Introduction:
The ferrite phase is a solid solution of carbon in iron. It has a body-centered cubic crystal structure and is relatively soft compared to other phases in steel. Increasing the amount of ferrite phase in steel can have several effects on its mechanical properties.

Strength:
Increasing the ferrite phase in steel can increase its strength. This is because ferrite has a lower carbon content, which reduces the formation of hard and brittle carbides. As a result, the steel becomes more ductile and less prone to fracture. The absence of carbides also reduces the likelihood of intergranular corrosion, which can further enhance the strength of the steel.

Hardness:
Contrary to the statement given in the question, an increase in the ferrite phase generally decreases the hardness of steel. Ferrite is a relatively soft phase, and increasing its proportion in steel leads to a decrease in overall hardness. Hardness is primarily determined by the presence of hard phases, such as martensite or carbides, which are not present in ferrite.

Ductility:
Increasing the ferrite phase in steel generally improves its ductility. Ferrite is a more ductile phase compared to other phases, such as martensite or bainite. The presence of ferrite allows for more plastic deformation before fracture occurs, making the steel more ductile and less prone to brittle failure.

Brittleness:
Increasing the ferrite phase in steel can reduce its brittleness. Ferrite is a relatively soft and ductile phase, and its presence can prevent the formation of harder and more brittle phases, such as martensite or bainite. This leads to a more ductile steel that is less prone to sudden and catastrophic failure.

Conclusion:
In summary, increasing the ferrite phase in steel can increase its strength, improve ductility, and reduce brittleness. However, it generally decreases the hardness of the steel. These changes in mechanical properties are primarily due to the absence of hard and brittle phases, such as carbides or martensite, in the ferrite phase.