Conditions for the localisation of plastic deformation in temperature sensitive viscoplastic materials

Abstract

We study the onset of localisation of plastic deformation for a class of materials that exhibit both temperature and rate sensitivity. The onset of localisation is determined via an energy bifurcation criterion, defined by the postulate that viscoplastic materials admit a critical (mechanical) energy input above which deformation becomes unstable and plastic localisation ensues. In analogy to the classical concepts of mechanics, the conditions for the onset of localisation in temperature-sensitive viscoplastic materials are reached at a critical stress. However, it is shown that in viscoplastic materials a material bifurcation occurs when the heat supply through mechanical work surpasses the diffusion capabilities of the material. This transition from near-isothermal stable evolution to near-adiabatic thermal runaway is the wellknown concept of shear heating. Here, it is generalised and the correspondence between this runaway instability and the localisation of plastic deformation in solid mechanics is detailed. The obtained phase space controlling the localisation is shown to govern the evolution of the system in the postyield regime. These results suggest that the energy balance essentially drives the evolution of the plastic deformation and therefore constitutes a physics-based hardening law for thermoviscoplastic materials.

Boudinage and folding as an energy instability in ductile deformation

“…This change from stable to unstable creep (Figure b.ii) is the inflection point of the eigenvalues of the critical Gruntfest number G r c [e.g.. Hobbs et al , , ; Veveakis et al , ], revealing a folded instability curve ( S curve). The saddle point G r c has been shown to define the transition of the system from steady state (homogeneous) deformation to a localization instability [ Paesold et al , ; Veveakis et al , ]. From the definition of G r as a dissipation measure, we conclude that this saddle point is an energy bifurcation threshold, defining the transition to localization.…”

“…These two equations are coupled, but using G r as a bifurcation parameter allows the equations to be decoupled and solved separately. According to Paesold et al [], this can be achieved in a two‐step procedure. First, a bifurcation analysis of the energy balance of equation determines the steady state.…”

“…In order to determine the conditions for the onset of localization, we therefore start our approach by considering constant stress boundary conditions. The first equation of the system together with the yield criterion provide the characteristics of the stress equilibrium, defining the directions in which potential localization will take place [ Paesold et al , ]. The bifurcation diagram of the second equation can be computed using the pseudo–arc length continuation technique [ Doedel et al , ; Keller , ].…”

“…Therefore, the critical turning point of G r admits smaller values when the structure approaches that of a thin layer, where l y ≪ l x , i.e., (Figure a). Paesold et al [] have obtained a semianalytic expression for the critical value of G r at the turning point G r c (see also Figure b), which reads …”

Robust numerical implementation of a 3D rate‐dependent model for reservoir geomechanical simulations

“…[29][30][31] Veveakis et al investigated a viscoplastic approach for pore collapse in saturated soft rocks 32 and particularly the effects related to temperature variation. 33 Another class of simplified one-dimensional models is based on elastic springs, plastic sliders, and viscous dashpots. These models have been widely used, and they are still attractive for their simplicity.…”