# Elasticity in Metals and Polymers

Hi friends,

In this article, I am discussing the elasticity in metals and polymers and some more related terms. You will find this information interesting and useful, I hope so.

Elasticity is a property, possessed by the materials of resuming its original shape upon removal any force, which has modified its form by stretching, compressing etc. All elastic materials are abided by the Hooke’s law, the value of modulus elasticity of a material depends upon the type of stress and strain produced.

# Explanation of Elasticity in Metals and Polymers

Matter is made up of ultra-microscopic particles known as ‘atoms’. The atoms of a solid are held together in a regular array by electric forces in a way as if they were connected by springs.

Under the forces the solid remains in its natural equilibrium state. Inside the solid, the distribution of positive and negative atomic charges is such that when the solid is in its natural equilibrium state, there is no net force between the atoms.

If, however, the solid is compressed by an external force, the distance between the atoms reduces. Now, the distribution of charges in the atoms changes in such a way that a net force of repulsion begins to act between the atoms. It is termed as ‘inter-atomic force’. On removal of external force, the inter-atomic force pushes the atoms back to their initial positions so that solid returns to its original size.

Similarly, when a solid is stretched by an external force, the inter-atomic space increases. In this case, the distribution of charges in the atoms again changes but now in such a way that there is a net force of attraction between the atoms. On removal of external force, the force of attraction between the atoms brings them close to each other to their initial positions.

In case the applied external force is very large, the distance between the atoms increases so much that the force of attraction between them becomes negligible. When this is the case, there is a permanent dislocation in the positions of the atoms and on removal of the external force, the solid does not return to its original size. If we go on increasing the load on a wire then ultimately the wire will break.

## Elastic After Effect

We know that bodies are deformed under external forces, but return to their original state on removal of deforming forces. It is observed that some bodies return to their original state immediately after the removal of force, while some take quite a long time to do so.

For instance, a quartz fiber immediately returns to its original shape when the twisting couple acting on it is removed, but a glass fiber takes hours to do so. The delay in returning to the original state by an elastic body after the removal of deforming forces is known as the ‘elastic-after-effect’.

Quartz and phosphor-bronze, being practically free from elastic-after-effect, are employed as suspensions in moving-coil galvanometers and electrometers.

## Elastic Fatigue

When a body is subjected repeatedly to alternating deforming forces, then it becomes less elastic. For instance, when a suspended wire carrying a disc at its end is set into torsional vibrations, it continues vibrating for some time.

During these vibrations, the wire is subjected repeatedly to an alternating twisting couple. Now, if the wire is again made to vibrate, then its vibrations die away quickly than before as if the wire has tired or become fatigue.

Thus, elastic fatigue is the property of an elastic body by virtue of which its behavior becomes less elastic under the action of repeated alternating deforming forces.

Elastic fatigue corresponds to physical fatigue in human beings. Just as a tired person becomes fresh after taking rest, an elastic body regains its full elasticity when allowed to rest for some time.

# What is elastic hysteresis?

A rubber wire does not obey Hooke’s law even for small stresses, and has no permanent strain even for quite large stresses. It has a large elastic region in its stress-strain curve, but it does not retrace the same curve during unloading. (In fact, for a given stress, the strain is less during loading than during unloading.)

In Figure, the portion OAB represents loading and the portion BCO represents unloading. This feature is known as ‘elastic hysteresis’ and the complete stress-strain closed curve is known as `hysteresis loop’.

## Resilience

It is the property of the material which enables it to store energy, and resist shock and impact. The ability of a material to store elastic energy without permanent deformation is termed its resilience.

The maximum amount of elastic energy that may be so stored in the material during its first loading cycle is called proof resilience. It corresponds to the area under the stress-strain diagram from the origin to the elastic limit, and is expressed in energy units such as J/m3.

Materials that have high resilience are used for springs. Annealed copper would make a poor spring because its elastic limit is very low; but cold-worked copper has a much higher elastic limit and resilience, and therefore makes a better spring. Thus, high resilience is associated with high elastic strength.

## Ductility, Malleability and Toughness

Ductility:  It is the quality of materials, which makes them being capable of extended by pulling and remains extended even after the force of pulling is removed.
A study of stress-strain curve for mild steel, as shown in Figure, shows that OA a straight line relationship exists. Point A is called proportional limit within which Hook’s Law applies.

B is the elastic limit point, i.e. the limit upto which material is capable of withstanding load without producing a permanent set. C is known as upper yield point and D is the lower yield point.

The position of the curve beyond lower yield point represents the plastic range. In this range the deformation increases more rapidly than stress, E is the maximum stress, the material can attain and F represents the breaking point.

The elongation from the yield point to the point of rupture is not recoverable and it is a measure of plasticity. The total elongation of a specimen at fracture expressed at a percentage of the gauge length is a measure of ductility. It reveals that greater the permanent extension, the more ductile the material is.

The ductility is of great importance in wire drawing. It is very valuable property to select the materials for chains, ropes etc. because they do not snap of while in service without giving sufficient alarm by elongation.

Malleability:  Malleability or “mass ductility” is the property of a material to be permanently extended in all directions, when hammered, or otherwise, worked into various shapes.

Toughness: The work per unit volume required to fracture a metal is called its toughness, and is equal to the total area under the stress-strain curve. It is a measure of the total energy-absorbing capacity of the metal, including both elastic and plastic deformation.

Some mild steels are tougher than hard steels because the plastic deformation at fracture for the latter may be quite small. Toughness shows some relationship to impact strength, i.e., resistance to shock loads, but the energy values measured in a static test and impact test do not agree for all metals or test conditions.

Toughness is desirable property in materials subjected to dynamic loads such as shocks or impact.