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The 3 stages of quenching are the Vapor Stage, the Boiling Stage, and finally the Convection stage. These stages are in reference to the interaction between the quenchant and the component being cooled. Vapor Stage: In this stage the super-heated component immediately vaporizes the quenchant. The gaseous quenchant now surrounds the component in a thin sheet, and the liquid quenchant is no longer in contact with the component and the heat therefore slowly seeps out of the component by radiation and limited conduction. Boiling Stage: As the vapor insulation degrades and collapses, the component begins to boil the quenchant. Due to the direct contact with the liquid quenchant, cooling occurs quicker than the vapor stage. Eventually, as the heat diffuses into the liquid, the interface temperature drops below boiling and the convection stage begins. This is a similar principle to that which allows this to occur (see video). This is called the Leidenfrost Effect (https://en.wikipedia.org/wiki/Leidenfrost_effect#:~:text=The%20Leidenfrost%20effect%20is%20a,the%20liquid%20from%20boiling%20rapidly.) Convection Stage: Finally, the convection stage occurs after boiling has ceased and the heat can only be transferred by convection. The rate of cooling gradually decays as the system approaches equilibrium. Please see the graphical illustration below.
Image courtesy of Globalspec.com
References: Understanding the Cooling Curve Test by D. Scott MacKenzie courtesy of Thermal Processing Magazine https://www.houghtonintl.com/sites/default/files/resources/article_-_understanding_the_cooling_curve_test_0.pdf