The ductility of a material with work hardening decreases.

Work hardening, also known as strain hardening, is the process by which a material becomes harder and stronger as it is deformed. During work hardening, the material undergoes plastic deformation, which causes dislocations to move and rearrange within the crystal lattice structure of the material.



1. Ductility and Plastic Deformation
Ductility is the ability of a material to undergo plastic deformation without fracture. It is a measure of the amount of strain a material can withstand before it breaks. A ductile material can undergo substantial plastic deformation before fracture, while a brittle material fractures with little or no plastic deformation.

2. Effect of Work Hardening on Ductility
During work hardening, dislocations within the crystal lattice become entangled and impede the movement of other dislocations. This leads to an increase in the strength and hardness of the material. However, it also makes it more difficult for the material to undergo further plastic deformation.

3. Strain Hardening Curve
The relationship between stress and strain during work hardening can be represented by a stress-strain curve. Initially, as the material is deformed, it exhibits an elastic behavior where it returns to its original shape once the applied load is removed. However, as plastic deformation continues, the material reaches a point where it starts work hardening. This is represented by a steep increase in stress with increasing strain.

4. Necking and Fracture
As the material undergoes further plastic deformation, it eventually reaches a point where it starts to neck. Necking is the localized reduction in cross-sectional area of the material. Due to the increased strength and decreased ductility caused by work hardening, the material becomes more susceptible to necking and ultimately fractures.

5. Conclusion
In conclusion, the ductility of a material decreases with work hardening. As the material undergoes plastic deformation and work hardening, its strength and hardness increase, but its ability to undergo further plastic deformation and elongation decreases. This is why the correct answer is option 'B' - decreases.