Properties of Materials

Density is a useful quantity because it allows us to compare different materials.

Question:

Spring constant, k, is a measure of how hard it is to bend or stretch a spring. A large spring constant means that the spring is stiff.

Extension is the length a material has stretched when a load is added. It is calculated by subtracting the original length of the material from the length when stretched.

Limit of proportionality is the endpoint of the linear section of a force–extension graph.

Elastic limit is the load above which a material is permanently deformed.

A material is said to be elastic when it returns to its original dimensions once the applied load is removed.

A material is said to be plastic when it is permanently deformed and does not return to its original dimensions once the applied load is removed.

Hooke’s Law: F = kΔl

Nearly all materials show Hooke’s law behaviour up to a point. The applied force beyond which materials no longer obey Hooke’s law will be different for each material.

Question:

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 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.

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.

A-C is the region of the elastic limit. Up to C, the material will go back to it’s original shape when released. Between C and D, is the elastic region, the object will not return to it’s original shape. This is known as plastic deformation.

Fmax is the maximum force that can be applied before breaking. Which occurs at delta L max.

The work done on the spring is equivalent to the Elastic strain energy, which is the energy stored by stretched materials.

E  =

Force constant is K.

In materials science the change in distance is denoted delta L.

Question:

The elastic properties of some materials, such as rubber, can be complex. When a rubber band is stretched it will return to its original length. However, the way in which it does this is very different from a metal wire. Figure 12.20 shows a typical force–extension curve for a rubber band:

(Applied to a solid by external force)

O–P on the graph represents the range of tensile stress for which the copper obeys Hooke’s law. The gradient of this section is the Young modulus for copper.

Point P represents the limit of proportionality for the material.

Point E on the graph represents the elastic limit. Up to point E, if the stress is removed, the sample of copper will return to its original length. Beyond this point, copper behaves plastically. It does not return to its original length.

The yield point of the material is given by Y. This is the value of stress beyond which the strain increases rapidly for small increases in stress.

The ultimate tensile stress (UTS) of copper is sometimes called the maximum strength or strength of the wire.