If you've spent any time playing Dead Space 3 you'll know how difficult it can be to acquire Tungsten early on in the game. As a crafting material, Tungsten's the rarest most valuable type of metal you can find in the game.
Throughout the game, there are many sealed areas that require Tungsten Torque Bars to open. You'll need the raw material to craft them. Typically, these areas will contain upgrade circuits and weapon parts, much as reward areas in previous games were locked away by Power Nodes you needed to also upgrade your weapons.
The following list will be updated with more locations for Tungsten and hidden artifacts throughout the game as we discover them.
You'll find some Tungsten in the Admiral's Office early on in Chapter 4. Right after the cutscene where Isaac zones out, shoot the buck's head that's hanging on the wall to find some Tungsten in a hidden compartment. You'll also get the achievement "Under a Buck" for this discovery.
You can find the following cache of Tungsten in the space derelict after you use the Mechanical SK-1P. You won't get any achievements for it, but it's a good find anyway.
You'll come across the following cache in the space surrounding the Terra Nova. Be sure to kill the pimples before going for the artifact or you'll probably die.