Metal removal in electric discharge machining takes place through

The correct option is melting and vaporization.

Step-by-Step Explanation:

1. Working Principle of Electric Discharge Machining (EDM):
Electric Discharge Machining (EDM) is a non-traditional thermoelectric machining process. In this process, material is removed from the workpiece using a series of rapidly recurring electrical spark discharges between an electrode (the tool) and the workpiece, which are both submerged in a dielectric fluid (such as kerosene or deionized water).

2. Mechanism of Metal Removal:
When a high voltage is applied across the small gap between the tool and the workpiece, the dielectric fluid breaks down and ionizes, creating a plasma channel. As a spark jumps across the gap, it produces extremely high localized temperatures (typically in the range of 8,000 to 12,000 degrees Celsius). This intense heat causes a small portion of the metal on both the workpiece and the tool surface to instantly melt and vaporize.

3. Ejection of Material:
When the current is interrupted, the plasma channel collapses, causing a sudden drop in pressure. This shockwave, combined with the flushing action of the circulating dielectric fluid, carries away the melted and vaporized metal debris, leaving behind a small crater on the surface of the workpiece.

4. Evaluating the Options:
- Ion displacement: Incorrect. Although ionization of the dielectric medium occurs to form the plasma channel, the physical removal of the metal is not caused by ion displacement.
- Melting and vaporization: Correct. The thermal energy of the spark directly melts and vaporizes the metal.
- Corrosive reaction: Incorrect. EDM is an electro-thermal process, not a chemical or corrosive one.
- Plastic shear: Incorrect. Plastic shear is the primary mechanism of material removal in conventional machining processes (like turning or milling), not in EDM.