Stress-Strain Graphs (OCR A Level Physics)

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Katie M

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Stress-Strain Graphs

  • Stress-strain curves give an indication of the properties of materials such as
    • Whether they are brittle, ductile or polymeric
    • Up to what stress and strain they obey Hooke's Law
    • Whether they exhibit elastic and/or plastic behaviour
    • The value of their Young Modulus

  • Each material has a unique stress-strain curve

Brittle

  • A brittle material is defined as

A material that fractures before plastic deformation

  • For a brittle material:
    • Elastic behaviour is shown until the breakpoint where the material snaps
    • There is no plastic deformation, and the loading and unloading curves are the same
    • Brittle materials include: glass, ceramic

Stress Strain Graph Brittle, downloadable AS & A Level Physics revision notes

The stress-strain graph for a brittle material

Ductile

  • A ductile material is defined as

A material that can withstand large plastic deformation without breaking

  • For a ductile material:
    • They generally experience elastic deformation up until their elastic limit
    • After this, they then undergo plastic deformation before reaching their ultimate tensile stress and breakpoint
    • For this reason, they can be easily hammered into thin sheets or drawn into long wires
    • Ductile materials include: copper

Stress Strain Graph Ductile, downloadable AS & A Level Physics revision notes

The stress-strain graph for a ductile material

Polymeric

  • A polymeric material is defined as:

A material made up of long, repeating chains of molecules

  • For a polymeric material:
    • They can endure a lot of tensile stress before breaking
    • There is no plastic deformation, but the unloading curve is different to the loading curve, as some energy has been lost as thermal energy
    • Polymeric materials include: rubber, polythene

Stress Strain Graph Polymeric, downloadable AS & A Level Physics revision notes

The stress-strain graph for a polymeric material

Stress-Strain Graph Examples, downloadable AS & A Level Physics revision notes

Stress-strain graph for different materials up to their breaking stress

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

Stress-Strain Graph, downloadable AS & A Level Physics revision notes

The important points shown on a stress-strain graph

  • The key points that are unique to the stress-strain graph are:
    • The elastic strain energy stored per unit volume is the area under the Hooke's Law (straight line) region of the graph

  • Yield Stress: 
      • The force per unit area at which the material extends plastically for a small increase in stress

  • 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 until 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

Worked example

The graph below shows a stress-strain curve for a copper wire.Stress-Strain Worked Example, downloadable AS & A Level Physics revision notesFrom the graph, state the value of:

(a) The breaking stress

(b) The stress at which plastic deformation begins

Part (a)

Step 1: Define breaking stress

    • The breaking stress is the maximum stress a material can stand before it fractures. This is the stress at the final point on the graph

Step 2: Determine breaking stress from the graph

    • Draw a line to the y axis at the point of fracture

Stress-Strain Worked Example

The breaking stress is 190 MPa

Part (b)

Step 1: Define plastic deformation

    • Plastic deformation is when the material is deformed permanently and will not return to its original shape once the applied force is removed
    • This is shown on the graph where it is curved

Step 2: Determine the stress of where plastic deformation beings on the graph

    • Draw a line to the y axis at the point where the graph starts to curve

Stress-Strain Worked Example (2)

Plastic deformation begins at a stress of 130 MPa

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.