Kampmann-Wagner Numerical Research Articles

Simulation of bcc-Cu precipitation in ternary Fe-Cu-M alloys

The precipitation of bcc-Cu in the ferrite matrix of Fe-Cu-M alloys, where M is Al, Mn and Ni, is simulated using the Kampmann-Wagner-Numerical (KWN) model with the classical nucleation theory (CNT) and the theory of diffusion-controlled growth by Zener and Kirkaldy. The instantaneous local equilibrium interfacial concentrations of Cu and M were calculated at every time interval, which revealed that the influence of M diffusion is insignificantly small no matter it is faster or slower than the diffusion of Cu. Whilst the capillarity-corrected Cu concentration at the interface in the matrix essentially dictated the growth and coarsening, the concentration of M in the particle affected by capillarity also had an appreciable influence on the number of Cu particles. Al decreased the Cu solubility in the bcc-Fe matrix, increased the number of Cu particles, and decreased the matrix supersaturation fastest. Mn decreased the number and increased the mean radius of bcc-Cu particles due to the increase in Cu solubility to a large extent. The effects of Ni on particle number were less pronounced than one would expect from experimental observations in multicomponent steel. The small changes in particle/matrix interfacial energy and strain energy of nucleus can alter significantly the evolution of particle number and size during aging.

Effect of Cu Addition on Precipitation and Growth Behavior of MnS in Silicon Steel Sheets

The influence of Cu addition on MnS precipitation and growth behavior in Fe-2.88Si-0.1Mn-xCu (x = 0, 0.25) has been investigated. SEM observation clarified that Cu addition has no effect on the morphology of MnS or its growth rate at early stage. In contrast, Cu addition suppresses the growth rate at the Ostwald ripening stage. At the early stage of growth, a plateau region was observed both with and without Cu addition. Neither the conventional diffusion limited growth nor the Ostwald ripening theory adequately explains these observations. Using the Kampmann–Wagner Numerical (KWN) model, it was possible to successfully reproduce such behavior, including the plateau region. The interfacial energy between ferrite and the MnS was evaluated by the KWN-model, and good agreement was found with previously reported values. The suppression in the growth rate at the Ostwald ripening stage by Cu addition can be explained by a 15 pct reduction in the interfacial energy which possibly occurs due to the segregation of Cu at the interface between MnS and ferrite. This segregation was experimentally confirmed by STEM-EDX analysis.

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.

Quantitative modeling and experimental verification of carbide precipitation in a martensitic Fe–0.16 wt%C–4.0 wt%Cr alloy

Precipitation of carbides during tempering of a martensitic Fe–0.16wt% C–4.0wt% Cr alloy has been investigated by experimental analysis and quantitative modeling. It is found that both M7C3 and M23C6 form, at low- and high-angle grain boundaries in the martensite, as well as, at dislocations inside individual laths of martensite, during tempering at 700°C. The applied Kampmann–Wagner numerical (KWN) modeling, utilizing CALPHAD thermodynamic and kinetic databases together with an assumption of local equilibrium and a constant tie-line, captures the main features of the precipitation, with a transient formation of metastable M23C6, and with M7C3 as the stable carbide. The predicted volume fraction and size are in reasonable agreement with extraction experiments for M7C3. However, for the metastable minority carbide M23C6, the modeling underestimates the size and overestimates the volume fraction within the transient time. With sound thermodynamic databases and physical parameter input, the adopted simplified modeling scheme is a valuable tool for materials design and optimization. Furthermore, by treating conditions at the phase interface more rigorously it is possible to account for different mechanisms of precipitation, such as e.g., non-partitioning local equilibrium, which could be important in systems where interstitial elements diffuse much faster than the substitutional ones.

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.

Modelling the Evolution of Multiple Hardening Mechanisms during Tempering of Fe–C–Mn–Ti Martensite

We model the hardness evolution of martensite during tempering as a linear addition of multiple hardening mechanisms that is combined with a microstructural Kampmann-Wagner-Numerical (KWN) model to simulate the nucleation and growth of TiC-precipitates during tempering. The combined model is fitted to the measured hardness evolution during tempering at 300 degrees C and 550 degrees C of martensitic steels with and without the addition of titanium. The model predicts TiC-precipitate sizes in agreement with experimental observations and generates fitting parameters in good agreement with literature. The microstructural components that give the highest contribution to the overall hardness are Fe3C precipitates (88 HV) and dislocations (54 HV). Both Fe3C- and dislocation-strengthening decreases rapidly during the initial stage and stabilise after 10 minutes of tempering. The model shows that the decrease in dislocation density due to recovery is slowed down due to the presence of TiC-precipitates. Titanium atoms in solid solution give a stable hardness contribution (25 HV) throughout the tempering process. TiC-precipitate strengthening generates a minor contribution (3.5 HV). The model shows that less than 1% of the equilibrium volume fraction of TiC-precipitates forms during isothermal tempering at 550 degrees C due to the large misfit strain (1.34 GJ/m(3)) and a limited density of potential nucleation sites in the martensite. The model shows that the hardness of tempered martensitic steels could potentially be increased by increasing the TiC-precipitate density by reducing the misfit strain.

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.

Optimizing materials properties using modeling tools to simulate solidification and heat treatment

To read more about her, turn to page 8. To join TMS, visit www.tms.org/Society/Membership.aspx. Computer aided materials design has become increasingly important in mode rn materials design and development. Many modeling tools have been developed or are currently under development within the scope of Integrated Computational Materials Engineering (ICME). These modeling tools are used to understand the effects of alloy chemistry and processing conditions on the evolution of microstructure and ultimately mechanical properties, so that the materials performance can be “designed” and “optimized” even before the materials are produced. The following three papers demonstrate such efforts for the simulation of three different processes: solidifi cation, homogenization, and precipitation. The paper titled “Modeling of Alloy Casting Solidifi cation” by J. Guo and M. Samonds presents casting simulation of the solidifi cation process. As stated in the paper: “Alloy casting solidifi cation processes involve many physical phenomena such as chemistry variation, phase transformation, heat transfer, fl uid fl ow, microstructure evolution, and mechanical stress.” Two commonly used approaches for microscopic modeling of solidifi cation are reviewed; the deterministic method and the stochastic method. The deterministic method is used for the simulation of phase fraction, dendrite grain size, and the secondary dendrite arm spaces. The as-cast room temperature yield strength can be calculated based on the microstructure predicted. The cellular automaton (CA) model based on the stochastic method can be used to simulate the dendritic structure at different solidifi cation stages. Defects formed during the casting process, such as porosity, hot tearing, and macrosegregation were then discussed in the paper. The formation of these defects is found to be related to thermodynamics, fl uid fl ow, thermal, and/or stress, and all these factors are intertwined. Next, “An Integrated Computational Tool for Precipitation Simulation” by Weisheng Cao et al. presents an integrated computational thermodynamics and kinetics approach to simulate the microstructural evolution and the corresponding mechanical properties during the precipitation process. Three built-in precipitation models for microstructure simulation at multi-levels were discussed in the paper, which are the JMAK model (Johnson–Mehl– Avrami–Kolmogorov) for the estimation of the overall transformation rate, the fast-acting model based on the Langer and Schwartz theory for the simulation of the evolution of particle number density and mean size, and the more advanced KWN (Kampmann & Wagner Numerical) model for the predication of the full evolution of particle size distribution (PSD) in addition to average quantities. The modeling tools were applied to study a model Cubased alloy and a number of Ni-based superalloys to demonstrate its capability in microstructural simulation. This paper also discusses the integration of the microstructure information with strengthening models for the prediction of the age hardening behavior. Aluminum alloys (AA6XXX series) are used to demonstrate the application in this regard. The paper titled “Microstructural Modeling of the Homogenization Heat Treatment for AA3XXX Alloys” by Qiang Du et al. mainly discusses the microstructure evolution during homogenization of AA3XXX alloys. The model developed by the authors is fully coupled with thermodynamic calculation, and is able to simulate the reduction of the microsegregation formed during solidifi cation, the nucleation, growth and coarsening of intra-granular dispersoids, and the growth/dissolution of inter-granular constituent particles during the homogenization process of AA3XXX alloys. Simulation was performed for an AA3003 alloy to predict the microstructure change under different homogenization heat treatment conditions. With the positive experimental validations of the simulation results the authors concluded that the model has a potential to be used as a valuable tool for optimizing the heat treatment parameters of the AA3XXX alloys.