Mean-field modelling of the intermetallic precipitate phases during heat treatment and additive manufacture of Inconel 718

Abstract

A multi-phase, multi-component mean-field model has been developed for simulating the intermetallic precipitation kinetics in Inconel 718. The aim of this work is to develop predictive capability to aid in process optimisation and explore precipitation kinetics during additive manufacturing (AM). The model has been calibrated to available experimental data, and then applied to predict precipitation kinetics during typical solid solution treatment and aging operations, and during AM. It is shown that a Computer Coupling of Phase Diagrams and Thermochemistry (CALPHAD) based modelling approach provides a unified particle growth rate which can capture the growth, coarsening and dissolution of γ ′ , γ * and δ precipitates under relevant heat treatment conditions. To apply the model to AM, finite element simulations of a simple rectangular build have been carried out, using a property switching method to simulate the material deposition. The component level simulation provides the thermal fields to calculate precipitation kinetics during deposition, also allowing for the examination of the heat affected zone in the substrate. The modelling approach can capture the repeated nucleation and dissolution of precipitates that occurs during AM. The model shows good agreement with experimental data when applied to predicting precipitation kinetics during heat treatment.

On the Evolution of Primary Gamma Prime Precipitates During High Temperature and High Strain Rate Deformation and Subsequent Heat Treatment in the Ni-Based Superalloy, RR1000

“…The precipitation kinetics simulation that was employed in this study is a mean-field formulation of the Svoboda et al particle growth model in a super-saturated matrix, [38] which has been then adapted to use a fast-acting surrogate model for the phase Gibbs energy and the diffusivities and chemical potentials of the alloying elements vs temperature. [39] The model also considers the effect of misfit strain between the matrix and precipitate phase on the free energy of the system as well as a temperature-dependent interfacial energy. Previous studies on common powder alloys for disc rotor applications have established the initial value of this interfacial energy, [40] and recent internal Single-Sensor Differential Thermal Analysis (SSDTA) data have been used to finely calibrate the model to match the onset and completion of precipitation.…”

A computational study on the three-dimensional printability of precipitate-strengthened nickel-based superalloys

“…Taking these length scale differences into account, a mean-field description of the particle size distribution is a suitable method for describing precipitate phase evolution during solidification. precipitation is based on the multi-component approach described by Anderson et al [26] and further developed in [27] to simulate intermetallic precipitation of IN718 during SLM. The number of particles per volume at a time t with radius r lying in the range r ≤ r < r + dr is F(r, t) dr, where F(r, t) is the particle radius distribution.…”

“…The state variables are initialized to contain the initial precipitate dispersions. A user subroutine has been written to convert the state variables into the required information such as the precipitate size distribution functions, then normalize and reformulate the problem, and solve the continuity method shown in equation (3.4) using a finite difference scheme reported in Anderson et al [27]. Sub-stepping is used within the user state variable subroutine applying a Courant-Friedrichs-Lewy condition to determine the appropriate time step to evolve the dispersions.…”

“…Calibration of the mean-field model parameters for IN718 has been carried out by Anderson et al [27] and these have been used in predicting precipitation of γ , γ * and δ in the FE simulations of a rectangular SLM build. The γ * and δ phase precipitates are non-spherically shaped and this has been taken into account in the mean-field model as described in §3.…”

Predicting Precipitation Kinetics During the Annealing of Additive Manufactured Inconel 625 Components

“…This involves using multiple techniques to calculate the thermo-mechanical loading to allow for the prediction of precipitation during SLM. The mean-field model is presented in [6], and describes the application of mean-field modelling of the intermetallic precipitates in Inconel 718, which is similar to Inconel 625 with the addition of γ precipitates which form due to the larger Al and Ti content in the alloy. The model presented in this work includes refinements to the description of heterogeneous nucleation and modifications to capture the sluggish nucleation kinetics of γ and δ in Inconel 625.…”