Mesoscopic Modeling of Discontinuous Dynamic Recrystallization: Steady-State Grain Size Distributions

2012 ◽  
Vol 706-709 ◽  
pp. 234-239 ◽  
Author(s):  
David Piot ◽  
Gilles Damamme ◽  
Frank Montheillet
Keyword(s):  
Grain Size ◽  
Steady State ◽  
Dislocation Density ◽  
Grain Boundary ◽  
Dynamic Recrystallization ◽  
Mesoscale Model ◽  
Boundary Migration ◽  
Internal Variables ◽  
Size Distributions ◽  
Grain Size Distributions

A simple mesoscale model was developed for discontinuous dynamic recrystallization. The material is described on a grain scale as a set of (variable) spherical grains. Each grain is characterized by two internal variables: its diameter and dislocation density (assumed homogeneous within the grain). Each grain is then 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 sizeviathe mobility of grain boundaries, which is coupled with (ii) a dislocation-density evolution equation, such as the Yoshie–Laasraoui–Jonas or Kocks–Mecking relationship, involving strain hardening and dynamic recovery, and (iii) an equation governing the total number of grains in the system due to the nucleation of new grains. The model can be used to predict transient and steady-state flow stresses, recrystallized fractions, and grain-size distributions. The effect of the distribution of grain-boundary mobilities has been investigated.

A Model of Discontinuous Dynamic Recrystallization and its Application for Nickel Alloys

2010 ◽  
Vol 638-642 ◽  
pp. 2543-2548 ◽  
Author(s):  
Gilles Damamme ◽  
David Piot ◽  
Frank Montheillet ◽  
S. Lee Semiatin
Keyword(s):  
Grain Size ◽  
Dislocation Density ◽  
Dynamic Recrystallization ◽  
Mesoscale Model ◽  
Boundary Migration ◽  
Internal Variables ◽  
Grain Size Distributions ◽  
Migration Equation ◽  
Spherical Grains ◽  
Transient And Steady State

A simple mesoscale model was developed for discontinuous dynamic recrystallization. The material is described on a grain scale as a set of (variable) spherical grains. Each grain is characterized by two internal variables: its diameter and dislocation density (assumed homogeneous within the grain). Each grain is then 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 dislocation-density evolution equation, such as the Yoshie–Laasraoui–Jonas or Kocks–Mecking relationship, involving strain hardening and dynamic recovery, and (iii) an equation governing the total number of grains in the system due to the nucleation of new grains. The model can be used to predict transient and steady-state flow stresses, recrystallized fractions, and grain-size distributions. A method to fit the model coefficients is also described. The application of the model to pure Ni is presented.

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.

The effect of cooling during deformation on recrystallized grain-size piezometry

Geology ◽  
2020 ◽  
Vol 48 (6) ◽  
pp. 531-535 ◽  
Author(s):  
Hamid Soleymani ◽  
Steven Kidder ◽  
Greg Hirth ◽  
Gordana Garapić
Keyword(s):  
Grain Size ◽  
Steady State ◽  
Traditional Approach ◽  
Shear Zones ◽  
Temperature Deformation ◽  
Shear Strain Rate ◽  
Size Distributions ◽  
Final Stress ◽  
Grain Size Distributions ◽  
Recrystallized Grain Size

Abstract Most exposed middle- and lower-crustal shear zones experienced deformation while cooling. We investigated the effect of the strengthening associated with such cooling on differential stress estimates based on recrystallized grain size. Typical geologic ratios of temperature change per strain unit were applied in Griggs Rig (high pressure-temperature deformation apparatus) general shear experiments on quartzite with cooling rates of 2–10 °C/h from 900 °C to 800 °C, and a shear strain rate of ∼2 × 10−5 s−1. Comparisons between these “cooling-ramp” experiments and control experiments at constant temperatures of 800 °C and 900 °C indicated that recrystallized grain size did not keep pace with evolving stress. Mean recrystallized grain sizes of the cooling-ramp experiments were twice as large as expected from the final stresses of the experiments. The traditional approach to piezometry involves a routine assumption of a steady-state microstructure, and this would underestimate the final stress during the cooling-ramp experiments by ∼40%. Recrystallized grain size in the cooling-ramp experiments is a better indicator of the average stress of the experiments (shear strains ≥3). Due to the temperature sensitivity of recrystallization processes and rock strength, the results may underrepresent the effect of cooling in natural samples. Cooling-ramp experiments produced wider and more skewed grain-size distributions than control experiments, suggesting that analyses of grain-size distributions might be used to quantify the degree to which grain size departs from steady-state values due to cooling, and thereby provide more accurate constraints on final stress.

Microstructures and Mechanical Properties of Magnesium Alloy ZK60 Sheets after Multi-Pass Hot Rolling

2019 ◽  
Vol 794 ◽  
pp. 113-120
Author(s):  
Yeong Maw Hwang ◽  
Yung Lin Wang
Keyword(s):  
Mechanical Properties ◽  
Grain Size ◽  
Magnesium Alloy ◽  
Dynamic Recrystallization ◽  
Hot Rolling ◽  
Size Distributions ◽  
Proposed Model ◽  
Grain Size Distributions ◽  
Deform 2D ◽  
Different Thickness

Magnesium alloys have been widely used in automotive, bicycle, aerospace industries. Improving the mechanical properties of the materials by various forming processes has been an important issue. Grain refinement is an effective method to improve material properties. In this study, single-pass and multi-pass hot rolling processes are carried out to generate dynamic recrystallization (DRX) and fine grains and to obtain better mechanical properties on the rolled products. A mathematical model linked with FEM software DEFORM-2D is proposed to predict the dynamic recrystallization ratio and the grain size distributions during various multi-pass hot rolling processes. The effects of different thickness reductions on the grain size distributions inside the sheet are discussed. Multi-pass hot rolling experiments of magnesium alloy ZK60 sheets are carried out and the metallographic microstructures are observed. The measured grain sizes are compared with the simulation results to verify the validity of the proposed model. The effects of different thickness reductions on the mechanical properties of the rolled magnesium alloy ZK60 sheets are also investigated.

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.

scholarly journals Grain Growth Anomaly in Ti-rich Strontium Titanate as Revealed by Electron Microscopy

2012 ◽  
Vol 18 (S5) ◽  
pp. 123-124
Author(s):  
L. Amaral ◽  
M. Fernandes ◽  
A. M. R. Senos ◽  
P. M. Vilarinho ◽  
M. P. Harmer
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Boundaries ◽  
Grain Growth ◽  
Strontium Titanate ◽  
Structural Changes ◽  
Sintering Temperature ◽  
Size Distributions ◽  
High Tunability ◽  
Grain Size Distributions

An anomaly in the dependence of the kinetics of grain growth on the temperature for strontium titanate (ST) ceramics is reported in this work. It consists of a decrease of the grain size with increasing sintering temperature. Recently, a drop in the grain boundary mobility of ST in the same temperature range was reported. These observations imply an unusual decrease of the grain size with the increase of the sintering temperature, in agreement with our present results. Although the mobility drop was related to structural changes in grain boundaries, the exact mechanism involved is still unknown. The understanding of this anomaly may offer an alternative way of controlling the microstructure and tuning the dielectric response of ST based compositions without the use of dopants. ST is characterized by high dielectric permittivity, high tunability and low dielectric losses, and is thus a particularly interesting material for capacitor or tunable microwave devices. These properties are very dependent on the stoichiometry, structure and microstructure, in which the role of grain boundaries is fundamentally important. Indeed, increasing attention has been paid to grain boundary structures and nonstoichiometry and to its relation with microstructure and electrical properties. Densification proceeds faster with decreasing Sr/Ti ratio (Ti-rich compositions). Sr-rich samples show narrow grain size distributions, while Ti excess favors enlarged grain size distributions and faceting of the grain boundaries.

scholarly journals Effect of Strain-Induced Precipitation on the Recrystallization Kinetics in a Model Alloy

2021 ◽  
Author(s):  
Mo Ji ◽  
Martin Strangwood ◽  
Claire Davis
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Avrami Exponent ◽  
Model Alloy ◽  
Size Distributions ◽  
Recrystallization Kinetics ◽  
Grain Size Distributions ◽  
Recrystallized Grain Size ◽  
Nb Addition

AbstractThe effects of Nb addition on the recrystallization kinetics and the recrystallized grain size distribution after cold deformation were investigated by using Fe-30Ni and Fe-30Ni-0.044 wt pct Nb steel with comparable starting grain size distributions. The samples were deformed to 0.3 strain at room temperature followed by annealing at 950 °C to 850 °C for various times; the microstructural evolution and the grain size distribution of non- and fully recrystallized samples were characterized, along with the strain-induced precipitates (SIPs) and their size and volume fraction evolution. It was found that Nb addition has little effect on recrystallized grain size distribution, whereas Nb precipitation kinetics (SIP size and number density) affects the recrystallization Avrami exponent depending on the annealing temperature. Faster precipitation coarsening rates at high temperature (950 °C to 900 °C) led to slower recrystallization kinetics but no change on Avrami exponent, despite precipitation occurring before recrystallization. Whereas a slower precipitation coarsening rate at 850 °C gave fine-sized strain-induced precipitates that were effective in reducing the recrystallization Avrami exponent after 50 pct of recrystallization. Both solute drag and precipitation pinning effects have been added onto the JMAK model to account the effect of Nb content on recrystallization Avrami exponent for samples with large grain size distributions.

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