|
|||||
 |
|
|
|
|
|
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 |
|
