On thermodynamics of crystal plasticity

A simple model for dynamic recrystallization during severe plastic deformation

“…we demandḋ = 0 for ρ < k 1 ρ S (with k 1 being a phenomenological constant less than 1 [13]). Therefore, Eq.…”

“…Note that the dislocation density ρ only accounts for statistical dislocations inside the grains and not for the geometrically necessary dislocations that constitute the grain boundaries whose energy enters explicitly as grain boundary energy. We employ the following formulation for the energy of the microstructure, following Berdichevsky's [13] proposal…”

“…With these findings at hand in addition to energetic suggestions by Berdichevsky [13], it becomes feasible to thermodynamically motivate and derive the evolution equations for grain size and dislocation density during dynamic recrystallization and apply these to ECAE.…”

Dislocation structure during microindentation

“…Therefore the free energy density per unit volume of the crystal with continuously distributed dislocations can be proposed in the form (Berdichevsky, 2006a(Berdichevsky, , 2006b wðe e ; qÞ ¼ 1 2 k tre e ð Þ 2 þ le e : e e þ lk ln…”

“…The material model proposed in this paper is based on the continuum dislocation theory (CDT) developed in Berdichevsky (2006aBerdichevsky ( , 2006b, Berdichevsky and Le (2007), Kaluza and Le (2011), Kochmann and Le (2008, 2009a, 2009b, Le and Sembiring (2008a, 2008b, 2009), Le and Nguyen (2010), Le andNguyen (2012, 2013) (see also the finite strain CDT proposed by Le & Günther (2014), Koster, Le, & Nguyen (2015)). We apply this material model to the two-dimensional plane strain problem of wedge indentation for single crystals having one active slip system on each side of the wedge.…”