Can I have a glass bed with only the center heated? I have a 15x15 cm heating resistor from my current printer (printing area: 12x12 cm).

I would like to switch to a glass bed and to rework my printer to increase the printing area to 20 cm (22x22 cm glass plate).

Would it be possible to use the old heating resistor placed only in the centre? this way I would have a smaller heated bed for ABS and a bigger one for PLA.

Would the glass crack due to non uniform heating? This is because glass has a conductivity of less than 5 W/mK, therefore the hot area will stay hot and basically never really spread the heat to the surrounding area. So the frame will be cold and the center hot, causing stresses.

Related: https://engineering.stackexchange.com/questions/31842/how-much-an-unevenly-heated-glass-plate-bows
If you're using borosilicate glass (aka pyrex) then it won't crack. You can get squares of ~20x20 cheaply off aliexpress.

If you're using window glass, picture frame class etc then you might have issues with cracking, it will depend on lots of factors like the wattage of your heater and the temperature of the room.

Your biggest problem will be that the bed heats very non-uniformly, which is unlike to give good print adhesion. I'd suggest a sheet of aluminium underneath the glass if possible, it will allow much more even heating.