Two-dimensional phase-field simulations of competitive dendritic growth during laser welding

Materials and Design 181 (2019) 107980

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Two-dimensional phase-field simulations of competitive dendritic growth during laser welding Mi Gaoyang a, Xiong Lingda b,⁎, Wang Chunming c, Jiang Ping b, Zhu Guoli b a b c

State Key Lab of Material Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan, China School of Mechanical Science and Engineering, Huazhong University of Science and Technology, China Wuxi Institute of Huangzhong University of Science and Technology, China

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• Competitive growth of dendrites with different crystalline orientations is studied. • The cellular dendrites first appear from planar interface nearby grain boundaries. • Dendrites with small inclined angle can overgrow dendrites with 00 inclined angle. • Lateral dendritic growth, grain boundary angle and side branch affect grain width.

a r t i c l e

i n f o

Article history: Received 18 April 2019 Received in revised form 6 June 2019 Accepted 26 June 2019 Available online 27 June 2019 Keywords: Phase-field model Competitive dendritic growth Laser welding Al-Cu alloy Crystalline orientation Grain boundary

a b s t r a c t A phase-field model is applied to study competitive dendritic growth between different grains with different crystalline orientations during laser welding of Al-Cu alloy. An unfavorable oriented (UO) grain is set to locate between two favorable oriented (FO) grains to study the dendritic growth behaviors at not only converging grain boundary (GB) but also diverging GB. It is found that the cellular dendrites appear firstly nearby the GBs at initial instability stage. At early competitive growth stage, the UO misalignment angle influences the competitive dendritic growth at both GBs. After completely entering competitive growth stage, the leading dendrites that are much faster than other dendrites at GBs firstly grow in lateral direction. The side branches growing from leading dendrites block growth path of nearby dendrites and change the UO/FO grain widths. The converging GB deflection angle and the side branch development at diverging GB as characteristic competitive dendritic growth behavior at relatively steady growth stage also significantly affect UO and FO grain widths. The numerical results are basically consistent with microstructure obtained by experiment. © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

⁎ Corresponding author. E-mail address: [email protected] (X. Lingda).

As a joining technology, laser welding is widely applied in the manufacturing industries. The solidification process and resulting microstructure determine the properties of weld joints [1]. For better understanding of the formation of microstructure in fusion zone, it is

https://doi.org/10.1016/j.matdes.2019.107980 0264-1275/© 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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M. Gaoyang et al. / Materials and Design 181 (2019) 107980

important to investigate the solidification process during laser welding. However, experimental observation of solidification behavior and the microstructure evolution during welding is hard to achieve. After decades of development, numerical simulation has offered a new approach to gain an insight of solidification behaviors in welding [2]. In recent years, the phase-field method has been introduced to study the solidification process in molten pool during welding. It introduces an order parameter (i.e. phase field) to indicate phase state and avoid complex front tracking [3]. Farzadi et al. [4] used phase-field model to simulate solidification microstructures in the molten pool during gas tungsten arc welding. However, the temperature gradient and pulling velocity applied in the model were constant values, which was not consistent with the fact that temperature gradient and pulling speed in the molten pool change over time. Zheng et al. [5] coupled 2-D double ellipsoid heat source model to phase-field model to investigate onset of initial morphological during the solidification of welding pool of Al-4%wt Cu alloy, which took the time-dependent temperature gradient and pulling velocity in molten pool into consideration. Wang et al. [6] coupled this model with flow-field model to study fluid velocity distribution near solid-liquid interface(S/L interface) for Al-4%wt Cu alloy GTAW. Besides, Wang et al. [7] investigated dendritic growth and solute concentration in forced convection for laser welding of Al-4%wt Cu alloy. Yu et al. [8] investigated the influence of preferred crystalline orientation on dendritic growth. It was found that the angle between the direction of crystalline orientation and direction of temperature gradient determined the morphology of microstructure and the growth direction of dendrites. Wang et al. [9] found that the dendrites in fusion zone were curved due to the change of S/L interface direction in a moving molten pool. By comparing numerical result applying different sets of welding parameter, Yu et al. [10] found that the initial instability dynamics was affected by the welding parameter which determined the thermal gradient and growth rate in the solidification process. However, the effect of competitive dendritic growth between different grains with different crystalline orientations on microstructure evolution has been neglected in above model. Dendrites with different crystalline orientations compete with each other during their growth process [11]. Tourret et al. [12] used phase-field modeling to study grain growth competition during thin-sample directional solidification. By analyzing data obtained by numerical results, they revised the grain boundary (GB) selection law. They [13] also found that noise close to the tip of a dendritic grain significantly favors that grain in the dendritic branching competition at the diverging GB. Chunwen Guo [14] et al. studied dendritic growth competition by 3-D phase-field simulation and found that the new primary arms could develop from the FO dendrites along two directions to occupy the gap left by the UO grains, which led to a faster overgrowth rate of the UO grains than that in the case of diverging growth in 2D. Zhou et al. [15] found the UO dendrites were able to overgrow the FO dendrite at converging GB in directional solidification of a nickel-base superalloy. Tomohori Takaki et al. [16] found that a relatively large amount of unexpected UO dendrites could survive during unidirectional solidification by a very-large-scale 3-D phase-field simulation. Takaki [17] set 3 dendrite groups with different crystalline orientation arrays to investigated the unusual growth phenomenon (the FO grain is overgrown by UO grain during directional solidification). When the grains on both sides grew towards the middle FO grain, the middle FO grain was easily overgrown even with very small inclination angle. In another study, Tomohiro [18] found the unusual growth phenomenon (FO dendrites were overgrown by UO dendrites) only occurred when the angle between crystalline orientation of UO grain and thermal gradient was less than 170 for a Ni-based super alloy. Li et al. [19] studied dendritic growth competition at the converging GB. It was found that the unusual growth phenomenon only occurred when the distance between FO dendrite and UO dendrite at converging GB decreased to a threshold value before the FO dendrite was eliminated. The above works has proved that dendritic growth competition significantly affects the dendritic morphology at grain

boundary and grain size. Therefore, it is essential to consider dendritic growth competition between different grains with different crystalline orientations in simulation of solidification process in molten pool during laser welding. In the present work, a phase-field model is used to study influence of dendritic growth competition between different grains with different crystalline orientations on microstructure evolution in molten pool during laser welding. Different grain arrays with different crystalline orientations were set to study the dynamics of dendrite evolution at all stage during welding. Finally, experiment has been conducted to verify the numerical result. 2. Models and experiments 2.1. Macroscopic model The transient condition macroscopic model developed by Zheng [5] is applied to obtain the time-dependent pulling speed Vp and thermal gradient G. The macrograph of molten pool is shown in Fig. 1. It is composed of two half ellipsoids. The rear ellipsoid is the solidification area of the molten pool. The yellow region showed in Fig. 1 is the computational domain. The depth and rear length of the solidification area are defined as al and bl respectively. The temperature at molten pool edge is the equilibrium liquidus temperature. Tp is the temperature value at the center of molten pool, which is maximum value of temperature in the molten pool. V is the welding velocity (i.e. the moving velocity of molten pool). α is the angle between pulling velocity of S/L interface and welding velocity. Vp(t) and G(t) are the pulling velocity and temperature gradient, respectively. Hence, Vp(t) and G(t) can be expressed as: a V 2t  V p ðt Þ ¼ pffiffiffiffiffiffi  l 2 4 V 2 t 2 al 2 −bl þ bl T p −T l ffi Gðt Þ ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1−V 2 t 2 V 2 t 2 þ al 2 2 bl

ð1Þ

ð2Þ

2.2. Phase-field modeling To simulate the solidification behavior in the molten pool, the phasefield model for welding of dilute binary alloy [20] is applied. The ‘frozen temperature approximation’ is adopted.   Z t 0 T ðz; t Þ ¼ T 0 þ Gðt Þ z− V p ðt 0 Þdt 0

ð3Þ

where T0 = T(Z0,t) is a reference temperature, G(t) is the temperature gradient along pulling direction. In the phase-field model, a continuous scalar field φ is introduced to determine the phase at every point. φ = +1 in solid phase and φ = −1 in liquid phase. The φ value continuously varies across S/L interface. The solute concentration is characterized by a dimensionless supersaturation field U, which can be expressed as U¼

 1 2kc=c∞ −1Þ 1−k 1−φ þ kð1 þ φÞ

ð4Þ

where k is equilibrium partition coefficient and c∞ is the global sample composition. The forms of governing equations of the phase field and supersaturation field in two dimension can be expressed by Eqs. (5) and (6),

M. Gaoyang et al. / Materials and Design 181 (2019) 107980

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Fig. 1. Macrograph of the molten pool.

0.8839 and a2 = 0.6267, DL is the diffusion coefficient in the liquid region and d0 = Γ/(|m|(1 − k)c0l ) is the capillarity length. lT is the dimensionless thermal length and can be expressed as:

respectively: " # Rt _2 z− 0 V p ðt 0 Þdðt 0 Þ ∂φ τ0 a n 1−ð1−kÞ lT ∂t _1 _ 11 0 0 0   ! 2  ∂a n 2  ∂a n ! _2 ! _ _ A þ ∂y @ ! AA ¼ W 2 @ ∇ a n ∇ φ þ ∂x @ ∇ φ a n ∇ φ a n

∂ð∂x φÞ ∂ ∂y φ " þ φ−φ3 −λgðφÞ U þ

z−

Rt 0

ð5Þ

# V p ðt 0 Þdðt 0 Þ lT

0 1   ! _ ! 1 þ k 1−k ∂U !B ∂φ ∇ φ C − φ ¼ ∇ @DL qðφÞ ∇ U þ a n W ½1 þ ð1−kÞU  ! A 2 2 ∂t ∂t ∇ φ

lT ¼

jmjð1−kÞc0l Gðt Þ

ð7Þ

where m is the liquidus slope of Al-Cu alloy, cl 0 ¼ c∞ =k is the equilibrium solute concentration on the liquid side of the interface. The form of the fourfold anisotropy of the surface tension in 2-D system can be expressed as: ð6Þ

1 ∂φ þ ½1 þ ð1−kÞU  2 ∂t

where axis z is the pulling direction of S/L interface. W is the interface width (length scale). τ0 is the relaxation time(time scale). g(φ) = (1φ2)2. q(φ) = (1-φ)/2. λ is a coupling constant for convergence. W and τ0 can be obtained via W = d0λ/a1 and τ0 = a2λW/DL, where a1 =

_ a n ¼ 1 þ ε0 cos4ðθ þ θ0 Þ

ð8Þ

where ε0 is the anisotropy strength, θ is the angle between the interface normal and pulling direction when θ0 is the misalignment angle between preferred crystalline orientation and temperature gradient direction as shown in Fig. 2.

Fig. 2. The schematic diagram of θ and θ0.

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2.3. Computational detail In order to study competitive dendritic growth at not only converging GB but also diverging GB, the initial condition is set as shown in Fig. 4. A 2D computational domain with grid size of 3000△x ∗ 2000△y was established (△x = △y = 0.8 W). The solid phase is consisted of 3 grains. An unfavorable oriented grain is set to locate between two favorable oriented grains. The middle UO grain width is 1600△x and the width of FO grains on both sides is 700△x. W is set to 3.4 ∗ 10−8 m for convergence. The upper and lower boundaries are set as zero-Neumann boundary condition. Periodic boundary conditions are applied to the other boundaries. A time step size △t = 0.02 (b△x2/4DLτ0) was chosen to applied in computation. The evolution of phase field and solute concentration field are obtained by calculating the governing Eqs. (5) and (6). The total number of iteration is 1.5 ∗ 106, corresponding to actual time 0.0582 s for the solidification process. The self-developed code was programmed by C. Finite difference method with CUDA 9.2 parallelization was used to solve the governing equations.

Fig. 3. 8 neighboring points around pointi,j.

In order to characterize crystalline orientations of different grains, an index field S is introduced to each point in computational domain at the beginning. S equals to 0 in the liquid, −1 in UO grains and 1 in FO grains respectively. When the φ value of the point in liquid region increases and exceeds −0.99, the S value of its 8 neighboring points as shown in Fig. 3 will be summed up. If the sum is N0, S value of this point is set to be 1 and its θ0 equals to θFO; If the sum is b0, S value of this point is set to be −1 and its θ0 equals to θUO. Once the S value of this point is not equal to 0, it does not change further [13]. In the present model, the crystalline orientation of FO grains is designed to be parallel to temperature gradient, which means θFO equals to 00. 50, 100, 200, 300, 400 and 450 are selected as θUO, that is, the values of misalignment angles between crystalline orientation of UO grain and temperature gradient direction due to the four-fold symmetry of the cubic crystal structure.

2.4. Experiment design and material properties Laser welding experiments were conducted to verify numerical results. The welded material is Al-4%wt Cu alloy 2A12. The thickness of the alloy was 4 mm. The laser welding experiment was conducted by an IPG YLR-4000 fiber laser with a peak power of 4.0 kW and an ABB IRB4400 robot as shown in Fig. 5. Pure argon at a flow rate of 1.5 m3/h was used for top surface shielding. The defocusing distance is 0 mm. The laser power was 3.0 kW and the welding speed was 1.8 m/min. Chemical composition of the material is shown in Table.1. After laser welding, the longitudinal section of the welded joint was cut from the workpiece. Microstructure of welded joint was observed by Scanning Electron Microscopy (SEM). The crystalline orientations of grains near fusion line were measured by Electron Back-Scattered Diffraction (EBSD).

Fig. 4. Initial set of planar crystal.

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Fig. 5. Welding devices: (a) IPG YLR-4000 fiber laser; (b) ABB IRB4400 robot.

The physical properties of aluminum alloy 2A12 used in the phasefield model are listed in Table 2 [21]. Table 1 The chemical composition of 2A12 in wt%.

3. Result and discussion

Element

Al

Cu

Mg

Mn

Wt%

94.38

3.92

1.08

0.62

Table 2 Physical properties of Al-4wt%Cu alloy.

The dendritic growth from fusion line during welding is consisted of four stages: linear growth stage, initial instability stage, competitive growth stage and relatively steady growth stage by Wang [22]. In the result and discussion section, the competitive dendritic growth behavior at these stages will be discussed in detail. 3.1. Linear growth and initial instability

Properties

Value

Unit

Alloy composition: c∞ Liquidus temperature: TL Liquidus slope: m Equilibrium partition coefficient: K Anisotropy of surface energy: ε0 Liquid diffusion coefficient: DL Gibbs-Thomson coefficient: Γ

4 922.9 −2.6 0.14 0.01 3.0 ∗ 109 2.4 ∗ 10−7

wt% K K/wt% / / m2/s K∗m

At the linear growth stage, the advancing velocity of UO S/L interface is the same as FO S/L interface. The S/L interface advances towards to liquid region as planar crystal. As the solute accumulates at the liquid side of S/L interface and the pulling velocity increases, the S/L interface undergoes a Mullins-Sekerka instability [21]. Fig. 6 shows the morphologies of S/L interface with different UO misalignment angles. The cellular dendrites appear firstly nearby the GBs. The dendrite tip heights at the GBs are shown in Fig. 7. At the GBs, what is surprising is that the UO cellular dendrite tips grow far ahead of the FO cellular dendrite tips when θUO b 300 for converging GB and θUO is b400 for diverging GB,

Fig. 6. S/L interface morphologies with different UO misalignment angles: (a) θUO = 50; (b) θUO = 100; (c) θUO = 200; (d) θUO = 300; (e) θUO = 400; (f) θUO = 450.

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Fig. 9. The φ difference value between the peak value at GB's UO side and the valley value at GB's FO side as a function of time. Fig. 7. The dendrite tip heights at the GBs.

respectively. However, the FO cellular dendrite tips catch up with the UO cellular dendrite tips when θUO ≥ 300 for converging GB and θUO ≥ 400 for diverging GB, respectively. As shown in Fig. 8a, the growth of UO cellular dendrite is faster than that of FO cellular dendrite at GBs. The solute diffusion around leading UO cellular dendrite tip affects the solute layer of FO dendrite tip when θUO is small. Therefore, the FO cellular dendrite tip velocity decreases and the UO cellular dendrite tips grows ahead of the UO crystal dendrite tips. Since dendrites of both crystals converge at converging GB, the solute diffusion around FO cellular dendrite also affects solute layer of UO cellular more easily than at diverging GB. When θUO is large, the FO cellular dendrite exceeds

UO cellular dendrite at converging GB more easily. Therefore, the critical angle for converging GB(i.e. 300) is smaller than the critical angle for diverging GB(i.e. 400). To illustrate the reason why cellular dendrites grow firstly at both GBs, the S/L interface φ and solute distribution when θUO is 100 at different time steps are shown in Fig. 8 as an example. It is found that the φ value of UO S/L interface is always higher than that of FO S/L interface at the beginning of linear growth stage. The function q(φ) = (1-φ)/2 in the supersaturation field governing equation indicates the solute diffusivity ability. Therefore, solute diffusivity at UO S/L interface is more difficult than that at FO S/L interface. At UO/FO GBs, the solute is easy to diffuse from UO side to FO side. At that circumstance, there will be

Fig. 8. The S/L interface φ and solute distribution when θUO is 100 as a function of time.

M. Gaoyang et al. / Materials and Design 181 (2019) 107980

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Fig. 10. Dendrite tip positions evolution at the beginning of competitive growth stage: (a) θUO = 50; (b) θUO = 100; (c) θUO = 200; (d) θUO = 300; (e) θUO = 400; (f) θUO = 450.

a solute concentration peak at FO side and a solute concentration valley at UO side, which makes the constitutional undercooling is higher at UO side. This phenomenon promotes cellular dendritic growth at GB's UO side and suppresses cellular dendritic growth at GB's FO side. Meanwhile, the solute diffusivity at UO side is going to be more difficult when the solute diffusivity at UO side is going to be easier over time. With efforts of above factors, the φ difference value between the peak value at GB's UO side and the valley value at GB's FO side increases with time. The φ difference value between the peak value at GB's UO side and the valley value at GB's FO side as a function of time is shown in Fig. 9. The differences increase over time. At the same time step, the differences increase with UO misalignment angle increasing, which means that increasing UO misalignment angle promotes the cellular dendritic growth at UO side of GB. 3.2. Competitive dendritic growth After interface loses its stability, the cellular dendrites keep growing and translate into dendrites. At the beginning of competitive dendritic growth stage, the dendrites at converging GB grow and start competing with each other. Fig. 10 shows the change of FO/UO dendrite tip positions at converging GB with time. It can be found that when θUO b 300, the UO dendrite grows towards the FO dendrite and suppresses the FO dendrite. FO dendrite grows along UO dendritic growth direction. However, when θUO ≥ 300, the UO dendrite grows towards the FO

dendrite and FO dendrite grows along UO dendritic growth direction at first. Nevertheless, FO dendrite tip grows faster than UO dendrite tip at pulling direction. When FO dendrite tip exceeds UO dendrite tip, the growth path of UO dendrite tip is blocked by FO dendrite. All of these are consistent with the competitive dendritic growth in initial instability stage. What is interesting is that the blocked UO dendrite does not stop growing but change its growth direction to the opposite direction as shown in Fig. 11. It is caused by the difference of solute concentration on the both sides of UO dendrite. When UO dendrite grows towards FO dendrite at first, solute accumulates between FO and UO dendrites at converging GB. At this circumstance, the solute concentration at this side of FO dendrite is higher than that of another FO dendrite side. So the constitutional undercooling at another side is higher, which promotes FO dendrite grows along UO dendrite direction. When UO dendritic growth path is blocked by FO dendrite, the solute between FO and UO dendrite at converging GB cannot diffuse to somewhere else. It is much higher than solute concentration on another UO dendrite side. Therefore, the constitutional undercooling at another UO side is higher, which promotes the UO dendrite to grow in the opposite direction. At diverging GB, UO and FO dendrite grows in opposite direction as shown in Fig. 12. When θUO b 300, UO dendritic deflection angle increases with the increasing of θUO. Fig. 13 shows UO dendritic deflection angle at early competitive growth stage as a function of UO misalignment angle. When θUO b 300, the UO dendritic deflection angle is approximately a proportional function of θUO. The scaling factor in the

Fig. 11. FO/UO dendritic growth competition at early competitive growth stage: (a) θUO = 50; (b) θUO = 100; (c) θUO = 200; (d) θUO = 300; (e) θUO = 400; (f) θUO = 450.

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Fig. 12. Dendrite tip position evolutions at the beginning of competitive growth stage: (a) θUO = 50; (b) θUO = 100; (c) θUO = 200; (d) θUO = 300; (e) θUO = 400; (f) θUO = 450.

function is 0.8. When θUO ≥ 300, UO dendritic growth model translates into seaweed-like model [23]. The dendritic growth velocity decreases sharply. With seaweed-like dendritic growth model, the dendritic deflection angle has no explicit relationship with θUO. Fig. 14 shows dendritic competitive growth after completely entering competitive growth stage. The white dashed line is GB between FO and UO dendrites. It is found that GB direction is significantly influenced by FO/UO dendritic growth competition at early competitive growth stage. The crystalline orientation of leading dendrite at early competitive growth stage will affect FO and UO grain widths. At converging GB, when θUO is 50, UO and FO dendrites grow at the same rate. No dendrite is suppressed after completely entering

competitive stage. When θUO is larger than 50, as we can see in Fig. 14b–f, the leading dendrites first grow along lateral direction, in accordance with the finding by Takaki [17]. The larger thermal undercooling at lower position is the main cause for the lateral dendritic growth. The well-developed side branches from lateral dendritic growth suppress the surrounding dendrites with slower growth rate. Moreover, the converging GB migrates along these side branches. When θUO is 100 or 200, the leading dendrite is UO dendrite. With θUO increasing, the distance that GB migrates to FO grain increases. When θUO is larger than 200, the leading dendrite is FO dendrite. The converging GB migrates to UO grain. When θUO is 50, the diverging GB does not migrate much as the converging GB. When θUO is 100, the leading dendrite at diverging GB is UO dendrite and diverging GB migrates along its side branch to FO grain. When θUO is larger than 100, the leading dendrite is FO dendrite and the diverging GB migrates to UO dendrite, except that when θUO is 200, the FO dendrite grows faster and finally catches up the leading UO dendrite. In addition, the side branches of FO dendrite develop better and the distance that diverging GB migrates laterally to UO grain increases with increasing θUO when θUO ≥ 300. With the effect of lateral side branch growth, FO/UO grain widths have changed. However, FO/UO grain widths are also influence by other factors. These factors will be discussed in Section 3.3. 3.3. Relatively steady growth

Fig. 13. UO dendritic deflection angle at early competitive growth stage as a function of UO misalignment angle.

As shown in Fig. 15, dendrite morphology at relatively steady growth stage (time step = 1.5 ∗ 106) is very different from dendrite morphology in Fig. 14 (time step = 106) at competitive growth stage. We measured the distance between FO dendrites at both side of UO grain as a characteristic datum to evaluate FO grain width. Fig. 16 shows it as a function of θUO. With large θUO (larger than 200), FO dendrites suppress UO dendrites and FO grain width increases with increasing θUO due to lateral growth of leading FO dendrite at converging GB and FO dendrite side branch development at diverging GB. UO dendrites are even completely overgrown when θUO is 450. With small θUO

M. Gaoyang et al. / Materials and Design 181 (2019) 107980

Fig. 14. Dendritic growth in lateral direction: (a) θUO = 50; (b) θUO = 100; (c) θUO = 200; (d) θUO = 300; (e)θUO = 400; (f) θUO = 450.

(smaller than or equal to 200), FO grain width decreases compared to the initial width 1400△x. It is notable that when θUO is 100 or 450, FO grain width increases much after completely entering competitive growth stage. When θUO is 100, FO dendrites are severely suppressed by UO dendrite at converging GB. When θUO is 450, UO dendrites are completely eliminated by FO dendrites, which is caused by a. the lateral growth of leading FO dendrite at competitive growth stage; b. converging GB deflection angle; c. side branch development of FO dendrite at diverging GB. Fig. 17 shows the deflection angle of converging GB at relatively steady growth stage. No FO dendrite is overgrown by UO dendrite at converging GB. When θUO is less than 200, the converging GB deflection angle is larger than 00. When θUO is larger than or equal to 200, the converging GB deflection angle is 00. With non-zero converging GB deflection angle, UO dendrite forces FO dendrite at converging GB to grow along converging GB direction. Meanwhile, UO grain width increases and FO grain width decreases. The dendritic spacing also affects converging GB direction. The UO dendrites at converging GB showed in Fig. 15b and c are not the initial UO dendrites at converging GB at competitive growth stage showed in Fig. 14b and c, which have been eliminated by FO dendrites at converging GB. When θUO is 100 in Fig. 14b, the UO dendritic spacing is 3.66 μm. After the initial UO dendrite at converging GB is eliminated, the UO dendrite next to it keeps approaching FO dendrite at converging GB. The UO dendrite spacing is smaller than a

Fig. 16. FO grain width as a function of UO misalignment angle.

Fig. 15. Dendrite morphology at relatively steady growth stage(time step = 150 ∗ 104): (a) θUO = 50; (b) θUO = 100; (c) θUO = 200; (d) θUO = 300; (e) θUO = 400; (f) θUO = 450.

9

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M. Gaoyang et al. / Materials and Design 181 (2019) 107980 Table 3 UO/FO grain crystalline orientation and temperature gradient.

Fig. 17. Deflection angle of converging GB at relatively steady growth stage.

Angle between grain orientation and temperature gradient

Diverging GB

Converging GB

2-D

3-D

2-D

3-D

UO FO

37.6 5.0

37.8 10.2

34.8 15.7

41.7 17.2

tip, the solute concentration around the lagged UO dendrite cannot interact with the solute concentration around FO dendrite at converging GB. Therefore, FO dendrite at converging GB keeps growing along its crystalline orientation and suppresses all the coming UO dendrites. Finally, converging GB deflection angle is 00 when θUO is 200. At diverging GB, side branches determine the GB position. As shown in Fig. 17, the diverging GB deflection angle is 00. The diverging GB position with small θUO(less than 300) are similar. With large θUO (larger than or equal to 300), FO dendrite grows much faster than UO dendrite at diverging GB as shown in Fig. 15. In this circumstance, side branches grow from FO dendrite due to the high constitutional undercooling and block the UO dendrite at diverging GB. 3.4. Experimental result

threshold value. Therefore, the solute concentration around the next coming UO dendrite interacts with that around FO dendrite at converging GB, which decreases undercooling and velocity of FO dendrite at converging GB. Finally, the next coming UO dendrite tip catches up with growing FO dendrite tip at converging GB [19]. When θUO is 200 in Fig. 14c, the UO dendritic spacing is 5.13 μm, which is larger than the threshold value. The FO dendrite tip has enough time to grow ahead of the next coming UO dendrite before the solute concentration around the next coming UO dendrite interacts with that around FO dendrite at converging GB. When FO dendrite tip is ahead of UO dendrite

Experiment was conducted to verify numerical result. SEM and EBSD were applied to observe microstructure and crystalline orientation. For Al-Cu alloy materials with a face-centered-cubic crystal structure, the trunk of dendrites (or cells) grow in the 〈100〉 direction [24]. Typical microstructure around GBs is presented by Fig. 18. By measuring 〈100〉 crystalline direction and temperature gradient direction, GB type was confirmed. Table 3 shows angle between UO/FO grain crystalline orientation and temperature gradient. According to Table 3, the 2-D angles are similar to corresponding 3-D angles, which means the FO/UO

Fig. 18. EBSD inverse pole map and pole figure: (a) diverging GB (b) converging GB.

M. Gaoyang et al. / Materials and Design 181 (2019) 107980

crystalline orientations are basically parallel to EBSD observation plane. In Fig. 18a, θFO is 5.00 and θUO is 37.60. Diverging GB direction is the same as temperature gradient. However, diverging GB position gradually migrates to UO grain. In Fig. 18b, θFO is 15.70 and θUO is 34.80. Converging GB migrates to UO grain and FO dendrites suppress UO dendritic growth. All these findings are basically generally consistent with numerical results. 4. Conclusion Competitive dendritic growth between different grains with different crystalline orientations during laser welding has been investigated using a 2-D phase-field model. Experiments have been conducted to verify the numerical result. The conclusion are as follows: (1) At initial instability stage, the cellular dendrites appear first nearby the GBs. (2) At early competitive growth stage, with small UO misalignment angle, UO dendrite grows faster than FO dendrites at GBs; with large UO misalignment angle, FO dendrite grows faster than UO dendrites at GBs. Besides, after completely entering competitive stage, the leading dendrites at GB first grow along lateral direction. (3) FO and UO grain widths are affected by 3 factors: a. the lateral growth of leading dendrite; b. converging GB deflection angle; c. side branch development of FO dendrites at diverging GB. However, it should be pointed out that dendrites grow in the 3-D space during welding in reality, which is more complicate than 2-D numerical simulation. 2-D phase-field numerical simulation cannot completely reveal the mechanism of microstructure evolution [25]. Besides, as shown in Fig. 1, S/L interface direction keeps changing during welding, leading to the curved growth of dendrites [26]. Therefore, it is essential to take the angle α between welding velocity and pulling velocity into consideration. The 3-D phase-field simulation of competitive dendritic competition in molten pool during welding with more accurate heat source model is our next goal of further study. CRediT authorship contribution statement Mi Gaoyang:Conceptualization, Writing - original draft, Software. Xiong Lingda:Investigation, Data curation, Writing - review & editing. Wang Chunming:Funding acquisition.Jiang Ping:Resources.Zhu Guoli:Supervision. Acknowledgement This work is supported by the National Natural Science Foundation of China (Grant No. 51705173), the Key Research and Development Program of Jiangsu Province of China (BE2016005-1) and Science and Technology Planning Project of Guangdong Province (Grant No. 2017B090913001). The authors are grateful to the Analysis and Test Center of HUST (Huazhong University of Science and Technology) and the State Key Laboratory of Material Processing and Die & Mould Technology of HUST, for their friendly cooperation. The authors acknowledge Ph.D Liu Jizi and postgraduate Qin Yonggui in Nanjing University of Science and Technology for many useful discussions. Data availability The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

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