The ductility of a material refers to its ability to deform under tensile stress without fracture. It is a desirable property for materials used in applications that require shaping or forming, such as metalworking or construction.

Work hardening, also known as strain hardening, is a process in which a material becomes stronger and more resistant to deformation as it is plastically deformed. This occurs due to the creation and interaction of dislocations within the material's crystal structure.

When a material undergoes work hardening, its ductility generally decreases. This is because the creation and interaction of dislocations restrict the movement of atoms within the crystal lattice, making it more difficult for the material to deform plastically. As a result, the material becomes more brittle and prone to fracture.

Here is a detailed explanation of why the ductility of a material with work hardening decreases:

1. Creation of dislocations: When a material is subjected to plastic deformation, dislocations are generated within its crystal lattice. Dislocations are line defects that disrupt the regular arrangement of atoms. They can move through the crystal lattice, allowing plastic deformation to occur. However, the presence of dislocations also hinders the movement of atoms and increases the material's resistance to further deformation.

2. Interaction of dislocations: As plastic deformation continues, dislocations can interact with each other, forming entangled networks or tangles. These tangles act as barriers to dislocation motion, making it more difficult for the material to deform. This results in an increase in the material's strength but a decrease in its ductility.

3. Strain hardening: The interaction of dislocations leads to strain hardening, which is the process by which a material becomes stronger and more resistant to deformation. Strain hardening occurs because the dislocations create internal stresses within the material, which resist further dislocation motion. This resistance to deformation causes the material to exhibit higher yield strength and tensile strength.

4. Decreased ductility: The increased resistance to deformation and the presence of dislocation tangles restrict the ability of the material to deform plastically. As a result, the material becomes more brittle and prone to fracture. This decrease in ductility is undesirable in many applications where the material needs to undergo extensive shaping or forming.

In conclusion, the ductility of a material with work hardening decreases. The creation and interaction of dislocations within the material's crystal lattice lead to an increase in strength but a decrease in ductility. This is due to the increased resistance to deformation and the formation of dislocation tangles, which restrict the material's ability to deform plastically.