Yield stress, proof stress, toughness, Young's modulus, Hooke's law.

Hooke's Law

  • "Stress is proportional to strain up to the PROPORTIONAL LIMIT (1)"
  • This means that any increase in stress will bring about a proportional increase in strain up to the proportional limit.
  • Written mathematically, the formula of Hooke's Law is:
\begin{align} E = \frac {\sigma}{\varepsilon} \end{align}
  • $E$ is a constant. (Young's Modulus[see below])
  • $\sigma$ is stress (Pa)
  • $\varepsilon$ is strain

Young's Modulus

  • Young's Modulus is a measure of the stiffness of a material.
  • It is also known as the Modulus of Stiffness/Elasticity
  • This is the constant that is represented in Hooke's Law (see above)

Proportional Limit

  • This is when an increase in stress no longer has a linear relationship with an increase in strain.
  • Sometimes this is known as the elastic limit.


  • This is the ability of a material to retain its shape after being deformed.
  • It can be found through the area under the curve up to the proportional limit.

Yield Stress

  • This is the Stress Value at the Progressive Yield Point (3).
  • This is when there is no relationship between an increase in stress and an increase in strain.
  • Is a useful value as the UTS point occurs after some deformation where this only begins to deform.

Proof Stress

  • An approximation for the Yield point/Elastic limit for materials that don't have a definite one due to their structure.
  • To find the approximation, a tangent is produced from the Proportional Limit. The points of intersection between the graph and the tangent defines the Proof Stress of the material.
  • The line may be moved slightly to accommodate for certain materials.
  • Examples are 0.1%/0.2% Proof Stress, where the tangent is produced from a point slightly (0.001) to the right of the Proportional Limit.


  • "A material's ability to absorb energy"
  • This is sometimes known as impact strength.
  • This can be found by finding the Area under the ENTIRE curve.