### Abstract

Language | English |
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Status | Published - 13 Jan 2019 |

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### Keywords

- dissipation potential function
- convexity
- rate of dislocation density
- flow instability criterion

### Cite this

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

**A dissipation potential approach to describe flow instability in alloys during hot deformation.** / Wang, Peng; Hogrefe, Katharina; PIOT, David; MONTHEILLET, Frank; Poletti, Maria Cecilia.

Research output: Contribution to conference › Abstract › Research › peer-review

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TY - CONF

T1 - A dissipation potential approach to describe flow instability in alloys during hot deformation

AU - Wang, Peng

AU - Hogrefe, Katharina

AU - PIOT, David

AU - MONTHEILLET, Frank

AU - Poletti, Maria Cecilia

N1 - 1. Kocks U. F.: Laws for Work-Hardening and Low-Temperature Creep, Journal of Engineering Materials and Technology-Transactions of the Asme, 1976, 98(1), 76-85. 2. Mecking H., Kocks U.F.: Kinetics of Flow and Strain-Hardening, Acta Metallurgica, 1981, 29(11), 1865-1875. 3. Ottosen N. S., Ristinmaa M.: The mechanics of constitutive modeling, Elsevier, 2005. 4. Regenauer-Lieb K., Yuen D.A., Fusseis F.: Landslides, Ice Quakes, Earthquakes: A Thermodynamic Approach to Surface Instabilities, Pure and Applied Geophysics, 2009, 166(10-11), 1885-1908. 5. Ziegler H.: Some extreme principles in irreversible thermodynamics with application to continum mechanics, Swiss Federal Institute of Technology, Zürich, 1962.

PY - 2019/1/13

Y1 - 2019/1/13

N2 - 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.

AB - 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.

KW - dissipation potential function

KW - convexity

KW - rate of dislocation density

KW - flow instability criterion

M3 - Abstract

ER -