Dissolution kinetics of irregular second phase in as-cast Cu-Ti alloys via a multi-particle dissolution model
Graphical abstract
Introduction
Dissolution of the second phase in the as-cast alloys, an important step in heat treatment process, influences a variety of materials processes in metal structural alloys, for instance, deformation [1], [2], [3], aging [4], [5], recrystallization [6], corrosion [7], [8] and wear [9], [10]. However, the corresponding works on the dissolution of the as-cast second phase are not well developed and focused on describing qualitatively the microstructure evolution by experiments [11], [12], [13]. The CALPHAD (CALculation of PHAse Diagrams) method, as a part of Integrated Computational Materials Engineering (ICME), is not only essential for understanding the thermodynamics and kinetics of phase transitions but also helpful in providing technical guidance to optimize the material manufacturing process [14], [15], [16], [17], [18], [19]. Thus, the CALPHAD-based dissolution models should be developed and satisfied for the dissolution treatment of different alloys systems.
To date, semi-empirical models [20], [21], [22], numerical methods [23], [24], phase-field method [25], [26], [27], [28] and CALPHAD-based computational kinetics tools [29], [30], [31] were applied to unveil the dissolution kinetics of a single particle and multi-particle systems. For the as-cast alloys, most research simplified the geometry of the irregular phase to a single size (average particle radius) spherical particle to simulate the dissolution process of the second phase [32]. However, considering the morphology and agglomeration of the as-cast second phase, the value of average particle radius is hard to obtain directly. Furthermore, the average particle radius causes the deviation between the simulation results and the actual situation, which is due to the incomplete dissolution of the second phase particles larger than the average radius [33], [34]. The self-coarsening of the precipitated phase during heating has been observed in several experimental studies [35], [36], but the existed dissolution models have not reflected this phenomenon. To solve above problems, a multi-particle dissolution model (spherical log-normal distribution) is established to simulate the dissolution of irregular second phase and the age-hardenable Cu-Ti alloy [37], [38], [39] is adopted to be a case study.
The purpose of the present work is to study the non-isothermal dissolution kinetics of the irregular solidified second phase in as-cast Cu-3.1Ti alloy via a multi-particle dissolution model based on the CALPHAD diffusion theory. Because of the complex morphology of the as-cast second phase, regularizing the shape of the solidified second phase is necessary. Based on the energy and mass conservation, the hypothetical spherical second phase particles satisfying a log-normal distribution are constructed to replace the irregular solidified Cu4Ti phase via high-throughput integrated calculations. The corresponded diffusion field around each particle could be determined based on the relative volume fraction of the second phase. In order to verify the extrapolation of this model, the dissolution of the irregular solidified Cu4Ti phase has been simulated under various heating processes and supported by the present experimental work. Moreover, the Kissinger–Akahira–Sunose (KAS) method enables the tracking of activation energy under different transformed volume fractions.
Section snippets
Multi-particle dissolution model
In this study, the second-phase dissolution modelling during non-isothermal solution processing is based on the moving phase boundary diffusion theory. In order to keep the mass balance at the phase interface, the moving boundary velocity can be calculated by the flux balance equation [40]:Where is the location of the interface, and are the diffusion fluxes of component at the interface on the matrix and second phase sides,
Dissolution experiments
Binary Cu-3.1Ti (3.1 wt%) alloy was made by vacuum induction melting and casting, using pure copper (99.99 wt%) and the Cu-Ti master alloy (50 wt%). In order to observe the dissolution of the solidified second phase, the samples with dimension of 10 mm × 10 mm × 5 mm were extracted from the middle of the ingot, then performed at heating rate 10C/min from 25C in the KSL-1200X muffle furnace. The solution-treated samples were quenched in cold water to freeze at 400C, 600C, 750C, 800C, 900C, and
Results
In present work, we use a CALPHAD-based multi-particle dissolution model to simulate the dissolved evolution of the Cu4Ti phases in the as-cast Cu-3.1Ti system during heating rate 10C/min in Fig. 1. The calculated results via the multi-particle dissolution model with initial particle size distribution show an excellent agreement with the experimental results. From the simulation results, an abnormal dissolution phenomenon is observed. It shows that Cu4Ti phase is initially self-coarsening
Model setup and validation
Figure 5 shows the initial microstructure of the as-cast Cu-3.1Ti alloy via optical microscope, SEM and XRD techniques. Fig. 5(a, b) show the irregular solidified second phase is segregated at the grain boundary with the effective volume fraction about 2.95%. The XRD result in Fig. 5(c) shows the solidified second phase is Cu4Ti phase.
The initial effective volume fraction and the approximate topography of the Cu4Ti phase are provided in Fig. 5 from the as-cast samples, then we can observe that
Conclusions
A multi-particle dissolution model has been constructed to investigate the dissolution process of the Cu4Ti phase in as-cast Cu-3.1Ti alloys.
Based on the mass balance and the energy conservation during solid-state phase transformation, a multi-particle spherical dissolution model is developed by integrating the CALPHAD-based diffusion theory (CALPHAD: CALculation of PHAse Diagrams) and high-throughput calculations.
The multi-particle dissolution model with the initial spherical log-normal
Data availability
Part of the data is presented in the paper and supplementary materials. Additional data related to this paper can be requested from the corresponding authors.
CRediT authorship contribution statement
Xingyu Xiao: Conceptualization, Data curation, Methodology, Writing - original draft. Renhai Shi: Conceptualization, Methodology, Supervision, Writing - review & editing. Qiang Du: Supervision, Writing - review & editing. Jianxin Xie: Funding acquisition, Project administration, Resources, Supervision, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors gratefully acknowledge Prof. Xinhua Liu at University of Science and Technology Beijing for supporting experimental research and discussion. Finally, the authors are grateful for the support from the National Natural Science Foundation of China (No. 52090041) and the Fundamental Research Funds for the Central Universities (No. 06500161).
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