Ductile and brittle materials

A ductile material is one such as copper which may be drawn out into a wire.
A brittle material is one like cast iron which will stretch and then break.

The variation of stress and strain

If a ductile material such as copper is stretched until it breaks and its stress and strain measured and plotted, a graph like that in Figure 1 may be obtained.

There are a number of important points about such a graph:
(a) OP is a straight line - in this region Hooke's law (discussed below) is obeyed.
(b) P is the limit of proportionality – up to P strain is proportional to stress.
(c) E is the elastic limit - up to E, if the load is removed the material will return to its original length (although the stress may not be proportional to the strain up to this point).
(d) Y is the yield point - between E and Y the material becomes plastic, that is, if the load is removed the material will contract but all the extension is not recoverable. The material follows the dotted line YS on the graph during contraction and the remaining extension is known as a permanent set.
(e) Z - after this point none of the extension is recoverable.
(f) B - this is the breaking stress beyond which the material will break.

A material like copper is known as ductile - that is, it will flow, and can be drawn out into a wire without fracture.

Materials such as glass that can be extended but do not show plastic deformation and will easily fracture are known as brittle materials.

A stress-strain curve for a ductile material is shown in Figure 1 and that for a brittle material is shown in Figure 2.

The repeated bending, heating and beating known as work hardening increases the strength of metals and is used in the manufacture of swords.

If the steel is heated and then rapidly cooled it will become more brittle but by heating a sample of steel and then slow cooling it the effect can be reversed.

The stress-strain relationship for some common materials should now be investigated such as the properties of climbing ropes. These should be strong, stretch if subjected to a sudden force but not stretch too much!