which occur under normal stress. Examples of plastic materials are clay and mild steel. In engineering, this is called yield.* For many ductile metals, tensile loading applied to a sample will cause it to behave in an elastic manner. Each increment of load is accompanied by a proportional increment in extension, and when the load is removed, the piece returns exactly to its original size. This is Hooke's law.* However, once the load exceeds some threshold (the yield strength), the extension increases more rapidly than in the elastic region, and when the load is removed, some amount of the extension remains. A generic graph displaying this behaviour is below.* Ductile materials can sustain large plastic deformations without fracture. However, even ductile metals will fracture when the strain becomes large enough.*

### Brittleness

A material is brittle if it is subject to fracture when subjected to stress i.e. it has little tendency to deform (or strain) before fracture.* When used in materials science, it is generally applied to materials that fail due to normal stress rather than shear stress, or when there is little or no evidence of plastic deformation before failure.* When a material has reached the limit of its strength, it usually has the option of either deformation or fracture. A naturally malleable metal can be made stronger by impeding the mechanisms of plastic deformation (reducing grain size, dispersion strengthening, work hardening, etc.), but if this is taken to an extreme, fracture becomes the more likely outcome, and the material can become brittle. Improving material toughness is therefore a balancing act.* This principle applies to other classes of material. Naturally brittle materials, such as ceramics (most famously glass), are difficult to toughen effectively. Most such techniques involve one of two mechanisms: to deflect the tip of a propagating crack, for instance by introducing natural weaknesses of limited extent, or to create carefully controlled residual stresses so that cracks from certain predictable sources will be forced closed, as in the case of toughened glass and pre-stressed concrete.*

### Ductility

Ductility is the physical property of being capable of sustaining large plastic deformations without fracture (in metals, such as being drawn into a wire). It is characterized by the material flowing under shear stress.* A ductile material is any material that yields under shear stress (as opposed to brittle fracture, which yields under normal stress). Gold, copper, and aluminium are highly ductile metals.*

### Electrical conductivity

Electrical conductivity is a measure of a material's ability to conduct an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current.* Conductivity is the reciprocal (inverse) of electrical resistivity, and has the SI units of siemens per metre (S m-1). It is commonly represented by the Greek letter σ, but κ or γ are also occasionally used.*

### Thermal conductivity

Thermal conductivity, λ or k, is the property of a material which relates its ability to conduct heat. It is the quantity of heat, Q, transmitted due to a temperature difference ΔT. The sample conducting the heat has a thickness L and a cross-section area A.*

thermal conductivity = heat flow rate × distance / (area × temperature difference)
λ = Q × L / (A × ΔT)

### Thermal expansivity

Thermal expansion is the tendency of matter to increase in volume when heated. For liquids and solids the amount of expansion will normally vary depending on the material's coefficient of thermal expansion.*

### Density

Density (symbol: ρ - Greek: rho) is a measure of mass per unit of volume. The higher an object's density, the higher its mass per volume. The average density of an object equals its total mass divided by its total volume. A denser object (such as iron) will have less volume than an equal mass of some less dense substance (such as water).* The SI unit of density is the kilogram per cubic metre (kg m-3)* although grams per cubic centimetre (g cm-3) is also used because the numbers are more convenient.

#### Density calculations

 Material Density (g cm-3) Mass (g) Volume (cm3) Polystyrene 1.05 6.08 Fireclay 2.4 6.63 Teflon 2.2 15.6 Kevlar 1.4 1.57 Nickel 8.9 6.99 Brick 1.92 1.03 Polythene 2.85 2.98 Aluminium 13.7 5.19 Stainless steel 12.7 1.64

### Resistance to chemicals

Chemical resistance is the ability of a substance to withstand exposure to acids, alkalis, solvents and other chemicals.

Some materials are chosen because they can be used in an environment which contains dangerous chemicals; or to protect vulnerable components, or people, against dangerous chemicals. An example is Teflon, which was developed to make valves which could handle the highly corrosive compound UF6 in the Manhattan project.

Permeation is a process by which a chemical can pass through a protective film without going through pinholes, pores, or other visible openings. Individual molecules of the chemical enter the film, and “squirm” through by passing between the molecules of the protective compound or film. In many cases the permeated material may appear unchanged to the human eye. [1]

Chemical permeation can be described in simple terms by comparing it to what happens to the air in a balloon after several hours. Although there are no holes or defects, and the balloon is tightly sealed, the air gradually passes through (permeates) its walls and escapes. This simple example uses gas permeation, but the principle is the same with liquids or chemicals. [2]

Degradation is a reduction in one or more physical properties of a material due to contact with a chemical. Certain materials may become hard, stiff, or brittle, or they may grow softer, weaker, and swell to several times their original size. If a chemical has a significant impact on the physical properties of a material, its permeation resistance is quickly impaired. [3]

### Assignment

1. Identify different examples of materials with each mechanical property listed above;
2. State why the value of each mechanical property is relevant to the use to which the material is to be put, and compare given values for each mechanical property;

## Methods for measuring physical properties

Manufacturers of materials need to be aware of methods for measuring physical properties. These could be used to test new materials or as a quality control check in a factory.

You will need to be aware of simple laboratory experiments to measure the values of physical properties. You will need to be able to measure the following physical properties for a range of materials including metals, ceramics, glass, polymers and composites:

• a mechanical property;
• density;
• electrical conductivity;
• thermal conductivity;
• resistance to chemicals;
• thermal expansion/contraction.

You will need to be aware of experiments that test the physical properties of materials. The specific experiments you should be aware of are:

• the determination of Hooke’s law and how to relate the relevant physical properties of the material (elasticity, elastic limit, permanent deformation, plasticity, break point) to the molecular structure of the material;
• Searle’s experiment to calculate the stiffness of a material and how this can then be related to the Young modulus of a material using the formula

You will need to be able to use this formula to calculate a value for the Young modulus of a material. You will then need to compare this value to given values and relate this to particular uses of a material.

You should show an awareness that in a commercial environment these experiments will often be done quite differently than in a school laboratory, sometimes on a much larger scale and often more rigorously.

### Searle’s method for finding the Young’s modulus of a wire

Searle’s method uses two wires of the same material, one of which will be loaded with various weights.

E = $\frac{F l}{A x}$

To calculate Young’s modulus we need to know:

• The cross-section area of the wire (A). This is measured by using a micrometer to determine the radius of the wire, and then using the formula area of circle = πr2. The radius must be measured in metres, and is typically 2 x 10-4 m. This gives an area of 1.26 x 10-7 m2.
• The length of the wire (l, measured in metres).
• The force and the extension.
• The weight of a 1 kg mass is 9.81 N.

We plot a graph of the extension (m, horizontal axis) against the weight (N, vertical axis).

The gradient of this graph (change in vertical measure / change in horizontal measure) is the ratio F/x. If we multiply this ratio by l and divide by A we have the Young modulus for the wire.

Measuring the extension:

The ‘business end’ of the apparatus is a device which holds the two wires parallel, and allows the extension of the loaded wire to be measured.

You need to label this diagram to show:

• Constant mass attached to stress the reference wire.
• Variable mass attached to stress the test wire.
• Flexible connectors.
• Level reference from one wire to the other.
• Thumbscrew with scale to level the reference.
• Clamps for wires.
• Reference wire.
• Test wire.

• Thermal expansion of the test wire is correct by thermal expansion of the reference wire.
• Long, thin wires allow maximum extension for minimum force.

Problems:

• Difficulty measuring the cross-section area.
• Extensions very small.
• Mass, not weight, is measured.
• Need high, secure mounting point unless apparatus adapted.

## Equations

There are three equations given in the specification that you need to know. See the relevant section for a fuller description in each case.

### Thermal conductivity

thermal conductivity = heat flow rate × distance / (area × temperature difference)
λ = Q × L / (A × ΔT)

### Density

density = mass / volume
ρ = m / V

where p=rho----> greek letter given to density

### Young modulus

The Young modulus of elasticity = stress / strain
E = $\frac{F l}{A x}$
stress = force/ area = F / A
strain = extension / length = x / l