Metal removal in electric discharge machining takes place through melting and vaporization.

Explanation:
In electric discharge machining (EDM), metal removal occurs through a controlled electric spark erosion process. The process involves the use of an electrically conductive workpiece and a tool electrode, typically made of copper or graphite. The workpiece and the tool electrode are immersed in a dielectric fluid, usually deionized water or a special EDM oil.

1. Melting:
When an electric potential difference is applied between the tool electrode and the workpiece, a series of high-frequency electric sparks are generated. These electric sparks cause localized heating at the surface of the workpiece. The intense heat generated by the electric sparks causes the localized area of the workpiece to melt.

2. Vaporization:
As the material melts, it also vaporizes due to the high temperatures reached during the spark discharge. The vaporized metal is expelled from the workpiece in the form of small particles or droplets. These metal particles are carried away by the dielectric fluid, effectively removing the material from the workpiece.

3. Displacement:
While melting and vaporization are the primary mechanisms of metal removal in EDM, there is also a certain degree of material displacement. The electric sparks create a high-pressure plasma channel between the tool electrode and the workpiece. This plasma channel exerts a force on the molten metal, causing it to be pushed away from the workpiece surface.

Advantages of Melting and Vaporization:
Melting and vaporization as the main mechanisms of metal removal in EDM offer several advantages:
- The process does not rely on mechanical force, allowing for the machining of complex shapes and difficult-to-machine materials.
- EDM can be used to machine electrically conductive materials, including hardened steels, exotic alloys, and even non-conductive materials that can be made conductive with the use of a special coating.
- The process produces minimal residual stresses and heat-affected zones, making it suitable for applications that require precise dimensional accuracy and surface finish.

In conclusion, metal removal in electric discharge machining primarily occurs through melting and vaporization. This process allows for the precise machining of electrically conductive materials, offering several advantages over traditional machining methods.