Kampmann-Wagner Numerical Model Research Articles

A direct particle tracking model for predicting homogeneous precipitation kinetics in Al-Sc alloys

The Kampmann-Wagner numerical (KWN) model, although been widely used in modeling the precipitation kinetics in solid solution alloys, has its own deficiency which is mainly reflected in two aspects: inability to track the growth history of individual particles and difficulty in describing the precipitation kinetics of non-spherical particles. In this work a direct particle tracking (DPT) model, which can well handle such issues, has been proposed and implemented. The main aim of this work is to check the validity and accuracy of the DPT model. To this end, the DPT model and two KWN models with different levels of accuracy have been applied to simulate the precipitation kinetics in two Al-Sc alloys. By comparing the numerical results with literature experimental data, it is found that the DPT model can well describe the microstructure evolutions during ageing of the Al-Sc alloys, and it has nearly the same accuracy as the KWN model with the governing equation solved by the high-resolution scheme (HR-KWN model). To reduce the amplitude of the oscillations formed in the particle size distribution (PSD) curves predicted by the DPT model, we need to set a small enough value for the time intervals divided in the nucleation stage.

On Evaluation of the Gibbs–Thomson Effect and Selection of Nucleus Size for the Kampmann–Wagner Numerical Model

On Evaluation of the Gibbs–Thomson Effect and Selection of Nucleus Size for the Kampmann–Wagner Numerical Model

Modeling the Precipitation of Aluminum Nitride Inclusions during Solidification of High‐Aluminum Steels

High‐aluminum advanced high‐strength steels have received increasing interest due to their excellent combination of strength and ductility. The control of nonmetallic inclusions in steel is among the most important issue for the production of high‐aluminum steel. This study proposes a model for the evolution of size distributions of AlN inclusions during solidification of steel based on the Kampmann–Wagner numerical model and microsegregation calculation. Both homogeneous (pure AlN) and heterogeneous precipitations (AlN+oxide or MnS) are described using homogeneous nucleation and free growth models of Greer et al. respectively. The model is applied to calculate the size distributions of AlN in high‐Al (up to 5%) Fe–Cr–Al steels and high‐ and medium‐manganese steels and validated by the experimental data in the literature. The model correctly describes the influence of cooling rates on the precipitation of AlN in Fe–Cr–Al steels and high‐manganese steels, and the sizes of AlN are reduced and the number densities of AlN inclusions are increased by increasing the cooling rate. The effects of nitrogen and aluminum concentration in medium‐manganese steel on inclusion precipitation are investigated by the model calculation. The increases in nitrogen and aluminum concentration facilitate the homogeneous precipitation of AlN inclusions.

Modeling the Precipitation Kinetics and Yield Strength of Mg-Gd-Y-Zr Alloys Based on An Improved Kampmann–Wagner Numerical Model and Modified Orowan Strengthening

Modeling the Precipitation Kinetics and Yield Strength of Mg-Gd-Y-Zr Alloys Based on An Improved Kampmann–Wagner Numerical Model and Modified Orowan Strengthening

Kawin: An open source Kampmann–Wagner Numerical (KWN) phase precipitation and coarsening model

Kawin, a new open-source implementation of the Kampmann–Wagner Numerical model of precipitation (concomitant nucleation, growth, and coarsening), is presented. An overview of the organization and capabilities of the program is provided, along with an outline of the constituent physics. Kawin is shown to be able to reproduce the results of state-of-the-art commercial software and experimental data for a variety of alloy systems under multiple precipitation conditions. Kawin is capable of simulating the bulk precipitation behavior of multiphase, multicomponent systems in response to complex heat treatments, and contains numerous innovative features to enhance model stability, improve flexibility and usability, and minimize computational expense. Kawin also incorporates sophisticated elastic energy calculations, traditionally ignored in this type of simulation but shown here to significantly impact the precipitation behavior of some systems. The inclusion of native strain calculations enables Kawin to predict the influence of internal or external stress fields on precipitation, as well as track the evolution of precipitate geometry throughout the course of a heat treatment. It is the hope of these authors that this software will facilitate the advancement of precipitation modeling as a tool for materials design.

Optimization of T5 heat treatment in high pressure die casting of Al–Si–Mg–Mn alloys by using an improved Kampmann-Wagner numerical (KWN) model

The increased use of lightweight aluminum die castings in the automotive industry leads to new die casting alloys and their heat treatment processes to meet performance requirements. In this paper, an integrated precipitation and strengthening framework based on an improved Kampmann-Wagner numerical (KWN) model was developed to predict the hardness and yield strength (YS) of high pressure die casting (HPDC) Al–11Si-xMg (x = 0.3 and 0.6) alloys during T5 aging (artificial aging after casting) process. The hardness and YS of the alloys were measured and compared with the predication results, for T5 treatment at 190 °C, 210 °C, 225 °C and 240 °C, respectively. The increased Mg content (from 0.3 to 0.6%) leads to the formation of Mg2Si phase during solidification, which effectively increases the hardness and YS in as-cast conditions. Also, the higher Mg content results in increased peak strengths because of higher precipitate density of needle-like Mg5Si6-β″ phase. This improved KWN model showed a good accuracy with experimental results. Mechanical property maps were generated to guide the design and optimization of T5 process window for these two important die casting aluminum alloys.

Characterization and modeling of concurrent precipitation in Mg-Al-Sn alloys using an improved Kampmann-Wagner numerical (KWN) model

The concurrent precipitation microstructure of Mg17Al12 and Mg2Sn phases in AT72 (Mg-7Al-2Sn) magnesium alloy was quantitatively characterized using Scanning Transmission Electron Microscopy (STEM) based techniques. An improved Kampmann-Wagner numerical (KWN) model taking into account of the effects of non-spherical precipitates on growth kinetics and coupled with multicomponent thermodynamic and kinetic databases of magnesium alloys was used to simulate the evolution of the concurrent precipitation microstructure. Furthermore, the age hardening behavior of AT72 alloy was predicted by coupling the improved KWN model with a classical precipitation strengthening model. Simulation results show that a lower aging temperature will lead to finer and higher number density of both types of precipitates, providing improved aging hardening response. The addition of Al to Mg-Sn alloys can increase the driving force and precipitation kinetics of Mg2Sn phase. High-throughput KWN simulation was performed on the Mg-Al-Sn alloy system to demonstrate the application of the improved KWN model in optimizing the composition and heat treatment procedure in precipitation strengthened alloys.

Modeling precipitation kinetics for multi-phase and multi-component systems using particle size distributions via a moving grid technique

The collection and coupling of thermodynamic data following the Calphad framework is important for the computational alloy and process design. The microstructure and the precipitation kinetics have a significant influence on the microstructure and mechanical properties of multi-component alloys in solid state; therefore, it is essential to account for solid state phase transformations via thermo-chemical process simulations. In this work an efficient numerical scheme for a Kampmann-Wagner numerical (KWN) model, which takes into account multi-component nucleation and growth theories via the coupling to the open thermodynamic software-package OpenCalphad, is developed and implemented. By the usage of the Calphad approach, it becomes feasible to describe complex multi-component alloy systems. The developed KWN model can take into account effects resulting from the generation or annihilation of vacancies by an off-equilibrium diffusion constant. For the solution of the particle size distribution an efficient and flexible moving grid algorithm is elaborated, which provides a robust and adaptive solution scheme for the simulation of nucleation, growth, coarsening and reversion. The model is applied to simulate the precipitation kinetics of recently published in-situ anomalous small angle X-ray scattering experiments studying reversion of an AA7xxx alloy and the identified model can reproduce the essential characteristics of these reversion experiments over a wide temperature range.

Diffusion-driven microstructure evolution in OpenCalphad

The diffusion process in multicomponent alloys has a significant influence on the evolution of the microstructure. The Calphad approach is a powerful method for describing the equilibrium state as well as the kinetics of non-equilibrium systems via the Gibbs energy. In this work, the principles of multicomponent diffusion theory are considered intensively, and an equation for the fluxes in the case of substitutional-interstitial diffusion is given for implementation. Additionally, the calculation of mobility matrices and thermodynamic factors is addressed. As an application case, substitutional diffusion is implemented in OpenCalphad and is used for calculating the growth rate for spherical precipitates from a supersaturated aluminum matrix. The growth rate has been integrated into the Kampmann–Wagner numerical model, which describes nucleation, growth, and coarsening for spherical precipitates. A AlMgZnCu alloy is considered, which has great significance in the field of materials processing.

Modeling of Microsegregation and Homogenization of 6xxx Al-Alloys Including Precipitation and Strengthening During Homogenization Cooling.

Control of the homogenization process is important in obtaining high extrudability and desirable properties in 6xxx aluminum alloys. Three consecutive steps of the process chain were modeled. Microsegregation arising from solidification was described with the Scheil–Gulliver model. Dissolution of Mg2Si, Si (diamond) and β-AlFeSi (β-Al5FeSi) to α-AlFeSi (α-Al12(FeMn)3Si) transformation during homogenization have been described with a CALPHAD-based multicomponent diffusion Dual-Grain Model (DGM), accounting for grain size inhomogeneity. Mg2Si precipitation and associated strengthening during homogenization cooling were modeled with the Kampmann–Wagner Numerical (KWN) precipitation framework. The DGM model indicated that the fractions of β-AlFeSi and α-AlFeSi exhibit an exact spatial and temporal correspondence during transformation. The predictions are in good agreement with experimental data. The KWN model indicated the development of a bimodal particle size distribution during homogenization cooling, arising from corresponding nucleation events. The associated strengthening, arising from solid solution and precipitation strengthening, was in good agreement with experimental results. The proposed modeling approach is a valuable tool for the prediction of microstructure evolution during the homogenization of 6xxx aluminum alloys, including the often-neglected part of homogenization cooling.

Precipitation Kinetics of AA6082: An Experimental and Numerical Investigation

The development of simulation tools for bridging different scales are essential for understanding complex joining processes. For precipitation hardening, the Kampmann-Wagner numerical model (KWN) is an important method to account for non-isothermal second phase precipitation. This model allows to describe nucleation, growth and coarsening of precipitation hardened aluminum alloys based on a size distribution for every phase which produces precipitations. In particular, this work investigates the performance of a KWN model by [1-3] for Al-Mg-Si-alloys. The model is compared against experimental data from isothermal heat treatments taken partially from [2]. Additionally, the model is used for investigation of the precipitation kinetics for a laser beam welding process, illustrating the time-dependent development of the different parameters related to the precipitation kinetics and the resulting yield strength.

Multiscale process simulation of residual stress fields of laser beam welded precipitation hardened AA6082

In this study, a multiscale modelling approach for the determination of residual stresses for the laser beam welded, precipitation hardened aluminium alloy AA6082-T6 is presented and applied. The material behaviour is described by an elasto-visco-plastic material model, specially suited for fusion welding processes. The microstructure evolution during the welding process has a direct influence on the macroscopic mechanical properties. The modelling approach accounts for the change in the microstructure via a Kampmann–Wagner Numerical model which takes into account the kinetics of the precipitates. The macroscopic mechanical properties are determined via classic dislocation theory, which accounts for the interaction between dislocations and precipitates. The temperature field of the welding process is described by a highly efficient semi-analytical approach. The solution of the temperature field in connection with a three dimensional moving heat source is achieved by using the method of Green’s functions. By employing the method of Green’s functions, it is possible to reduce the numerical effort significantly. The results of this modelling approach are compared to temperature, hardness as well as residual stress measurements, obtained from synchrotron X-ray diffraction, for welded sheets to clarify the accuracy of the applied model.

A novel approach to investigate delta phase precipitation in cold-rolled 718 alloys

This paper proposes a numerical alternative to the lengthy experimental approaches typically employed to characterize delta phase precipitation in 718 alloys. A high-throughput experimental case study is first performed on cold-rolled alloy 718 of known composition and initial microstructure. Direct resistance heating is used to generate highly heterogeneous thermal fields, which enables investigation of a wide range of temperatures with relatively few experiments. Through a coupled finite element and Kampmann-Wagner numerical model, topographies of delta phase characteristics resulting from the complex heat treatments are generated. The predicted precipitation state shows good agreement with scanning electron microscopy observations of the heat-treated samples, demonstrating the validity of the proposed numerical approach.

Modeling over-ageing in Al-Mg-Si alloys by a multi-phase CALPHAD-coupled Kampmann-Wagner Numerical model

The formation of the equilibrium precipitation phase during ageing treatment of Al-Mg-Si alloys is preceded by a series of metastable phases. Given longer ageing time, higher ageing temperature or elevated temperature service condition, β″, the main hardening phase, would be replaced by the more stable metastable phases such as β′, B′, U1 and U2. The post-β″ microstructure evolution, called “over-ageing”, leads to a steep drop in the hardness evolution curve. This paper aims to predict directly over-ageing in Al-Mg-Si alloys by extending a CALPHAD-coupled Kampmann-Wagner Numerical (KWN) framework towards handling the coexistence of several different types of stoichiometric particles. We demonstrate how the proposed modeling framework, calibrated with a limited amount of experimental measurement data, can aid in understanding the precipitation kinetics of a mix of different types particles. Simulation results are presented with some earlier reported transmission electron microscopy measurements [1,2] to shed light on how the alloy composition and ageing treatment influence the post- β″ phase selection.

Precipitation Modeling in Nitriding in Fe-M Binary System

Precipitation of fine alloy nitrides near the specimen surface results in significant surface hardening in nitriding of alloyed steels. In this study, a simulation model of alloy nitride precipitation during nitriding is developed for Fe-M binary system based upon the Kampmann–Wagner numerical model in order to predict variations in the distribution of precipitates with depth. The model can predict the number density, average radius, and volume fraction of alloy nitrides as a function of depth from the surface and nitriding time. By a comparison with the experimental observation in a nitrided Fe-Cr alloy, it was found that the model can predict successfully the observed particle distribution from the surface into depth when appropriate solubility of CrN, interfacial energy between CrN and α, and nitrogen flux at the surface are selected.

Precipitation of Non-Spherical Particles in Aluminum Alloys Part I: Generalization of the Kampmann–Wagner Numerical Model

Particles precipitated during aging treatments often have non-spherical shapes, e.g., needles or plates, while in the classical Kampmann–Wagner Numerical (KWN) precipitation model, it is assumed that the particles are of spherical shape. This model is here generalized resulting in two correction factors accounting for the effects induced by the particles’ non-spherical shape on their growth kinetics. The first one is for the correction of the growth rate. It is derived from the approximate solution of the diffusion problem on spheroidal coordinate and verified by the three-dimensional numerical solutions for cuboid particles. The second factor is for the energetic correction due to the particle surface curvature. It is derived from chemical potential equality (or Gibbs energy minimization principle) at equilibrium for non-spherical particles and provides a correction factor for the Gibbs–Thomson effect. In the accompanying paper, the two correction factors are implemented into a multi-component KWN modeling framework, and the resulting improvements on the model’s predictive power are demonstrated.

Precipitation of Non-spherical Particles in Aluminum Alloys Part II: Numerical Simulation and Experimental Characterization During Aging Treatment of an Al-Mg-Si Alloy

This is the second part of the investigation on the precipitation of needle-shaped particles. In part I, two particle aspect ratio-dependent correction factors are introduced to describe the effects of non-spherical precipitate shape on precipitate growth kinetics. In this part II, the two factors are integrated into a CALPHAD-coupled multi-component Kampmann–Wagner numerical model to predict precipitation kinetics of needle-shaped metastable particles during aging treatment of an Al-Mg-Si alloy. The predictions are compared with transmission electron microscopy observations on precipitate number density, volume fraction, and size distribution. Improved agreement is reported, and in particular, the shape of the predicted particle size distribution density function becomes more realistic.

An extension of the Kampmann–Wagner numerical model towards as-cast grain size prediction of multicomponent aluminum alloys

The Kampmann–Wagner numerical (KWN) model, which has been widely adopted as a precipitation modeling framework accounting for concurrent nucleation, growth and coarsening kinetics, was extended to predict the as-cast grain size of inoculated multicomponent aluminum alloys. In the model, the heterogeneous nucleation of grains on inoculant particles was modeled based on the free growth criterion, while the influence of the solute on the nucleation behavior, in terms of the solute suppressed nucleation (SSN) effect, was rigorously defined and integrated. In order to fully address the solidification behavior of multicomponent alloys, a coupling of the KWN model to CALPHAD was carried out. These extensions allow the treatment of two different nucleation-ceasing mechanisms induced by grain growth: recalescence stifling and solute segregation stifling. Given melt composition, inoculation and heat extraction rate, the model is able to predict maximum nucleation undercooling, cooling curve and the final as-cast grain size of multicomponent alloys without invoking the binary equivalence assumption used in the existing models. The proposed model was tested with a variety of binary and multicomponent aluminum alloys, and the predictions were compared with the experimental measurement results and previous grain size prediction models. The simulation results show that the SSN effect has a negligible influence on the nucleation behavior and the final grain size during isothermal melt solidification, but a strong influence on the ceasing of grain nucleation during directional solidification. Reasonable agreement was obtained between the model prediction and measurement results on a direct chill casting experiment of an AA5182 alloy. Our work proves that the application of the precipitation modeling framework for the solidification problem is successful.

Modelling precipitate nucleation and growth with multiple precipitate species under isothermal conditions: Formulation and analysis

This study extends the Kampmann–Wagner-Numerical model for the nucleation and growth of precipitates. We introduce a multi-component theoretical framework for the value of the frequency of atomic attachment to a growing particle, which compares well with literature. The growth of precipitates is modelled using Zener approximations and the Gibbs–Thomson effect, where all chemical elements influence the growth rate. The model is discretised using finite-volume and time-integration techniques and subsequently applied under isothermal conditions to an industrial HSLA steel containing Nb(C,N)-, AlN- and MnS-precipitates. The simulations show the importance of the multi-component and multi-phase approach as some of the secondary phases have significant effects on other phases.

Evolution of size distribution of shearable ordered precipitates under homogeneous deformation: Application to an Al-Li-alloy

Based on the model of the “pseudo Portevin-Le Chaˆtelier effect” by Bréchet and Estrin, a quantitative description is developed for the homogeneous precipitation of small, coherent and hence shearable ordered second-phase particles when small and homogeneous plastic deformation of constant strain rate is exerted. A modified Gibbs-Thompson equation is derived for the re-dissolution of a sheared particle. The growth on shrinkage of the sheared particle is described phenomenologically. By means of a modified Kampmann-Wagner numerical model, the evolution of the precipitate structure, i.e. the size distribution under plastic deformation, is simulated for the example of an aged Al Li alloy. Three regimes of the precipitation process, i.e. nucleation, growth and coarsening are treated to be “concomitant” instead of being “consecutive”. The hardening stress owing to precipitation is calculated. It is demonstrated that the strain-rate sensitivity of the hardening stress turns negative under certain conditions. This is of relevance for the Portevin-Le Chaˆtelier effect.