1. To understand stress, strain and Young’s modulus
Know the distinction between stress and strain
Be familiar with stress-strain curves
Be able to calculate the Young Modulus of a material
Be able to describe an experiment to measure the Young Modulus of a material

2. Which is stronger?
Spiders make their webs from a natural protein polymer called fibroin. A single strand of spider silk can be stretched by up to 40% of its length before it breaks. As well as being very elastic, it is as strong as steel but has one sixth of the density.

3. Stretching materials
Imagine extending a wire by pulling at its ends. The extension will depend on
The original length of the wire
Its diameter
The tension in the wire
The material the wire is made from
If we change the thickness of a spring or its length then the values of the force needed and extension observed will change
More useful ways to compare the behaviour of specific materials under tensile forces is to compare two other quantities: stress and strain

4. Key definition Stress = 𝐹𝑜𝑟𝑐𝑒 𝐶𝑟𝑜𝑠𝑠−𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎
Stress is the force per unit cross sectional area. It has units of Nm-2 or Pa.
Stress = 𝐹𝑜𝑟𝑐𝑒 𝐶𝑟𝑜𝑠𝑠−𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 N
𝜎= 𝐹 𝐴
Pa or Nm-2 m2

5. Key definition Strain = 𝑒𝑥𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
Strain is the extension per unit length.
It has no units as it is the ratio of 2 lengths and is therefore dimensionless. It is given the symbol ∈
Strain = 𝑒𝑥𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
∈= 𝑥 𝐿

6. Stress – Strain graph for a ductile material
Stress proportional to strain from the origin to P (limit of proportionality) (obeys Hooke’s Law)
E is the elastic limit, elastic deformation occurs up to this point
Y1 and Y2 are upper and lower yield points, where the material extends rapidly
The UTS (ultimate tensile strength) – max stress the material can withstand before it breaks
Beyond the UTS, material may become longer and weaker and eventually snaps . This is the breaking strength
Ductile materials can be easily drawn into a wire or hammered into a sheet. Eg low carbon steel

7. Stress-strain graph for a brittle material
Eg Glass, ceramics
Elastic behaviour up to the breaking strength
Ultimate tensile strength is the same as breaking strength for a brittle material
No significant plastic deformation before fracture
Stress
Strain

8. Polymeric materials
Polymeric materials are materials that consist of long molecular chains.
These behave differently depending on their molecular structure and temperature
Stress
Strain
Rubber
Polythene

9. Young’s Modulus E Young’s Modulus = 𝑆𝑡𝑟𝑒𝑠𝑠 𝑆𝑡𝑟𝑎𝑖𝑛 = 𝜎 ∈ = A x
Within the limit of proportionality, stress is directly proportional to strain.
Young’s Modulus (E) is the ratio of stress to strain for a given material
Young’s Modulus = 𝑆𝑡𝑟𝑒𝑠𝑠 𝑆𝑡𝑟𝑎𝑖𝑛 = 𝜎 ∈
Pa or Nm-2
A x
F L = E

10. Young’s Modulus from a graph
Stress
Strain 𝜎 ∈
𝐸= 𝜎 ∈
Young’s Modulus =
𝐆𝐫𝐚𝐝𝐢𝐞𝐧𝐭 𝐨𝐟 𝐥𝐢𝐧𝐞𝐚𝐫 𝐫𝐞𝐠𝐢𝐨𝐧 𝐨𝐟 𝐚 𝐬𝐭𝐫𝐞𝐬𝐬−𝐬𝐭𝐫𝐚𝐢𝐧 𝐠𝐫𝐚𝐩𝐡

11. Young’s Modulus
A material with a large Young’s modulus is stiffer than one with a smaller Young’s Modulus
Material
Young’s Modulus (Pa)
Diamond
1.2 x 1012
Iron
2.1 x 1011
Copper
1.2 x 1011
Aluminium
7.1 x 1010
Lead
1.8 x 1010
Rubber
2.0 x 107

12. Example
An object of weight 790N is suspended vertically from a crane on a steel cable 5.0m long and 6.00mm in diameter. The Young Modulus of the material of the cable is 2.0 x 1011 Pa. Calculate the extension in the cable.

13. You try
Questions from the sheet