316L激光粉末床熔覆IN718偏析带形成过程的模拟

图1 激光粉末床熔覆示意图

Fig.1 Schematic of laser powder bed cladding

为在保证计算精度的前提下提高求解效率，本模型主要假设如下：(1) 模型中只考虑固相和液相，且两相体积分数之和f_s + f_l = 1；(2) 激光光源作用在熔池表面，且能量呈Gaussian分布；(3) 熔融流体在熔池中为不可压缩、层流的Newton流体；(4) 粉末为连续的固相，熔化后再凝固；(5) 忽略蒸汽和反压力的作用；(6) 不考虑凝固收缩；(7) 晶粒无运动；(8) 不考虑元素间的相互作用和再分配；(9) 由于实验中IN718粉末层较少，熔覆涂层稀释率较高，IN718合金的影响相对较小，模型中的热物性参数主要参考316L不锈钢，液相线温度主要根据2种材料中的元素含量计算获得。本工作只考虑Fe、Cr和Ni 3种主要元素，将多元合金简化为等效的Fe-X (X = Ni、Cr)二元系。等效初始质量分数( ${\bar{c}}_{0}$ )、等效分配系数( $\bar{k}$ )、等效液相线斜率( $\bar{m}$ )和等效溶质扩散系数( $\bar{D}$ )可由下式计算得到^[9]：

{\bar{c}}_{0} = \sum_{i = 1}^{N - 1} c_{0_{i}}

(1)

{\bar{c}}_{0} \cdot \bar{m} = \sum_{i = 1}^{N - 1} m_{i} c_{0_{i}}

(2)

{\bar{c}}_{0} \cdot \bar{m} / \bar{k} = \sum_{i = 1}^{N - 1} m_{i} c_{0_{i}} / k_{i}

(3)

{\bar{c}}_{0} \cdot (1 - \bar{k}) \cdot \bar{D} = \sum_{i = 1}^{N - 1} c_{0_{i}} (1 - k_{i}) D_{i}

(4)

式中，下标i表示第i个二元系中的物理性质，N为合金中的元素个数，c₀为初始元素的质量分数，k为溶质元素的分配系数，m为溶质元素的液相线斜率，D为溶质元素的扩散系数。

本模型中将计算域中的每一个网格单元作为一个元胞，每个元胞有液相胞、固相胞和界面胞 3种状态，根据元胞的固相体积分数和角点生长算法实现元胞在不同状态之间的转换^[10,11]。固/液界面的推移由固/液界面的溶质通量平衡确定^[12~15]：

V_{n} c_{l}^{*} (1 - \bar{k}) = ({\bar{D}}_{s} (\frac{\partial c_{s}}{\partial x} + \frac{\partial c_{s}}{\partial y}) - {\bar{D}}_{l} (\frac{\partial c_{l}}{\partial x} + \frac{\partial c_{l}}{\partial y})) \cdot n

(5)

式中， V_n为固/液界面的法向生长速度，m/s； $c_{l}^{*}$ 为固/液界面的液相平衡浓度； ${\bar{D}}_{s}$ 为等效固相扩散系数； ${\bar{D}}_{l}$ 为等效液相扩散系数；c_s为固相溶质浓度；c_l为液相溶质浓度； n 为界面法向量。沿x方向的生长速率表达式为：

$V_{x}=\frac{1}{\Delta x(1-\bar{k}) c_{1, \mathrm{P}_{0}}^{*}}\left\{\bar{D}_{\mathrm{s}}\left[\left(c_{\mathrm{s}, \mathrm{P}_{0}}^{*}-c_{\mathrm{s}, \mathrm{~L}}\right) f_{\mathrm{s}, \mathrm{~L}}+\left(c_{\mathrm{s}, \mathrm{P}_{0}}^{*}-c_{\mathrm{s}, \mathrm{R}}\right) f_{\mathrm{s}, \mathrm{R}}\right]+\right. \\ \left.\bar{D}_{1}\left[\left(c_{1, \mathrm{P}_{0}}^{*}-c_{1, \mathrm{~L}}\right)\left(1-f_{\mathrm{s}, \mathrm{~L}}\right)+\left(c_{1, \mathrm{P}_{0}}^{*}-c_{1, \mathrm{R}}\right)\left(1-f_{\mathrm{s}, \mathrm{R}}\right)\right]\right\}$(6)

式中，V_x 为液/固界面在x方向上的生长速率，m/s；Δx为网格尺寸； $c_{s}^{*}$ 为固/液界面的固相平衡浓度；下标P₀、L和R分别表示当前界面胞及与其左右两侧的相邻胞。液/固界面在y方向上的生长速率(V_y )的计算表达式与V_x 类似。当经过时间步长(Δt)后，界面胞中固相率的增量(Δf_s)为：

Δ f_{s} = \frac{Δ t}{Δ x} (V_{x} + V_{y} - V_{x} V_{y} \frac{Δ t}{Δ x})

(7)

c_{l}^{*} = \frac{T - T_{f} - Γ κ f (φ, θ)}{\bar{m}}

(8)

式中，T为液态金属的温度；T_f为纯Fe的熔点；Γ为Gibbs-Thompson系数；κ为枝晶尖端的曲率；f(φ, θ)为各相异性函数^[16,17]。κ和f(φ, θ)的计算公式为：

κ = \frac{1}{Δ x} [1 - 2 (f_{s} + \sum_{i = 1}^{N_{u}} f_{s}^{i}) / (N_{u} + 1)]

(9)

f (φ, θ) = 1 - 15 ε c o s (4 (φ - θ))

(10)

式中， $f_{_{S}}^{i}$ 为邻胞的固相体积分数，N_u为邻胞的个数，ε为各向异性参数，θ为晶粒生长方向与x轴的夹角，φ为界面法向量与x轴的夹角。

1.1.1 基本控制方程

在激光熔覆过程中，熔池中的质量、能量、溶质传输与熔体流体运动相互影响并耦合作用，因此模型中考虑了四大守恒方程^[18~20]：(1) 质量守恒方程；(2) 动量守恒方程；(3) 能量守恒方程；(4) 溶质守恒方程。

质量守恒方程表达式为：

\frac{\partial}{\partial t} (f_{l} ρ_{l}) + \nabla \cdot (f_{l} ρ_{l} u_{l}) = - M_{l s}

(11)

\frac{\partial}{\partial t} (f_{s} ρ_{s}) = M_{l s}

(12)

式中，ρ_l和ρ_s分别为液相和固相密度； u_l为熔体的流速；t为时间；M_ls为液相向固相的传输质量，其表达式为M_ls = Δf_s·ρ / Δt。

动量守恒方程为：

\frac{\partial}{\partial t} (f_{l} ρ_{l} u_{l}) + \nabla \cdot (f_{l} ρ_{l} u_{l} \otimes u_{l}) =

- f_{l} \nabla p + \nabla \cdot τ_{l} - U_{l s} + F_{M}

(13)

式中，p为压力； τ₁为应力-应变张量； U_ls为液相与固相动量交换量； F_M为引起Marangoni流的动量源项，表达式为 $F_{M} = \frac{\partial γ}{\partial T} \cdot \nabla T_{l}$ ，其中， $\frac{\partial γ}{\partial T}$ 为表面温度张力系数，∇T_l为熔池中液相温度梯度。

能量守恒方程为：

\frac{\partial}{\partial t} (f_{l} ρ_{l} h_{l}) + \nabla \cdot (f_{l} ρ_{l} u_{l} h_{l}) = \nabla \cdot (f_{l} k_{q l} \nabla T_{l}) - Q_{l s} + Q_{q l}

(14)

\frac{\partial}{\partial t} (f_{s} ρ_{s} h_{s}) = \nabla \cdot (f_{s} k_{q s} \nabla T_{s}) + Q_{l s} + Q_{q s}

(15)

式中，h_l和h_s分别为液相和固相的焓；k_ql和k_qs分别为液相和固相的热导率；T_l和T_s分别为液相和固相的温度；Q_ls为液相和固相间的能量交换项；Q_ql和Q_qs分别为液相和固相吸收的激光能量，激光热源以源项的方式植入能量方程。

Gaussian热源通量(q(r))表达式为:

q (r) = A \cdot \frac{2 P}{π R^{2}} e x p (- \frac{2 r^{2}}{R^{2}})

(16)

式中，A为激光利用率，P为激光功率，R为激光光斑半径，r为距离斑点中心的距离。

溶质守恒方程为：

\frac{\partial}{\partial t} (f_{l} ρ_{l} c_{l}) + \nabla \cdot (f_{l} ρ_{l} u_{l} c_{l}) = \nabla \cdot (f_{l} ρ_{l} {\bar{D}}_{l} \nabla c_{l}) - C_{l s}

(17)

\frac{\partial}{\partial t} (f_{s} ρ_{s} c_{s}) = \nabla \cdot (f_{s} ρ_{s} {\bar{D}}_{s} \nabla c_{s}) + C_{l s}

(18)

式中，C_ls为液相与固相之间的溶质传输量，凝固时 $C_{l s}$ = $\bar{k} \cdot c_{l}^{*}$ ∙M_ls，熔化时C_ls = c_s∙M_ls。

1.1.2 形核模型

针对凝固形核过程，本模型采用连续形核模型来描述液相中的非均匀性形核，形核密度增量(dn，n为形核密度)与过冷度(ΔT)之间服从Gaussian分布^[21,22]，表达式为：

\frac{d n}{d (Δ T)} = \frac{n_{m a x}}{\sqrt[]{2 π} Δ T_{σ}} e x p (- \frac{1}{2} {(\frac{Δ T - Δ T_{n}}{Δ T_{σ}})}^{2})

(19)

式中，ΔT_n和ΔT_σ 分别为形核过冷度的均值和标准偏差，K；n_max为最大形核率。因此，对于任意过冷度的晶粒密度(n(ΔT))可由以下公式求得：

n (Δ T) = \int_{0}^{Δ T} \frac{d n}{d (Δ T)} d (Δ T)

(20)

在一个时间步长内，过冷度增量为δ(ΔT)，则一个时间步长内的晶粒密度增量(δn)可表示为:

δ n = n [Δ T + δ (Δ T) - n (Δ T)] =

\int_{Δ T}^{Δ T + δ (Δ T)} \frac{d n}{d (Δ T)} d (Δ T)

(21)

因此当前元胞的形核概率为P_n = δn·V_c，V_c为元胞的体积。当该元胞的形核概率大于一个(0, 1)的随机数时，该元胞发生形核，由液相胞转变成界面胞，并在(-0.25π, 0.25π)内赋予其随机生长方向。

1.2 数值求解

本模型采用2D正方形网格，图2所示为计算域网格及边界条件，其中流体域尺寸为14 mm × 1.2 mm，网格尺寸为10 μm × 10 μm，其余网格从上到下依次增大，粉末层简化为固相，高度设置与实验结果一致。模型边界为壁面，初始温度为室温300 K，初始溶质质量分数根据式(1)确定。

图2

图2 计算域的边界条件和网格

Fig.2 Characteristics of boundary conditions and grids in the computational domain (g—acceleration of gravity; T_w—wall boundary condition)

本模型采用PC-SIMPLE算法求解上述控制方程，时间步长设置为1 × 10^-4 s，每个时间步长内，最多迭代60次即可保证计算的收敛。该模型在8个超线程CPU (AMD EPYC 3.0GHz)上并行运算3 d。模拟计算中的热物性参数如表1^[23]所示，此外工艺参数与实验过程保持一致。

表1 模型中的热物性参数^[23]

Table 1 Thermophysical parameters in the model^[23]

Parameter	Symbol	Value	Unit
Melting point of pure Fe	T_f	1805.15	K
Reference densities of liquid and solid	ρ_l, ρ_s	8000	kg·m^-3
Specific heat	c_p	500	J·kg^-1·K^-1
Thermal conductivity of solid	k_qs	19.2	W·m^-1·K^-1
Thermal conductivity of liquid	k_ql	209.2	W·m^-1·K^-1
Latent heat	Δh_f	250000	J·kg^-1
Viscosity	μ_l	0.0042	kg·m^-1·s^-1
Volume heat-transfer coefficient	H^*	1 × 10⁹	W·m^-2·K^-1
Temperature coefficient of surface tension	∂γ / ∂T	-4.3 × 10^-4	N·m^-1·K^-1
Maximum nucleation density	n_max	1 × 10⁹	m^-3
Average nucleation undercooling	ΔT_n	15	K
Nucleation undercooling deviation	ΔT_σ	5	K

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2 实验设计

2.1 实验设备及材料

为了验证模型的可靠性，如图3所示搭建了激光熔覆实验平台。采用最大功率为1 kW的Laserline LDF400-1000光纤耦合半导体激光器作为热源，利用STAUBLI TX90 型六自由度机器人控制熔覆头的移动，同轴水冷装置增加激光器散热。为了控制熔覆过程的氧化，采用纯度为99%的高纯度Ar气作为保护气体。基板材料为316L不锈钢，尺寸为110 mm × 70 mm × 8 mm，选用球形粒径为53~150 μm的IN718粉末作为铺粉材料，基板和粉末材料的化学成分如表2所示。

图3

图3 激光粉末床熔覆工作平台示意图

Fig.3 Schematic description of work platform for laser powder bed cladding

表2 316L基板和IN718粉末的化学成分 (mass fraction / %)

Table 2 Chemical compositions of 316L substrate and IN718 powder

Material	Fe	Ni	Mn	Al	Ti	Nb	Si	Cr	Mo	C
316L	Bal.	10.0	1.55	-	-	-	0.55	16.5	2.08	0.020
IN718	18.1	Bal.	0.04	0.54	0.97	4.92	0.20	19.2	2.08	0.045

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2.2 实验方法

实验前用角磨机去除316L基板材料表层氧化膜层，同时将IN718粉末材料放置在温度为393.15 K的真空干燥箱中连续烘烤2 h，去除粉末中的水分，保证熔覆质量。实验工艺参数如表3所示。

表3 激光熔覆工艺参数

Table 3 Laser cladding process parameters

Process parameter	Symbol	Value	Unit
Laser power	P	900	W
Scanning speed	v	8	mm·s^-1
Powder thickness	H_p	0.2	mm
Laser beam radius	R	1	mm
Laser defocusing amount	L_h	15	mm

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实验结束后，采用电火花切割技术取样，分别沿着激光扫描方向和垂直于激光扫描方向取试样若干，经热镶嵌、磨样、抛光后用体积比为C₂H₅OH∶HCl∶FeCl₃ = 20∶4∶1的腐蚀液制备金相。利用AXIO Scope A1光学显微镜(OM)观察试样熔池形貌，采用XFlash型能谱仪(EDS)分析沉积层的元素分布。

3 实验结果与分析

3.1 模型验证

t = 0.93 s时熔池形貌的OM像和模拟结果如图4所示。实验结果显示，熔高(H)大于铺粉厚度(H_p)，经对比相关研究，主要有以下2个原因^[24~26]：(1) 熔池中心的温度较高，压力低于周围的大气压，熔池外围粉末在空气压力作用下被推向熔池中心；(2) 由于熔体在表面张力的作用下发生Marangoni对流，该流动会将周围的部分粉末卷入熔池中，最后使熔高大于初期铺粉厚度。由于本模型中未考虑空气相的作用，此处不讨论实验与模拟结果的熔高差异。但是通过比较模拟与实验的熔深，结果表明其相差约为5.5%，说明了本模型具有一定可靠性。同时，在模拟过程中，由于IN718粉末液相线温度低于基体的液相线温度，因此在熔池的前端由于粉末与基体材料未充分混合，出现了类似台阶形貌的熔池。但是受熔融流体流动的影响，粉末与基体材料经过初步混合，其液相线温度差异减小，最终在熔池后端出现较为光滑的凝固界面。

图4

图4 时间t = 0.93 s时熔池形貌的OM像和模拟结果

Fig.4 OM image (a) and simulation result (b) of melt pool at t = 0.93 s (H—molten height; B—depth of fusion; H_L = H + B)

该模型在初始化时，将流体域内划分成平均尺寸为83 μm的晶粒，并为每个晶粒设置随机生长方向，在激光辐照时发生熔化并随着光斑移动实现再凝固。如图5所示为t = 1.27 s时凝固组织形貌的模拟结果。在凝固过程中，在熔覆层底部，晶粒根据基材初始取向在温度场演化作用下实现外延生长，并逐渐发生倾斜；在熔覆层的中部，由于形核作用，部分枝晶被新生晶粒阻塞，并伴随新晶粒竞争生长；在熔覆层的顶部，由于顶部散热作用，熔体形核能力增强，晶粒明显增多，并且随着凝固继续，晶粒进一步长大。综上所述，由于凝固组织存在相互竞争生长，部分晶粒在温度场作用下择优生长，形成具有一定取向的组织形貌，该模拟结果与已有的研究结果^[27,28]类似，进一步验证了本模型的合理性。由于本工作主要研究成分的分布，晶粒生长不再赘述。

图5

图5 t = 1.27 s时模拟的晶粒生长过程

Fig.5 Simulation of grain growth process at t = 1.27 s

3.2 温度场分布

图6为t = 0.15 s、t = 0.47 s、t = 0.80 s以及t = 1.13 s时的温度场演变云图，其中T_max为当前时刻熔池中心最高温度，黑色线表示熔池轮廓线，此时f_l = 0.5。熔池边界内为液相的Fe元素分布情况，熔池边界外为固相的Fe元素分布情况。由图可知，在t = 0.15 s之前激光的热输入量大于基体的热输出并形成熔池，此时熔池中心温度快速上升；在t = 0.15~0.45 s时因熔池尚未达到稳定，熔深持续增加，所以熔池温度继续增大；在t = 0.45 s后，熔池形貌达到稳定，此时激光的热输入量与熔池散热趋于平衡。在激光扫描方向上，熔池前方的等温线被压缩，等温线分布密集，温度梯度大，而熔池后方的等温线被拉伸，导致等温线分布稀疏，温度梯度较小。

图6

图6 不同时刻的温度场分布云图

Fig.6 Temperature field distributions at t = 0.15 s (a), t = 0.47 s (b), t = 0.80 s (c), and t = 1.13 s (d) (f_l—volume fraction of liquild, T_max—maximum temperature. Black lines show the contour lines of melt pool)

3.3 熔池流体流动特征

图7为t = 0.15 s、t = 0.47 s、t = 0.8 s以及t = 1.13 s时的流场矢量图，其中u_max为当前时刻熔体的最大流动速率。在Marangoni剪切力的作用下，熔池具有由内向外的流动模式^[29]，而且熔池中的最大流动速率发生在熔池边缘附近。在t = 0.15 s时，熔池尚未完全成型，此时熔池中的u_max为0.3219 m/s；在t = 0.15~0.47 s时，随着熔池持续吸收激光能量，熔体温度升高，在表面张力作用下，熔池中心的热量被熔体传导至熔池边缘，使得熔池尺寸不断增大，熔池边缘的温度梯度增大，u_max增大；在t = 0.47 s以后，由于熔池基本成型，熔池中的u_max趋于稳定。

图7

图7 不同时刻的流场分布矢量图

Fig.7 Vector plots of flow field distribution at t = 0.15 s (a), t = 0.47 s (b), t = 0.80 s (c), and t = 1.13 s (d) (u_l—flow velocity of melt pool, u_max—maximum flow velocity)

3.4 熔覆层中元素分布结果

图8为t = 1.17 s时Fe元素的分布云图。模拟结果显示，随着熔池深度不断增加，Fe元素含量也不断增加且有明显的分布不均匀现象。在熔深较小时，熔池中的熔体元素主要是粉末中的元素，凝固后的Fe元素含量也较低。随着熔深不断增大，在Marangoni力作用下，随着熔体的流动基体元素被不断地卷入熔池上部，熔池上部的元素被带到熔池底部，凝固后的Fe元素含量不断增加。由于熔池中的流动不断变化，使得熔池中的元素混合程度不同，熔池后端的液相线温度也不断地变化，熔池形貌也随之变化，形成浓度高、低相间分布呈条纹丝带状的偏析带。

图8

图8 t = 1.17 s时Fe元素的分布云图

Fig.8 Distribution nephogram of Fe element at t = 1.17 s

为了验证模拟的预测结果，做了相同工艺参数下的激光粉末床熔覆实验，图9a为沿激光扫描方向中间截面的OM像。可以看出，颜色深浅不一，说明被腐蚀的程度不同，元素分布不均匀。对图9a中的虚线方框区域进行EDS面扫描，结果如图9b~d所示。可见，在该选区内Fe、Ni元素存在明显的分布不均匀现象，而Cr元素分布较为均匀。在Fe元素富集的地方，Ni元素贫瘠，呈现浓度高、低相间分布的现象，呈条纹丝带状式样，即偏析带，与模拟结果保持一致。

图9

图9 沿激光扫描方向中间截面的OM像和元素的EDS面扫描

Fig.9 OM image of the middle section along the laser scanning direction (a); and EDS scanning maps of elements Fe (b), Ni (c), and Cr (d) of dashed area in Fig.9a

为了定量对比实验与模拟结果中Fe元素的含量变化，从图8中选取熔池稳定后的一个区域(图8中方框区域)和图9a中的虚线方框区域，提取激光扫描方向(x方向)和垂直于激光扫描方向(y方向) Fe元素的含量，对比结果如图10所示。可以看出，Fe元素含量分布不均匀，分布趋势保持一致，模拟与实验结果吻合较好。

图10

图10 x方向和y方向上的Fe元素含量的模拟(图8)与实验(图9a)结果对比图

Fig.10 Comparisons of simulated (Fig.8) and experim-ental (Fig.9a) results of Fe content in the x (a) and y (b) directions

3.5 偏析带形成机理

图11为t = 1.02 s、t = 1.03 s、t = 1.04 s、t = 1.05 s、t = 1.06 s以及t = 1.07 s时Fe元素分布的模拟结果。将熔池边界内的区域分为3个部分，红色部分主要为基板中的Fe元素含量，绿色部分主要为粉末中的Fe元素含量，剩下的橙黄色为基板与粉末中Fe元素的混合区域。熔池中液相线的温度随溶质浓度的不同而不同，在Marangoni力驱动下，当熔池底部的元素更多地被带入熔池后端时，熔池后端的液相线温度升高，促进了熔池后端的凝固，形成一道Fe元素的高浓度区域，如图11a~c所示。随时间增加，熔池后端形貌变为“鼓包”状，熔池中的流速增加，使得熔池前端的元素更多地被卷入熔池后端，熔池后端的液相线温度降低，推迟熔池后端的凝固，形成一道Fe元素的低浓度区域，如图11d~f所示。熔池后端形貌逐渐变得平坦，熔池中的流速逐渐降低，又会使得熔池底部的元素更多地被卷入熔池后端，这种现象会不断地出现在后续的凝固过程中。

图11

图11 不同时刻Fe元素的分布

Fig.11 Distributions of Fe element at t = 1.02 s (a), t = 1.03 s (b), t = 1.04 s (c), t = 1.05 s (d), t = 1.06 s (e), and t = 1.07 s (f) (Black lines show the contour lines of melt pool)

图12为偏析带形成过程的示意图，图中红色部分主要为基体中的Fe元素，绿色部分主要是粉末中的Fe元素，T_p表示粉末的液相线温度，T_b表示基体的液相线温度，T_a为实际凝固的液相线温度。熔池底部(红色)的Fe元素被流动带入熔池后端，熔池后端的液相线温度升高，使得T_a偏向T_b，凝固时间提前，熔池后端快速凝固，形成Fe元素的高浓度区域，如图12a和b所示。当熔池前端(绿色)的Fe元素更多地流入熔池后端，熔池后端的液相线温度降低，使得T_a偏向T_p，减缓熔池后端的凝固，如图12c所示。随着凝固的进一步进行，熔池后端边界向前推进，形成Fe元素的低浓度区域，如图12d所示。固/液界面的推移速率由界面胞与邻胞的溶质浓度差异确定，而熔池中的流动存在波动，使得熔池后端的形貌不断发生变化，凝固后的Fe元素浓度也存在差异，该现象会不断出现在后续的凝固过程中。因此，增加熔池中元素混合的均匀性，可以降低偏析程度，在实验过程中，可以适当提高激光功率和降低扫描速率以便提高熔覆层的质量。

图12

图12 偏析带形成的示意图

Fig.12 Schematics of the formation of the segregation bands

(a) T_a at the rear end of the molten pool tends to T_b (T_p—liquidus temperature of powder; T_a—actual solidification liquidus temperature; T_b—liquidus temperature of matrix; Red and green dots represent Fe element in matrix and in powder, respectively)

(b) solidification creates a region of high concentration of Fe element

(d) solidification creates a region of low concentration of Fe element

4 结论

(1) 基于元胞自动机方法和Eulerian多相流算法建立了在316L不锈钢基板上激光熔覆IN718合金的二维熔化凝固模型，模拟结果表明，Fe元素含量高、低相间分布，呈条纹丝带状，与实验结果吻合较好，证明了本模型的可靠性。

(2) 熔池中的熔体在Marangoni力驱动下，将熔池底部和熔池前端的元素卷入熔池后端，使得熔池中的液相线温度发生变化，导致熔池后端的形貌在温度场和溶质场共同作用下发生周期性波动，进而影响熔池中流体的流速，最终造成Fe元素分布不均匀，形成偏析带。

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