A flow instability criterion for alloys during hot deformation

Peng Wang*, Katharina Hogrefe, David Piot, Frank Montheillet, María Cecilia Poletti

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


Flow instability is an intrinsic behavior of materials, especially during hot deformation, and it will be intensified and propagate internal defects, and finally lead to various damages in the significant perturbation. Some phenomenological models in the literature could present the flow instability behavior, but not available for describing the microstructure changes. To overcome this problem, we introduce a dissipation potential as a function of the plastic strain rate, the dislocation density rate, and the heat transfer rate, 퐷(휺̇, 휌̇푑is, 풒; 휀, 휌푑is, 휃), coupled with strain, dislocation density, and temperature as the boundary condition to record the microstructure evolution and describe the flow instability. In this function, the stored energy rate marks the dislocation density evolution, i.e., the transient microstructure changes, and one parameter 휂, is introduced to evaluate the efficiency of metallurgy. And the flow instability criterion is derived from the principles of maximum dissipation (or maximum entropy production rate) and orthogonality proposed by HANS ZIEGLER. We obtain the necessary conditions of the flow instability are that the dissipation potential is with entirely positive values due to the large plasticity, and the dissipation potential 퐷(휺̇, 휌̇푑is, 풒; 휀, 휌푑is, 휃) is convex, i.e., the associated Hessian matrix is semi-positive. In this work, the function was applied to describe the behavior of Ti6Al4V during hot deformation, and a Kocks-Mecking type model was used to describe the flow stresses as well.

Original languageEnglish
Pages (from-to)319-326
Number of pages8
JournalProcedia Manufacturing
Publication statusPublished - 1 Jan 2019
Event9th International Conference on Physical and Numerical Simulation of Materials Processing: ICPNS 2019 - HSE Moscow Institute of Electronica and Mathematics (MIEM HSE), Moscow, Russian Federation
Duration: 10 Oct 201915 Oct 2019


  • Convexity of the dissipation function
  • Dislocation density rate
  • Flow instability criterion
  • Maximum dissipation
  • Stored energy rate

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering
  • Artificial Intelligence

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