Stress-strain graphs

In a nutshell

Stress-strain graphs are useful in helping to understand the properties of different kinds of materials. The features of these graphs, which are the elastic limit, the limit of proportionality, the yield points, the ultimate tensile strength and the breaking point, give us more information about the behaviours of different types of materials.

Definitions

limit of proportionality	Up until this point the stress is proportional to strain and Hooke's law is obeyed.
elastic limit	Up until this point the material will return to its' original shape once the stress is removed.
yield point	The yield point is where a lot of strain occurs with constant (or reduced) stress.
ultimate tensile strength	This is the maximum value of stress the material can withstand.
fracture/failure	This is the point the material breaks.

Stress-strain graphs

Stress-strain graphs are a graphical way of observing the relationship between stress and strain for a given material. The formulae for stress and strain both have dimensional quantities which means that regardless of the size of the material being tested, the stress strain graph will be the same for each material.

There are three different stress-strain graphs that you need to be aware of.

Ductile materials

Physics; Materials; KS5 Year 12; Stress-strain graphs

A	Stress
B	Strain
1	Limit of proportionality
2	Elastic limit
3	Yield point
4	Ultimate tensile strength
5	Failure

The stress-strain curve for a ductile material such as copper is shown above. There are 5 points that need to be remembered.

Note: Ductile is defined as the ability to be drawn out into a thin wire.

Limit of proportionality

The limit of proportionality is the the first part of the graph from the origin to the part where the graph starts to curve.

Elastic limit

The elastic limit normally follows fairly close after the limit of proportionality but is dependent on the material. There is no distinctive feature on a stress strain curve which indicates the elastic limit.

Yield point

The yield point is identifiable by a flat section following the curve after the limit of proportionality. Some materials have a drop in stress and an increase in strain, which looks more like a bump on a stress strain curve.

Ultimate tensile strength

The ultimate tensile strength is the highest point on the graph, signified by the greatest value of stress.

Failure

Failure is identified as the end of the graph. Where the curve ends signifies the break, or fracture, of the material.

Brittle materials

Brittle materials undergo little to no plastic deformation before fracture.

As a result, they break quite easily and the resulting stress-strain graphs usually show a straight line through the origin. These materials follow mostly elastic deformation until they break.

Physics; Materials; KS5 Year 12; Stress-strain graphs

A	Stress
B	Strain
1	Strong and stiff brittle material
2	Weak and stiff brittle material
3	Weak and less stiff brittle material

Example

A tough brittle material would be something like cast iron. Cast iron is strong and tough but will not plasticly deform and will fracture after a short amount of strain.

A fragile brittle material would be something like glass. Glass will not take a lot of stress before fracturing and again, will not plasticly deform before fracturing.

Polymeric materials

Polymeric materials are defined as substances with large chains of similarly bonded molecules. This chemical composition gives them their unique stress strain graph.

Polymeric materials will normally undergo a huge amount of strain with little amount of applied stress. This is due to the molecules being stretched out.

Physics; Materials; KS5 Year 12; Stress-strain graphs

A	Stress
B	Strain
1	Truncation

Note: Sometimes the stress strain curves for polymeric materials will be truncated if plotted on the same axes as a brittle or a ductile material. This is because some polymeric materials can stretch up to $1000+ \%$ their original length! Truncated means that the graph is shortened to allow all of the curve to be shown on the axes.

Polymeric materials include materials like polyethene which shopping bags are made out of.

Loading and unloading curves

The loading and unloading curves for polymeric materials are different to normal. This is due to work being done stretching the atoms and molecules away from their equilibrium position.

The change in work done between the loading and unloading curves is normally transferred as thermal energy.

Physics; Materials; KS5 Year 12; Stress-strain graphs

A	Stress
B	Strain

Loading and unloading curve for polyethene

Physics; Materials; KS5 Year 12; Stress-strain graphs

A	Stress
B	Strain

Loading and unloading curve for rubber

Note: Rubber is a polymeric material and has a distinctive shaped curve and is called a hysteresis loop.