Thermal and Mechanical interplay in Microstructural evolution of Al3X precipitates (X = Sc, Zr, Er) in binary Aluminium alloy: An integrated Phase-field simulations and ab initio study

Abstract

Thee microstructural changes resulting from the addition of trace amounts of Sc, Zr, and Er to aluminium are not comprehensively addressed in the current archival literature. The Al-X (X=Sc, Zr, Er) alloy exhibits broad application potential as it forms trialuminides like Al3X (X=Sc, Zr, Er), which confer remarkable thermal stability to the alloy. Furthermore, its low density, high specific strength, and excellent oxidation resistance, similar to the γ′ Ni3Al (L12) ordered precipitates in Ni-based alloys, make it an excellent candidate for use in automobile and aerospace manufacturing. In this alloy, precipitates often exhibit a variety of morphologies, which are influenced by specific heat treatment conditions. Many studies fail to consider the complex interplay between thermal, mechanical, and chemical factors during precipitation, nucleation, and coarsening in heat treatment. For instance, the generation of internal stresses and their correlation with various factors are not adequately accounted for in these alloys, primarily due to experimental limitations in quantifying such stresses. Additionally, the intricate relationship between the material's elastic properties and chemical kinetics can explain several discrepancies in the observed changes in precipitate morphology across different studies, which is a relatively less explored aspect. This thesis seeks to bridge this gap by investigating the complex relationships between the chemical mechanical and thermal factors and their impact on the Al-X (X=Sc,Zr,Er) alloy's microstructure. The generation of misfit, a key characteristic of coherent precipitate evolution, is highly significant in the microstructure as it leads to the generation of internal stresses during precipitate coarsening. These internal stresses interact with dislocations, obstructing their motion and playing a crucial role in material reinforcement. Factors such as the difference in thermal expansion coefficients between the matrix and precipitate, the presence of transition metal impurities in solid solution, and the occurrence of vacancies are pivotal in determining the lattice misfit between the precipitate and matrix. Understanding the generation of these internal stresses and their correlation with the aforementioned factors is crucial for accurately predicting the final precipitate morphologies and resulting microstructure. An essential consideration during any solid-state transformations is that, despite their independent influences, the concentration and stress/strain gradients surrounding precipitates exhibit substantial overlap, exerting mutual influence during nucleation, growth, and ripening. This interdependence is termed "chemomechanical" coupling. Consequently, similar to composition changes induced by precipitate growth, variations in composition may also arise due to internal stress. This effect can elucidate many of the discrepancies observed in the reported microstructures of several systems. In this context, theoretical studies hold substantial relevance. The phase-field approach has emerged as a potent method for modeling various microstructure evolution processes. Among the different phase-field models, the multiphase field model has demonstrated significant potential in studying microstructure evolution in the solid state. By effectively employing numerical simulations using a multiphase field model and incorporating phenomena such as the temperature dependence of lattice misfit and composition dependence of elastic constants into the model, the various microstructural characteristics during precipitate coarsening can be thoroughly investigated. A suitable mathematical model is incorporated into the multiphase field simulation to account for the temperature-dependent nature of lattice misfit. To establish the dependency of elastic constants on the alloy composition, ab-initio calculations are performed. Both of these aspects are considered in the present study with the aim of resolving discrepancies in precipitate morphology observed in the Al-X (X=Sc, Zr, and Er) alloy. Additionally, an in-depth analysis of various microstructural features during precipitate growth, such as composition field and internal stress distribution, is conducted. The obtained results are correlated with previous experimental findings and analyzed using appropriate analytical methods for validation. The entire thesis is divided into seven chapters, with the breakdown as follows: Chapter one of the thesis provides a formal introduction to high-temperature aluminium alloys, such as nickel-based superalloys, followed by an exploration of the Knipling criteria for the development of a castable, creep-resistant aluminium alloy. It discusses how the addition of Sc, Zr, and Er effectively meets these criteria, the development of lattice misfit in these alloys, the factors influencing it, and offers a brief introduction to the multiphase field model and chemo-mechanical coupling. This chapter also includes an outline of the work conducted in the thesis. In Chapter Two of the dissertation, an extensive literature survey is conducted on general high-temperature aluminium alloys, Al-Sc, Al-Zr, and Al-Er alloys, focusing on their precipitation studies and the various reported morphologies. Additionally, different numerical methods such as the phase-field method, multiphase field method, and Density Functional Theory are reviewed. A brief overview of studies on the temperature dependence of misfit and the composition dependence of elastic constants is also provided. The research gap in the precipitation coarsening of the Al-X (X=Sc, Zr, Er) alloy is identified, and the research plan to address this gap is summarized within the literature review. Chapter Three of the thesis provides an overall outline of the modelling and simulation aspects of this research. It elaborates on the derivation of the governing time evolution equation, the driving forces involved in precipitation, and the method for homogenizing the elastic constants at the interfaces. Following this, the similation procedure, which involves the parameters used for the simulation and how they are obtained is also explained. The theory of temperature dependence of misfit and the model used are also detailed in this section. Additionally, the density functional method framework employed in the study and the method for obtaining the composition dependence of elastic constants are elaborately described. Chapter Four of the thesis conducts an initial investigation into the coarsening characteristics of the Al-X (X=Sc, Zr, and Er) system with a 12-hour heat treatment duration. The study employs the multiphase field method and incorporates the elastic effects as proposed by Khachaturyan. The chapter primarily examines the elastic interactions and composition distribution within the aluminium matrix, emphasizing key parameters such as temperature and aging time during the stages of precipitate growth and coarsening. Chapter Five of the dissertation extends the previous analysis to a 50-hour heat treatment duration to address the variations in reported precipitate morphology observed at longer durations. By incorporating temperature-dependent misfit effects into the phase-field model, a detailed analysis of stress and strain field distribution, composition distribution, and morphology evolution in Al–Sc, Al–Zr, and Al–Er alloys is conducted. Through a comprehensive analysis of thermal and mechanical interactions, this chapter aims to achieve a more refined simulation of microstructure evolution. In Chapter Six of the thesis, an examination of precipitate growth and microstructure evolution over an extended aging time of 100 hours is conducted. To accurately capture these processes, the thermal, chemical, and mechanical interdependencies influencing precipitate evolution are incorporated into the simulation. This more intricate framework is adopted to address the disparity in reported morphologies of precipitates and to overcome limitations in accurately examining microstructure evolution during prolonged aging times. The elastic constants of the Al-X (X=Sc, Zr, and Er) matrix solid solution, which vary with composition, are precisely determined through density functional theory (DFT) calculations. By incorporating the temperature dependence of misfit and providing the coupling factor that correlates elastic constant and alloy composition as input to the multiphase field simulation, a comprehensive investigation of the composition, stress distribution, and morphology of precipitates is conducted in this section. The Seventh and final chapter comprises a brief summary of the work and the inferences presented in the thesis.