Warning: Chromates are toxic and carcinogenic. Destroy them with ascorbic acid before washing down the drain. Hydrochloric acid is corrosive. Do not apply to skin. Nickel compounds are also carcinogenic.
You will need:
18/10 stainless steel object
12VDC power supply
2 Alligator clips
Ordinary iron nail or screw
Stainless steel is well known for its corrosion resistance. Despite this, we will split up 18/10 stainless steel into its three constituent elements. The 18/10 stands for percent of chromium/percent of nickel. 18/0 stainless steel is more boring as there are only two elements to separate.
Let's analyze this problem to see whether you can design the experiment. Stainless steel is resistant to oxidation by oxygen but not by chlorine. Therefore, sodium bicarbonate electrolyte is out of the question as only oxygen gas will be produced. What compounds can produce chlorine? Sodium chloride is one of the most common ones. The acid produced should dissolve the protective layer of the stainless steel, exposing it to further corrosion. As you should know, the anode oxidizes, and the cathode reduces. So the stainless steel should go to the anode. Since the electrode is not affected during reduction, any metal can be used. Because of iron's ready availability, it is used as a cathode. The oxides or hydroxides are produced during this corrosion.
Here are the properties of the elements:
Iron: 2 common oxidation states, none higher than 3, Fe2O3 insoluble in ammonia
Nickel: 1 common oxidation state, Ni(OH)2 soluble in excess ammonia
Chromium: 2 common oxidation states, water soluble +6 oxidation state
So, to separate chromium, we need to oxidize it so we can leach it out of the remaining oxides. Bleach is an oxidant, so that can be used. To separate nickel, we need to leach it out as the ammine complex. This involves much washing with ammonia. Then, only iron is left.
Electrolyze the stainless steel. You will see a dark green precipitate that will gradually turn brownish-green. Electrolyze as long as you like, replenishing water as needed. Filter and dry the precipitate. After placing it in a container, add excess sodium hypochlorite (bleach). Stir and let it sit for a day. Stir it again. A yellow solution of sodium chromatewill form. Filter and keep both the filtrate and the precipitate. Evaporate the filtrate until only a small amount is left. While doing this, wash the precipitate with water. Place the precipitate back in a container, then add an excess of ammonia. After a while, a blue solution of nickel(II) ammine complex should form. Keep this covered for several days as the ammonia leaches out the nickel. Then filter and keep both the filtrate and the precipitate. Evaporate the filtrate until only a small amount is left. Then rewash the precipitate, following the steps above. Continue rewashing until the solutions become colorless. Then you have pure iron oxide. Now you have three solutions and one solid: chromate, nickel ammine, and iron oxide. Add ascorbic acid to the chromate. It will turn light green and a chromium(III) solution will form. Concentrate the solution by boiling. Electrolysis it using a smooth cathode and any anode may form chromium metal. Electrolyze the nickel ammine solution using a smooth cathode and any anode. Nickel powder should form at the cathode. You may use a strong magnet to pick up the nickel powder if it gets mixed with the solution. Dissolve the iron oxide in hydrochloric acid and add ascorbic acid. A green solution should form of an iron(II) complex. Electrolyze the solution using a smooth cathode and any anode. Pure iron powder should form at the cathode. Use a magnet to take it out of solution.
If this big experiment works, you have separated stainless steel into its constituents using nothing but household chemicals and basic supplies.
There are better and more reliable ways of obtaining the metals, but they do not use solely common household products.