Grain Growth In Metals Research Articles

Persistence of abnormal grain growth in the presence of grain boundary complexion transitions: Thermodynamic analysis and phase field modeling

An anomalous feature in polycrystalline grain growth in metals and ceramics is the rapid abnormal growth of a few grains relative to the surrounding matrix grains. In certain systems, this phenomenon is reported to be associated with the presence of first order phase transitions in the grain boundaries often referred to as complexion transitions. The fundamental question of how the growth advantage of abnormally growing grains persists in this context is not yet well understood. We present a thermodynamically consistent mechanism by which abnormal grain growth may occur. The presence of two complexion transitioned boundaries at a triple junction provides a driving force for partial wetting at the triple junction leading to the formation of a quadruple junction. The subsequent dissociation of the quadruple junction into two partial wetting triple junctions favors the persistence of abnormal grain growth. We incorporate this dissociation process into a multi-order parameter phase field model and demonstrate the occurrence of abnormal grain growth without the need for mobility advantage or additional driving forces. The results from simulations of abnormal grain growth capture experimentally observed microstructural features such as peninsular and island grains. Through a systematic study we show that the initial fraction of complexion boundaries plays a significant role in abnormal grain growth and that maximum abnormal grain growth is observed when the fraction of complexion boundaries is less than about 2%.

Monte-Carlo-Assisted Phase Field Simulations of Grain Structure Evolution during the Welding Process

A Monte-Carlo-assisted phase field model for the simulation of grain growth in metals and alloys is presented. The simulation time in this model is connected to real time through an experimental data-based kinetic model. Site selection probability is introduced to simulate grain structure evolution under non-isothermal conditions. The grain evolutions with temporal and spatial distributions of temperature during the welding process are comprehensively reproduced. The average size and topological texture of the generated grains in the fusion zone and heat-affected zone are examined. The computed results are compared to experimental data for laser-welding two alloys: Fe–6.5 wt.%Si and low-carbon steel. The applications of real-time–temperature based phase field simulation to material processing indicate significant promise for understanding grain structures during the welding process or additive manufacturing processes.

Investigation of Full-field and Mean-field Models for Pure Grain Growth Simulations

Mean-field approaches are commonly used in the simulation of grain growth in metals as they are easier to implement. However, mean-field models only track the evolution of average grain diameter as a function of temperature and time, while they neglect the effect of actual grain size distribution, which limits their applicability. Recently introduced full-field models of grain growth – either by level-set and phase field methods- allow to overcome the barriers of mean-field methods, but they are computationally much more demanding. In this article, the main goal is to investigate the applicability of both approaches for the pure grain growth in a solid with an initial Gaussian grain size distribution. The main idea is to keep the average grain size constant while altering the grain size distribution by modifying the standard deviation. DIGIMU software, which uses the level-set approach - is used for this purpose. The conclusion is that full-field models are beneficial to observe changes during grain growth; alternatively, mean-field models deduce approximately the same results as full-field models for a Gaussian distribution within a shorter time. However, it is found that mean-field models overlook certain important stages of the evolution of the microstructure, while full-field method captures all the details. Therefore, the model to investigate the grain growth mechanism should be selected accordingly.

Effect of thermo-mechanical processes on microstructure evolution in austenitic stainless steels

The mechanical properties of steels are strictly connected to chemical composition as well as to microstructural features obtained after thermo-mechanical processing. As a consequence, recrystallization and grain growth are relevant to the mechanical properties of steels, thus suggesting the necessity of mathematical models able to predict the microstructural evolution after thermo-mechanical cycles. In particular, in stainless steel grades, mechanical characteristics, and a proper microstructure with an adequate grain size distribution, are very important in order to achieve the required formability and deep drawing properties for many applications. This paper deals with the study of microstructural changes, such as grain size variations and recrystallized volume fraction in stainless steels during isothermal treatments through the application of a mathematical model, able in general to describe the primary recrystallization and grain growth in metals. The developed model takes into account the recrystallization phenomenon and Zener drag effect. A general continuity equation is proposed describing in continuous way recrystallization and grain growth phenomena without taking into account textures effect. The influence of input parameters is analyzed.

Recrystallization and Grain Growth Phenomena in Stainless Steels for Different Thermo-Mechanical Processes

The mechanical properties of steels are strictly connected to chemical composition as well as to microstructural features obtained after thermo-mechanical processing. As a consequence, recrystallization and grain growth are relevant to the mechanical properties of steels, thus suggesting the necessity of mathematical models able to predict the microstructural evolution after thermo-mechanical cycles. In particular, in stainless steel grades, mechanical characteristics, and a proper microstructure with an adequate grain size distribution, are very important in order to achieve the required formability and deep drawing properties for many applications. This paper deals with the study of microstructural changes, such as grain size variations and recrystallized volume fraction in stainless steels during isothermal treatments through the application of a mathematical model, able in general to describe the primary recrystallization and grain growth in metals. The developed model takes into account the recrystallization phenomenon and Zener drag effect. A general continuity equation is proposed describing in continuous way recrystallization and grain growth phenomena without taking into account textures effect. The influence of input parameters is analyzed.

Critical assessment 30: Grain growth – Unresolved issues

ABSTRACTGrain growth is a broad field of study that covers several scientifically and technically interesting characteristics. Normal grain growth kinetics and its associated parabolic growth law and self-similar size distributions, grain boundary pinning, abnormal grain growth, the effect of triple junctions and quadruple points as well as grain growth in thin films are the most important current topics of grain growth research. In this critical assessment of grain growth in metals, we present and discuss some of the most important unresolved issues that have been a subject of research for many years.

Physical Modelling of Recrystallization and Grain Growth in Steels: Analysis of Free Parameters

The mechanical properties of steels are strongly affected by grain size and chemical composition variations. Many industrial developments have been carried out both from the point of view of composition variation and grain size in order to exploit the effect of these variables to improve the mechanical proprieties of steels. It is also evident that recrystallization and grain growth are relevant to the mechanical properties of steels, thus suggesting the necessity of mathematical models able to predict the microstructural evolution after thermo-mechanical cycles. It is therefore of primary importance to study microstructural changes, such as grain size variations of steels during isothermal treatments through the application of a mathematical model, able in general to describe the primary recrystallization and grain growth in metals. This paper deals with the recrystallization and grain growth modelling of steels based on the statistical theory of grain growth originally developed by Lücke [1] and here integrated to take into account the effect of recrystallization and Zener drag effect. A general continuity equation is proposed describing in continuous way recrystallization and grain growth phenomena without taking into account textures effect. The effect of input parameters is analyzed.

Roughening Transition of Interfaces and its Effect on Grain Growth in Metals and Ceramics

Roughening Transition of Interfaces and its Effect on Grain Growth in Metals and Ceramics

Scaling of Monte Carlo simulations of grain growth in metals

The term microstructure defines many properties of metals that have practical significance. The final microstructure established during metal-forming processes is determined by the grain growth, recrystallization and recovery phenomena. Since these phenomena represent stochastic processes, they require a statistical treatment, and therefore, the Monte Carlo (MC) method is often used to simulate them. However, the MC method does not provide physical time and length scales, and thus a scaling procedure is required to map the simulation results to the physical material behavior. In this paper, we compare MC simulation results with theoretical models and experimental observations for grain growth of metals at different temperatures to obtain scaling relationships between physical time/length scales and the MC step/cell size. These scaling relationships can then be employed in multi-scale modeling of metal-forming processes.

A Paradox of Decreasing Entropy in Multiscale Monte Carlo Grain Growth Simulations

Grain growth in metals is driven by random thermal fluctuations and increases the orderliness of the system. This random process is usually simulated by the Monte Carlo (MC) method and Cellular Automata (CA). The increasing orderliness results in an entropy decrease, thus leading to a paradoxical apparent violation of the second law of thermodynamics. In this paper, it is shown that treating the system as a multiscale system resolves this paradox. MC/CA simulations usually take into consideration only the mesoscale entropy. Therefore, the information entropy of the system decreases, leading to an apparent paradox. However, in the physical system, the entropy is produced at the nanoscale while it is consumed at the mesoscale, so that the net entropy is growing.

Multiscale effects in crystal grain growth and physical properties of metals

A multiscale approach for the simulation of physical properties of metals is suggested and discussed. Grain growth in metals involves interactions at three distinct scale levels: the atomic scale (length of crystal lattice spacing), microscale (grain length) and macroscale. A simulation scheme should include these three levels. The crystalline microstructure is simulated by the Monte Carlo method. The average grain radius is then used to determine the yield strength from the Hall-Petch relationship for large grains and the inverse Hall-Petch relationship for submicron-sized grains. The yield strength is then supplied to a continuum macroscale model. The normal grain growth, which has a theoretical solution for grain size as a function of time, is discussed in detail as a case study and conclusions are drawn with regard to more complex situations such as dynamic recrystallization.

Abnormal Grain Growth in Metals

Grain growth may occur in two forms, normal grain growth, characterized by a constant grain size distribution during growth, and abnormal grain growth, where one or more abnormally large grains may form in the microstructure. The presence of abnormally large grains in an otherwise uniform microstructure may be detrimental to the mechanical properties of a polycrystalline structure. Little is understood of the exact cause of abnormal grain growth. The annealing conditions leading to the onset of abnormal grain growth have been investigated via a series of grain growth experiments carried out on an Al-4wt%Cu alloy. The structure of which consisted of equiaxed grains (<8μ) pinned by a fine dispersion of sub-micron second phase particles, which may dissolve upon annealing. Minority texture components may experience accelerated growth due to a higher energy and mobility compared to the surrounding grain structure. The combination of these two events may result in the abnormal growth of some grains. SEM imaging and EBSD data has then made it possible to characterize the influence of particle dissolution and grain boundary misorientation on the onset of abnormal grain growth. The stability of ‘island grains’ found to exist internally in abnormally large grains has also been investigated in relation to the misorientation relationship and localized second phase volume fraction found there. There was only weak evidence of special misorientation relationships between the island grains and the abnormally large grains in which they exist, and although there was evidence of an enhanced fraction of pinning particles at island grain boundaries, this was also true of boundaries in general. The larger size of island grains is their dominant characteristic, and grains which become island grains may have been incipient abnormal grains.

An analytical and experimental investigation on the normal grain growth in metals using the Monte Carlo method

The prediction of material microstructure is of great interest to the material designers since the property and performance of materials depend strongly on their microstructures. In this work, a Monte Carlo approach is used to investigate the normal grain growth of aluminum and pure copper. The grain growth was calculated at certain temperatures using the grain growth law and compared with the simulation results by varying the Q as a parameter of simulation lattice orientation for pure aluminum. Also the results predicted by the Monte Carlo method showed a good agreement with the experimental results of grain growth of pure cooper. It was found that increase in Q increases the accuracy of the predicted results and the Monte Carlo method can be used to assess both the grain growth mechanism as well as the grain rotation in the microstructure simulation.

Analysis of the recrystallization and grain growth processes in AISI 316 stainless steel

A theoretical and experimental study on the recrystallization and grain growth processes on AISI 316 stainless steel is here reported. Experimental data are analyzed according to a mathematical model based on statistical assumptions able to describe simultaneously recrystallization and grain growth in metals. Taking into account the classical constitutive equations of the Taylor's theory, the model adopts two parameters: the dislocation density and the initial number of nuclei. The predictions of the model are in good agreement with experimental results. As cross check of the model predictions, the independent parameter “dislocation density” is found to properly correlate to the mechanical properties of the steel, to X-ray diffraction measurements and to transmission electron microscopy measurements. A comparison with an analogue study on AISI 304 stainless steel is also reported, enhancing the effect of molybdenum in inhibiting recrystallization and grain growth.

Three-Dimensional Monte Carlo Simulation of Primary Recrystallization and Grain Growth in Metals with Texture

In the present paper the the Monte Carlo (MC) method is applied for the simulation of primary recrystallization and grain growth in metallic materials. Both processes are influenced by the distribution of the crystallographic orientations in the material. In the case of strong textures, most of the grain boundaries have a low misorientation. Such low angle boundaries are generally assumed to have a mobility much lower than the mobility of high angle boundaries. In the present MC-model, these anisotropic mobilities are realised by introducing modified flip rates. The three-dimensional simulations show the strong influence of the initial texture and of the mobilities on the growth kinetics as well as on the evolution of the texture. It is demonstrated that deviations from the parabolic time law of grain growth and texture alterations, both observed experimentally, can be simulated in a quite satisfying manner. Furthermore, the application of the method to model primary recrystallization is discussed. It turns out that the growth of the nuclei influenced by the local surrounding (grain boundaries, misorientation, defect density) can be simulated very well by the MC-model.

Grain growth in metals with strong textures: Three-dimensional Monte Carlo simulations

The commonly used Monte Carlo technique has been applied to simulate normal as well as texture-controlled grain growth on 100 3-square lattices. For the case of normal grain growth the simulations yield a grain growth exponent of n ≈ 0.5, provided the modifications of Radhakrishnan and Zacharia [B. Radhakrishnan, T. Zacharia, Simulation of curvature-driven grain growth by using a modified Monte Carlo algorithm, Metall. Mater. Trans. A 26A (1995) 167.] are implemented into the algorithm. Microstructures with a strong initial texture exhibit texture changes if the grain boundaries have anisotropic mobilities.

Real time-temperature models for Monte Carlo simulations of normal grain growth

Two different models for the simulation of normal grain growth in metals and alloys are presented. These models demonstrate the application of real time-temperature based Monte Carlo (MC) simulation to materials processing. A Grain Boundary Migration model coupled the MC simulation to a first principle grain boundary migration model. The results of this simulation were shown to correlate well with the experimental results for isothermal grain growth in zone refined tin. An Experimental Data Based model coupled the MC simulation with experimental grain growth data. The results from this simulation were shown to correlate well with the grain growth during continuous heating of a beta titanium alloy.

Analytical modelling of grain growth in metals and alloys in the presence of growing and dissolving precipitates—I. Normal grain growth

The present investigation is concerned with analytical modelling of grain growth in metals and alloys in the presence of growing and dissolving precipitates. In Part I, the different components of the normal grain growth model are outlined and differential equations presented which allow the mean grain size to be calculated as a function of time and temperature. These equations have then been solved for fixed starting conditions by means of analytical and numerical methods to evaluate the matrix grain coarsening behaviour during isothermal heat treatment. The results are presented in the form of novel “mechanism” maps (by utilizing the concept of group variables) which show the conmpetition between the various processes that lead to normal grain growth in metals and alloys in the presence of unstable second phase particles. An analytical approach to the modelling of abnormal grain growth is described in an accompanying paper (Part II).

Analytical modelling of grain growth in metals and alloys in the presence of growing and dissolving precipitates—II. Abnormal grain growth

The present investigation is concerned with analytical modelling of grain growth in metals and alloys in the presence of growing and dissolving precipitates. In Part II the modelling methodology presented in Part I for normal grain growth has been further developed and applied to abnormal grain growth. The judicious construction of the constitutive equations makes full use of both dimensionless parameters and calibration techniques to eliminate poorly known kinetic constants. The results are presented in the form of novel “mechanism” maps (by utilizing the concept of group variables) which show the competition between the various processes that lead to abnormal grain growth during heat treatment. This approach has made it possible to fit many of the apparently conflicting results into a more consistent picture and establish a simple criterion for the initiation of abnormal grain growth under different pinning conditions. It is concluded that the key to a verified, quantitative understanding of the phenomenon of abnormal grain growth lies primarily in the recognition of the important effect of precipitate stability on the secondary recrystallization kinetics.

Computer-aided analysis of grain growth in metals

Isothermal grain growth in aluminium, copper and α-iron was investi8ated experimentally at elevated temperatures and quantitatively interpreted by computer simulation on the base of a statistical model described in [4,5,6]. As it is demonstrated for the grain growth kinetics, the experimental data can be fitted satisfactorly