Explain the differences in grain structure for a metal that has been cold worked and one that has been cold worked and then recrystallized.

Cold working, also known as work hardening or strain hardening, is a process where a metal is mechanically deformed at temperatures below its recrystallization temperature. This mechanical deformation introduces defects, also called dislocations, in the metal's lattice structure, which impede the movement of other dislocations. As a result, the metal becomes harder and stronger but less ductile.

Recrystallization is a heat treatment process where a cold-worked metal is heated to a temperature above its recrystallization temperature but below its melting point. At this temperature, the new grains will nucleate, grow, and replace the existing deformed grains formed during cold working, and the dislocations will be reduced. The recrystallization eliminates the effects of cold working, returning the metal to its original ductile state with lower strength and hardness.

Cold working results in the elongation of grains in the direction of the applied stress due to mechanical deformation. The dislocations within the grains increase due to the cold working process, which causes the grains to become misoriented and distorted, leading to an increase in the overall strength and hardness of the metal. However, the increased dislocation density also causes a decrease in ductility due to the hindered movement of dislocations. The grains will appear elongated and have irregular shapes with different sizes.

When a cold-worked metal undergoes recrystallization, new grains start to nucleate and grow, consuming the existing distorted and elongated grains formed during cold working. This process results in smaller, more uniformly sized and equiaxed grains with fewer dislocations. The new grains will be free from the distortions and stresses caused by the cold working process, restoring the original ductility, and decreasing the strength and hardness. In conclusion, a cold-worked metal has elongated, misoriented, and irregularly shaped grains with increased dislocation density, resulting in higher strength and hardness but lower ductility. On the other hand, a metal that has been cold worked and then recrystallized has smaller, uniformly sized, and equiaxed grains with reduced dislocation density, leading to a decrease in strength and hardness but an increase in ductility.