4.8 Stress-Strain Graphs

• Stress-strain curves give an indication of the properties of materials such as
  • 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
  • The value of their breaking stress

• Each material has a unique stress-strain curve

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

Comparing Force-Extension to Stress-Strain Graphs

The key features of the graph which are also on the force-extension graph are:

• Limit of proportionality, beyond which Hooke's law no longer applies
• The elastic limit, before which a material returns to its original length or shape when the deforming force is removed
• The yield point beyond which the material continues to stretch (more strain is seen) even though no extra force is being applied to it (without additional stress)
• Elastic deformation where the material will return to its original shape when the load is removed
• Plastic deformation where the material will not return to its original shape when the load is removed

The important points shown on a stress-strain graph

The stress-strain graph is also used to find;

• The Young Modulus is found from the gradient of the straight part of the graph
• Breaking stress (also called fracture stress) is the stress at the point where the material breaks
  • At the yield point the atoms in the material had started to move relative to each other, at the breaking stress they separate completely
  • Breaking stress is not the same as ultimate tensile stress which is marked on many graphs

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