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:
(1)
\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.

#### Resilience

• 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.

#### Toughness

• "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.
page revision: 2, last edited: 04 Oct 2011 01:21