Numerical simulation of precipitation in multicomponent Ni-base alloys

A comprehensive particle size distribution model has been developed for the simulation of gamma' precipitation in multicomponent Ni alloys. Nucleation, growth and coarsening of the precipitates are described by a particle size distribution. The growth rate of each precipitate class is calculated with a multi-component diffusion model formulated for non-diagonal matrices of diffusion coefficients. The model is fully coupled with CALPHAD calculations of the thermodynamic equilibrium at the interface, including a direct treatment of the effect of curvature through modification of the Gibbs free energy. An optimization strategy was developed to minimize the computational cost. The model was used to simulate ageing heat treatment at 600 degrees C of Ni-7.56 at.% Al-8.56 at.% Cr, which was studied experimentally by Booth-Morrison and others (Booth-Morrison C, Weninger J, Sudbrack CK, Mao Z, Noebe RD, Seidman DN. Acta Mater 2008;56:3422; Mao Z, Booth-Morrison C, Sudbrack CK, Martin G, Seidman DN. Acta Mater 2012;60:1871). The comparisons showed that the precipitation stages of gamma' precipitates are correctly captured by the numerical model. It was shown that non-diagonal diffusion coefficients substantially influence the selection of the operating tie-line and the overall transformation kinetics. With non-diagonal diffusion matrices, complex phenomena such as uphill diffusion of Cr due to the Al gradients were evidenced and explained. (C) 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Simulation de la formation des microstructures dans les superalliages à base de nickel de type AM1 durant la solidification et les traitements thermiques

Luc Rougier

Nickel base superalloys are used for the manufacturing of monocrystalline turbine blades, due to their outstanding mechanical properties at high temperature. The mechanical properties strongly depend on the presence of γ’ precipitates in the γ matrix. Improper size or spatial distribution of the precipitates is one of the possible defects that can appear during the processing of turbine blades. In order to anticipate such defects and optimize the processes, numerical simulation can be used to predict the formation and evolution of precipitates as a function of the alloy chemistry and heat treatment conditions. Numerical models can also be used to analyze the influence of microsegregation, which develops during solidification and does not entirely disappear during the solution heat treatment. A modeling approach has been developed to simulate the formation of microstructure in AM1-type nickel based superalloys during the main processing steps. Two distinct numerical models were developed for the simulation of microsegregation, on one hand, and precipitation on the other hand. An existing microsegregation model [1] was modified to take into account important specificities of Ni-base superalloys, such as non-diagonal matrices of diffusion coefficients. The model was applied to several alloys to predict the evolution of the composition profiles, and the formation/dissolution of interdendritic phases during solidification and the solution heat treatment. A new precipitation model was developed in order to predict the formation and evolution of γ' precipitates during heat treatment [2]. The model is based on the description of the precipitate size distribution, which is tracked based on nucleation and growth laws, taking into account coarsening through the Gibbs-Thomson effect. The time evolution of average quantities, such as the average radius, the number density of precipitates and volume fraction is deduced from the particle size distribution. The model is coupled to the phase diagram software Thermo-Calc, which makes it possible to calculate equilibrium concentrations and nucleation driving force in multicomponent industrial alloys. The coupling to Thermo-Calc is also exploited to compute the effective diffusion coefficients from a mobility database. The microsegregation and precipitation models were applied to ternary Ni-Al-Cr alloys and to the industrial CMSX-4 and AM1 superalloys. The results of the simulations were compared with experimental data collected from the literature and atom probe tomography measurements carried out during the project. The simulation results showed to be globally in good agreement with the experiments. The accuracy of the thermodynamic database turned out to be one of the most important factors for quantitative prediction, in particular for precipitation. Chained simulations were performed on Ni-Al-Cr and AM1 alloys in order to assess the sensitivity of precipitation kinetics with respect to microsegregation. The calculations showed that the radius, volume fraction and number density of precipitates are substantially influenced by the residual segregation in industrial heat treatments. The effect of residual segregation on precipitation kinetics decreases however during coarsening at long ageing times. In summary, the simulation approach developed in this project allows for the formation of microstructures in industrial Ni-based superalloys to be analyzed in detail. The application of chained microsegregation and precipitation calculations to AM1 superalloys permitted to analyze the influence of the solidification conditions on the microstructure after heat treatment.

EPFL2013

Numerical Simulation of Solidification, Homogenization, and Precipitation in an Industrial Ni-Based Superalloy

Charles-André Gandin, Alain Jacot, Luc Rougier

A comprehensive simulation approach integrating solidification, homogenization, and precipitation during aging has been used to predict the formation of gamma/gamma' microstructures in the AM1 nickel-based superalloy. The particle size distribution of intradendritic gamma' precipitates after aging was calculated with a multicomponent diffusion model coupled with CALPHAD thermodynamics for the equilibrium at the interface. The influence of residual microsegregation after homogenization and quenching was analyzed through different initial conditions obtained from calculations of the concentration profiles in the primary gamma dendritic microstructure during solidification and the homogenization heat treatment. While the global sequence of precipitation remains qualitatively the same, substantial differences in the final volume fraction of gamma' precipitates were predicted between the core and the periphery of a former dendrite arm, for typical homogenization and aging conditions. To demonstrate the relevance of the developed simulation approach, the model was also used to investigate modified precipitation heat treatments. The simulations showed that relatively short heat treatments based on slow continuous cooling could potentially replace the extended isothermal heat treatments which are commonly used. Slow continuous cooling conditions can lead to similar gamma' precipitates radii and volume fractions, the main differences with isothermal heat treatments lying in a narrower particle size distribution.

Springer2016

Numerical simulation of microstructure formation during solidification and heat treatments of Ni-base superalloys

Paolo Di Napoli, Charles-André Gandin, Alain Jacot, Luc Rougier

A comprehensive modelling approach has been developed for the simulation of microstructure formation during solidification and heat treatment in Ni-base superalloys. The microsegregation taking place during solidification is simulated using the pseudo-front tracking (PFT) technique. This finite volume method calculates the concentration profiles in primary γ and the proportion of liquid and γ′ in the interdendritic regions. The same model is then used to describe the dissolution of the interdendritic γ′ particles during the subsequent solution heat treatment. The concentrations in primary γ predicted with the PFT model are then used to calculate the evolution of the γ′ precipitates and their size distributions at different locations in a dendrite arm during heat treatment. This is achieved with a precipitate size distribution (PSD) model. The classes of the distribution are created and tracked based on classical nucleation theory and a semi-analytical model for the growth of the precipitates as a function of their radius and the matrix supersaturation. The PFT and PSD models are both coupled with Thermo-Calc, which is used for the computation of the concentrations at the γ/liquid and γ/γ′ interfaces, for the Gibbs-Thomson effect in precipitates, and to calculate non-diagonal diffusion matrices based on a mobility database. The precipitation model was applied to a Ni-Al-Cr alloy and the results were compared with experimental data from the literature. Experimental and simulation results are in good qualitative agreement. The main phenomena taking place during precipitation, i.e. nucleation, growth and coarsening, are well reproduced by the precipitation model. Some discrepancies were observed on the precipitate number density, which were attributed to the homogeneous nucleation model. The full modelling sequence was then applied to Ni-Al in order to assess the influence of an incomplete homogenization heat treatment on the formation of γ′ precipitates.