I am going to build this 12 volt mobile inverter box. I thought circuit breakers might be a good idea but I dont know if they will wprk on 12 VDC motorcycle battery. Would these breakers work or will I have to order DC ones?

They will work up to 24V (the limit for contacts without any special arc supression), but I would expect the voltage drop, so power losses would be quite high compare to the working power.

The most common way to protect 12VDC power distribution networks mainly in cars is becoming the use of "Smart FET's" (a combination of a power FET, predriver in one common package, e.g. NCV8452, NCV8460,...) handling the load failures and mainly the selectivity (identifying and disconnecting only the faulty branch, let the others operate; usually used one per function like lamp, motor,...), in combination with classic filament fuses used as a back up (when the MOSFET itself fails,...; these usually disconnect larger functional groups).
These FET's are then used for normal functional power switching (switching ON/OFF the lights,...)

I know Sq D QO series 120 volt Ac also will do 48 volt DC.  It used in some solar Home install.

I know older thermal magnetic  challanger breakers
Works quite well. Even not rated for it .

Lets break it up to :

Will the breaker trip in response to overcurrent

What will happen when and after the breaker trips



As long as the breaker is closed, there is only minimal voltage drop across it. It can sense the current and thats it

Breakers have thermal and magnetic trip elements in them :

The thermal handle low overcurrents, and take long time to heat up and trip - from a hour or more for "light" overload (1.5x rated current or so) down to about 10 seconds for high currents of a "bad contact" short circuit

The magnetic handle high overcurrents, and trip instantly - thats mostly for "good contact" short circuits that draw really big currents

The magnitude of current at which the magnetic part takes over the thermal one is on the order of several times the rated current. In our European breakers, it is on the order of 3x..5x rated current for B type ("low inrush") and 5x..10x rated current for C type ("high inrush") breaker types

The thermal part trips by a bimetal strip heating from I2R, it will trip just the same for AC and DC

The magnetic part trips by pulling a latch that release the spring with an electromagnet coil. It will work on DC, but can trip at a different current than on AC. For example, while with AC the alternating field "shakes" the latch from under the spring, in DC it can only pull straight and will have to pull harder (so higher current) before it release the breaker



As soon as one of the tripping systems activated, the contacts are starting to move apart. They interrupt very large currents (short circuit etc) and have to be able to cut out the arc that pulls between the contacts moving apart, before the arc destroys the breaker

The breaker has arc interruption capability of few kA up to 10 kA, sometimes higher - once (after that it has to be replaced), or lower current (100's A) multiple times, but all that is in AC - the breaking depends on the arc going out at zero crossing, then cooling down and venting the hot air through a seres of metal plates

In DC there is no zero crossing so the arc that can be drawn is way longer lasting

The hotter the arc is, the more conductive it is, so the less voltage drop is across it. Now same as with HID, the arc will go out if the arc voltage exceed the available supply voltage. So while for 12V the supply is really limited, for 48V not so much - i would trust a sand filled fuse more than an AC rated breaker if the 48V system has big batteries that are capable of more than few A of short circuit current

The thing is, for the sake of robustness, the mains breakers are designed with rather high power dissipation of their "thermal" trigger. The higher power dissipation means the energy available to actuate the trigger mechanism becomes higher, so you do niot have to worry that much about the friction or so, so it stay perfectly working even in worse conditions.
When you have 120V total, spending 0.5..1V for more reliable operation of the breaker is no bug deal to care about, it is just less than a percent. But the same drop would be on 12V, but there it means 5..10% of the power, so not that negligible anymore and that is the problem I had in mind. If that is of no problem, the normal breakers will work well up to the contact limit.
Therefore for the 12V you will need something with less drop, so something with more sensitive mechanics.

As making the mechanics more sensitive and still very reliable is quite difficult task, it is not the way the industry went.
It really goes in the way of few wire-blow fuses (as the main safety device) supplemented by the semiconductor switches (to make the need to replace the fuses very rare event and to isolate the faulty branch from the others).

I'm with funkybulb on the square d breakers.  They also make resettable ATM fuses both in push button reset and auto reset.