Kampmann-Wagner Numerical Research Articles

Implementing numerical algorithms to optimize the parameters in Kampmann–Wagner Numerical (KWN) precipitation models

The Kampmann–Wagner Numerical (KWN) model of precipitation is a powerful tool to simulate the precipitation of the second phase considering the nucleation, growth, and coarsening. Some quantities such as interfacial energy and nucleation site number density are required to accomplish the simulation. Practically, those quantities are hard to measure in the experiment directly, and the derivation of those quantities through modeling can also be costly. In this work, we hereby adopt the minimization algorithm implemented in the open-source Scipy Python package to derive that important information in terms of very limited experimental data. The convergence and robustness of different algorithms are discussed. Among those algorithms, the Nelder–Mead and Powell algorithms are successfully applied to optimize multiple parameters during KWN modeling. This work will shed light on the design of experiments/processes and facilitate integrated computational materials engineering (ICME).

High-Precision Numerical Simulation Study of the Aging Precipitation Behavior in Al-Li Alloys Based on Improved Kampmann-Wagner Numerical (KWN) Model

High-Precision Numerical Simulation Study of the Aging Precipitation Behavior in Al-Li Alloys Based on Improved Kampmann-Wagner Numerical (KWN) Model

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 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

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.

Importance of Microstructure on Precipitation in Tempering of Martensitic Steels

Precipitation hardening is one of most effective strengthening mechanisms in steels, and much research has been performed in the past. To evaluate the contribution of precipitates, the quantitative features of precipitates including mean size and particle size distribution etc., are vital and needed. However, the predictive modeling of precipitation is still a challenge so far, especially on a quantitative level. Thus, in the present work, precipitation of carbides after tempering of martensitic Fe-Cr-C alloys, consisting of hierarchically arranged substructures within the prior-austenite grains, namely packets and blocks of individual laths, up to 1000h has been investigated. Experimental measurements using electron microscopy and modeling using a Langer-Schwartz theory with the Kampmann-Wagner -Numerical (KWN) method have been conducted. The importance of a proper definition of the initial microstructure for predictive modeling is discussed, in terms of the comparison of calculated and experimental results.

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.

TaC Precipitation Kinetics During Cooling of Co−Re‐Based Alloys

Cobalt−rhenium (Co−Re) alloys are developed for high‐temperature applications at ≈1200 °C and are strengthened by dispersion of nanosized tantalum carbide (TaC) precipitates. Herein, the precipitation behavior during cooling from supersolution depending on the cooling rate and the addition of chromium is presented. The phase composition (matrix phases and TaC) is analyzed from the wide‐angle neutron diffraction patterns measured in situ during temperature cycling. The precipitation of nanosized TaC particles is measured by in situ and ex situ neutron and X‐ray small‐angle scattering. The in situ measurements are used to extract the temperature‐dependent volume fraction of the precipitates; the final size distribution after cooling is extracted from the ex situ measurements. A Kampmann−Wagner's numerical (KWN) model is adapted to isochronal cooling processes. The in situ measurements give the unique possibility to calibrate the model parameters, whereas the ex situ measurements are used to assess the model predictions.

Modelling precipitation hardening in an A356+0.5 wt%Cu cast aluminum alloy

The behavior of a A356+0.5 wt%Cu alloy used to manufacture cylinder heads was studied. Samples were solutionized, quenched and aged at 200 °C for 0.1, 1, 10 and 100 h. TEM characterization showed that for the short aging durations (up to 10 h), the dominating hardening precipitates were β″ rods, while for the long aging duration (100 h), the dominance shifted to the Q-phase (Q′, Q″ precipitates). The length and diameter of the β″ rods were measured to produce size distributions which were later used to calibrate and validate the precipitation model. The physics-based precipitation kinetics model relies on classical nucleation/growth/coarsening equations adapted for the precipitation of Mg–Si precipitates in the aluminum matrix. Indirect coupling to Thermo-Calc software was used in order to determine the essential thermodynamic variables such as the driving force for precipitation and the solubility product for the model. Recent developments regarding the correction of the growth rate equations and the curvature effect were used to take into account the elongated morphology of precipitates. A Kampmann-Wagner Numerical (KWN) based model was used to track the evolution of the size distributions during nucleation, growth and coarsening of the β precipitates. The yield strength of the alloy was modelled using the Pythagorean sum of the contributions of intrinsic strength, solid solution strengthening and precipitation hardening. Both models showed good accuracy when compared to experimental results.

Modeling Precipitation Hardening and Yield Strength in Cast Al-Si-Mg-Mn Alloys

An integrated precipitation and strengthening model, incorporating the effect of precipitate morphology on precipitation kinetics and yield strength, is developed based on a modified Kampmann–Wagner numerical (KWN) framework with a precipitate shape factor. The optimized model was used to predict the yield strength of Al-Si-Mg-Mn casting alloys produced by vacuum high pressure die casting at various aged (T6) conditions. The solid solution strengthening contribution of Mn, which is a common alloying element to avoid die soldering, was included in the model to increase the prediction accuracy. The experimental results and simulations show good agreement and the model is capable of reliably predicting yield strength of aluminum die castings after T6 heat treatment, providing a useful tool to tailor heat treatment for a variety of applications.

Modelling grain growth with the generalized Kampmann-Wagner numerical model

The multi-phase Kampmann-Wagner Numerical (KWN) model, which had been successfully applied for modeling particle precipitation (i.e. Ostwald ripening), is extended toward grain growth modeling. The extensions consist of adopting grain topology- and size-dependent growth rate equation obtained from either the reported parameterization of phase field simulations results or theoretical analysis. Global volume conservation equation is imposed in the extended model to reflect the spacing filling constraints that grains do not overlap and no voids appear. The extended model has been applied to simulate ideal grain growth, grain growth with the initial states of lognormal/normal/Weibull distributions, bi-modal grain size distribution and arbitrary Voronoi tessellations, and the simulation results have been verified by Hillert's asymptotic solution and phase field simulation results. The extension has enabled the KWN approach applicable to model grain growth thus reducing the threshold for the establishment of an efficient Integrated Computational Materials Engineering modeling framework.

Model for Inclusion Precipitation Kinetics During Solidification of Steel Applications in MnS and TiN Inclusions

A simulation model for inclusion precipitation kinetics during solidification of steel was proposed in this work. With the aim to calculate the inclusion size distribution during solidification of steel, the microsegregation calculation combined with the Kampmann–Wagner numerical (KWN) model for nucleation and growth of inclusion was incorporated into the present simulation model for calculating the evolution of inclusion size distribution during solidification of steel. The inclusion agglomeration due to Brownian collisions was also taken into account. The present simulation model was first applied in simulating precipitation of MnS during steel solidification and validated by the experimental data available in the literature. The effects of cooling rates and sulfur concentrations on the precipitation of MnS were investigated by the model calculations. Then, the present simulation model was applied in simulating the precipitation of TiN inclusions during steel solidification. The calculated mean size was found to be in good agreement with data available in the literature. Finally, the model was employed for studying the effects of interfacial tension between TiN and steel due to sulfur concentration change and cooling rates on the inclusion precipitation kinetics. It was found that interfacial tension between TiN and steel has a crucial influence on the precipitation of TiN. With an increase of the cooling rate, the size distribution of TiN transforms from the lognormal distribution to the bimodal distribution.

High-Throughput and Systematic Study of Phase Transformations and Metastability Using Dual-Anneal Diffusion Multiples

This article highlights the capabilities of dual-anneal diffusion multiples (DADMs) in performing high-throughput and systematic studies of phase transformations and metastability. DADMs create wide ranges of solid solution compositions through elemental interdiffusion during a first anneal at a high temperature. After quenching to ambient temperature, each diffusion multiple can be cut into several slices, and each slice is further annealed individually at a lower/second temperature. Phase transformations take place in the supersaturated regions of the solid solution compositions that are formed during the first anneal, leading to various precipitates due to different driving force, interfacial energy, and other factors as composition varies across the regions in the sample. By subjecting the sliced diffusion multiples individually to different anneal durations and different second anneal temperatures, very large datasets can be collected on phase transformation kinetics and evolution of precipitate morphology as a function of composition, time, and temperature. Metastable phases and their transitions to more stable phases have been systematically observed in the Fe-Cr-Mo ternary system across a wide range of composition, temperature, and anneal time, thus providing a large amount of information on metastability of the phases. The solvi of the metastable and stable phases can be systematically collected for more reliable CALPHAD assessments of the Gibbs free energy of the metastable phases. By adjusting the interfacial energy value in simulations using models such as the Kampmann–Wagner Numerical (KWN) model and matching the simulated precipitate sizes at different compositions with experimentally measured sizes of the corresponding compositions in a DADM, the interfacial energy value can be obtained. Opportunities and challenges in using DADMs to collect large datasets on precipitation kinetics and morphology will be explained to enable full utilization of the capabilities of DADMs in the future. This review not only presents experimental results collected to date, but also explains the vast more datasets that can be collected from DADMs in the future. An approach that iteratively and holistically integrates experimental results with model predictions is advocated as a very effective means to advance the understanding of various phase transformation mechanisms. In this way, the new mechanistic understanding can be integrated to more robust models to simulate the “abnormal” behaviors that are observed in DADMs, especially related to sequential precipitations of phases that are common in engineering alloys. Examples are also shown to illustrate the systematic nature of DADMs as a result of their continuously varying composition regions in catching unusual phenomena and emergent trends that are easily missed during studies using discrete compositions afforded by individual alloys.

Challenges and opportunities in thermodynamic and kinetic modeling microalloyed HSLA steels using computational thermodynamics

Most High Strength Low-Alloy (HSLA) steels rely on the control of the carbonitrides of Ti, Nb and V to achieve their properties. To properly control the distribution and size of precipitates the knowledge of the thermodynamics of the Fe–C–N-(Ti,Nb,V) systems is essential. Furthermore, understanding the kinetics of dissolution and precipitation of the carbonitrides is fundamental to properly design these steels and their processing. In this work, we emphasize Ti and Nb behavior in HSLA steels. First, the thermodynamic information concerning the stability of their carbonitrides in steel is reviewed, highlighting the difficulties associated with the variable C/N ratio of the carbonitrides and with the fact that there is also miscibility between Ti, Nb and V in the carbonitrides of the “NaCl” structure. These difficulties make the use of the compound energy formalism (CEF) and of computational thermodynamics extremely recommended. To demonstrate this, some frequently used solubility products are compared to results obtained with current computational thermodynamics databases. Currently, many efforts have been made to model the kinetics of dissolution and precipitation of these particles in steel. We focus on the potential advantages of using computational thermodynamics methods both for diffusion and for nucleation, growth and coalescence, in special using software based on Kampmann-Wagner numerical (KWN) theory. The potential of these methods is demonstrated in some selected applications. We emphasize the importance of interfacial energy in these models. Frequently the interfacial energy is used as an adjustable parameter in these models. Even when this is done, the models can be very useful for steel and process design, as long as the user is aware of the limitations associated to the adjustment.

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.

Influence of retained austenite and Cu precipitates on the mechanical properties of a cold-rolled and intercritically annealed medium Mn steel

A low carbon Cu-bearing medium-Mn steel (Fe-0.05C-5.7Mn-1.9Cu-2.0Ni-0.4Si) was cold rolled and then intercritically annealed (IA) between 640 °C and 680 °C for 180 s. Ultrafine multi-phase microstructure (∼300 nm grain size) was obtained in this single short time annealing, composed of recovered martensite, fresh martensite, more than 20% retained austenite and copious (1022 m−3) nanosized (∼6 nm in radius) Cu precipitates. A good combination of strength (YS (yield strength) of 1037 MPa and UTS (ultimate tensile strength) of 1210 MPa) and ductility (19% UEL (uniform elongation) and 23% TEL (total elongation)) was obtained at an annealing temperature of 640 °C, with the former enhanced by Cu precipitates, ∼200 MPa, and the latter, improved by significant fraction of stable retained austenite. The microstructure was studied by SEM (scanning electron microscope), TEM (transmission electron microscopy) and XRD (X-ray diffraction). It is observed that Cu precipitates distribute heterogeneously in the amount of Cu precipitates adjacent to martensite/retained austenite interface obviously higher than that predicted based on the average bulk composition. According to thermodynamic analysis through Thermo-calc, DICTRA and Kampmann–Wagner Numerical (KWN-) simulation, the influence of Mn, Ni and Si on the bcc (body-centered cubic) miscibility gap shows that the precipitation of Cu particles could be facilitated by Si, a ferrite stabilizer, and inhibited by the presence of Mn and Ni, both austenite stabilizers. As a result, Cu precipitation is promoted in the diffusion zone formed during IA adjacent to martensite/retained austenite interface.

Precipitation and strengthening modeling for disk-shaped particles in aluminum alloys: Size distribution considered

For an ICME (Integrated Computational Material Engineering) modeling framework used for the age-hardening aluminum alloy design and heat treatment parameters optimization, it is critical to take into account the geometric shape of precipitates, as it is tightly related to the precipitation kinetics and particles' hardening effect. The aim of this paper is to present such an ICME modeling approach to describe the precipitation of disk-shaped hardening particles during aging treatment and predict the final yield strength. The classical Kampmann–Wagner Numerical (KWN) model is extended to consider the influence of disk-shaped particle morphology on growth kinetics. The extension consists of two correction factors to the growth rate equation and to the Gibbs-Thomson effect. The extended model, coupled with a metastable thermodynamic database, is applied to simulate precipitation kinetics of Al-Cu and Al-Mg-Zn alloys during aging treatment. The predicted microstructural features are in reasonable agreement with the reported experimental observations. Furthermore, a strengthening model for disk-shaped particles, which considers the size distributions of precipitates, is developed. The predicted yield strengths are compared with reported tensile test results and with predictions from other strength models. Unlike other models, the proposed strength model can reveal the strength contribution from disk-shaped precipitates without an additional tuning parameter for accounting for the impact of the mean particle spacing in the slip plane.

Effective evaluation of interfacial energy by matching precipitate sizes measured along a composition gradient with Kampmann-Wagner numerical (KWN) modeling

A dual-anneal diffusion multiple was utilized to generate a composition gradient via a first anneal at a high temperature followed by a second anneal at a lower temperature to induce phase precipitation as a function of composition/supersaturation. By adjusting the interfacial energy value in simulations using the classical nucleation and growth theories as implemented in the Kampmann-Wagner numerical (KWN) model and matching the simulated average precipitate sizes at different compositions with the experimental measurements along the composition gradient, the Ni3Al/fcc interfacial energy in the Ni-Al system at 700 °C was effectively determined to be ~12 mJ/m2.