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.

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.

Influence of Niobium Content on the Hot Mechanical Behavior of Nickel Alloys

2016 ◽  
Vol 879 ◽  
pp. 1251-1257
Author(s):  
N. Matougui ◽  
David Piot ◽  
M.L. Fares ◽  
Frank Montheillet
Keyword(s):  
Solid Solution ◽  
Mechanical Behavior ◽  
Strain Hardening ◽  
Dynamic Recovery ◽  
Equivalent Strain ◽  
Rheological Parameters ◽  
Niobium Content ◽  
Hot Torsion ◽  
Nickel Base ◽  
Von Mises

Nickel-base superalloys are usually employed for large forged parts in aerospace industry. A comprehensive understanding of their mechanical behavior during hot working is required, especially for manufacturers in order to enhance the in-service properties. In this context, the first part of the work aims at investigating the mechanical behavior of nickel during hot deformation, with particular emphasis on the influence of niobium additions in solid solution. For this purpose, a series of wrought model alloys including pure nickel and Ni-Nb alloys (Ni-0.01, 0.1, 1, 2, 5 and 10 wt. % Nb) were prepared and deformed by hot torsion at temperatures ranging from 800 to 1000 °C degrees and at three (von Mises equivalent) strain rates of 0.03, 0.1 and 0.3 s-1. Afterwards, the key rheological parameters that characterize strain hardening and dynamic recovery were determined through a simple analytical method based on the classical Laasraoui-Jonas constitutive equation, allowing reasonable fit for the flow curves for all studied Ni-Nb alloys. In this way, the effect of niobium solutes on the fundamental mechanisms of deformation was well highlighted. In the second part, three usual models describing strain hardening and dynamic recovery, referred to as the Laasraoui-Jonas (LJ), Kocks-Mecking (KM), and power law (PW) equations are compared within the range of moderate strains. Transformation formulae are derived, allowing the parameters of one law to be computed from the parameters of any of the two others. The theoretical derivations are illustrated by the specific case of a Ni-Nb alloy in the solid solution domain.

Hot Working of High-Purity Nickel-Niobium Alloys

2007 ◽  
Vol 539-543 ◽  
pp. 2966-2971
Author(s):  
Frank Montheillet ◽  
S. Girard ◽  
Christophe Desrayaud ◽  
S. Lee Semiatin ◽  
J. Le Coze
Keyword(s):  
Activation Energy ◽  
Solid Solution ◽  
Steady State ◽  
Flow Stress ◽  
Dynamic Recrystallization ◽  
High Purity ◽  
Rate Sensitivity ◽  
Pure Nickel ◽  
Large Strains ◽  
Niobium Alloys

The present work deals with the influence of niobium in solid solution on the dynamic recrystallization of pure nickel. High-purity nickel and two model nickel-niobium alloys were deformed to large strains via torsion at temperatures between 800 and 1000°C. Niobium additions considerably increased the flow stress, while they lowered the strain-rate sensitivity and increased the apparent activation energy. EBSD of the steady-state microstructures revealed strong grain refinement. Substructure development was favored, whereas thermal twinning was reduced by niobium. More generally, discontinuous recrystallization kinetics were considerably decreased.

Modeling of Grain-Boundary Mobility and Nucleation Rate during Discontinuous Dynamic Recrystallization in Ni-Nb Alloys and a High-Purity Alloy Derived from SAE 304L

2016 ◽  
Vol 879 ◽  
pp. 1501-1506 ◽  
Author(s):  
David Piot ◽  
Guillaume Smagghe ◽  
Frank Montheillet
Keyword(s):  
Grain Size ◽  
Steady State ◽  
Grain Boundary ◽  
Dynamic Recrystallization ◽  
Grain Boundaries ◽  
Nucleation Rate ◽  
High Purity ◽  
Boundary Mobility ◽  
Niobium Content ◽  
Grain Boundary Mobility

A simple mesoscale model has been developed for discontinuous dynamic recrystallization. Each grain is considered in turn as an inclusion, embedded in a homogeneous equivalent matrix, the properties of which are obtained by averaging over all the grains. The model includes: (i) a grain-boundary migration-equation driving the evolution of grain size via the mobility of grain boundaries, which is coupled with (ii) a single-internal-variable (dislocation density) constitutive model for strain hardening and dynamic recovery, and (iii) a nucleation equation governing the total number of grains by the nucleation of new grains. All the system variables tend to asymptotic values at large strains, in agreement with the experimentally observed steady-state regime.With some assumptions, both steady-state stress and grain-size are derived in closed forms, allowing immediate identification of the mobility of grain boundaries and the rate of nucleation. An application to Ni–Nb-pure-binary model alloys and high-purity 304L stainless steel with Nb addition is presented. More specifically on one hand, from experimental steady-state stresses and grain sizes, variations of the grain boundary mobility and the nucleation rate with niobium content are addressed in order to quantify the solute-drag effect of niobium in nickel. And on the other hand, the Derby exponents were investigated varying separately the strain rate or the temperature.

Modeling Grain Boundary Mobility during Dynamic Recrystallization of Metallic Alloys

2010 ◽  
Vol 638-642 ◽  
pp. 2303-2308 ◽  
Author(s):  
Frank Montheillet ◽  
Gilles Damamme ◽  
David Piot ◽  
S. Lee Semiatin
Keyword(s):  
Grain Boundary ◽  
Dynamic Recrystallization ◽  
Mesoscale Model ◽  
Solute Drag ◽  
Solute Concentration ◽  
Metallic Alloys ◽  
Second Phase ◽  
Boundary Mobility ◽  
Grain Boundary Mobility ◽  
Second Phase Particles

A simple analytical model is proposed for estimating grain boundary mobility during dynamic recrystallization in metallic alloys. The combined effects of solutes (solute drag) and second phase particles (Zener pinning) on mobility are considered. The approach is based on (and is consistent with) a recently published mesoscale model of discontinuous dynamic recrystallization. The dependence of grain boundary mobility on solute concentration and particle size is summarized in the form of two-dimensional maps.

Introducing Solute Drag in Irregular Cellular Automata Modeling of Grain Growth

2004 ◽  
Vol 467-470 ◽  
pp. 1045-1050 ◽  
Author(s):  
Koenraad G.F. Janssens ◽  
Elizabeth A. Holm ◽  
Stephen M. Foiles
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Grain Growth ◽  
Boundary Energy ◽  
Solute Drag ◽  
Solute Concentration ◽  
Local Concentration ◽  
Boundary Mobility ◽  
Grain Boundary Mobility ◽  
Dynamics Simulations

In this paper we discuss the principles of a combined approach to solve the problem of solute drag as it occurs in microstructure evolution processes such as grain growth, recrystallization and phase transformation. A recently developed irregular grid cellular automaton is used to simulate normal grain growth, in which the energy of the grain boundaries is the driving force. A new, discrete diffusion model is used to simulate solute segregation to the grain boundaries. The local concentration of the solute is then taken into account in the calculation of the local grain boundary mobility and/or grain boundary energy, thereby constituting a drag force. The relation between solute concentration and grain boundary mobility/energy is derived from molecular dynamics simulations.

High Strain Rate Superplasticity in a Zr and Sc Modified 7075 Aluminum Alloy Produced by ECAP

2008 ◽  
Vol 584-586 ◽  
pp. 164-169 ◽  
Author(s):  
Krystof Turba ◽  
Premysl Malek ◽  
Edgar F. Rauch ◽  
Miroslav Cieslar
Keyword(s):  
Aluminum Alloy ◽  
High Strain Rate ◽  
Strain Rate ◽  
High Strain ◽  
Rate Sensitivity ◽  
7075 Aluminum Alloy ◽  
Fine Grained ◽  
Angular Pressing ◽  
Average Grain Size ◽  
Elongation To Failure

Equal-channel angular pressing (ECAP) at 443 K was used to introduce an ultra-fine grained (UFG) microstructure to a Zr and Sc modified 7075 aluminum alloy. Using the methods of TEM and EBSD, an average grain size of 0.6 1m was recorded after the pressing. The UFG microstructure remained very stable up to the temperature of 723 K, where the material exhibited high strain rate superplasticity (HSRSP) with elongations to failure of 610 % and 410 % at initial strain rates of 6.4 x 10-2 s-1 and 1 x 10-1 s-1, respectively. A strain rate sensitivity parameter m in the vicinity of 0.45 was observed at temperatures as high as 773 K. At this temperature, the material still reached an elongation to failure of 430 % at 2 x 10-2 s-1. These results confirm the stabilizing effect of the Zr and Sc additions on the UFG microstructure in a 7XXX series aluminum alloy produced by severe plastic deformation.

Superplastic Behavior of a Cu-Cr-Zr Alloy Subjected to ECAP

2016 ◽  
Vol 838-839 ◽  
pp. 404-409
Author(s):  
Roman Mishnev ◽  
Iaroslava Shakhova ◽  
Andrey Belyakov ◽  
Rustam Kaibyshev
Keyword(s):  
Grain Size ◽  
Dislocation Density ◽  
Strain Rate ◽  
Temperature Interval ◽  
Rate Sensitivity ◽  
Tensile Tests ◽  
Superplastic Behavior ◽  
Average Grain Size ◽  
Gauge Section ◽  
Zr Alloy

A Cu-0.87%Cr-0.06%Zr alloy was subjected to equal channel angular pressing (ECAP) at a temperature of 400 °C up to a total strain of ~ 12. This processing produced ultra-fine grained (UFG) structure with an average grain size of 0.6 μm and an average dislocation density of ~4×1014 m-2. Tensile tests were carried out in the temperature interval 450 – 650 °C at strain rates ranging from 2.8´10-4 to 0.55 s-1. The alloy exhibits superplastic behavior in the temperature interval 550 – 600 °C at strain rate over 5.5´10-3 s-1. The highest elongation-to-failure of ~300% was obtained at a temperature of 575 °C and a strain rate of 2.8´10-3 s-1 with the corresponding strain rate sensitivity of 0.32. It was shown the superplastic flow at the optimum conditions leads to limited grain growth in the gauge section. The grain size increases from 0.6 μm to 0.87 μm after testing, while dislocation density decreases insignificantly to ~1014 m-2.

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