Incorporating the influence of the temperature into a mesoscopic continuum description of dislocation systems

Understanding the collective behaviour of dislocations is a key issue of recent research activity on dislocation theory. Around the micron scale a continuum description operating with continuous fields (like stored and geometrically necessary dislocation densities) seems to be an efficient approach for describing phenomena like pattern formation or size effects. The aim of the present paper is to incorporate the influence of temperature and dislocation climb into the time evolution equations of the different dislocation densities. For a system of straight dislocations a Fokker–Planck type equation is derived. By performing a coarse graining procedure it is shown that thermal noise and climb lead to the appearance of additional gradient-like terms.