High School Physics

Ductile and Brittle materials beyond elastic limit & their force-extension graph

Ductile materials can be formed into wires by stretching them. They show ductility. A brittle material is one that shows little, or no, plastic deformation before breaking. In this post, we will discuss (1) ductile material & ductility, (2) force-extension graph of ductile material like copper wire (3) Brittle material (4) force-extension graph of brittle materials like high-carbon steel (5) fracture of ductile & brittle material & their differences

Ductile material & Ductility

Wires obey Hooke’s law because the bonds between the metal atoms act like springs. When the wire is stretched the bonds lengthen slightly. When the force is removed, the bonds return to their original length.

However, if the force applied is too great, and the elastic limit is exceeded, then the metal atoms will be able to move past one another and the wire lengthens. This is known as ductility and is a very useful property as it allows metals to be formed into thin wires.

The wire formed shows plastic behaviour and will not return to its original length when the force is removed. Ductile behaviour is also an example of plastic deformation.

force-extension graph of a ductile material (copper wire)

A typical force–extension
graph for a copper wire. The wire shows
plastic behaviour when it is stretched
beyond the elastic limit.
figure 1: A typical force-extension graph for a copper wire. The wire shows plastic behaviour when it is stretched beyond the elastic limit.

In Figure 1 the dotted line represents the extension measured as the force is removed from the loaded wire.

It can be seen that the wire has permanently lengthened because, even with no applied force, there is still a measurable extension.

Brittle material

Some materials do not show plastic behaviour but are brittle and break when the elastic limit is exceeded. Cast iron and glass are two examples of brittle materials.

force-extension graph of a Brittle material (high-carbon steel)

Figure 2 shows a typical force-extension graph for high-carbon steel, which is also a brittle material. The material fractures and breaks. It does not show plastic behaviour.

Force–extension curve for high-carbon mild steel.
figure 2: Force–extension curve for high-carbon mild steel.

Fracture of ductile and brittle materials & their difference

The way in which ductile and brittle materials fracture is also different.

In a ductile material, the sample of material will elongate and ‘neck’ before it breaks. On a force-extension graph, necking occurs in the plastic region of the graph.

In a brittle material, there is no change in the shape of the material because it does not undergo plastic behaviour. A straight break in the material is seen.

figure 3: Ductile and brittle fracture.

Figure 3 shows the difference between the two types of fracture.

See also  Dimensional formula of Modulus of elasticity - how to find it?
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