What prevents fissile materials from fully undergoing nuclear fission? As I have realised, most of the Uranium and Plutonium inside an Atomic Bomb do not actually fission together, even if the critical mass is used. In fact, for Little Boy, only 1.09 kg out of 64 kg of the uranium fissioned, while Fat Man only had 1 kg out of 6.19 kg of plutonium fissioned. Eventually, nuclear fusion is used to compensate for this low conversion, atomic bombs stuffed in nuclear bombs to make more destruction.
I do not fully know what causes this to happen. I initially believed it to be something to do with the extra radioactive materials flying everywhere, but that might not be the only issue, especially when referring to implosion-types, which ensure that the entire ball of fissile material is compressed in all directions. I also cannot find any proof that this is really the case. Just what really prevents the fissile material from undergoing nuclear fission?
 A: A detailed answer is probably not appropriate on this stack. (Note that when I posted this answer it was on the world building stack, not the physics stack. On the physics stack a detailed answer would be far better.)
But very briefly, it has to do with efficiency and the speed the thing blows itself apart. The time for burn rate to rise and the time the device starts to explode compete. So the nuclei are flying apart before more than a small portion are used up.
Consider a compression type device, with a shaped charge that compresses a sphere of Plutonium. In some designs there is also a tamper. This is a shell of material around the core that acts to reflect many neutrons back into the core, further reducing the required critical mass.
The characteristic time of increase of burn rate is extremely sensitive to the geometry of the fissile material. If the mass is just below critical at its non-compressed density, then a very small compression puts it over. If it can be put far enough over such that it reaches prompt critical, then the doubling time for energy output is in the range of a few micro seconds.
But recall that the mass only needs to expand a very small amount to fall below criticality again. So, as the energy is released and the explosion starts its very early stages, it does not have to go far to cause the reaction to effectively halt. So if the original chemical explosion only reduced the radius of the core by, say, 1% (not the actual number, but to have a number) then the explosion only has to progress far enough to overcome that 1% to stop the reaction. If the explosion kicks the tamper away, the reaction stops.
There are a bunch of additional effects that would be difficult to calculate. I can't even tell you whether they speed things up or slow them down just off hand. For example, each fission leaves fragments of the original nuclei. Some of those are strong neutron absorbers. There is a temperature effect. Hot nuclei are moving, so it changes the effective energy spectrum for the reaction.
But the dominant effect is competition between the speed of the burn and the speed of the core exploding. If it explodes too quickly you get what is known as a "fizzle."
A: As I noted above in the comments, Reed's paper is a wonderful overview of the conditions in a bomb, going back to Serber's Los Alamos Primer. As noted in the introduction to Reed's paper:

One full page of the Primer was devoted to a hand-drawn
graph that illustrated the evolution of neutron density, energy
density, and pressure within an exploding bomb core as a
function of time. While based on an approximate treatment
of neutron diffusion for the purpose of informing his audience
as to the orders of magnitude they would be dealing
with, Serber’s plot still stands as a remarkable example of
effective graphical display of information.

Reed repoduces the Serber plot in Figure 1:

Note the tiny bar labeled 'Efficiency' down in the lower right corner, and compare with the pressure and temperature lines, both of which are significantly exceeding the core of the Sun. One does not reach even 1% efficiency until neutron generation #36, and 100% efficiency is reached in neutron generation #41. The trick, of course, is holding it all together long enough to contain the extremes of energy density, temperature, and pressure before flying apart.
A fun quote from near the end of the (short) paper is:

"A density
of a few quadrillion neutrons per cubic centimeter
sounds fantastic but, in reality, corresponds to fission of less
than one part in a million of the 235U contained in any cubic
centimeter of the core."

