A dissipation potential approach to describe flow instability in alloys during hot deformation

Flow instability is the onset of heterogeneous flow intensifying flow localization and leading to further damage in alloys during hot deformation. Some phenomenological approaches in the literature do not account for the microstructure changes of the material. In order to overcome this problem, we introduce a dissipation potential approach as a function of the plastic strain rate, the evolution rate of dislocation density and the heat flux, D(ε ̇_p,ρ ̇,q), to describe the flow instability during hot deformation. This approach considers the principle of orthogonality proposed by HANS ZIEGLER and describes large plastic flow with far-from-equilibrium thermodynamics. Moreover, the evolution rate of dislocation density ρ ̇is involved and the transient energy dissipation comprises mechanical part due to dislocation movement and thermal part by heat transfer. The necessary condition for stable flow is that the dissipation potential D(ε ̇_p,ρ ̇,q)is convex, i.e. the associated Hessian is non-negative. This approach connects the continuum mechanics, non-linear non-equilibrium thermodynamics and microstructure evolution when dealing with hot deformation problems. In this work, the approach was applied to describe the behavior of Ti6Al4V during hot deformation, and using a Kocks-Mecking type model to describe the flow stresses as a function of the dislocation density.