Explanation:

Ductility is a property of a material that allows it to deform under tensile stress without fracturing. It is a measure of how much a material can be stretched without breaking. Work hardening refers to the increase in the strength and hardness of a material as it is deformed. Work hardening occurs when a material undergoes plastic deformation, causing dislocation movement and rearrangement of the crystal structure.

The relationship between ductility and work hardening is as follows:

1. Work Hardening:

When a material is subjected to plastic deformation, dislocations are generated and move through the crystal lattice. These dislocations interact with one another and create obstacles that hinder their movement. As a result, the material becomes harder and stronger. Work hardening is characterized by an increase in yield strength and tensile strength of the material.

2. Effect on Ductility:

Work hardening has a significant impact on the ductility of a material. As the material work hardens, the dislocation density increases, and the movement of dislocations becomes more restricted. This increase in dislocation density leads to a decrease in the ability of the material to deform plastically without fracturing. The material becomes less ductile and more prone to brittle fracture.

3. Decrease in Ductility:

As the material undergoes work hardening, it becomes less ductile. The increased dislocation density and restricted dislocation movement make it more difficult for the material to undergo plastic deformation. This results in a decrease in ductility and an increase in the likelihood of brittle fracture.

4. Example:

For example, consider a piece of metal that is initially ductile. When the metal is subjected to plastic deformation, such as stretching or bending, it undergoes work hardening. As a result, the metal becomes harder and stronger but also less ductile. If the deformation is continued beyond a certain point, the metal may eventually fracture due to the decreased ductility.

Conclusion:

The ductility of a material decreases as it undergoes work hardening. Work hardening increases the strength and hardness of the material but restricts its ability to deform without fracturing. Therefore, the correct answer is option 'B': Decreases.