When liquid steel cools it forms crystal structures. But this happens at different places within the steel at the same time. And these crystals that start in different places form in different orientations. Where they meet there will be a much weaker structure as the crystals do not connect well. It is much easier for the steel to break where these different crystal structures meet then in a continuous structure. When you forge the steel you are moving the crystals around so they meet at other orientations throughout the process. When they meet at different orientation they form weak bonds which will get broken in the next hammer hit but when they meet at the correct orientation they form a continuous strong crystal.
There are also a few other crystal defects which can be fixed by forging. Sometimes as the crystals form and solidify there may be a gap in the crystal structure as there happened to not be an atom there at the time. This creates a tiny weak spot and when the hammer hits the crystal the atoms will shift around filling this hole and creating a hole a different place. So you force these holes out to the edge of the crystal. Similarly you might have areas of too much carbon or too much iron which again creates weaker crystals and the hammering process will force these around to form a continuous strong alloy. It is not uncommon to see excess carbon flake off the outside of a steel piece as it is being forged. The same happens with any trapped oxygen or even air pockets.
Cast iron forms large crystals as it cools. The large crystals are strong within themselves, but weakly bound to each other by the intervening matrix, making cast iron brittle. Repeatedly heating and working the metal breaks up the large crystals into smaller ones, and improves the binding matrix between the crystals. Careful heat management during cooling (by quenching, annealing and insulation) provides additional control over crystal formation and matrix, giving forged iron much more strength and the ability to take an edge.
Cast metal is poured into a cast in a liquid state. Mold fills up, metal cools down and becomes solid. Forged metal is essentially compressed metal. The metal is heated enough to be malleable and then struck with hammers, which compresses the metal and makes it more dense. So a piece of forged metal compared to an equally sized piece of cast metal actually has more material, more mass, and is thus heavier, it’s just been pounded down to the same size, but the density compared to volume is higher. Each metal has a natural density it settles to but forged metal is forced to become more dense. This means that aside from heavier it’s also stronger. Since pounding something into an exact shape with gigantic hydraulic hammers is not exactly easy, forged parts are usually machined out of a bigger block of forged metal. In contrast cast parts come out of the cast pretty much done, only needing minor processing to remove casting marks and imperfections, basically just surface finish.
So Forged metal is stronger but also more expensive.
Liquid metal has gas and other impurities dissolved into it. Solid iron can’t dissolve as much, so as the metal solidifies it concentrates the impurities towards the front forming a horribly weak mess at the last place to solidify, with gas pockets and non- metallics. Forging breaks these up, do any cracks are smaller. It’s the size of the biggest crack that determines the toughness of the metal.
Forging also helps the strength through making the crystal grains smaller. The grain boundaries aren’t weak, but to stretch metal, you need to move slices of atoms called ‘dislocations’. These are hard to push through grain boundaries, do small grains make for strong metals. In most steels, heating and cooling will make the grain size smaller too.
I am a metallurgist.
I just wanted to add that SG irons (spheriodal graphite) are cast and will give a lot of steels a run for their money – so it’s not a universal fact. Components made traditionally from forged steel – like engine crankshafts – are increasingly commonly replaced with cast SG iron variants since its way cheaper to cast.
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