About

Minimally 3 fully engaged threads. Look at a nut.
However, for optimum thread engagement, a common rule of thumb is 1 1/2 times the diameter of the screw.

So, for a 1/4″ diameter screw, you need (1.5 x .25)=.375″ of thread depth.
For a 1/4-20 screw you have

(length of thread x pitch) = number of threads
(.375 x 20)= 7.5 threads

The idea is for the screw to break instead of stripping out the threads in the tapped hole. A longer length of engagement leads to a stripped out hole.

The most common reason is that the male and female threads are made of the same material. During tightening, as pressure builds between the contacting and sliding thread surfaces, protective oxides are broken, possibly wiped off, and interface metal high points (such as rough threads) shear or lock together. This cumulative clogging-shearing-locking action causes increasing adhesion called “galling”. Thread galling is most prevalent with parts made of stainless steel, aluminum, titanium, and other alloys which self-generate an oxide surface film for corrosion protection. In the extreme, galling leads to seizing – the actual freezing together of the threads. If tightening is continued, the fastener can be twisted off or its threads ripped out.

Lubricating the internal and/or external threads frequently eliminates thread galling. The suggested lubricants should contain substantial amounts of molybdenum disulfide (moly), graphite, mica, or talc. Some proprietary, extreme pressure waxes may also be effective. You must be aware of the end use of your parts before settling on a lubricant. Stainless steel is frequently used in high vacuum applications, which may make some lubricants unacceptable.

Using different stainless alloy grades for the mating parts reduces galling. The idea here is that the materials of mating parts have different hardnesses. If one of the components is 316 and the other is 304 they’re less likely to gall than if they’re both of the same alloy grade. This is because different alloys work-harden at different rates.

To prevent breaking taps try these helpful hints:

a. use the correct drill size for the tapped hole and the material
b. chamfer the hole
c. lubricate the tap
d. use the proper size tap wrench
e. use a sharp tap
f. use a thru hole if at all possible, blind holes don’t allow the chip to evacuate. Think venting.
g. for every 1/4 turn of the tap in, turn the tap at least a 1/2 turn back out to break the chip.
h. tap 1/2 the hole depth, then clear out the chips and go back in and finish tapping the hole.