Vol. 11, No. 2, 2016

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ISSN: 1559-3959
Conditions for the localisation of plastic deformation in temperature sensitive viscoplastic materials

Martin K. Paesold, Andrew P. Bassom, Klaus Regenauer-Lieb and Manolis Veveakis

Vol. 11 (2016), No. 2, 113–136
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 well-known 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.

Keywords
bifurcation analysis, localisation of plastic deformation, energy balance, slip lines
Milestones
Received: 16 April 2015
Revised: 19 October 2015
Accepted: 24 October 2015
Published: 23 February 2016
Authors
Martin K. Paesold
School of Mathematics and Statistics
University of Western Australia
35 Stirling Hwy
Crawley WA 6009
Australia
CSIRO Earth Science and Resource Engineering
26 Dick Perry Avenue
Kensington, WA 6151
Australia
Andrew P. Bassom
School of Mathematics and Physics
University of Tasmania
Private Bag 37
Hobart TAS 7001
Australia
School of Mathematics and Statistics
University of Western Australia
35 Stirling Hwy
Crawley, WA6009
Australia
Klaus Regenauer-Lieb
School of Petroleum Engineering
University of New South Wales
Tyree Energy Technologies Building
Anzac Parade
Kensington NSW 2052
Australia
Manolis Veveakis
School of Petroleum Engineering
University of New South Wales
Tyree Energy Technologies Building
Anzac Parade
Kensington NSW 2052
Australia
School of Mathematics and Statistics
University of Western Australia
35 Stirling Hwy
Crawley, WA6009
Australia