arXiv subjects

Kamalnath Kadirvel

Publications and source records attributed to Kamalnath Kadirvel.

5 recordsLinked to original sources

arXiv2023

Phase Field Method for Inhomogeneous Modulus Systems

One of the advantages of the phase-field method (PFM) is its ability to incorporate elastic interactions that dominate solid-state processes including phase transformations and plastic deformation. As mechanical equilibrium is attained much faster than chemical equilibrium, the former should be used as a constraint explicitly in deriving the governing equations of time-evolution of PFM order parameters. Current models for elastically anisotropic and inhomogeneous media in the literature do not impose such a constraint in their governing equations. In particular, they ignore the dependence of the total strain on the order parameters while evaluating the variational derivative of the elastic energy (VDEE). There is no mathematical proof to support this treatment and the fundamental thermodynamic consistency of such a models could be challenged. In this work, we present a rigorous and physically transparent formulation of PFM governing equations for elastically anisotropic and inhomogeneous media in which the mechanical equilibrium is explicitly used as a constraint. From our formulation, we show that VDEE computed in the Leo-Lowengrub-Jou (1998) (LLJ) model is thermodynamically consistent. We also show that the Wang-Jin-Khachaturyan (2003) (WJK) model has significant error in VDEE calculation. We proposed a first-order correction term to the WJK model which nullifies the error in VDEE and makes the model thermodynamically consistent. Also, we computed the VDEE by a numerical method with-out using any assumptions and compared the numerical VDEE with the LLJ, WJK and modified WJK models.

cond-mat.mes-hall↗

arXiv2023

Microstructural engineering by heat treatments of multi-principal element alloys via spinodal mediated phase transformation pathways

Nanoscale multi-phase microstructures observed in multi-principal element alloys (MPEAs) such as $\rm AlMo_{0.5}NbTa_{0.5}TiZr$, $\rm Al_{0.5}NbTa_{0.8}Ti_{1.5}V_{0.2}Zr$, $\rm TiZrNbTa$, $\rm AlCoCrFeNi$ and $\rm Fe_{15}Co_{15}Ni_{20}Mn_{20}Cu_{30}$ that exhibit promising mechanical or functional properties may have evolved through spinodal-mediated phase transformation pathways (PTPs). The microstructures in such MPEA systems could be further engineered for targeted applications by appropriately designing the alloy composition and heat-treatment schedule. In this study, we investigate systematically how different heat treatment schedules such as single-step isothermal aging, two-step isothermal aging and continuous cooling alter the interplay among the various factors associated with alloy composition, such as volume fraction of individual phases, lattice misfit and modulus mismatch between the co-existing phases. We have determined the degree to which these factors influence significantly the spinodal-mediated PTPs and the corresponding microstructures by use of high-throughput phase-field simulations. In particular, we demonstrate that the microstructural topology (i.e., which phase forms the continuous matrix and which phase forms discrete precipitates) in the same MPEA having an asymmetric miscibility gap could be inverted simply by a continuous cooling heat treatment. Further, we reveal a rich variety of novel hierarchical microstructures that could be designed using two-step isothermal aging heat treatments in MPEA systems with symmetric or asymmetric miscibility gaps. These simulation results may shed light on novel microstructure design and engineering for the above-mentioned MPEA systems.

cond-mat.mtrl-sci↗

arXiv2022

Microstructural Design via Spinodal-Mediated Phase Transformation Pathways in High-Entropy Alloys (HEAs) using Phase-Field Modelling

Understanding the phase transformation pathways (PTPs) and microstructural evolution in multi-phase HEAs will aid alloy and process designs to tailor the microstructures for specific engineering applications. In this work, we study microstructural evolution in two-phase HEAs where a disordered parent phase separates into a mixture of two phases: an ordered phase ($β'$) + a disordered phase ($β$) upon cooling following two different PTPs: (i) congruent ordering followed by spinodal decomposition in the ordered phase and then disordering of one of the ordered phases, i.e., $β\rightarrow β' \rightarrow β_1' + β_2' \rightarrow β+ β_2'$ and (ii) spinodal decomposition in the disordered phase followed by ordering of one of the disordered phases, i.e., $β\rightarrow β_1 + β_2 \rightarrow β_1+β'$. We systematically investigate the effects of equilibrium volume fractions of individual phases, free energy landscapes (in particular, the location of the critical point of the miscibility gap relative to the compositions of the final two equilibrium phases), and elastic modulus mismatch between the two equilibrium phases on the microstructural evolution of these HEAs. We focus on the following morphological characteristics: bi-continuous microstructures vs. precipitates + matrix microstructures, ordered matrix + disordered precipitates vs. disordered matrix + ordered precipitates, and the discreteness of the precipitate phase. This parametric study may aid in multi-phase HEA design for desired microstructures.

cond-mat.mtrl-sci↗

arXiv2021

Exploration of Spinodal Decomposition in Multi-Principal Element Alloys (MPEAs) using CALPHAD Modeling

Researchers attributed the orderly arranged nanoscale phases observed in many multi-principal element alloys (MPEAs) to spinodal/spinodal-mediated phase transformation pathways. However, spinodal decomposition is not well understood in multicomponent systems. Although the theoretical background is available, CALPHAD databases were not used to explore the miscibility gap in MPEAs. In this work, we develop a CALPHAD framework utilizing the Hessian of free energy to study the stability of solid solutions in MPEAs. In particular, we utilize the geometry of higher dimensional Gibbs simplex in conjunction with the Hessian to calculate concentration modulations in early stages of spinodal decomposition. We apply this framework to a diverse set of multi-phase MPEAs that have been studied in the literature including TiZrNbTa (BCC/BCC), Fe15Co15Ni20Mn20Cu30 (FCC/FCC), Al0.5NbTa0.8Ti1.5V0.2Zr (BCC/B2), AlCo0.4Cr0.6FeNi (BCC/B2) and Al0.5Cr0.9FeNi2.5V0.2 (FCC/L12). We show that the MPEA systems are unstable only to certain concentration modulations which could be further explored to design microstructurally engineered alloys.

cond-mat.mtrl-sci↗

arXiv2021

Phase-Field Modelling of Transformation Pathways and Microstructural Evolution in Multi-Principal Element Alloys

The recently developed refractory multi-principle element alloy (MPEA), AlMo$_{0.5}$NbTa$_{0.5}$TiZr, shows an interesting microstructure with cuboidal precipitates of a disordered phase ($β$, bcc) coherently embedded in an ordered phase ($β'$, B2) matrix, unlike the conventional Ni-based superalloys where the ordered phase ($γ'$, L12) is the precipitate phase and the disordered phase ($γ$, fcc) is the matrix phase. It becomes critical to understand the phase transformation pathway (PTP) leading to this microstructure in order to tailor the microstructure for specific engineering applications. In this study, we first propose a possible PTP leading to the microstructure and employ the phase-field method to simulate microstructural evolution along the PTP. We then explore possible PTPs and materials parameters that lead to an inverted microstructure with the ordered phase being the precipitate phase and the disordered phase being the matrix phase, a microstructure similar to those observed in Ni-based superalloys. We find that in order to maintain the precipitates as highly discrete particles along these PTPs, the volume fraction of the precipitate phase needs to be smaller than that of the matrix phase and the elastic stiffness of the precipitate phase should be higher than that of the matrix phase.

cond-mat.mtrl-sci↗