Grain Growth Equation Research Articles

Modeling Dynamic Recrystallization Behavior in a Novel HIPed P/M Superalloy during High-Temperature Deformation.

The dynamic recrystallization (DRX) features and the evolution of the microstructure of a new hot isostatic pressed (HIPed) powder metallurgy (P/M) superalloy are investigated by hot-compression tests. The sensitivity of grain dimension and DRX behavior to deformation parameters is analyzed. The results reveal that the DRX features and grain-growth behavior are significantly affected by deformation conditions. The DRX process is promoted with a raised temperature/true strain or a reduced strain rate. However, the grains grow up rapidly at relatively high temperatures. At strain rates of o.1 s−1 and 1 s−1, a uniform microstructure and small grains are obtained. Due to the obvious differences in the DRX rate at various temperatures, the piecewise DRX kinetics equations are proposed to predict the DRX behavior. At the same time, a mathematical model for predicting the grain dimension and the grain growth behavior is established. To further analyze the DRX behavior and the changes in grain dimension, the hot deformation process is simulated. The developed grain-growth equation as well as the piecewise DRX kinetics equations are integrated into DEFORM software. The simulated DRX features are consistent with the test results, indicating that the proposed DRX kinetics equations and the established grain-growth model can be well used for describing the microstructure evolution. So, they are very useful for the practical hot forming of P/M superalloy parts.

Microstructural modelling of above β-transus heat treatment of additively manufactured Ti-6Al-4V using cellular automata

A heat treatment is an essential part of the metal additive manufacturing process chain. If an additively manufactured part, made of Ti-6Al-4 V, is heated above its β transus temperature, the columnar prior-β grains will become equiaxed β grains. This work quantitatively models this transition and the subsequent cooling down to room temperature by using the well-established cellular automata (CA) technique. Using this microstructural model allows visualisation of the local variation in the microstructure. The final microstructure consists of both the equilibrium phase α and β, organised in laths. This paper shows that the developed CA is capable of modelling the microstructural evolution during the entire above-β transus heat treatment. In order to get an accurate simulation of the microstructural change during such a heat treatment, the nucleation and grain growth functions are dependent on temperature. Since there exists a thermal gradient throughout the simulated cube, the local values of these functions will vary, leading to spatial differences in the nucleation frequency and growth velocity of new β grains. The model is verified by comparing the transformed volume fraction with a typical Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation for isothermal grain growth. However, the JMAK equation insufficiently describes the grain growth during the initial stage of the heat treatment, namely while heating up to above the β transus temperature. Finally, the simulations of the second half of the heat treatment show that there are underexplored mechanisms during the growth of α laths when cooling down to room temperature. The simulations show, that it is not a requirement to nucleate α in the centre of the former β grains to form basketweave α. Moreover, the basketweave morphology in the simulated microstructures is a result of the difference between the viewing plane of the microstructure and the plane in which the laths grow, with a pure Widmanstätten morphology only appearing when the planes are parallel.

Modeling Microstructure Evolution in a Martensitic Stainless Steel Subjected to Hot Working Using a Physically Based Model

The microstructure evolution of a martensitic Stainless steel subjected to hot compression is simulated with a physically based model. The model is based on coupled sets of evolution equations for dislocations, vacancies, recrystallization, and grain growth. The advantage of this model is that with only a few experiments, the material-dependent parameters of the model can be calibrated and used for a new alloy in any deformation condition. The experimental data of this work are obtained from a series of hot compression, and subsequent stress relaxation tests performed in a Gleeble thermo-mechanical simulator. These tests are carried out at various temperatures ranging from 900 to 1200 °C, strains up to 0.7, and strain rates of 0.01, 1, and 10 s−1. The grain growth, flow stress, and stress relaxations are simulated by finding reasonable values for model parameters. The flow stress data obtained at the strain rate of 10 s−1 were used to calibrate the model parameters and the predictions of the model for the lower strain rates were quite satisfactory. An assumption in the model is that the structure of second phase particles does not change during the short time of deformation. The results show a satisfactory agreement between the experimental data and simulated flow stress, as well as less than 5 pct difference for grain growth simulations and predicting the dominant softening mechanisms during stress relaxation according to the strain rates and temperatures under deformation.

Phase transformations and grain growth behaviors in superalloy 718

The phase transformation and grain growth behaviors of commercial Ni-Fe-base superalloy 718 at 1323, 1373, 1423 and 1473 K were investigated through DSC and SEM methods. The transformation temperatures of γ + NbC→L and γ→L were determined as 1495 and 1555 K, respectively, and TiN was shown to gradually dissolve into the formed L. The pinning effect caused by Nb-rich carbide (NbC) and Ti-rich nitride (TiN) was observed, and the mean size of the grains increased with holding time at each temperature. The grain growth exponent, m, was confirmed to be 4, indicating that grain growth was controlled by the coarsening of the precipitate through grain boundary diffusion. The grain boundary diffusion of Nb and N was confirmed to control the coarsening of NbC and TiN, respectively. The major factor for γ grain growth was confirmed to be the coarsening of NbC, and the activation energy for grain growth was calculated as 417 kJ·mol−1. The equations for grain growth were determined as G4-G04 = 0.10 × 106 × t (1323 K), G4-G04 = 0.49 × 106 × t (1373 K), G4-G04 = 2.01 × 106 × t (1423 K) and G4-G04 = 3.89 × 106 × t (1473 K), for all four temperatures respectively. The predicted grain growth curves were in good agreement with the experimental data.

A Study of Growth of Austenite Grains in a Steel Microalloyed with Ti and Nb

The growth of austenite grains and the dissolution of carbonitrides under heating of a structural steel microalloyed with niobium and titanium are studied. The microstructure of the steel is investigated with the help of light and transmission electron microscopes. The content of elements in precipitated particles is determined using an energy dispersive spectrometer. The kinetic equation of grain growth is derived and the critical temperature above which the carbonitrides stop to hinder grain growth is determined. Recommendations are given on the temperature modes of hot rolling.

Iron grain growth kinetics during carbothermic reduction of ilmenite concentrates with microwaves

ABSTRACTThe iron grain growth kinetics during the carbothermic reduction of ilmenite concentrates in the microwave field were investigated and described by using iron grain size dt and a parameter (attenuation voltage U) of microwave-absorbing characteristics. The results demonstrated that there was a linear relationship between ln dt and 1/T during the iron grain growth, and the kinetic model equation for the iron grain growth in the microwave field was deduced as: ln ; the activation energy of the iron grain growth at the initial stage and the late stage in the microwave field were calculated to be 31.04 and 69 kJ/mol. It was found that there was also a linear relationship between ln U and 1/T. The iron grain growth described by using the attenuation voltage (U) of microwave-absorbing characteristics and the grain size dt had the same rule, the activation energy at initial stage was small and became big at the late stage. The results suggested that the iron grain growth could be described by using a parameter of microwave-absorbing characteristics during the carbothermic reduction of ilmenite concentrates in the microwave field, if ignored the specific values of the activation energy, just used the changing trends of the activation energy, which could help us utilize the microwave technology in the ilmenite concentrate processing and the recovery of the byproducts of metallic iron.

Microstructure stability of ultra-fine grained magnesium alloy AZ31 processed by extrusion and equal-channel angular pressing (EX–ECAP)

Thermal stability of the ultra-fine grained (UFG) microstructure of magnesium AZ31 alloy was investigated. UFG microstructure was achieved by a combined two-step severe plastic deformation process: the extrusion (EX) and subsequent equal-channel angular pressing (ECAP). This combined process leads to refined microstructure and enhanced microhardness. Specimens with UFG microstructure were annealed isochronally at temperatures 150–500°C for 1h. The evolution of microstructure, mechanical properties and dislocation density was studied by electron backscatter diffraction (EBSD), microhardness measurements and positron annihilation spectroscopy (PAS). The coarsening of the fine-grained structure at higher temperatures was accompanied by a gradual decrease of the microhardness and decrease of dislocation density. Mechanism of grain growth was studied by general equation for grain growth and Arrhenius equation. Activation energies for grain growth were calculated to be 115, 33 and 164kJ/mol in temperature ranges of 170–210°C, 210–400°C and 400–500°C (443–483K, 483–673K and 673–773K), respectively.

PREDICTION OF GRAIN GROWTH IN HYBRID WELDING HAZ OF TCS STAINLESS STEEL

According to the formula of grain growth under isothermal condition, the kinetics equation of ferritic grain growth in heat affected zone (HAZ) was obtained, which was combined with the calculated thermal cycles to predict the grain growth in HAZ of TCS stainless steel under the new-type welding procedure-hybrid welding. The grain sizes in HAZ of TCS stainless steel have been calculated for three welding conditions. Simulation results are validated by the average grain sizes measured on the metallographic images of the welding joint of TCS stainless steel. Preliminary discussion has been made on correlation of the grain growth with the thermal cycles and the effect of local variation in thermal cycles on the grain growth.

Plain Carbon Strip Q235 Grain Growth in Reheating Progress

Before hot rolling the ingot of plain carbon steel Q235 should be heated to austenite temperature to decrease distortion resistance. The grain size will affect the following hot rolling process. In this paper, the behaviour of Q235 grain growth in reheat furnace was studied with the method of physical simulation. To achieve the equation of grain growth in heating progress, the samples was carried out in different peak temperature and holding time at the Gleeble1500. With the kinetics equation grain size can be calculated and the results provide a basis for the setting of progress parameter during reheating of ingot.

Numerical Simulation of Microstructure Evolution of TC6 Alloy Blade during Finish Forging

In order to predict the evolution of microstructure and grain size in TC6 alloy blade finish forging process and optimize the parameters, a series of constitutive equations for dynamic recrystallization and grain growth were developed and implemented into a 3D FE simulator. The grain size has been illustrated for the upsetting of TC6 alloy and the calculated grain size is in a good agreement with the experimental results, which shows that the microstructure prediction tool was validated and reliable. Then the distribution of stress, strain, temperature and microstructure, grain size and deformation has been predicted in TC6 alloy blade forging successfully using the 3D FEM at 930°C deformation temperature, 250°C die temperature and 50mm/s deformation velocity. The results show that the temperature of blade edge is higher than that of center because heat transfer, friction work and deformation work. The equivalent stress and strain have the same distribution as temperature after forging and the refined grain is obtained because of dynamic rescrystallization occurred with larger deformation. The uniform distribution of grain size are obtained in the blade and the shape after finish forging under the condition of technology parameters meet the user’s requirement comparing the calculated deformation with experimental results.

Grain Growth Evaluation in HAZ of Welded Pipes Using Dimensionless Parameters and Optimum Pre-Exponential Constant for Seam Weld and Seamless Pipes

Kinetic strength in grain growth is evaluated for HAZ of welded pipes. Austenite grain growth is dependant on the thermal cycle and the material properties. In this research the influence of thermal cycle is evaluated using characteristic time constant and characteristic temperature. These dimensionless parameters were calculated for the points lying in HAZ using temperature/time profile derived from Rosenthal equation for the heat transfer. The grain growth is assumed diffusion controlled and Arrhenius temperature dependency is applied for the rate of growth in grains. In an experimental investigation the welded pipes were sectioned longitudinally and the grain size in parent metal and HAZ were measured based on ASTM E 112 by using Planimetric Counting. The obtained data was compared with the result of the model and the appropriate kinetic constant which is calibrated the equation of grain growth is introduced for the seam weld and seamless pipes.

EFFECT OF Nb SOLUTE DRAG AND NbC PRECIPITATE PINNING ON THE RECRYSTALLIZATION GRAIN GROWTH IN LOW CARBON Nb-MICROACLOYED STEEL

A kinetic equation for austenite grain growth has been derived concerning the mutual effect of NbC and Nb solute in low carbon Nb-microalloyed steels. It is shown that both solute drag of Nb in solid solution and pinning of NbC particles inhibit the grain boundary migration during grain growth after recrystallization in low carbon Nb-microalloyed steels. At high temperatures the NbC pinning plays a dominate role for retarding the austenite grain growth with less Nb solute drag effect. An obvious Nb solute drag restraint was, however, observed at relatively low temperatures. Also, the theoretical calculations are in good agreement with experimental results. The effectiveness of drag effect of soluble atoms and pinning effect of precipitates can be characterized by a p factor. The pinning of precipitates and solute drag of soluble atoms are more effective for suppressing grain growth as p> 0a nd p< 0, respectively. And the ratio of Nb in solute and Nb in precipitate as p=0 reaches the priority and most effectively retards the grain growth. In the traditional hot rolling or austenitizing temperature range, a strong suppression for grain growth after recrystallization could be obtained due to those fine NbC particles smaller than 10 nm in Nb-microalloyed steels.

Simulation and Analysis on Microstructure Evolution of Large Generator Retaining Ring during Multi-Fire Forging

In order to investigate microstructure evolution of Mn18Cr18N retaining ring during the multi-fire forging, a series of constitutive equations for dynamic recrystallization, static recrystallization, meta-dynamic recrystallization and grain growth were developed and implemented into a Deform FE simulator. The single-axial hot upsetting test has been performed to investigate the process of microstructure evolution and to show validity and effectiveness of the developed program. Then based on the modified boundary condition, hot forging process for 300MW retaining ring was put into effect. The results have displayed that the microstructure prediction tool was validated by comparing the simulated grain structure with that of the experiment and it could provide a reference to optimize forging processes in the production of retaining ring.

Kinetic equation of the effect of thickness on grain growth in nanocrystalline films

This paper presents an anisotropy Monte Carlo algorithm to simulate grain growth in nanocrystalline films. The results indicate that a thickness effect appears only when the average grain size reaches 0.8–1.2 times the film thickness. A grain size-thickness factor is introduced to modify Burke’s grain growth kinetic equation, better describing the whole process of grain growth in both simulation and Ni/SiO2 nanocrystalline multilayer films. A more universal kinetic equation of grain growth is further suggested.

Numerical prediction of austenite grain size in a bar rolling process using an evolution model based on a hot compression test

A microstructure evolution model was formulated by characterizing the kinetics of static (SRX) and metadynamic (MDRX) recrystallization in consideration of the experimental data using single and double compression tests of AISI 4135 at various temperatures and strain rates. The evolution model consisted of equations for SRX, MDRX, and grain growth was implemented into an in-house finite element program to simulate the process. Numerical prediction of austenite grain size (AGS) evolution during a hot bar rolling of AISI 4135 was conducted and presented. The predicted results were compared with the experimental data obtained from the hot bar rolling and the numerical results based on other AGS models available in the literature which were derived based on torsion tests. The present model determined in the current investigation based on compression tests shows better agreement with the experimental data than the earlier works. The critical strains determined from compression tests were relatively smaller than those from the torsion tests, which influenced the overall recrystallization and grain growth behaviors. Also, the current model was beneficial to understand the effect of recrystallization behavior and control the microstructure evolution during hot bar rolling.

A thermal spike model of grain growth under irradiation

The experimental study of grain growth in nanocrystalline metallic foils under ion irradiation showed the existence of a low-temperature regime (below about 0.15–0.22Tm), where grain growth is independent of the irradiation temperature, and a thermally assisted regime where grain growth is enhanced with increasing irradiation temperature. A model is proposed to describe grain growth under irradiation in the temperature-independent regime, based on the direct impact of the thermal spikes on grain boundaries. In the model, grain-boundary migration occurs by atomic jumps, within the thermal spikes, biased by the local grain-boundary curvature driving. The jumps in the spike are calculated based on Vineyard’s analysis of thermal spikes and activated processes using a spherical geometry for the spike. The model incorporates cascade structure features such as subcascade formation, and the probability of subcascades occurring at grain boundaries. This results in a power law expression relating the average grain size with the ion dose with an exponent equal to 3, in agreement with the experimental observations. The model is applied to grain growth observed in situ in a transmission electron microscope in a wide range of doses, temperature, and irradiation conditions for four different pure metals, and shown to predict well the results in all applicable cases. Some discussions are also presented on the expansion of the model to the thermally assisted regime. The paper is organized in six sections. Section I gives background and literature review, while Secs. II and III review experimental methods and results for in situ grain growth under irradiation. Section IV derives the model proposed to find the grain-growth equation in the nonthermal regime, and in Sec. V the model is applied to the results. In Sec. VI grain growth in the thermally assisted regime is discussed and Sec. VII presents the conclusions.

From distribution functions to evolution equations for grain growth and coarsening

During precipitate coarsening or grain growth, the distribution function of the effective radii usually approaches a steady state. Time-independent distribution functions are obtained by normalizing these functions to a constant total volume of the studied objects and by normalizing the radius of each object to the mean or critical radius. It is well known that different evolution equations for the object radii lead to different steady-state distribution functions, which can be determined experimentally or by computational simulations. This paper presents an inverse-problem method, by which the evolution equations for the object radii can be derived from the steady-state distribution functions. The evolution equations for both grain growth and coarsening kinetics are determined considering the most common steady-state distribution functions, and the results are discussed.

Effects of yttrium on recrystallization and grain growth of Mg-4.9Zn-0.7Zr alloy

Recrystallization and grain growth in Mg-4.9Zn-0.7Zr and Mg-4.9Zn-0.9Y-0.7Zr alloys as a function of temperature on deformation were investigated with regards to hot rolling and annealing. The influence of yttrium addition on the microstructure was examined by X-ray diffraction (XRD), optical microscopy (OM), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The results indicated that yttrium addition promoted nucleation of recrystallization during hot rolling process. The grain size of Mg-4.9Zn-0.7Zr alloy samples grew significantly with annealing temperature (300–400 °C) and holding time (0–120 min), while the microstructure of the alloy with yttrium addition remained unchanged and fine. The activation energy of grain boundary migration for Mg-4.9Zn-0.9Y-0.7Zr alloy samples (56.34 kJ/mol) was higher than that for Mg-4.9Zn-0.7Zr (42.66 kJ/mol) owing to the pinning effect of Y-containing particles. The proposed growth models of recrystallized grains for the two studied alloys conformed well to E. Robert's grain-growth equation. Besides, the ultimate strength and yield strength of the alloys with yttrium addition were improved with good plasticity.

A Study of the Microstructure and Grain Size at the Welding Heat Affected Zone of a Ferrite Stainless Steel

A method of Monte Carlo combined with welding experiments was adopted to study the grain size and microstructure in welding heat affected zone of the ferrite stainless steel. Firstly, the kinetic equation of grain growth was established with the experimental data . Then , a simulation procedure based on the kinetic equation was worked out. Agreement between Monte Carlo simulation result and the real experiment results was obtained.

Grain size measurement methods and models for nanograined WC–Co

Development of nanograined WC–Co presents challenges for grain size measurement. In this study, standard and nanocrystalline WC–Co powders are processed by conventional and spark sintering. The resulting microstructures are characterized by image analysis of scanning electron microscopy micrographs, X-ray line broadening, and magnetic coercivity. The results are analyzed and a property map relating coercivity to WC grain size is developed. Equations for interface-controlled grain growth are transformed into the master sintering curve form and are used to analyze the grain size data from the three measurement techniques.