Stress-Strain Graphs (OCR AS Physics)

• 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

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

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

The stress-strain graph for a polymeric material

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

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

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

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

Plastic deformation begins at a stress of 130 MPa