Precipitation of γ′ in the γ binder phase of WC-Al-Co-Ni cemented carbide: A phase-field study

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 68 (2020) 101717

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Precipitation of γ0 in the γ binder phase of WC-Al-Co-Ni cemented carbide: A phase-field study Yingbiao Peng a, Yong Du b, *, Matthias Stratmann c, Jianzhan Long d, Yuling Liu b, Hong Mao b, Helena Zapolsky e a

College of Metallurgical and Materials Engineering, Hunan University of Technology, Zhuzhou, Hunan, 412008, PR China Research Institute of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, PR China OpenPhase Solutions GmbH, Wasserstraße 494, D-44795, Bochum, Germany d State Key Laboratory of Cemented Carbide, Zhuzhou, Hunan, 412000, PR China e Groupe de Physique des Mat�eriaux, UMR 6634 CNRS, University of Rouen, Avenue de L’Universit�e 76301, Saint Etienne Du Rouvray, 76801, France b c

A R T I C L E I N F O

A B S T R A C T

Keywords: Al–Co–Ni binder Precipitation Multi-phase-field CALPHAD database Order/disorder transition Long-term aging

High-temperature properties of WC-Co cemented carbides can be greatly improved by introducing ordered γ0 precipitates (L12 structure) into disordered γ Co-binder matrix (fcc structure). The microstructure evolution of γ0 precipitates in γ matrix was investigated by using multi-phase-field (MPF) method. In order to avoid indistin­ guishable miscibility during MPF simulations, a phenomenon caused by mistaking the chemical free energies of γ and γ0 phase for each other, the thermodynamic driving force and diffusivities were taken from CALPHAD da­ tabases with the Gibbs energies of ordered and disordered phases separated according to a single Gibbs energy expression in a thermodynamic database. The interfacial energy between γ and γ0 phases was estimated based on a thermodynamic model applied to coherent interfaces. The elastic strain energy was introduced to reproduce the cuboidal shape of the ordered γ0 precipitates. Specially, the MPF approach was applied to study the morpho­ logical evolution of γ þ γ0 microstructure as a function of concentration, temperature and aging time. It was shown that with increasing of Al concentration the cuboidal shape of precipitates appears at early stages of growth. After long term aging at 1373K the γ0 /γ interface becomes semi-coherent and some γ-channels are formed. The simulation results are in good agreement with experimental data and have demonstrated the ability of the model to capture the major structural characteristics of microstructural evolution in Al–Co–Ni binder system during long-term heat treatment. Based on the knowledge of microstructure evolution, it is possible to design the optimal process parameters efficiently instead of expensive and time-consuming experiments.

1. Introduction WC-Co cemented carbides are regarded as the tooth in industries due to the combination of high hardness and good fracture toughness [1,2]. In order to overcome the shortages of traditional Co binder, such as weak oxidation/corrosion resistance and low high-temperature hard­ ness, strengthening the Co binder phase has been the subject of many investigations [3–7], among which the adoption of binder phase with nano-particle precipitates has attracted more and more interests [4–7]. For instance, the presence of η nano-precipitates in the binder phase can significantly improve the hardness and wear resistance of cemented carbides [4,5]. Recently, Al–Co–Ni composite binder phase with ordered γ0 precipitates (L12 structure) coexisting with disordered γ binder matrix

(fcc structure) was developed and introduced into cemented carbides [6, 7]. High-temperature properties and corrosion resistance of cemented carbides can be greatly improved by such a kind of γ/γ0 binder phase [6–8]. To improve performance of these materials and optimize the process parameters, the knowledge of microstructural evolution during aging process is necessary. However, only few experimental studies are available about the microstructure evolution in WC-Al-Co-Ni cemented carbide [6,7]. Nowadays, the phase-field simulations have been widely applied to investigate microstructure evolution in various materials. In particular, considering their technical importance, a large number of phase-field simulations have been done to investigate microstructural evolution in Ni-based superalloys, ranging from solidification [9,10], dissolution [9],

* Corresponding author. E-mail address: [email protected] (Y. Du). https://doi.org/10.1016/j.calphad.2019.101717 Received 3 August 2019; Received in revised form 2 November 2019; Accepted 24 November 2019 Available online 7 December 2019 0364-5916/© 2019 Elsevier Ltd. All rights reserved.

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precipitation [11–15], and coarsening [16,17] to inter-diffusion [18]. However, for the Al–Co–Ni system, a kind of Co-base binder in cemented carbides, no phase-field simulation on the microstructure evolution has been reported [19]. The multi-phase-field (MPF) method developed by Steinbach and his co-workers [20–29] has been successfully applied to study microstructure evolution in different multicomponent alloys during various materials processes. In order to quantitatively simulate the microstructure evolution of industrial alloys, it is necessary and a trend to couple with the CALPHAD (CALculation of PHAse Diagrams) databases, which can provide realistic chemical driving force, diffusion potentials, and chemical mobility at any composition and temperature. For most of the systems containing order/disorder transition, the or­ dered and disordered phases are described by a single Gibbs energy function. However, when coupling to such kind of thermodynamic da­ tabases during phase-field simulations, the chemical free energies of γ and γ0 phases always exchange for each other irregularly. It means the Gibbs energy for γ or γ0 phase may be right in one step but change to the value of the other phase in the next step, which makes it difficult to couple to such thermodynamic databases during time-continuous pha­ se-field simulations [10–12,25]. For the Al–Co–Ni system acting as one kind of composite binder phase in cemented carbides, the thermody­ namic descriptions of the ordered/disordered phases in this system are unsurprisingly using a single Gibbs energy function. Thus, there is an urgent need to remedy this situation so as to perform phase-field sim­ ulations of technical importance. Considering the key process parameters like alloy composition and heat treatment, the microstructure evolution of γ0 precipitates in γ ma­ trix of the ternary Al–Co–Ni system according to the variables of alloy composition, aging temperature and aging time is studied by using MPF method while coupling to CALPHAD databases, in which both disor­ dered and ordered phases are described by a single Gibbs energy func­ tion. The main focus of the present work is to investigate the morphology evolution of γ0 precipitates during growth and coarsening stages. It has been revealed that the topological inversion between matrix and precipitates not only take place under applied load but also without applied load during long-term aging [29–32]. Therefore, the long-term aging process was also considered in the present simulations.

f chem ¼

N X

( f elast ¼

1 2

N X

� φα εijtot;a

α¼1

~i ¼ phase composition ciα , μ i.

εijtot;a

and

εij*;a

(5)

εkl*;a

∂fchem;α ∂ciα

is the diffusion potential of component

are total strain and eigenstrain of a phase. Cijkl a are elas­ ij

temperature-dependent quantities. However, in the present work these quantities are considered to be constant in concentration and tempera­ ture but differ for the individual phases. This treatment has been applied in other works [26–28]. Inserting the free energy densities Eqs. (3)–(5) into Eqs. (1) and (2) leads to Ref. [22]. ! ! # " N N X μαβ X π2 π2 φ_ α ¼ r2 φγ þ 2 φγ þ ΔGαβ (6) σ βγ σ αγ N γ¼1 η 8η β¼1 In cases where the exact dynamics of multiple junctions are of minor importance, the so-called antisymmetric approximation of Eq. (6), which resigns from thermodynamic consistency at the multiple junc­ tions, is used [22,23]. � � � � N X π2 π pffiffiffiffiffiffiffiffiffiffi φ_ α ¼ φα φβ ΔGαβ μαβ σ αβ φβ r2 φα φα r2 φβ þ 2 ðφα φβ Þ þ η 2η β¼1 (7) where ΔGαβ ¼ ΔGchem;αβ þ ΔGelast;αβ is the sum of the chemical and me­ chanical driving forces between the a and b domains. The chemical part of the driving force (between the precipitate and matrix phase) is given by � � ∂ ∂ ΔGchem;αβ ¼ ​ f chem ∂φβ ∂φα (8) � � � ~i ciα ciβ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ¼ fchem;α ciα þ fchem;β ciβ þ μ where chemical free energy density fchem;α , fchem;β and diffusion potential

μ~i can be obtained directly from CALPHAD-type thermodynamic data­

base. In order to deal with the diffuse interface used in MPF method, a homogenization scheme [26–28] is applied across the interfaces where ij

εij*;eff and effective compliance matrix ½Cijkl eff �

effective strain εtot;eff

linearly weighted by phase fields.

εijtot;eff h

Cijkl eff

εij*;eff ¼ i

1

N X

¼

N X

� φα εijtot;α

α¼1

"

#

εij*;α

�

1

are

(9)

1

(10)

φα Cijkl α

α¼1

Thus, Eq. (5) can be simplified as ! ! 1 kl kl f elast ¼ εijtot;eff εij*;eff Cijkl ε ε eff tot;eff *;eff 2

where μαβ is the interface mobility, N is the local number of phases and η P is the interfacial thickness. The condition Nα¼1 φα ¼ 1 is always fulfilled. The interfacial energy density is given by Refs. [21,23]:

η

) �

�

ticity moduli of a phase. In general, ε*;a and Cijkl a are concentration- and

Ω

α6¼β

�

εij*;a Cijkl εkltot;a a

where fchem;α ðciα Þ is the chemical free energy density of phase a with the

The evolution of the phase field of α phase, φα , is modeled using a generalized form of the time dependent Ginzburg-Landau equation [21]: � � N X π 2 μαβ δF δF φ_ α ¼ (2) 8ηN δφα δφβ α¼16¼β

η2 rφ rφ þ φα φβ π2 α β

(4)

and

In the MPF model, a general free energy contains various contribu­ tions, such as chemical, interfacial, elastic, magnetic, and so on [20–23]. In our case only first three contributions will be considered. Then, F is described by integrating different free energy densities over a domain Ω, such as chemical energy density f chem , interfacial energy density f intf , and elastic energy density f elast . Z � chem � f (1) F¼ þ f intf þ f elast dΩ

� N X 4σ αβ

! φα ciα

α¼1

a¼1

2. Multi-phase-field model

f intf ¼

N X

� ~ i ci φα fchem;α ciα þ μ

�

(11) �

(3)

and finally, the elastic driving force, ΔGelast;αβ ¼ ​

∂ ∂φβ

∂ ∂φα

� f elast , can

be obtained using Eq. (11) (for more details about the process, see Refs. [26,27]).

where σ αβ the interfacial energy between α and β phases. The chemical and elastic free energy densities are weighted linearly with the phase fractions as [23]. 2

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Calphad 68 (2020) 101717

!

ε ijtot;eff

ΔGelast;αβ ¼ ​ � klmn � Cβ

1

(�

εij*;eff Cijkl eff

!

εkl*;a

�

εkl*;β

� 1 � klmn � Cα 2

directly coupling to CALPHAD databases [9–12,44], certain thermody­ namic databases describing ordered and disordered phases separately were chosen. However, these databases are usually out of date and thus not as precise as those describing ordered/disordered phases by a single Gibbs energy. Moreover, for some systems of technical importance, only the one describing ordered/disordered phases using a single Gibbs en­ ergy is available. Consequently, there is an urgent need to avoid this situation. The disordered γ (fcc) and ordered γ0 (L12) phases in the Al–Co–Ni system are described with the sublattice models (Al, Co, Ni)1.0 and (Al, Co, Ni)0.75(Al, Co, Ni)0.25, respectively. A single Gibbs energy function simultaneously describing ordered and disordered phases was derived by Dupin et al. [45]. Then, for the Al–Co–Ni system, the Gibbs energy function for both disordered γ (fcc) and ordered γ0 (L12) phases can be expressed as: � 0 0 0 0 0 L12 0 yAl ; yCo ; yNi ; y00Al ; y00Co ; y00Ni Gm ¼ Gfcc m ðxAl ; xCo ; xNi Þ þ Gm (14) 2 GL1 m ðxAl ; xCo ; xNi Þ

1

!) Cmnop eff

ε

op tot;eff

ε

op *;eff

(12)

Neglecting the stress effect on diffusion, the evolution equation for concentration can be derived as [26]. ! ! N N X X δF c_i ¼ r (13) Mα r i ¼ r φα Mα r~ μiα δcα α¼1 α¼1 where Mα represent the chemical mobilities in phase a and can be directly obtained from the CALPHAD-type kinetic database. The phase-field model used in the present work incorporates a diffused interface with the width of 5 grid points, which is close to the width of γ channels. This decreases the distance between neighboring particles and eventually touch each other and coalescence occurs owing to the minimization of the interfacial energy, which leads to the topo­ logical inversion. However, the dis-joining potential between γ0 pre­ cipitates rises significantly for a decreasing γ channel width [29]. As a result, a wetting condition is employed by increasing the interfacial energy of γ0 -γ’ by a factor of three times as compared with the γ-γ0 interfacial energy in order to consider the influence of dis-joining pressure [28,29]. Moreover, the lattice misfit between γ and γ0 phases elastically stabilizes the γ0 precipitates and restrict the coalescence [28, 29]. Eventually, in the current approach the topological inversion be­ tween γ and γ0 phases is modeled by artificially lowering the eigenstrain as well as the consideration of the wetting condition, which is similar to the work of Ref. [28,29]. The governing equations mentioned above have been successfully implemented in an open source package OpenPhase [33], which is suitable for studying microstructure evolution in various materials and processes. Especially, the thermodynamic driving force and diffusivities can be coupled to real CALPHAD-type databases in OpenPhase software, and thus adopted in the present simulations. A detailed introduction about the core modules of OpenPhase and their implementation as well as the parallelization is presented by Tegeler et al. [34].

in which xAl ; xCo ​ and ​ xNi are the mole fractions of Al, Co and Ni in fcc 0 0 0 or L12 phase, yAl ; yCo ​ and ​ yNi are the site fractions of Al, Co and Ni in the first sublattice, and y00Al ; y00Co ​ and ​ y00Ni in the second one. The first term

0

Gfcc m ðxAl ; xCo ; xNi Þ represents the Gibbs energy of the disordered fcc

phase. When the site fractions in both sublattices are equal, i.e.yAl ​ ¼ 0

0 y00Al ; yCo

¼ ​ ​ and ​ yNi ¼ ​ the last two terms cancel each other, ​ indicating a disordered state. Based on the above thermodynamic model, it is possible to separately express the Gibbs energies for indi­ vidual fcc and L12 phases according to the parameters restored in thermodynamic database, the first term for fcc phase and three terms together for L12 phase. In the present work, a data file containing completely independent Gibbs energy expressions and their derivatives as well as the diffusivities of disordered γ (fcc) and ordered γ0 (L12) phases has been coupled to OpenPhase software. Three different alloy compositions (i.e., A1: 17.5Al-12.5Co–70Ni, A2: 19.5Al-10.5Co–70Ni and A3: 21.5Al-8.5Co–70Ni with at. pct) aging at different temperatures (i.e., 1373 K and 1173 K) are chosen to investigate the effect of alloy composition and heat treatment on the grain growth of precipitates. Fig. 1 shows the calculated isothermal sections of the Al–Co–Ni system at 1373 K and 1173 K by using the thermodynamic database from Wang et al. [42], where the initial alloy compositions are indicated by green dots. The calculated equilibrium mole fraction of γ0 phase along with Al concentration at 1173 and 1373 K according to Wang et al. [42] is presented in Fig. 2. As can be seen in Fig. 2, a small change of Al concentration makes a large difference of the amount of γ0 precipitate. Besides, with the decrease of Al concentration,

3. Simulation condition 3.1. CALPHAD coupling Chemical free energy, thermodynamic factor and diffusion potential are essential to obtain a quantitative description of system with phasefield model (PFM). For a long period, the chemical free energy in PFM was obtained via some simple functions like parabolic equations and Landau polynomials [35–38]. Recently, coupling to CALPHAD data­ bases has attracted more and more attentions, e.g. linking to a data file containing Gibbs energy, chemical potential and diffusivity via some external software packages [11,12], or using linearly approximated phase diagrams [39,40]. One important feature of OpenPhase software [33] is that realistic thermodynamic driving force and diffusivity in­ formation can be provided by coupling to CALPHAD databases via the TQ interface in Thermo-Calc software [41] or directly linking to a data file containing chemical free energy and its derivatives, and atomic mobility information. For the Al–Co–Ni system, the thermodynamic database from Wang et al. [42] and the diffusivity database from Deng et al. [43] are adopted. The Gibbs energies for both disordered γ phase (fcc structure) and or­ dered γ0 phase (L12 structure) is described by a single Gibbs energy function [42], which is widely accepted in the thermodynamic description of order/disorder transitions nowadays. However, such a treatment will result in an indistinguishable miscibility when coupling to CALPHAD databases via TQ interface. As a result, in the previous phase-field simulations involving ordered/disordered transitions by

y00Co

0

y00Ni ,

Fig. 1. Calculated Al–Co–Ni phase diagram in Ni-rich region at 1373 K (dashed lines) and 1173 K (solid lines) according to the thermodynamic database from Wang et al. [42]. The initial alloy compositions are appended in the figure. 3

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Calphad 68 (2020) 101717

xIF i ¼

� � BI � BII � BII 1 ΩBI m ⋅xi þ 1 Ωm ⋅xi � BI � � � 1 Ωm þ 1 ΩBII m

(20)

Table 1 shows the crystal structure information of γ and γ0 phases, including the partial molar volume of Al, Co and Ni [49–51]. The interfacial energy between γ and γ0 phases can be calculated based on Eqs. (15)–(20) with the combination of thermodynamic Gibbs energies performed by using Thermo-Calk software [41]. In the present work, the compositions of targeted alloys are set close to the tie line in the γ and γ0 two-phase region. As a result, the interfacial energies between γ and γ0 phases for three alloys are the same at each temperature, which are 0.015 J⋅m-2 at 1173 K and 0.011 J⋅m-2 at 1373 K, respectively. 3.3. Lattice misfit and elastic constant In the case of the γ→γ0 phase ordering involved in the precipitation process, four translation variants of the ordered L12 phase can appear [52]. Wang and Khachaturyan [53] and Yang et al. [54] emphasized the importance of anti-phase domain boundaries preventing the coalescence of γ0 precipitates. With the presence of an anti-phase boundary, narrow channels of γ would form. However, the experimental microstructure morphology does not show such narrow channels, seeing Fig. 6 in Sec­ tion 4.1. Moreover, a tendency to form uniform γ-channel width after long-term aging can be seen in Fig. 7 in Section 4.3, which has been also found in other experiments [55]. Consequently, only one translation variant of the L12 phase is considered in our model. The eigenstrain of

Fig. 2. Calculated equilibrium mole fraction of γ0 phase along with Al con­ centration at 1173 K and 1373 K based on the thermodynamic database from Wang et al. [42].

the influence of aging temperature on the amount of γ0 precipitate be­ comes more significant. 3.2. Interfacial energy

⇀*

transformation ε α in Eq. (5) is regarded as the lattice misfit between the precipitate γ0 and the matrix γ, and can be expressed as [11,12]:

Kaptay [46] has proposed a thermodynamic model to calculate the interfacial energies of coherent interfaces. However, when this model was applied to the ordered/disordered phases with their Gibbs energies expressed by a single Gibbs energy function, the composition of the interface cannot be solved using the equation regarding the chemical potential. Most recently, we proposed a thermodynamic model to calculate coherent interfacial energy [47]. The interfacial energy σIF between γ (fcc) and γ0 (L12) phases in the Al–Co–Ni system can be expressed as: E

GIF m

σ IF ¼ 2⋅

GIF m

ΩIF m

where αγ0 and αγ are the lattice parameters of γ0 and γ phases, respec­ tively. For the Al–Co–Ni system, no experimental data for the lattice parameters and elastic constants of γ and γ0 phases are available. In the present simulations, the lattice parameter and elastic constants of the γ0 phase are taken from first-principle calculated data from Wu and Li [56]. Due to the lack of data, the lattice parameter and elastic constants of the γ phase are simply set to be equal to those of the Ni–Al alloy [57,58]. The lattice parameters and elastic constants of γ and γ0 phases applied in the present simulations are listed in Table 2. Based on Eq. (21), the lattice misfit of γ/γ0 interface is calculated to be 0.00285.

(15)

IF where GIF m and Gm are the molar Gibbs energies of the interface phase at the interfacial composition and the equilibrium two-phase mixture at the interfacial composition, respectively, which can be expressed as: E

IF IF IF IF IF IF GIF m ¼ xAl ⋅μAl þ xCo ⋅μCo þ xNi ⋅μNi

(16)

E

(17)

BI; ​ BII BI; ​ BII IF BI; ​ BII GIF þ xIF þ xIF m ¼ xAl ⋅μAl Co ⋅μCo Ni ⋅μNi

3.4. Other numerical parameters Due to the fact that 3-D phase-field simulation coupled with CAL­ PHAD databases and stress field is really time consuming, only the simulation of alloy A2 aging at 1373 K was performed in a 3-D domain with 32 � 32 � 32 grids (grid space of 0.01μm). For other cases, sim­ ulations were performed in a 2-D square domain with 128 � 128 grids (grid space of 0.01μm). The interface thickness is 5 grids. The simulation temperatures are 1373 and 1173K. The interfacial mobility μαβ ¼ 6.0 � 10-14 m4/J-s is used to guarantee the diffusion-controlled growth.

where xIF i is the mole fraction of component i (i ¼ Al, Co and Ni) at the interface, μθi presents the chemical potential of component i in phase q (q ¼ IF, BI or BII). Ωθm is the molar area in phase q, which can be expressed as follows: Ωθm ¼ ​ Ω0Al ⋅xθAl þ Ω0Co ⋅xθCo þ Ω0Ni ⋅xθNi �2=3

(21)

δ ¼ (αγ0 –αγ)/αγ

4. Results and discussion

(18) (19)

In the present simulations, γ0 phase was set to precipitate from an

where NA is the Avogadro’s number, Ω0i and V 0i are the partial molar area and partial molar volume of component i, respectively. f represents the geometry factor and a value f ¼ 1.091 was chosen for cubic phase [47]. As the composition of each interfacial layer is assumed to be as the same as that of adjoining bulk phase at the original state, it can be expressed as the following equation [48]:

Table 1 Crystal structure information of γ and γ0 phases with the occupation of Al, Co and Ni.

Ω0i ¼ f ⋅ V 0i

⋅N 1=3 A

4

Element

Phase

Cell volume, nm3

Multiplicity

Molar volume, cm3/mol

Ref.

Al Co Ni

γ, γ0 γ, γ0 γ, γ0

0.0664 0.0453 0.0440

4 4 4

9.993 6.822 6.626

[49] [50] [51]

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them become slightly cuboidal. At t ¼ 1500 s, γ0 particles continue to grow and the precipitates in A1 and A2 alloys show clearly the cuboidal morphology. When t ¼ 4000 s, γ0 grains in all the alloys become much more cuboidal. Moreover, it can be seen that large precipitates continue growing based on the consumption of small ones, indicating the begin­ ning of coarsening stage. As can be seen, the volume fraction of γ0 precipitates increases significantly from alloy A1 to alloy A3, which is in consistence with the calculated equilibrium results, seeing Fig. 2. As we known, the me­ chanical properties of materials largely depend on volume fraction of precipitates, their mean radius and mean distance between particles. Then, for WC-Al-Co-Ni cemented carbides, it can be an efficient way to improve the mechanical properties of these materials by slightly increasing the concentration of Al while keeping that of Ni constant in order to increase the volume fraction of γ0 precipitates. As shown in Figs. 4 and 5, when increasing the Al concentration of the alloys, the cuboidal shape of γ0 precipitates occurs earlier. However, the cuboidal shape of γ0 precipitates in the alloy A3 aging at 1373 K and alloys A1, A2 and A3 aging at 1173 K is not so obvious than that of the alloys A1 and A2 aging at 1373 K, which indicates a possible guidance of controlling the precipitate shape. Fig. 6(a) presents the simulated result of alloy A2 containing 47 vol. % γ0 precipitate aged 4000s at 1373K. Fig. 6(b) shows the SEM image of the binder phase of a WC-Al-Co-Ni cemented carbide aging at 1373 K for 3600 s, which contains 45.83 vol.% γ0 precipitate in the binder phase [59]. As can be seen, the presently simulated microstructure agrees well with the experimental one, thereby vilidating the reliability of the CALPHAD databases and numerical parameters applied in the present work.

Table 2 Lattice parameters and elastic constants of γ and γ0 phases. Phase

Lattice parameters, nm

γ γ0

0.35819 0.35717

Elastic constants, GPa

Ref.

C11

C12

C44

235.0 244.1

156.2 144.4

118.2 127.4

[57,58] [56]

initially supersaturated γ matrix. A given number of prime particles were randomly distributed in the simulation domain. The particle den­ sities were approximately determined according to experimentally detected grain size, volume of simulation domain and thermodynami­ cally calculated equilibrium volume fraction of precipitates. Fig. 3 presents the 3-D microstructure evolution of alloy A2 aging at 1373 K for 50 s, 300 s, 1500 s and 4000 s, respectively. As can be seen, at early stages of growth γ0 precipitates have a spherical morphology. With the increase of precipitate size, the elastic energy increases and finally the shape of precipitates become cuboidal. 4.1. Effect of alloy composition In order to study the effect of alloy composition on microstructure evolutions, three alloys (i.e., A1: 17.5Al-12.5Co–70Ni, A2: 19.5Al10.5Co–70Ni and A3: 21.5Al-8.5Co–70Ni with at. Pct) were chosen with the concentration of Al and Co slightly changed. Figs. 4 and 5 present the phase-field-simulated microstructure evolutions of alloys A1, A2 and A3 when aging at 1373 K and 1173 K for different time steps. As can be seen in Figs. 4 and 5, small γ0 particles randomly precipitate in γ matrix at t ¼ 50 s in all these alloys. As expected, the number of precipitates increases with increase of Al concentration. At this stage, the shape of precipitates for all alloys is spherical. Later, at t ¼ 300s, γ0 particles grow and some of

Fig. 3. Phase-field-simulated microstructure evolution (3D) in A2 alloy aging at 1373K, showing the growth of γ0 precipitates. 5

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Fig. 4. Phase-field-simulated microstructure evolution (2D) in A1, A2 and A3 alloys aging at 1373 K. The γ0 precipitates are indicated in red and disordered matrix in blue. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 5. Phase-field-simulated microstructure evolution (2D) in A1, A2 and A3 alloys aging at 1173 K. The γ0 precipitates are indicated in red and disordered matrix in blue. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

6

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Fig. 6. (a) Simulated microstructure of alloy A2 containing 46.85 vol.% γ0 precipitate, (b) microstructure of the binder phase of WC-Al-Co-Ni cemented carbide containing 45.83 vol.% γ0 precipitates at the equilibrium state after aging at 1373 K for 3600 s [59].

Fig. 7. (a)–(c) Simulated microstructure evolution of alloy A2 along with the relative simulation time where γ0 precipitates showing in red color and γ matrix showing in blue color. Microstructure of alloy A2 after aging at 1373 K for 4000 s and (a) 0% long-term aging time, (b) 50% long-term aging time, and (c) 100% longterm aging time. (d) SEM micrograph of WC-Al-Co-Ni cemented carbide containing 45.83 vol.% γ0 precipitates after aging at 1373 K for 100 h [59].

4.2. Effect of aging temperature

A1 is the largest one while alloy A3 the smallest one, which is in consistence with the calculated equilibrium phase diagram results, seeing Fig. 2. Consequently, when the composition of a commercial alloy needs to maintain, changing aging temperature would be another effective way to design the amount of precipitate. The other aspect is the geometric shape of γ0 precipitate. Besides of amount and particle size, geometric shape of precipitate would be another factor affecting the mechanical properties of materials [11]. As can be seen in Figs. 4 and 5, the shape of γ0 precipitate in alloys A1, A2 and A3 aging at 1373 K is

Heat treatment is another key factor affecting the subsequent mi­ crostructures. In the present work, alloys A1, A2 and A3 aging at two different temperatures 1373 K and 1173 K were chosen as the target. As can be seen in Figs. 4 and 5, aging temperature affects the sub­ sequent microstructures mainly in two aspects. One is the volume fraction of γ0 precipitate. When aging temperature decreases from 1373 K to 1173 K, the change of the volume fraction of γ0 precipitate in alloy 7

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much more cuboidal compared with those aging at 1173 K. This dis­ crepence may be caused by the presently applied different values of interfacial energies between γ/γ0 phases at different aging temperatures, i.e., 0.015 J⋅m-2 at 1173 K and 0.011 J⋅m-2 at 1373 K. The shape of precipitates depends from the ration between the interfacial and elastic energy. The larger interfacial energy is, the more spherical shape becomes.

Acknowledgements The financial support from the National Natural Science Foundation of China (grant no. 51601061), Sino-German Center for Promotion of Science (grant no. GZ 1208), and Special Funds for the Construction of Hunan Innovation Province (grant no. 2019GK2052) is greatly acknowledged. References

4.3. Effect of long-term aging

[1] H.E. Exner, Physical and chemical nature of cemented carbides, Int. Met. Rev. 24 (4) (1979) 149–173. [2] V.K. Sarin (Ed.), Comprehensive Hard Materials, first ed., Elsevier, Amsterdam, Netherlands, 2014, p. 123. [3] K. Nishigaki, H. Doi, N. Yukawa, M. Morinaga, T. Koie, Binder phase strengthening through γ0 precipitation of WC-Co-Ni-Cr-Al hard alloys, in: Proceedings of the 11th International Plansee Seminar, vol.85, 1985, pp. 487–508. [4] I. Konyashin, F. Lachmann, B. Ries, A.A. Mazilkin, B.B. Straumal, C. Kübel, L. Llanes, B. Baretzky, Strengthening zones in the Co matrix of WC-Co cemented carbides, Scr. Mater. 83 (2014) 17–20. [5] I. Konyashin, F. Schafer, R. Cooper, B. Ries, J. Mayer, T. Weirich, Novel ultracoarse hardmetal grades with reinforced binder for mining and construction, Int. J. Refract. Metals Hard Mater. 23 (2005) 225–232. [6] J. Long, W. Zhang, Y. Wang, Y. Du, Z. Zhang, B. Lu, K. Cheng, Y. Peng, A new type of WC-Co-Ni-Al cemented carbide: grain size and morphology of γ0 -strengthened composite binder phase, Scr. Mater. 126 (2017) 33–36. [7] J. Long, K. Li, F. Chen, M. Yi, Y. Du, B. Lu, Z. Zhang, Y. Wang, K. Cheng, K. Zhang, Microstructure evolution of WC grains in WC-Co-Ni-Al alloys: effect of binder phase composition, J. Alloy. Comp. 710 (2017) 338–348. [8] A. Suzuki, T.M. Pollock, High-temperature strength and deformation of γ/γ0 twophase Co-Al-W-base alloys, Acta Mater. 56 (2008) 1288–1297. [9] Y. Wang, A.G. Khachaturyan, Acta Metall. Mater. 43 (1995) 1837–1857. [10] U. Grafe, B. B€ ottger, J. Tiaden, S.G. Fries, Coupling of multicomponent thermodynamic databases to a phase field model: application to solidification and solid state transformations of supperalloys, Scr. Mater. 42 (2000) 1179–1186. [11] N. Ta, L. Zhang, Y. Du, Design of the precipitation process for Ni-Al alloys with optimal mechanical properties: a Phase-Field Study, Metall. Mater. Trans. A 45 (2014) 1787–1802. [12] N. Ta, L. Zhang, Y. Tang, W. Chen, Y. Du, Effect of temperature gradient on microstructure evolution in Ni-Al-Cr bond coat/substrate systems: a Phase-field study, Surf. Coat. Technol. 261 (2015) 364–374. [13] R.D. Kamachali, E. Borukhovich, N. Hatcher, I. Steinbach, DFT-supported phasefield study on the effect of mechanically driven fluxes in Ni4Ti3 precipitation, Model. Simul. Mater. Sci. Eng. 22 (2014), 034003. [14] C. Schwarze, A. Gupta, T. Hickel, R. DarvishiKamachali, Phase-field study of ripening and rearrangement of precipitates under chemomechanical coupling, Phys. Rev. B 95 (2017) 174101. [15] A.M. Jokisaari, S.S. Naghavi, C. Wolverton, P.W. Voorhees, O.G. Heinonen, Predicting the morphologies of γ0 precipitates in cobalt-based superalloys, Acta Mater. 141 (2017) 273–284. [16] J. Kundin, L. Mushongera, T. Goehler, H. Emmerich, Phase-field modeling of the γ¢-coarsening behavior in Ni-based super alloys, Acta Mater. 60 (2012) 3758–3772. [17] J.Z. Zhu, T. Wang, A.J. Ardell, S.H. Zhou, Z.K. Liu, L.Q. Chen, Acta Mater. 52 (2004) 2837–2845. [18] K. Wu, Y.A. Chang, Y. Wang, Scr. Mater. 50 (2004) 1145–1150. [19] C. Wang, M.A. Ali, S. Gao, J.V. Goerler, I. Steinbach, Combined phase-field crystal plasticity simulation of P- and N-type rafting in Co-based superalloys, Acta Mater. 175 (2019) 21–34. [20] I. Steinbach, F. Pezzolla, B. Nestler, M. Seeß elberg, R. Prieler, G.J. Schmitz, J.L. L. Rezende, A phase field concept for multiphase systems, Physica D 94 (1996) 135–147. [21] I. Steinbach, F. Pezzolla, A generalized field method for multiphase transformations using interface fields, Physica D 134 (1999) 385–393. [22] J. Eiken, B. B€ ottger, I. Steinbach, Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application, Phys. Rev. 73 (2006), 066122-066129. [23] I. Steinbach, Phase-field models in materials science, Model. Simul. Mater. Sci. Eng. 17 (2009), 073001. [24] L. Zhang, M. Stratmann, Y. Du, B. Sundman, I. Steinbach, Incorporating the CALPHAD sublattice approach of ordering into the phase-field model with finite interface dissipation, Acta Mater. 88 (2015) 156–169. [25] L. Zhang, I. Steinbach, Y. Du, Phase-field simulation of diffusion couples in the Ni–Al system, Int. J. Mater. Res. 102 (2011) 371–380. [26] I. Steinbach, M. Apel, Multi phase field model for solid state transformation with elastic strain, Physica D 217 (2006) 153–160. [27] R.D. Kamachali, C. Schwarze, M. Lin, M. Diehl, P. Shanthraj, U. Prahl, I. Steinbach, D. Raabe, Numerical benchmark of phase-field simulations with elastic strains: precipitation in the presence of chemo-mechanical coupling, Comput. Mater. Sci. 155 (2018) 541–553. [28] M.A. Ali, J.V. G€ orler, I. Steinbach, Role of coherency loss on rafting behavior of Nibased superalloys, Com, Mater. Sci. 171 (2020) 109279.

Topological phase inversion during creep process, i.e. the precipitate gradually becoming the matrix phase, has been widely investigated in the literature [60–62]. Recently, Goerler et al. [29] studied the topo­ logical phase inversion in Ni-base superalloys after long-term aging treatment by means of Phase-field simulation. Goerler et al. [29] found that the driving force for phase inversion during long-term aging process is due to the loss of coherency of the precipitates, which is caused by the accumulation of dislocations at the interfaces. In the present work, the microstructure evolution of γ/γ0 binder phase in WC-Al-Co-Ni cemented carbide during long-term aging process was investigated with the consideration of the coherency loss of the γ0 precipitates. It was per­ formed by gradually releasing the lattice misfit between γ and γ0 phases and the interfacial energy between γ0 and γ0 phases like the way used by Goerler et al. [29]. The γ/γ0 microstructures from the presently simu­ lated results and experimentally detected one are shown in Fig. 7. Fig. 7 (d) presents the SEM micrograph of WC-Al-Co-Ni cemented carbide containing 45.83 vol.% γ0 precipitates after aging at 1373 K for 100 h [59]. Since it is impossible to perform a realistic time-scale simulation according to the experimental long-term aging process for 100 h, the present simulation is accelerated by accelerating the reduction of the misfit. During the long-term aging process, the microstructure evolution involves mainly two mechanisms. One is Ostwald ripening, which is driven by surface energy minimization. Additionally, γ-channels are no longer stable due to the formation of interfacial dislocations in the γ/γ0 interfaces and therefore the γ0 precipitates are able to coalesce [29]. As can be seen in Fig. 7(b), some small γ0 precipitates are dissolved into γ matrix according to the Ostwald ripening process, which is the main microstructure evolution at the early stage of long-term aging process. As the aging time goes on, the misfit between γ and γ0 phase is accom­ modated and the γ-channels gradually disappear, seeing Fig. 7(c). 5. Conclusions The microstructure evolution of γ0 precipitates in γ binder phase of WC-Al-Co-Ni cemented carbide is studied by means of multi-phase-field method. The CALPHAD databases are used to provide the thermody­ namic driving force and diffusivities during the simulation. The Gibbs energies of γ and γ0 phases are separately restored in a data file coupling to OpenPhase software in order to avoid the indistinguishable misci­ bility when coupling to CALPHAD databases via TQ interface. The effect of alloy composition and aging heat treatment on microstructure evo­ lution was extensively studied. The long-term aging heat treatment on the microstructure evolution was also investigated. The presently simulated results are compared where possible against experimental data, thereby vilidating the reliability of the CALPHAD databases and numerical parameters applied in the present work. The present work opens a way to design and optimize the processing parameters like alloy composition and heat treatment schedule in order to develop new highperformance materials. Declaration of competing interest The authors declared that they have no conflicts of interest to this work. 8

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Calphad 68 (2020) 101717

[29] J.V. Goerler, I. Lopez-Galilea, L.M. Roncery, O. Shchyglo, W. Theisen, I. Steinbach, Topological phase inversion after long-term thermal exposure of nickel-base superalloys: experiment and phase-field simulation, Acta Mater. 124 (2017) 151–158. [30] M.V. Acharya, G.E. Fuchs, The effect of long-term thermal exposures on the microstructure and properties of CMSX-10 single crystal Ni-base superalloys, Mater. Sci. Eng. A 381 (2004) 143–153. [31] M. Gebura, J. Lapin, Morphological changes of γ0 in Ni-based superalloy during long-term ageing, Metals (2008) 1–8, 2008. [32] J. Lapin, M. Gebura, T. Pelachov, O. Bajana, Microstructure degradation of nickel base single superalloy CMSX-4, Metals 2009 (2009) 1–8. [33] www.openphase.de. [34] M. Tegeler, O. Shchyglo, R.D. Kamachali, A. Monas, I. Steinbach, G. Sutmann, Parallel multiphase field simulations with OpenPhase, Comput. Phys. Commun. 215 (2017) 173–187. [35] Y. Wang, D. Banerjee, C.C. Su, A.G. Khachaturyan, Field kinetic model and computer simulation of precipitation of L12 ordered intermetallics from fcc solid solution, Acta Mater. 46 (1998) 2983–3001. [36] G. Rubin, A.G. Khachaturyan, Three-dimensional model of precipitation of ordered intermet, Acta Mater. 47 (1999) 1995–2002. [37] D. Banjerjee, R. Banerjee, Y. Wang, Formation of split patterns of γ0 precipitates in Ni-Al via particle aggregation, Scr. Mater. 41 (1999) 1023–1030. [38] L.Q. Chen, Y.Z. Wang, The continuum field approach to modeling microstructural evolution, J. Occup. Med. 48 (1996) 13–18. [39] K. Cheng, L. Zhanga, C. Schwarze, I. Steinbach, Y. Du, Phase-field simulation of liquid phase migration in the WC-Co system during liquid phase sintering, Int. J. Mater. Res. 107 (4) (2016) 309–314. [40] W. Guo, I. Steinbach, C. Somsen, G. Eggeler, On the effect of superimposed external stresses on the nucleation and growth of Ni4Ti3 particles: a parametric phase field study, Acta Mater. 59 (2011) 3287–3296. [41] www.thermocalc.de. [42] Y. Wang, P. Zhou, Y. Peng, Y. Du, B. Sundman, J. Long, T. Xu, Z. Zhang, A thermodynamic description of the Al-Co-Ni system and site occupancy in Co þ AlNi3 composite binder phase, J. Alloy. Comp. 687 (2016) 855–866. [43] P. Deng, Y. Du, W. Zhang, C. Chen, C. Zhang, J. Zhang, Y. Peng, P. Zhou, W. Chen, CSUDDCC2: an updated diffusion database for cemented carbides, in: P. Mason, et al. (Eds.), Proceedings of the 4th World Congress on Integrated Computational Materials Engineering, 2017, pp. 169–179. [44] L. Zhang, I. Steinbach, Y. Du, Phase-field simulation of diffusion couples in the Ni–Al system, Int. J. Mater. Res. 102 (2011) 371–380. [45] N. Dupin, I. Ansara, B. Sundman, Thermodynamic re-assessment of the ternary system Al-Cr-Ni, CALPHAD 25 (2001) 279–298.

[46] G. Kaptay, On the interfacial energy of coherent interfaces, Acta Mater. 60 (2012) 6804–6813. [47] Y. Liu, S. Liu, Y. Du, Y. Peng, C. Zhang, S. Yao, A general model to calculate coherent solid/solid and immiscible liquid/liquid interfacial energies, CALPHAD 65 (2019) 225–231. [48] C. Zhang, Y. Du, A Novel Thermodynamic model for obtaining solid-liquid interfacial energies, Metall. Mater. Trans. A 48 (2017) 5766–5770. [49] S. Popovic, B. Grzeta, V. Ilakovac, R. Kroggel, G. Wendrock, H. L€ offler, Lattice constant of fcc Al-rich α-phase of Al–Zn alloys in equilibrium with GP zones and β(Zn)-phase, Phys. Status Solidi A 130 (1992) 273–292. [50] M. Singh, M. Barkei, G. Inden, S. Bhan, High-temperature X-ray diffraction study on Co75Sn25 alloy, Phys. Status Solidi A 87 (1985) 165–168. [51] J.W. Cable, Y. Tsunoda, Magnetic moments and short-range order in CoMn and NiMn alloys, J. Magn. Magn. Mater. 140/144 (1995) 93–94. [52] R. Oguma, T. Eguchi, S. Matsumura, S.K. Son, Domain growth and off-phase boundary structures in L12-type ordering, Acta Mater. 54 (2006) 1533–1539. [53] Y. Wang, A.G. Khachaturyan, Shape instability during precipitate growth in coherent solids, Acta Metall. Mater. 43 (1995) 1837–1857. [54] M. Yang, H. Wei, J. Zhang, Y. Zhao, T. Jin, L. Liu, X.F. Sun, Phase-field study on effects of antiphase domain and elastic energy on evolution of γ¢ precipitates in nickel-based superalloys, Comput. Mater. Sci. 129 (2017) 211–219. [55] I. Lopez-Galilea, S. Huth, W. Theisen, T.H. Fockenberg, S. Chakraborty, Effect of high pressure and high temperature on the microstructural evolution of a single crystal Ni-based superalloy, J. Mater. Sci. 48 (2013) 348–358. [56] Q. Wu, S. Li, Alloying element additions to Ni3Al: site preferences and effects on elastic properties from first-principles calculations, Comput. Mater. Sci. 53 (2012) 436–443. [57] A.B. Kamara, A.J. Ardell, C.N.J. Wagner, Lattice Misfits in four binary Ni-base γ/γ¢ alloys at ambient and elevated temperatures, Metall. Mater. Trans. A 27 (1996) 2888–2896. [58] S.V. Prikhodko, J.D. Carnes, D.G. Isaak, A.J. Ardell, Elastic constants of a Ni-12.69 at.%Al alloy from 295 to 1300 K, Scr. Mater. 38 (1998) 67–72. [59] J. Long, Study on the Relationship between Microstructure and Property of Co-NiAl Bonded Cemented Carbide, Ph.D. Thesis, Central South University, 2017. [60] A. Epishin, T. Link, U. Brueckner, P.D. Portella, Kinetics of the topological inversion of the γ/γ0 -microstructure during creep of a nickel-based superalloy, Acta Mater. 49 (2001) 4017–4023. [61] P. Caron, C. Ramusat, F. Diologent, Influence of the γ0 fraction on the γ/γ0 topological inversion during high temperature creep of single crystal superalloys, in: Proceedings of the 11th International Conference on Superalloys, 2008, pp. 159–167. [62] J. Boisse, N. Lecoq, R. Patte, H. Zapolsky, Phase-field simulation of coarsening of γ precipitates in an ordered γ0 matrix, Acta Mater. 55 (2007) 6151–6158.

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