If Pu-239 is irradiated in a neutron flux, will a fizzle detonation occur? How much flux would be required? I understand that adding flux does not change criticality. I'm not looking for K values here, just an estimate of the added neutron flux required to disable a typical ICBM warhead. I would like to compare it to flux levels in reactors and other neutron sources.
As noted in comments, neutrons will cause fissions to occur. If enough fissions occur over a short time period, the fissile material will heat up and possibly start to melt the warhead and/or the sudden thermal expansion would cause it to blow apart. Everything depends on the magnitude of flux added and the time involved.
A useful and understandable answer led to some useful hits. https://www.nuclear-power.net/nuclear-power/reactor-physics/reactor-dynamics/subcritical-multiplication/subcritical-multiplication-factor/
I think I understand the time dependence and asymptotic value of the neutron flux.
I'm still wondering what flux would be required to melt Pu from the heat of induced fission. Pu heat capacity= 0.13 J/(gK), and heat of fusion = 2.84 kJ/mol, and heat released from fission = 198.5 MeV. The fission rate = Neutron flux)(microscopic cross section)*(number density of nuclei).
I think I can work it out from that. Corrections appreciated. I'll assume adiabatic because I want a rapid heatup. I think neutron fluxes ranging from 10^10 to 10^14 neutrons/cm2/s (depending on the position within the reactor) are available.
Doesn't this make you wonder why I want to know?
 A: The warhead fissile material is in a subcritical configuration.  If exposed to an external neutron source, the configuration is a "subcritical mass with an external neutron source", and the flux $(neutrons/cm^2/sec)$ approaches a constant value proportional to the strength of the external neutron source and inversely dependent on  one minus the subcritical multiplication factor, $1 - k$.  The actual calculation is complicated, and analytical approximations are given in the text, Lamarsh Nuclear Reactor Theory.  An accurate calculation considering the exact geometry, and all the materials present besides the fissile primary, would require applying weapons neutron kinetic codes (on massively parallel computing machines) developed by Los Alamos and Lawrence Livermore National Laboratories, and would be different for different warhead nuclear packages, such as the W78 and the W87 for the current ICBMs.  There have been calculations done to assess the effectiveness of hardening measures in the warhead to protect against extraneous neutron sources from enemy nuclear weapon detonations during delivery of the warhead; these studies are classified, so I cannot give you any more detailed information.
Except for certain conditions the warhead is inside a reentry vehicle, inside the missile, inside a silo, so it would require a massive external neutron source to affect the warhead to any significant extent.
