Influence of Strain-Hardening and Dynamic Recovery on DDRX Steady State

2021 ◽  
Vol 1016 ◽  
pp. 194-199
Author(s):  
Frank Montheillet ◽  
David Piot
Keyword(s):  
Steady State ◽  
Strain Hardening ◽  
Dynamic Recovery ◽  
Constitutive Parameters

Relationships between macroscopic and microscopic constitutive parameters associated with steady state DDRX are derived for a material in which strain-hardening and dynamic recovery are described by the Yoshie-Laasraoui-Jonas equation. First examples are given for illustration.

scholarly journals Influence of Boundary Migration Induced Softening on the Steady State of Discontinuous Dynamic Recrystallization

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3531
Author(s):  
Frank Montheillet
Keyword(s):  
Grain Size ◽  
Steady State ◽  
Grain Boundary ◽  
Dynamic Recrystallization ◽  
Strain Hardening ◽  
Dynamic Recovery ◽  
Boundary Migration ◽  
Rate Sensitivity ◽  
Steady State Condition ◽  
Average Grain Size

During discontinuous dynamic recrystallization (DDRX), new dislocation-free grains progressively replace the initially strain-hardened grains. Furthermore, the grain boundary migration associated with dislocation elimination partially opposes strain hardening, thus adding up to dynamic recovery. This effect, referred to as boundary migration induced softening (BMIS) is generally not accounted for by DDRX models, in particular by “mean-field” approaches. In this paper, BMIS is first defined and then analyzed in detail. The basic equations of a grain scale DDRX model, involving the classical Yoshie–Laasraoui–Jonas equation for strain hardening and dynamic recovery and including BMIS are described. A steady state condition equation is then used to derive the average dislocation density and the average grain size. It is then possible to assess the respective influences of BMIS and dynamic recovery on the strain rate sensitivity, the apparent activation energy, and the relationship between flow stress and average grain size (“Derby exponent”) of the material during steady state DDRX. Finally, the possible influence of BMIS on the estimation of grain boundary mobility and nucleation rate from experimental data is addressed.

scholarly journals Constitutive Modelling of Polylactic Acid at Large Deformation Using Multiaxial Strains

Polymers ◽  
2021 ◽  
Vol 13 (17) ◽  
pp. 2967
Author(s):  
John Sweeney ◽  
Paul Spencer ◽  
Glen Thompson ◽  
David Barker ◽  
Phil Coates
Keyword(s):  
Steady State ◽  
Stress Relaxation ◽  
Strain Hardening ◽  
Small Strain ◽  
Limited Range ◽  
Constitutive Modelling ◽  
True Stress ◽  
Final Strain ◽  
Transverse Stresses

Sheet specimens of a PLLA-based polymer have been extended at a temperature near to the glass transition in both uniaxial and planar tension, with stress relaxation observed for some time after reaching the final strain. Both axial and transverse stresses were recorded in the planar experiments. In all cases during loading, yielding at small strain was followed by a drop in true stress and then strain hardening. This was followed by stress relaxation at constant strain, during which stress dropped to reach an effectively constant level. Stresses were modelled as steady state and transient components. Steady-state components were identified with the long-term stress in stress relaxation and associated with an elastic component of the model. Transient stresses were modelled using Eyring mechanisms. The greater part of the stress during strain hardening was associated with dissipative Eyring processes. The model was successful in predicting stresses in both uniaxial and planar extension over a limited range of strain rate.

Effects of membrane hardness and scaling analysis for capsules in planar extensional flows

2014 ◽  
Vol 745 ◽  
pp. 487-508 ◽  
Author(s):  
P. Dimitrakopoulos
Keyword(s):  
Steady State ◽  
Strain Hardening ◽  
Edge Length ◽  
Scaling Analysis ◽  
Normal Forces ◽  
Shearing Resistance ◽  
Slender Spindle ◽  
Physical Insight ◽  
Extensional Flows ◽  
Local Edge

AbstractIn this paper, we investigate computationally the effects of membrane hardness on the dynamics of strain-hardening capsules in planar extensional Stokes flows. As the flow rate increases, all capsules reach elongated steady-state configurations but the cross-section of the more strain-hardening capsules preserves its elliptical shape while the less strain-hardening capsules become lamellar. The capsule deformation in strong extensional flows is accompanied with very pointed edges, i.e. large edge curvatures and thus small local edge length scales, which makes the current investigation a multi-length interfacial dynamics problem. Our computational results for elongated strain-hardening capsules are accompanied with a scaling analysis which provides physical insight on the extensional capsule dynamics. The two distinct capsule conformations we found, i.e. the slender spindle and lamellar capsules, are shown to represent two different types of steady-state extensional dynamics. The former are stabilized mainly via the membrane’s shearing resistance and the latter via its area-dilatation resistance, associated with the elongation tension normal forces and thus both types differ from bubbles which are stabilized mainly via the lateral surface-tension normal forces. Our steady-state deformation results can be used to identify the elastic properties of a real capsule, i.e. the membrane’s shear and area-dilatation moduli, utilizing a single experimental technique.

Modelling Dynamic Recovery and Recrystallization of Metals by a New Non-Equilibrium Thermodynamics Approach

2007 ◽  
Vol 558-559 ◽  
pp. 517-522
Author(s):  
Ming Xin Huang ◽  
Pedro E.J. Rivera-Díaz-del-Castillo ◽  
Sybrand van der Zwaag
Keyword(s):  
Steady State ◽  
High Temperature ◽  
Flow Stress ◽  
Dislocation Density ◽  
Dynamic Recovery ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Equilibrium Thermodynamics ◽  
Burgers Vector ◽  
Non Equilibrium

A non-equilibrium thermodynamics-based approach is proposed to predict the dislocation density and flow stress at the steady state of high temperature deformation. For a material undergoing dynamic recovery and recrystallization, it is found that the total dislocation density can be expressed as ( )2 ρ = λε& b , where ε& is the strain rate, b is the magnitude of the Burgers vector and λ is a dynamic recovery and recrystallization related parameter.

A Theoretical Analysis of the Rheological Parameters Associated with DDRX

2018 ◽  
Vol 941 ◽  
pp. 2257-2263 ◽  
Author(s):  
Frank Montheillet ◽  
David Piot
Keyword(s):  
Steady State ◽  
Strain Hardening ◽  
Rate Sensitivity ◽  
Solute Concentration ◽  
Rheological Parameters ◽  
Boundary Mobility ◽  
Niobium Alloys ◽  
Grain Boundary Mobility ◽  
Average Grain Size ◽  
Hot Torsion

The macroscopic strain rate sensitivitymand apparent activation energyQare derived from their microscopic counterparts associated with strain hardening, grain boundary mobility, and nucleation rate in the case of steady state discontinuous dynamic recrystallization (DDRX). The case of solid solutions, involving effects of the solute concentration on strain hardening and boundary mobility, is also taken into consideration. Moreover, three distinct Derby exponents are introduced to refine the correlation between steady state flow stress and average grain size. Hot torsion data and micrographic observations on a set of nickel-niobium alloys are used to assess the predictions of this tentative approach.

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