Stress & Strain (AQA A Level Physics): Revision Note

Tensile stress & strain

• Opposite forces can deform an object

• If the forces stretch the object, then they are tensile forces

• Tensile forces lead to the two properties of materials known as tensile stress and tensile strain

Tensile stress

• Tensile stress is defined as the force exerted per unit cross-sectional area of a material

$\sigma =\frac{F}{A}$

• Where:

  • $\sigma$ = tensile stress (Pa)

  • $F$ = force applied (N)

  • $A$ = cross-sectional area (m²)

• The ultimate tensile stress is the maximum force per original cross-sectional area a wire is able to support until it breaks

• σ is the Greek letter lower-case 'sigma'

• σ has the units of pascals (Pa), which is the same units as pressure (also force ÷ area)

Tensile strain

• Strain is the extension per unit length

• This is a deformation of a solid due to stress in the form of elongation or contraction

$\mathrm{Tensile}\mathrm{strain}=\frac{∆L}{L}$

• Where:

  • $∆L$ = extension (m)

  • $L$ = original length (m)

• The strain is a dimensionless unit because it’s the ratio of lengths

• Sometimes strain might be written as a percentage

  • For example, extending a 0.1 m wire by 0.005 m would produce a strain of (0.005 ÷ 0.1) × 100 = 5 %

Stress-strain curves

• Stress-strain curves describe the properties of materials such as whether they are brittle, ductile and up to what stress and strain they obey Hooke's Law and have elastic and / or plastic behaviour

• Each material will have a unique stress-strain curve

• There are important points on the stress-strain graph, some are similar to the force-extension graph

• The key points that are unique to the stress-strain graph are:

  • Yield Stress: The force per unit area at which the material extends plastically for no / a small increase in stress

  • The elastic strain energy stored per unit volume is the area under the Hooke's Law (straight line) region of the graph

  • Breaking point: The stress at this point is the breaking stress

    • This is the maximum stress a material can stand before it fractures

  • Elastic region: The region of the graph up till the elastic limit

    • In this region, the material will return to its original shape when the applied force is removed

  • Plastic region: The region of the graph after the elastic limit

    • In this region, the material has deformed permanently and will not return to its original shape when the applied force is removed