This work investigates the influence of Mg–Zn–Ca alloy compositions and rapid cooling conditions on microstructural evolution, with a focus on the formation and behaviour of intermetallic phases such as Mg 2 Ca, MgZn, and Ca 2 Mg 6 Zn 3 during solidification. To achieve this, a combination of experimental characterisation and computational modelling was employed. The Scheil model, extended to ternary alloy systems, was used to simulate micro-segregation during solidification, while a multicomponent mean-field model was applied to predict solid-state phase transformations and the evolution of second-phase particles. CALPHAD-based thermodynamic calculations were integrated to refine the prediction of segregation pathways and phase distributions under non-equilibrium conditions. The model successfully differentiates solidification paths based on alloy composition, predicting that Mg–0.8Zn–0.2Ca (wt%) first forms Mg 2 Ca phase segregation, whereas Mg–6.8Zn–0.2Ca (wt%) primarily segregates MgZn. Experimental validation using SEM–EDS characterisation confirms these predictions. Finally, intermetallic phase formation diagrams under different solidification conditions are presented, providing insights into the control of intermetallic phase formation in Mg–Zn–Ca alloys.

This study aims to utilize a combined machine learning (ML) and CALculation of PHAse Diagrams (CALPHAD) methodology to design hardmetal matrix phases for metal-forming applications that can serve as the basis for carbide reinforcement. The vast compositional space that high entropy alloys (HEAs) occupy offers a promising avenue to satisfy the application design criteria of wear resistance and ductility. To efficiently explore this space, random forest ML models are constructed and trained from publicly available experimental HEA databases to make phase constitution and hardness predictions. Interrogation of the ML models constructed reveals accuracies >78.7% and a mean absolute error of 66.1 HV for phase and hardness predictions respectively. Six promising alloy compositions, extracted from the ML predictions and CALPHAD calculations, are experimentally fabricated and tested. The hardness predictions are found to be systematically under- and overpredicted depending on the alloy microstructure. In parallel, the phase classification models are found to lack sensitivity toward additional intermetallic phase formation. Despite the discrepancies identified between ML and experimental results, the fabricated compositions show promise for further experimental evaluation. These discrepancies are believed to be directly associated with the available databases but, importantly, have highlighted several avenues for both ML and database development.

The gamma' precipitate coarsening kinetics in additively manufactured Ni-based superalloys needs to be investigated to predict the microstructure stability at high temperature. Therefore, we investigate the gamma' precipitate coarsening kinetics in a laser powder bed fusion IN738LC Ni-based superalloy at 900 degrees C. We find that the initial bimodal gamma' precipitate size distribution at 24 h of ageing time changes to unimodal distribution at 168 h of ageing time at 900 degrees C. We perform the mean-field modelling to understand the transition physics using gamma-gamma' composition and gamma' volume fraction obtained using atom probe tomography and find that the modelling results are consistent with the experimental observation. Based on the modelling, we found that the gamma' volume fraction is an important parameter in the mean-field modelling, which is slightly higher than the equilibrium value due to the non- equilibrium composition of gamma-gamma' phases in the additively manufactured superalloy. Furthermore, the gamma/gamma' interfacial energy is predicted to increase from bimodal to unimodal distribution due to an increase in Ti/Al ratio in gamma' precipitate, which increases the gamma' precipitate coarsening kinetics. It is also found that the gamma/gamma' interfacial energy and z factor have more influence on the gamma' precipitate coarsening kinetics than the mobility parameter in additively manufactured IN738LC. In conclusion, the gamma' precipitate coarsening kinetics in additively manufactured Ni-based superalloy is predicted to be slightly faster than the alloy with equilibrium composition of phases.

Automated stereological methods are presented for approximating the 3D size distribution of unimodal or bimodal precipitate dispersions considering 2D and 1D measurements taken from polydisperse spherical non-penetrating particle dispersions. A method to quantify the uncertainty of the approximation as a function of the number of sampled particles is presented and demonstrated to experimental data. The derivation and verification of the analytical stereological expressions used are included. Two procedures are presented for estimating the 3D size distribution of bimodal particle populations depending upon the relative size of the two particle populations. If the particles can be characterised using micrographs of the same magnification, it is possible to estimate the volume fraction of each particle population. For cases where micrographs have been taken at different magnification, an estimate of the area fractions of the particle populations is needed to combine the datasets and allow for the approximation of the 3D size distribution. These methods are useful for use in determining the initial particle size distribution for use in modelling and determining the appropriate number of micrographs and particles to measure when characterising a precipitate dispersion.

In this work a novel mathematical framework, that fully describes the fusion and vapourisation state transitions in multi-component systems, has been applied to assist in understanding the fundamental mechanisms of defect formation and chemical homogenisation in the laser powder bed fusion process (L-PBF). Specifically, the role of vapourisation and condensation of the multi-component metallic substrate is investigated to determine the importance of properly capturing the state transitions when understanding the substrate evolution. The framework is applied to a ternary metallic system; it is revealed that entrained vapour bubbles in chemically dissimilar flows promote greater homogenisation during the condensation and collapse of these bubbles when compared to non-condensing phases. It is further shown that as the laser power density is increased, there is a greater tendency for preferential element evaporation of the lighter elements; this preferential element evaporation is quantified numerically for the first time, and shown to be a non-linear function of power density.

The ability to accurately predict the time evolution of precipitate size distributions is fundamental to optimising heat treatments and mechanical properties of engineering alloys. Mean-field models of the particle growth rates assume that diffusion fields between neighbouring particles are weakly coupled reducing the problem to a single particle embedded in an effective medium. This regime of behaviour is expected to be satisfied for low volume fraction alloys. However, these assumptions are not fulfilled in many applications of interest where strong interactions between precipitates holds. Correction factors are often introduced to account for the accelerated rate of diffusion caused by the overlapping of diffusion fields between neighbouring precipitates. This paper applies the Wang–Glicksman–Rajan–Voorhees (WGRV) discrete point-source/sink model to compare descriptions of competitive growth. This includes assessing correction factors to the mean-field particle growth rate derived by Ardell, Marqusee and Ross, and Svoboda and Fischer in addition to Di Nunzio’s pairwise interaction model. The WGRV model is used as a benchmark to compare different approximations of competitive growth that apply similar assumptions. This is followed by the application of the models to simulate precipitation kinetics during long term aging kinetics observed in the nickel-based superalloys IN738LC and RR1000. It is shown that the competitive growth correction factors are accurate for volume fractions of 20% and under-predict the acceleration of precipitate kinetics predicted at 40%. The WGRV model is able to capture the coarsening kinetics observed in both IN738LC and RR1000 with reasonable accuracy. The WGRV model determines particle growth rates as a function of the immediate neighbourhood and provides an improved prediction of the coarsening behaviour of tertiary particles in RR1000 in comparison to the mean-field approximation, however over-estimates the growth rate of the tertiary particles compared to experimental data.

This article elucidates the need to consider the inherent spatial transfer function (blur), of any thermographic instrument used to measure thermal fields. Infrared thermographic data were acquired from a modified, commercial, laser-based powder bed fusion printer. A validated methodology was used to correct for spatial transfer function errors in the measured thermal fields. The methodology was found to make a difference of 40% to the measured signal levels and a 174 °C difference to the calculated effective temperature. The spatial gradients in the processed thermal fields were found to increase significantly. These corrections make a significant difference to the accuracy of validation data for process and microstructure modeling. We demonstrate the need for consideration of image blur when quantifying the thermal fields in laser-based powder bed fusion in this work.

A theoretical treatment on the oxide-controlled dwell fatigue crack growth of a γ ’ strengthened nickelbased superalloys is presented. In particular, this study investigates the influence of an externally applied load and variations in the γ ’ dispersion on the grain boundary oxide growth kinetics. A dislocation-based viscoplastic constitutive description for high temperature deformation is used to simulate the stress state evolution in the vicinity of a crack at elevated temperature. The viscoplastic model explicitly accounts for multimodal γ ’ particle size distributions. A multicomponent mass transport formulation is used to simulate the formation/evolution of an oxide wedge ahead of the crack tip, where stress-assisted vacancy diffusion is assumed to operate. The resulting set of constitutive and mass transport equations have been implemented within a finite element scheme. Comparison of predicted compositional fields across the matrix/oxide interface are compared with experiments and shown to be in good agreement. Simulations indicate that the presence of a fine γ ’ size distribution has a strong influence on the predicted ow stress of the material and consequently on the relaxation in the vicinity of the crack-tip/oxide wedge. It is shown that a unimodal dispersion leads to reduced oxide growth rates（parabolic behavior） when compared to a bimodal one. Stability conditions for oxide formation are investigated and is associated with the prediction of compressive stresses within the oxide layer just ahead of the crack tip, which become progressively negative as the oxide wedge develops. However, mechanical equilibrium requirements induce tensile stresses at the tip of the oxide wedge, where failure of the oxide is predicted. The time taken to reach this critical stress for oxide failure has been calculated, from which dwell crack growth rates are computationally derived. The predicted rates are shown to be in good agreement with available experimental data.

The precipitation kinetics of gamma prime in the nickel based superalloy RR1000 has been characterised after solid-solution heat treatments and isothermal aging conditions relevant to service conditions. Multimodal precipitate dispersions are formed within the alloy. Numerical methods are presented for determining the three dimensional size of the particle populations combining information obtained from Scanning Electron microscopy and Transmission Electron microscopy. This information has been used to develop a multicomponent mean-field model descriptive of precipitation kinetics. The smallest particle population increases in mean size during isothermal aging at 700 BC where classical mean-field models of coarsening kinetics suggest that these particles should dissolve. A phenomenological model has been proposed to capture this behaviour within a statistical formulation that is applicable to both processing and service conditions. (C) 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The prediction of solidification microstructures associated with additive manufacture of metallic components is fundamental in the identification scanning strategies, process parameters and subsequent heat treatments for optimised component properties. Interactions between the powder particles and the laser heat source result in complex thermal fields in and around the metal melt pool, which will influence the spatial distribution of chemical species as well as solid-state precipitation reactions. This paper demonstrates that a multi-component, multi-phase precipitation model can successfully predict the observed precipitation kinetics in Inconel 625, capturing the anomalous precipitation behaviour exhibited in additively manufactured components. A computer coupling of phase diagrams and thermochemistry (CALPHAD)-based approach captures the impact of dendritic segregation of alloying elements upon precipitation behaviour. The model was successful in capturing the precipitation kinetics during annealing considering the Nb-rich and Nb-depleted regions that are formed during additive manufacturing.

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.

This paper presents a computational framework to study the differences in process-induced microvoid and precipitate distributions during selective laser melting (SLM) of two nickel-based superalloys representative of low (IN718) and high (CM247LC) volume fraction precipitate-strengthened alloys. Simulations indicate that CM247LC has a higher propensity to form process-induced microvoids than IN718. Particle sintering is predicted to be strongly influenced by the powder size distribution. For deposition thickness of approximately 40 μm, thermal gradients during cooling are predicted to be larger for CM247LC than IN718 and consequently expect the development of larger residual stresses for a high volume fractionγ′ alloy. A coupled mean field/finite-element approach has been used to predict the precipitate distributions across a simple rectangular build and during a subsequent hot isostatic pressing (HIP) cycle. Unimodal and multi-modal particle distributions are predicted for IN718 and CM247LC at the end of the SLM, respectively. A higher volume fraction ofγ′ is predicted for CM247LC at the end of the SLM process. During HIP, simulations indicate a dramatic increase in theγ′ volume fraction in CM247LC, which can result in a reduction in stress relaxation and lead to a ductility drop.

In this paper, an integrated computational materials science approach for selective laser melting (SLM) at the mesoscale is presented. A particle dropping model was developed to simulate the representative powder-bed particle distribution of a measured titanium alloy powder. Thermal fluid flow and resulting microstructural evolution of a set of laser scanned single tracks with different powder layer thicknesses and scanning speeds during SLM were also studied using both computational and experimental approaches. The simulated powder particle distribution was found to be consistent with experimental measurement. The thermal fluid flow model predicts that single laser scanned tracks become increasingly irregular-shaped with increased powder layer thickness and increased laser scanning speed. These findings were reinforced by scanning electron microscopy analysis. The more dispersed dissipation of the localised heat for thicker powder layers is understood to cause increased melting and evaporation. This can lead to increased Marangoni force and recoil pressure which in turn destabilises the melt flow. The use of an argon atmosphere speeds up the solidification process when compared with air but does not affect the morphology of single tracks significantly. The predicted microstructure was consistent with the electron backscattered diffraction data. The microstructure-based modelling methodology considering the representative powder size distribution provides a good predictive capability for the laser-powder interaction behaviour, surface structure and porosity development.

A multi-scale, multi-physics modelling framework of selective laser melting (SLM) in the nickel-based superalloy IN718 is presented. Representative powder-bed particle distribution is simulated using the measured size distribution from experiment. Thermal fluid dynamics calculations are then used to predict melting behaviour, sub-surface morphology, and porosity development during a single pass scanning of the SLM process. The results suggest that the pores and uneven surface structure are exacerbated by increasing powder layer thicknesses. Predicted porosity volume fraction is up to 12% of the single track when 5 statistical powder distributions are simulated for each powder layer thickness. Processing-induced microstructure is predicted by linking cellular automatons - finite element calculations indicate further that the cooling rate is about 4400 degrees C/s and grain growth strongly follows the thermal gradient giving rise to a columnar grain morphology if homogeneous nucleation is assumed. Random texture is likely for as-fabricated SLM single pass with approximately 8 mu m and 6 mu m grain size for 20 mu m and 100 mu m powder layer thickness fabrication. Use has been made of the cooling history to predict more detailed microstructure using a gamma" precipitation model. With the short time scale of solidification and rapid cooling, it becomes less likely that gamma" precipitation will be observed in the condition investigated unless a prolonged hold at temperature is carried out. Future work on extension of the proposed multiscale modelling approach on microstructure predictions in SLM to mechanical properties will be discussed.

A multi-component mean field model has been applied to predict the particle evolution of the γ′ particles in the nickel based superalloy IN738LC, capturing the transition from an initial multimodal particle distribution towards a unimodal distribution. Experiments have been performed to measure the coarsening behaviour during isothermal heat treatments using quantitative analysis of micrographs. The three dimensional size of the γ′ particles has been approximated for use in simulation. A coupled thermodynamic/mean field modelling framework is presented and applied to describe the particle size evolution. A robust numerical implementation of the model is detailed that makes use of surrogate models to capture the thermodynamics. Different descriptions of the particle growth rate of non-dilute particle systems have been explored. A numerical investigation of the influence of scatter in chemical composition upon the particle size distribution evolution has been carried out. It is shown how the tolerance in chemical composition of a given alloy can impact particle coarsening behaviour. Such predictive capability is of interest in understanding variation in component performance and the refinement of chemical composition tolerances. It has been found that the inclusion of misfit strain within the current model formulation does not have a significant affect upon predicted long term particle coarsening behaviour. Model predictions show good agreement with experimental data. In particular, the model predicts a reduced growth rate of the mean particle size during the transition from bimodal to unimodal distributions.

In this paper, an integrated computational materials science approach for selective laser melting (SLM) at the mesoscale is presented. A particle dropping model was developed to simulate the representative powder-bed particle distribution of a measured titanium alloy powder. Thermal fluid flow and resulting microstructural evolution of a set of laser scanned single tracks with different powder layer thicknesses and scanning speeds during SLM were also studied using both computational and experimental approaches. The simulated powder particle distribution was found to be consistent with experimental measurement. The thermal fluid flow model predicts that single laser scanned tracks become increasingly irregularshaped with increased powder layer thickness and increased laser scanning speed. These findings were reinforced by scanning electron microscopy analysis. The more dispersed dissipation of the localised heat for thicker powder layers is understood to cause increased melting and evaporation. This can lead to increased Marangoni force and recoil pressure which in turn destabilises the melt flow. The use of an argon atmosphere speeds up the solidification process when compared with air but does not affect the morphology of single tracks significantly. The predicted microstructure was consistent with the electron backscattered diffraction data. The microstructure-based modelling methodology considering 1 the representative powder size distribution provides a good predictive capability for the laserpowder interaction behaviour, surface structure and porosity development.

The dies used in the extrusion of nickel based super alloys are subject to severe mechanical and thermal stresses, resulting in shortened life and high manufacturing costs. It is necessary to understand the dominant damage mode in order to guide improvements for increased tool life. The operation under examination consists of the hot extrusion of a nickel based superalloy using nitrided hot work tool steel, glassed workpieces and graphite lubrication. The investigation was conducted through a combination of metallurgical analysis, metrology and finite element analysis. Out of the damage modes observed under these conditions, the plastic deformation of the substrate was found to be the cause for tool failure. This paper discusses the relationship between plastic deformation of the substrate and the formation of scoring marks, which fail the die.