Abstract

This article presents a fully three-dimensional numerical study on the process of melt pool evolution. To overcome the simplifications used in many existing studies, an enthalpy method is developed for the phase change, and an accurate interface capturing method, i.e., the coupled volume-of-fluid and level set (VOSET) method, is employed to track the moving gas–liquid interface. Meanwhile, corresponding experimental studies are carried out for validation. The obtained numerical results show the formed interface morphology during the process of melt pool with its typical sizes and are quantitatively consistent with those data measured in experiments. Based on the numerical results, the thermodynamic phenomena, induced by the interaction between heat and momentum exchange, occurring in the formation of melt pool are presented and discussed. Mechanisms of the melt pool evolution revealed in the present study provide a useful guidance for better controlling the process of additive manufacturing.

1 Introduction

Directed energy deposition, as one of the most popular additive manufacturing techniques, is a subject of growing interest and widely used in aerospace, biomedical, and other national industries due to its unique advantages, such as manufacturing flexibility and tailoring multifunction component [1,2]. However, quality problems such as cracking and roughness could seriously affect the further popularization of this technology [3]. Researchers are committed to improving fabrication quality by improving the energy–powder interaction process in the manufacturing process [4,5]. As an essential stage of additive manufacturing, the melt pool evolution process of melting broadening and solidification shrinkage attracts the attentions of researchers. Effective control of the melt pool evolution process by increasing the cooling rate and reducing surface deformation can improve product quality significantly [6]. Cunningham et al. [7] established a simplified relationship between operational parameters, and free surface shape of the titanium alloy melt pool used a high-speed x-ray imaging and attempted to prevent the pore formation going forward. Many researchers have found better fabrication parameters by adjusting and controlling the mode and parameters of the scanning laser and other factors [810], and they have successfully improved the actual manufacturing process after many experiments.

However, the study on the melt pool formation mechanism is far from enough, and clarifying the basic evolution mechanism of melt pool is important for improving efficiency. Choi et al. [11] developed a numerical model based on the assumption of only pure conduction heat transfer mode to obtain temperature distribution in a plate and revealed that the peak temperatures changed linearly with the changes of the heating source. Lei et al. [12] numerically analyzed the competitive influence of Marangoni flow and evaporation on temperature and melt pool shape evolution process using a 2D model. Ha and Kim [13] explored the influence of surface tension and surface deformation on weld pool evolution, and the results showed that the surface tension effect and the deformation of the weld pool surface are noticeable as Pe number increases and We number decreases. Han et al. [14] furtherly exhibited those phenomena using a 3D model, and the deformation surface also had been investigated under a fixed laser beam condition. Ding et al. [15] numerically investigated the effects of two different laser scan patterns on the thermal behavior and fluid flow of melt pool under the same energy input, and the results agreed well with the experimental data. Ebrahimi et al. [16] found that the accuracy of numerical predictions in simulations of the melt pool flow is significantly enhanced, as the dynamically adjusted energy flux distribution and the changing thermo-physical material properties were utilized. Hozoorbakhsh et al. [17] implemented a transient three-dimensional model using the ansys fluent platform. The thermal phenomena and characterization in laser micro-welding were characterized by the developed model. Chakraborty [18] simulated melting and solidification stages in a copper–nickel metal welding pool, and the energy and momentum transport characteristics obtained under both laminar and turbulent flow models were also compared. He et al. [19] further investigated the mushy zone evolution during the melt pool shrinking process, finding that the mushy zone grew rapidly and reached the maximum size when the melt pool vanished, but the solidification rate gradually increased. Besides, Tseng and Li [20] investigated the wetting and morphology of the initial melt pool under a moving selective laser, and they observed that the melt pool showed a periodic sloshing motion and oscillation as the wetting was enhanced by the Marangoni flow. Most of these studies focused on the flat surface melt pool model, thermal conductivity phase change model without consideration of the Marangoni convection or the flow and heat transfer phenomena in the melt pool. These studies have great reference significance for understanding the evolution of melt pool, but they cannot clearly describe the basic principle of energy-driven materials motion during the construction of melt pool. This is unfavorable for further flexible control of melt pool.

In addition, as the driving source in the melt pool evolution process, the input laser energy is significantly important; however, most researches on the input laser are just limited to the definition of thermal boundary [21,22]. There are few studies on the conservation of energy input and dissipation in the melt pool formation process. It is important to clarify the energy input and distribution to maximize energy saving and emission reduction in the process of the additive manufacturing process. Moreover, the self-shrinkage characteristics of the melt pool after laser quenching (power off) are often neglected. In fact, it plays an important role in improving the smoothness of the fabricating products, and the research on these characteristics is needed [23].

To accurately and comprehensively investigate the evolution phenomena and explore the formation mechanism, the surface deformation capture should not be neglected. The smooth surface of a melt pool protected by surface tension can be easily destroyed under the action of strong Marangoni convection and evaporation effect. Furthermore, the deformed surface that is also called the key hole in the welding pool study plays a notable role in energy transport and momentum variation. Numerous interface tracking methods have been proposed in the previous studies. Moving mesh technology based on the arbitrary Lagrangian–Eulerian method [24,25], surface capture technology based on nonorthogonal mesh [26], and multiphase model (the volume of fraction (VOF) [27] and level set (LS) [14]) can accurately track the surface deformation of the melt pool. In conclusion, from previous studies, how important of the surface tension and its temperature gradient effect in melt pool evolution have been clarified, and how to quantify the effect of melt pool evaporation and vapor recoil force have been obtained. Especially, the methods to track keyhole evolution, implement boundary conditions, and capture melt pool–air interface are known well here. Those aspects provide better methodology in our model establishment and research innovation. Thus, based on the previous literature, a numerical melt pool model incorporated an excellent surface tracing technique named the coupled volume-of-fluid and level set (VOSET) method, which combined the advantages of the VOF and LS methods [28,29], and was built in our previous study [30,31]. Results showed that the model can accurately capture the deformation of the melt pool interface.

However, because the initial research object was only to develop a two-dimensional numerical model, its assumptions were relatively simplified, and it was difficult to use for irregular and asymmetric problems. It is necessary to expand the two-dimensional model to a more comprehensive three-dimensional model in this study. Based on the previous developed 2D model, a three-dimensional melt pool numerical model was incorporated by the VOSET method. Then, a set of laser heating copper plate experiment system was built to validate the developed three-dimensional model. Finally, the basic evolution phenomena and mechanisms of temperature, velocity, free interface deformation, and melt pool dimension were investigated under the fixed and moving laser energy input conditions. Furthermore, the melt pool energy distribution, the melt pool asymmetric evolution under moving laser condition, and the self-shrinkage characteristics after laser quenching are explored in depth in this article.

2 Model Formulation

2.1 Model Description.

The geometry model established in this study, as shown in Fig. 1(a), has a computed domain size of 80 mm × 80 mm × 80 mm. The upper half of the cavity on the z-direction is the area where the laser and inert gas exist, the lower half is the metal substance, and the irradiation point of the laser beam is located at the center of the metal upper surface. As the high heat flux laser deposits on the metal surface, the metal temperature increases rapidly. Once the surface temperature exceeds the melting point, the solid metal begins to melt and the melt pool appears on the surface. In this physical process, the heat transfer phenomenon includes heat deposition and transfer on the metal, heat dissipation after heating up of the metal, and the latent enthalpy absorption and release. The momentum transport mainly involves the effects of the Marangoni force, the surface tension, the buoyancy force, and the vapor recoil force. The melt pool is derived from an extremely complex energy and momentum coupling process, and the detailed thermal dynamic interaction is shown in Fig. 1(b). The basic physical properties of materials used in this study are also listed in Table 1.

Fig. 1
The schematic of numerical model for the laser-based melt pool: (a) geometry model and (b) the schematic physical melt pool model
Fig. 1
The schematic of numerical model for the laser-based melt pool: (a) geometry model and (b) the schematic physical melt pool model
Close modal
Table 1

Material properties used in the study

VariablesValueVariablesValue
Metal density5000 kg/m3Gas density1.225 kg/m3
Metal liquid viscosity0.01 Pa·sGas viscosity0.0005 Pa·s
Metal specific heat470 J/(kg·K)Gas specific heat1005 J/(kg·K)
Metal thermal conductivity100 W/(m·K)Gas thermal conductivity0.035 W/(m·K)
Melting temperature1800 KSolidification temperature1600 K
Metal emissivity0.5Evaporation temperature2800 K
Coefficient of surface tension1.9 N/m
Thermal expansion coefficient0.0004
Metal latent heat of fusion220 kJ/kg
Metal evaporation latent heat6020 kJ/kg
Coefficient of surface tension temperature gradient−0.00043 N/(m·K)
VariablesValueVariablesValue
Metal density5000 kg/m3Gas density1.225 kg/m3
Metal liquid viscosity0.01 Pa·sGas viscosity0.0005 Pa·s
Metal specific heat470 J/(kg·K)Gas specific heat1005 J/(kg·K)
Metal thermal conductivity100 W/(m·K)Gas thermal conductivity0.035 W/(m·K)
Melting temperature1800 KSolidification temperature1600 K
Metal emissivity0.5Evaporation temperature2800 K
Coefficient of surface tension1.9 N/m
Thermal expansion coefficient0.0004
Metal latent heat of fusion220 kJ/kg
Metal evaporation latent heat6020 kJ/kg
Coefficient of surface tension temperature gradient−0.00043 N/(m·K)

2.2 Mathematic Model and Numerical Implementation.

The whole computational domain includes the pool region, the solid region, and the surrounding inert gas region. The physical models of different solution regions are different. For example, the melt pool involves fluid flow, melting, and heat transfer, whereas, in the solid phase, only heat conduction exists. However, there is a continuous melting and solidification near the interface between solid and liquid, which is a coexistence region of the solid and liquid known as the mushy region. Furthermore, the mushy region is always treated as a porous region in the literature [1,32]. Therefore, to simplify numerical computation, the porous-enthalpy model and the interface capture model are introduced and assembled into the general Navier–Stokes equations. The porous-enthalpy model is used to compute the melt pool, the solid, and the mushy region. The interface capture model (VOSET method) is applied to track the substance and the inert gas zone. Then the different regions can be well identified and solved using the same governing equations, thus greatly reducing the amount of computation. Besides, to make the model simplified, some assumptions are made on the basis of accuracy in simulation, as listed in Table 2. The mathematical equations are presented as follows [24,33]:

ρt+(ρui)xi=0
(1)
(ρui)t+(ρuiuj)xj=xj(μuixj)pxiK0(1fl)2fl3+ζui+ρgiβ(TT0)+FL/G
(2)
(ρh)t+(ρujh)xj=xj(λTxj)(ρΔhfl)t+(ρujΔhfl)xj+Q
(3)
where t is time (s), ui is the i velocity component (m/s), xi is the i coordinate directions component (m), ρ is the density (kg/m3), p is the fluid pressure (Pa), µ is the dynamic viscosity (Pa·s), λ is the material thermal conductivity (W/(m·K)), and T (K) and h (J/kg) are the temperature and enthalpy, respectively. The third term on the right-hand side of Eq. (2) is the Carman-Kozeny function, which is derived from the Darcy law and indicates the flow dissipation in the computing domain. The dissipation only exists in the zone consisting of the solid and liquid phase and sharply increases with the solid phase percentage increasing, just as there exists a porous region. The introduced function could well recognize the aforementioned liquid, solid, and mushy region in the lower half part of the model. fl is the liquid volume fraction in the zone, which is defined as follows:
fl=1,ifTTm;TTsTmTs,ifTm>TTs;and0,ifT<Ts
(4)
where Tm and Ts are the metal melting and solidification temperature (K), respectively.
Table 2

Assumptions made in mathematic model establishment

VariablesAssumption
Laser beamGaussian distribution; attenuation and scattering are ignored
Material propertiesIsotropic and homogeneous; temperature independent
Heat loss from thermal convectionIgnored
Melt pool and surrounding inert gasFluid flow is laminar and incompressible
Buoyancy driven flowBoussinesq approximation
VariablesAssumption
Laser beamGaussian distribution; attenuation and scattering are ignored
Material propertiesIsotropic and homogeneous; temperature independent
Heat loss from thermal convectionIgnored
Melt pool and surrounding inert gasFluid flow is laminar and incompressible
Buoyancy driven flowBoussinesq approximation

K0 is the permeability coefficient, which needed to be carefully selected. If the value is too larger, the source term cannot reach 0 when the fl is 1; on the contrary, if the value is too smaller, the source term can’t guarantee a zero velocity when fl is 0. Besides, the value of the permeability coefficient in the enthalpy-porosity method can affect the results of melt pool simulations. For a nonisothermal phase change problems, the sensitivity increases with increased mushy zone thickness and increased fluid flow velocities perpendicular to the solid/liquid interface, the selection of permeability coefficient also need to considerate this factor. According to literature [34], a Pe* number is proposed to predict and evaluate the influence on accuracy of result, the recommended number Pe* < 1 indicates insensitivity to the permeability coefficient. In this study, the Pe* number is also calculated as follows: Pe* = umaxΔTmL/α/(ThTc) = 0.15. Hence, the result is insensitivity to the permeability coefficient, and the selection of it in this study only need to satisfy the two flow criterions. In Refs. [14,35], a liquid fraction dependent function: K0 = 0.13fl−3/2 is selected; in Refs. [16,24], a value of 107 is recommended. Both of the two selection can satisfy the requirement, however, for the first K0, the value gradually increases with the decreasing fl and the value is small before the fl reduces to 0.1, this process will lead an excessive flow; as for the second K0, the value is too bigger, it will depress the flow in mushy zone even the fl is enough larger. Therefore, in our study, referring to the previous studies [19,32], a value of 1600 is selected to realize an adequate flow in mushy zone. ζ is a small number to avoid a zero denominator (1.0 × 10−4).

The other part of the porous-enthalpy model is a track function of the change of latent enthalpy, as shown in the second term (induced by the change of melting fraction versus time) and third term (induced by convection effect in mushy zone) on the right-hand side of Eq. (3), which can accurately describe the temperature change in the region when the phase change occurs with the latent heat absorption/release [32], and Δh is the material latent enthalpy (J/kg). The fourth term on the right-hand side of Eq. (2) is the buoyancy force term, which describes the natural convection induced by the density variation because of the temperature difference, and the Boussinesq approximation is used. gi is the i gravitational acceleration component (m/s2), and β is the coefficient of volume thermal expansion.

Based on the continuum surface force model [36], the momentum (FL/G) and energy (Q) source terms are expressed as follows:
Q=(2ηPlaserπR2exp(2r2R2)εσ(T4T4)ρV0exp(U/Tsurf)Lv)δ(ϕ)
(5)
FL/G=(γκn+dγdTs(T)+AB0Tsurf1/2exp(U/Tsurf))δ(ϕ)
(6)

The first term on the right-hand side of Eq. (5) is the laser heat depositing on the metal surface, and the second and third terms are the heat radiation and the heat evaporation on the surface when the temperature is high, respectively. η is the radiative absorptivity, Plaser is the laser energy density (W/m2), R is the laser radius (m), r is the distance from computing grid to laser center (m), ε is the emissivity, σ is the Stefan–Boltzmann constant (5.67 × 10−8 W/(m2·K4)), T is the ambient temperature (300 K), Lv is the evaporation latent heat of metal (J/kg), and δ(ϕ) is the derivative of the smooth Heaviside function. V0 is the sound velocity in melt pool (it is 3500 m/s in this study). U = MaLv/Nakb, where Ma is the atomic mass (kg), Na is the Avogadro’s number (6.02 × 1023), and kb is the Boltzmann constant (1.38 × 10−23 J/K). Tsurf is the melt’s surface temperature. In Eq. (6), the first two terms on the right-hand side are the surface tension and Marangoni force, respectively. The third term is the vapor recoil force, which takes effect when temperature is high. γ is the surface tension coefficient (N/m), κ is the curvature, n is the normal vector on free interface, dγ/dT is coefficient of surface tension temperature gradient, and ∇s is a tangential Hamiltonian. A = 0.55 is the surrounding pressure dependence coefficient, and B0 = 1.78 × 1010 Pa is the evaporation constant [33].

The definition of VOSET method is expressed as follows [28,29,37]:
Ct+(vC)=0,n=C/|C|
(7)
n=ϕ/|ϕ|,whereϕ=d,ifC>0.5;0,ifC=0;andd,ifC<0.5
(8)
where C is the volume of fluid, ϕ is the signed distance function, d is the shortest distance from grid point (i, j, k) to interfaces, and the precise normal vector is reconstructed by the signed distance function.

The 3D melt pool model was solved using an in-house developed code, which can define all the boundaries and phenomena more exactly. The controlling equations are solved by the discrete SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm based on the finite volume method. The convection term is discretized using a higher order monotone upwind central scheme, and the diffusion term is addressed by the central difference scheme. When comes to the VOSET process, a second-order projection method is applied. The detail numerical implementation information also can be found in our previous article [30,31]. Finally, a relative variation of temperature and speed between two adjacent iteration, which predefined precision value is 5 × 10−7, is set as the convergence and termination criterion for the procedure computation. Besides, the laser beam parameters used in the study are presented in Table 3.

Table 3

Laser beam parameters used in the study

VariablesValue
Fixed laser conditionMoving laser condition
Laser power2200 W2200 W
Laser scanning speed0 m/s0.01 m/s
Laser radius0.0005 m0.0005 m
Energy absorptivity0.60.6
Interaction time100 ms100 ms
Quenching time150 ms150 ms
VariablesValue
Fixed laser conditionMoving laser condition
Laser power2200 W2200 W
Laser scanning speed0 m/s0.01 m/s
Laser radius0.0005 m0.0005 m
Energy absorptivity0.60.6
Interaction time100 ms100 ms
Quenching time150 ms150 ms

3. Results and Discussion

3.1 Model Validation.

Before validating the correctness of the numerical model, it is necessary to carry out the mesh independency test. In this study, a fluid flow distance in one-time step Lgrid is benchmarked and used to obtain the various grid numbers by the dimensionless formula αLedge/Lgrid, where the Ledge is the model border length. The interface morphology of the formed melt pool in 100 ms and the corresponding run time for the selected four grid numbers (under α = 0.8, 1.0, 1.25, and 1.5, respectively) are shown in Fig. 2. Considering both of the computational accuracy and time, the grid number computed by α = 1.25 was chosen here.

Fig. 2
Grid independence test
Fig. 2
Grid independence test
Close modal

To validate the numerical model established in this study, a temperature and morphology measurement experimental system was established with a laser heating copper plate as shown in Fig. 3. The experimental system was mainly composed of four parts: the inert gas loading system, the infrared temperature-measuring system, the laser heating system, and the scanning electron microscope system. The inert gas loading system continuously filled argon gas into a sealed test space to protect the high-temperature copper plate from oxidizing. The main components are the blower, the suction machine, the high-pressure argon supply bottle, and the SIEMENS gas component detector. The function of the infrared temperature measurement system was to measure the surface temperature of the copper plate in the laser heating process and to adjust the position of the measuring point immediately. The main components included the adjustable eyepiece temperature-measuring thermometer and the controllable electric-moving platform. The laser heating system included the controlled solid laser launcher, the measured copper plate, and the electric control rotating platform. The laser was deposited on the copper plate surface to form the melt pool, and the electric control rotating platform was applied to ensure the rapid switch of the testing parts for the purpose of duplicating tests. The scanning electron microscope system was designed to observe the detailed morphology of the melt pool in the experiment, and a tungsten filament scanning electron microscope system and some experimental specimens were included.

Fig. 3
The experimental platform setup for temperature and surface morphology measurements for the laser-based melt pool
Fig. 3
The experimental platform setup for temperature and surface morphology measurements for the laser-based melt pool
Close modal

The detailed melt pool temperature measurement methods and procedures in this article are shown as follows.

  • Fabrication of experimental pieces: grinding and polishing the copper substrate, which has the same material and thickness under the same condition, and cutting the substrate to several same size experimental pieces, then putting them on the electric control rotating platform.

  • Setting of temperature measurement points: six points that along the diameter direction have been predefined, including the melt pool central point (also the laser beam center) and others five points (the distances of those point to center point are 0.7 mm, 2.4 mm, 3.8 mm, 5 mm, and 8 mm).

  • Temperature measurement on central point versus time: calibrating the laser center on the center of piece, aligning the measurement center of the thermometer to the laser center, and finally loading the laser energy until 100 ms.

  • Temperature measurement on others predefined points: switching the test pieces and aligning the laser and measurement center on the same position on piece. Then, controlling the electric-moving platform to move along the radial direction and approaching the predefined first point (0.7 mm, the thermometer fixed on the electric-moving platform). Loading the laser energy, reading the temperature on the first point and writing the data in 50 ms and 100 ms.

  • Completing the temperature measurement of other points step by step according to the aforementioned steps, and finally accomplishing the first time experiment measurement.

  • Reducing error by multiple experiments: five times experiments have been conducted for each point under the same condition. After rounding off the data points with large differences and giving the data uncertainties analysis, an average value of all the experiment measurement data on one point is obtained as the final result.

The data uncertainty is used to describe the dispersion degree of the measured data, the bigger data uncertainty, the greater data fluctuation and the lower measure reliability. There are two kinds of data uncertainties, one is computed from the statistical method (class A) and the other is derived from the experimental equipment (class B). For the class A data uncertainty, it is always computed according to the Bessel function:
uA(x¯)=1n(n1)i=1n(xix¯)2
(9)
where n is the experiment time, xi is the i experimental result, and x¯ is the average of all the experiments. For the class B data uncertainty, it is always computed as follows:
uB(x)=ΔB/kp
(10)
where ΔB is the experimental equipment measure error (here is 0.5% of the measured temperature according the equipment manual). kp is a reliability factor, and for a 99% confidence interval, kp is 2.58. From Eqs. (9) and (10), the total data uncertainty is computed as follows:
u(x)=uB2(x)+uA2(x¯)
(11)
Based on Eqs. (9)(11), the data uncertainties in this study are obtained. The maximum and average temperature uncertainty for the experiment of laser center temperature evolution versus time are 20.3 K and 11.54 K, respectively. The maximum and average uncertainty for the fixed point temperature measurement on 50 ms are 13.9 K and 11.4 K; as for on the 100 ms, the maximum and average uncertainty are 15.8 K and 12.4 K. For a high-temperature (∼103 order) melt pool experiment, the uncertainty is small, which indicates an accurate experiment result.

Figure 4(a) is a side-by-side comparison of the top-view morphology of the melt pool obtained from numerical simulation (the color denotes temperature distribution) with results obtained from experimental data. It can be seen that the morphology of the melt pool obtained from numerical simulation aligns closely with that results obtained experimentally in the copper plate heating process with a fixed laser beam. Results pertaining to melt pool temperature distributions are shown in Fig. 4(b). The measured temperature of five different points from the melt pool center (0.7, 2.4, 3.8, 5.0, and 8.00 mm) at 50 and 100 ms are shown for both the numerical model and experimental conditions. Besides, melt pool center temperatures versus time are also measured. Results show that the trends of melt pool temperature are the same for both numerical model and experiment. Quantitatively, the mean temperature error of the five measurement points at 50 ms is 9.3%, and it decreases to 7.2% at 100 ms. Meanwhile, the mean temperature error on the pool center at various times is 11.3%. The overprediction in temperature by the numerical simulation likely is due to the strong reflection effect on the laser from the smooth copper plate, and the data measurement in experimental condition shows greater error even if the energy density is very large. Similar results were reported in some previous studies [38,39]. As the temperature continuously increases, the melt pool appears and the reflection effect significantly reduces, and the deviation between the simulation and the experiment also quickly reduces. This trend can be clearly observed when looking at temperature variation in the pool center at different times. When the measured temperature is lower than the melting point (1250 K), the mean error of the simulation and the experiment is 14.3%, but the error reduces to 8.1% when the melt pool forms and grows up.

Fig. 4
Numerical model validation based on the experimental data: (a) the melt pool morphology (after solidification) and (b) the temperature distribution
Fig. 4
Numerical model validation based on the experimental data: (a) the melt pool morphology (after solidification) and (b) the temperature distribution
Close modal

Figure 5 shows the comparison of dimension of the melt pool among the present 3D model, the previous 2D model, and Ref. [14]. It can be found that the results of 3D model are more accurate than that of the 2D model, and the error reduces significantly. The mean and maximum absolute errors for the width and depth under moving laser beam condition are 0.073 mm, 0.114 mm and 0.029 mm, 0.075 mm, respectively, and the corresponding mean and maximum relative errors are 16%, 10.2% and 17%, 6.7%, which are acceptable in the melt pool simulation. These two test problems combined together illuminate that the present simulation method of flow and heat transfer in a melt pool is convincing.

Fig. 5
Validation of the melt pool dimension
Fig. 5
Validation of the melt pool dimension
Close modal

3.2 Melt Pool Evolution Phenomena Under Fixed Laser Beam

3.2.1 Temperature and Velocity.

Figure 6 shows the temperature and velocity distribution of the free interface in the middle cross section of the melt pool. Under the action of high-energy density of the laser beam, the maximum temperature of solid surface increases rapidly, increasing from room temperature to 3000 K in 20 ms. Then, although the maximum temperature in the region continues increasing with the continuous energy deposition, its increase rate drops down and the temperature increase is only about 280 K over the next 80 ms. As for the average temperature in the melt pool, it plateaus around 2330 K after a quick increase from 300 K in 10 ms and reaches equilibrium easier. Meanwhile, due to the Gaussian distribution of the heat source, the temperature distribution on the solid surface also shows the Gaussian distribution from the center to the melt pool periphery as shown in Fig. 7(a). The temperature drops sharply to room temperature in a smaller radius, showing a large temperature gradient over the whole heat affected area.

Fig. 6
Variations of the maximum and average temperature, maximum velocity, and average ΔPe number in the region versus time
Fig. 6
Variations of the maximum and average temperature, maximum velocity, and average ΔPe number in the region versus time
Close modal
Fig. 7
The axisymmetric evolution phenomena in the melt pool: (a) the temperature contour and (b) the velocity vector
Fig. 7
The axisymmetric evolution phenomena in the melt pool: (a) the temperature contour and (b) the velocity vector
Close modal

It is well known that the surface tension of liquid materials is extremely susceptible to temperature, and the existence of surface temperature gradient will lead to great differences in surface tension. In addition, a large surface tension gradient could induce the Marangoni convection on the metal surface, which is known as the Marangoni force. The higher the surface temperature gradient, the more vigorous Marangoni convection. For liquid metals with negative surface tension temperature gradient coefficient, the induced Marangoni force is in the opposite direction compared to the surface temperature gradient. In the melt pool, the highest temperature is located at the center, and the temperature gradient direction is from periphery to center. Therefore, the induced Marangoni convection presents a horizontal distribution from center to periphery at the surface. In addition, the vapor recoil force is also proved to be significant near the laser center [24], and the material there is squeezed by the force. Under the combined effects of these two forces, the liquid in the center is transported to the melt pool edge as shown in Fig. 7(b). During the evolution process of the melt pool, with the increasing surface temperature gradient, the induced surface velocity also continuously increases. From Fig. 6, it can be found that the maximum velocity in melt pool increases to 0.15 m/s from 0 m/s within 20 ms. However, when the surface temperature variation gradually reaches dynamic equilibrium, the temperature gradient changes become small and the velocity variation becomes increasingly smaller, and in following up 80 ms, the velocity only increase about 0.05 m/s.

In the melt pool formation procedure, the main driving source also changes. Figure 6 also shows the variation of the average grid Pe number (ΔPe = (Σρuδx/n)) [31], which indicates the effects of convection and diffusion versus time in the melt pool. ρ is the liquid density in grid (kg/m3), u is the liquid velocity in grid (m/s), µ is the liquid dynamic viscosity in grid (Pa·s), δx is the grid length (m), and n is the grid number in the melt pool. It can be observed clearly that ΔPe number is smaller than 0.5 before 5 ms, which indicates the melt pool evolution is dominated by the diffusion effect at the initial stage, owing to the not yet formed or very weak convection in the melt pool. Nevertheless, with the rapid increase of temperature and the induced fluid velocity, the convection effect gradually takes the leading position and the heat transfer in the region also increases (from 5 ms to 20 ms, the ΔPe number sharply increases to about 2). As time goes on, the variation of the ΔPe number becomes slower and finally reaches a maximum value of 2.35, corresponding to an equilibrium melt pool convection process.

3.2.2 Melt Pool Morphology.

During the melt pool evolution process, the flat surface of the melt pool is gradually deformed. Under the driving of Marangoni convection, the material in the center of melt pool is continuously transported to the periphery. Hence, a deep hollow is formed at the center, while a wave hump is formed after the transported material is accumulated at the edge as shown in Fig. 8. With the continuous material transport, the hollow in the center becomes increasingly deeper, while the hump becomes higher and wider.

Fig. 8
The variations of the free surface in the melt pool versus time
Fig. 8
The variations of the free surface in the melt pool versus time
Close modal

Furthermore, a quantitative study of the morphology evolution of the melt pool is also shown in Fig. 9, which shows the variations of the length, depth–length ratio, and width–length ratio of the melt pool, and the deformation of the free surface versus time. The detailed definitions of those parameters are shown in Fig. 9(b), respectively. As the pool grows larger with the increasing time, both length and depth of the melt pool increase obviously. However, due to the dominating horizontal convection, the tangential evolution is more vigorous and length increases more rapidly compared to depth (the initial depth–length ratio is about 0). When heat and convection gradually reach an equilibrium state, the increase of melt pool dimension slows down and eventually reaches its own equilibrium. The melt pool length and the depth–length ratio tend to balance at values of 1.42 mm and 0.25, respectively; however, the width–length ratio always stays at 1.0 because of the Gaussian boundaries condition. Due to the continuous transport of material from the fixed center to the periphery, free surface deformation of the hollow always becomes deeper and the hump becomes higher. Therefore, the deformation continuously increases with longer duration as shown in Fig. 9(a) (from 90 ms to 100 ms, the deformation still increases about 0.03 mm), but the overall deformation amplitude increase becomes smaller as shown in Fig. 8.

Fig. 9
The variations of melt pool morphology versus time under the fixed laser condition: (a) the melt pool morphology and (b) parameters definition
Fig. 9
The variations of melt pool morphology versus time under the fixed laser condition: (a) the melt pool morphology and (b) parameters definition
Close modal

3.2.3 Energy Input and Distribution.

Figure 10 shows the variations of energy input and distribution during the laser melting process. For the input energy in the melt pool, it can be mainly distributed into two parts, energy dissipation and energy increase. Energy dissipation includes heat conduction from the melt pool to other workpiece parts, heat radiation, convection, and evaporation of the melt pool surface. Since nature heat convection is far smaller than heat radiation for high-temperature surface (the surface average temperature is 2300 K at 10 ms), its dissipation effect is considered negligible and classified into the else energy term. Energy increase is also classified into the else energy term.

Fig. 10
The variations of energy input and distributions during the melting process: (a) the variations of energy in the melt pool and (b) the variations of percentage of energy distributions
Fig. 10
The variations of energy input and distributions during the melting process: (a) the variations of energy in the melt pool and (b) the variations of percentage of energy distributions
Close modal

At the initial laser deposition stage, the heat dissipation from the melt pool is little, as shown in Fig. 10(a), the else energy term is largest (56%) as shown in Fig. 10(b). Most of the input energy remains in the pool, making the temperature increase, melt pool broaden, and free surface deform. However, as the temperature gradually increases and passes the evaporation point, both heat radiation and evaporation components increase quickly. Simultaneously, heat conduction increases as well due to the increasing conduction area caused by the growing melt pool dimension. However, the energy input increases by the continuous increase of the temperature of the heating area due to the increasing surface deformation. The energy increase in the melt pool still decreases, and its percentage decreases quickly from 56% to about 1% since the increase of energy dissipation is faster than that of the input energy. The percentage of heat radiation and evaporation increases from 8% to 24% and 2% to 11%, respectively, and the heat conduction increases from 34% to 63%, which takes the dominant role as shown in Fig. 10(b). The else energy term almost approaches zero at 50 ms as shown in Fig. 10(a). At this moment, all the input energy in the melt pool is used to compensate for heat conduction, convection, radiation, and evaporation from the melt pool. The heat deposition and dissipation in the melt pool are dynamically balanced based on the continuous temperature feedback. Without further obvious energy increases or decreases in the melt pool, variations in temperature, velocity, and morphology become stabilized and the melt pool evolution at this stage enters a quasi-steady state stage.

3.2.4 Surface Shrink.

In this study, the self-shrink character of the free surface is also investigated. As shown in Fig. 11, which presents the free surface shape at various time, the free surface deformation reduces about 0.13 mm immediately after quenching within 4 ms. Especially for the period from 2 ms to 4 ms, owing to the sharp reduction of surface temperature (about 1200 K/4 ms), the melt pool dimension disappears continuously (clearly, the melt pool length and depth decrease about 75% and 100%, as shown in Fig. 12). Thus, the Marangoni force in melt pool also decreases; and the reverse transport effect in the melt pool energized by the surface tension force and the gravitational force gradually dominates the melt pool evolution, which delivers the material from periphery to center. As shown in Fig. 12(a), the velocity vector direction is reversed compared to that before quenching. Therefore, the hollow gradually becomes shallower, the hump becomes flatter, the deformation shrinks, and the free surface tends to be flat.

Fig. 11
The free surface shrinkage at various time periods
Fig. 11
The free surface shrinkage at various time periods
Close modal
Fig. 12
The free surface shrinkage formation mechanism after quenching: (a) reverse transport, (b) temperature contour near surface at 6 ms after quenching, and (c) the melt pool vanishing process
Fig. 12
The free surface shrinkage formation mechanism after quenching: (a) reverse transport, (b) temperature contour near surface at 6 ms after quenching, and (c) the melt pool vanishing process
Close modal

From 4 ms to 8 ms, the surface deformation still continues to decrease about 0.06 mm, but the shrinkage amplitude reduces quickly, owing to the weaker and weaker convection effect on melt pool surface induced by increasing porosity resistance. Besides, the relative slower temperature reduction of the surrounding inert gas near the free surface efficiently improves the free surface shrinkage process. As shown in Fig. 12(b), at 6 ms, the surrounding gas temperature is about 1900 K; however, the melt pool surface temperature is only about 1700K. Attributed to the continuous heat transfer from surrounding gas to surface, the surface melt and fluid flow are strengthened, and the shrinkage time is extended, although the induced shrinkage speed and efficiency are poorer than before. Figure 11 shows that in a long period after 8 ms, the free surface only changes about 0.002 mm, which almost can be ignored.

3.3 Melt Pool Evolution Phenomena Under Moving Laser Beam

3.3.1 Basic Evolution Process and Formation Deviation.

It has been mentioned in previous sections that a flat solid surface evolves into a centrally symmetrical-deformed surface with a hump and hollow under a fixed laser heat source, as shown in Figs. 4 and 7. Compared with the evolution phenomena of the melt pool under a fixed laser beam, the evolution of the melt pool under a moving laser presents different phenomena. Figure 13 displays the surface shape morphology and temperature of the workpiece for experiment and simulation. When a moving laser is used, a continuous, smooth, equal width, and uniform height bulge is formed on the sweeping path behind the rear edge of the melt pool. In the experimental condition, there is a group of discontinuous welding lump due to the fact that a pulsed laser is used. A corrected continuous energy input is used in the numerical simulation for simplification. Moreover, there is no obvious wave hump formed near the front edge of the melt pool, whose height is evidently lower than the rare bulge and is basically flat with the original surface.

Fig. 13
The morphology of the free surface and its trail edge on the sweeping path
Fig. 13
The morphology of the free surface and its trail edge on the sweeping path
Close modal
Figure 14 shows the evolution process of temperature and velocity on the free surface of the melt pool central cross section along the laser scanning direction versus time. The yellow region indicates the melt pool zone, and the red line indicates the location of the laser center where is also the highest temperature point. In the initial stage of laser scanning procedure of the first 20 ms, the red line divides the yellow area almost equally and the laser center is basically located at the pool center. The velocity and temperature fields are slightly asymmetrical with slightly larger on the left side. The melt pool evolution approaches the Gaussian evolution (axisymmetric) at this moment. However, with continuing laser scanning and increasing the melt pool dimension, the melt pool axisymmetric evolution is destroyed, and then, the asymmetric effect is strengthened. The melt pool area (yellow zone) on the left side of the laser center (red line) is gradually greater than that on the right side, the highest temperature region shifts to the front edge of the melt pool, and the velocity on the rear edge becomes higher (from 0.06 m/s at 20 ms to 0.1 m/s at 80 ms). Since the laser center keeps moving toward the front edge, the inverse Marangoni velocity is then induced in some regions of the front edge and the convection effect on the front edge is continuously destroyed and becomes weaker (from 0.05 m/s at 20 ms to 0.03 m/s at 80 ms). At the same time, a quantitative evolution of the asymmetric phenomena is also explored as displayed in Fig. 14(b). rA is the index to indicate those evolution and expressed as follows:
rA=LldululTl¯LrdururTr¯
where the subscript r and l represent the right and left sides, respectively, of the melt pool divided by the laser center, L is the length of each side, and du is the distance of the maximum velocity position to the laser center. T and u are temperature and velocity of each side, respectively. From this figure, it can be found that the asymmetric evolution continuously increases once the melt pool emerges and reaches equilibrium stage at about 60 ms, after then the evolution presents a quasi-steady stage. Applying the quantitative asymmetric evolution index as the indication to distinguish the stage of melt pool maybe an alternative method; however, it needs further verification.
Fig. 14
The asymmetric evolution process of temperature and velocity on the free surface: (a) the temperature and velocity evolution on scanning center line and (b) quantitative evolution versus time
Fig. 14
The asymmetric evolution process of temperature and velocity on the free surface: (a) the temperature and velocity evolution on scanning center line and (b) quantitative evolution versus time
Close modal

For the convective dominated melt pool evolution process, as shown in Fig. 15, the average ΔPe number is more than 1.1 after 20 ms, and the velocity distribution directly affects the morphology formation. For a fixed laser heating source, the transport process is always axisymmetric from the fixed center to the periphery. However, for a moving laser source, the velocity becomes faster on the rare edge and slower on the front edge due to the gradually increasing asymmetric effect in the melt pool. The material transport capacity toward the front edge is weakened and toward the rare edge is enhanced. Under this vigorous leftward flow, the material at the laser center is continuously transported to the rear edge, which makes the hollow formed by the laser center at the previous moment to be filled. In addition, the interface near the rear edge is continuously elevated, and then, a bulge is formed. Simultaneously, a new hollow in the melt pool is evolving at the new laser center near the front edge at this moment, and the hollow and the front edge are pushed forward along laser scanning direction as shown in Fig. 16. At the same time, due to the destruction of rightward convection, the material transport capacity is decreased, and there is no obvious hump formation in the front edge region.

Fig. 15
The variations of the maximum and average temperature, maximum velocity, and average ΔPe number in the region versus time
Fig. 15
The variations of the maximum and average temperature, maximum velocity, and average ΔPe number in the region versus time
Close modal
Fig. 16
The free surface evolution process under the moving laser scanning condition
Fig. 16
The free surface evolution process under the moving laser scanning condition
Close modal

Similar to the fixed laser beam condition, the maximum and average temperatures of the melt pool do not change when the pool evolution approaches a certain stage, and the induced maximum surface velocity and the average ΔPe number also change slightly as shown in Fig. 15. Besides, the asymmetric evolution in the melt pool tends to be stable (the area ratios on the two sides of the red line basically maintain around 2.2), and the melt pool evolution gradually enters the quasi-steady state stage.

3.3.2 Melt Pool Morphology.

Influenced by the asymmetric evolution on the scanning direction, the melt pool shape under a moving heating source is quite different from that under a fixed heating source. Figure 17 shows that the melt pool under a fixed laser source exhibits an axisymmetric evolution process. However, the melt pool is no longer axisymmetric for a moving laser source. In the laser scanning direction, the forward convection on the front edge is gradually destroyed and weakened, so the front edge becomes increasingly narrower, while the rear edge becomes increasingly wider due to the increasing convection effect as shown in the XZ plane in Fig. 17. When comes to the YZ plane, which is perpendicular to the laser scanning direction, it can be seen that the melt pool shape is still symmetrical with respect to the XZ plane. This is because that the asymmetry exists only in the scanning direction, and the evolution of the melt pool perpendicular to the scanning direction has no active mutagenesis factor under the Gaussian heat source distribution. The melt pool evolution under a moving laser source presents a plane symmetry feature along the central scanning section.

Fig. 17
The various melt pool shape during the evolution process: (a) moving laser and (b) fixed laser
Fig. 17
The various melt pool shape during the evolution process: (a) moving laser and (b) fixed laser
Close modal

Figure 18 shows the detailed transient evolution phenomenon of the free surface under a moving laser beam. In the initial evolution stage, the asymmetric effect in the melt pool is weaker, and the hump is formed on the front edge, and the free surface is approximately axisymmetric before 20 ms. As the melt pool evolution gradually reinforces, the hollow of the free surface continuously deepens, but the front hump gradually disappears due to the enhancement of the asymmetry effect. Meanwhile, the continuous bulge is gradually formed. However, in this stage, the transport in the melt pool is unstable, and the formed bulge on the rare edge is uneven. When the velocity and temperature evolution in the melt pool enters a quasi-steady state stage (about 60 ms), the material transport tends to be stable and the bulge at the trailing edge becomes smooth and even.

Fig. 18
The variations of the free surface in the melt pool versus time under the moving laser condition
Fig. 18
The variations of the free surface in the melt pool versus time under the moving laser condition
Close modal

Figure 19 shows the quantitative analysis of evolutions of the melt pool dimension and free surface deformation under the moving laser condition. For the melt pool dimension, its variation trends versus time are essentially the same as that under a fixed laser beam, which is rapidly increasing at first and then gradually approaches a quasi-steady evolution state (0.95 mm at 100 ms). Besides, the length evolution is much faster than that of the depth, and the depth–length ratio increases gradually at initial and maintains about 0.3 when evolution enters the steady state. However, the variation of the width–length ratio is different from that under a fixed laser beam. The width–length ratio of a fixed laser is always 1.0, but the ratio of a moving laser gradually reduces and at last remains about 0.9. It indicates that the evolution speed of the melt pool in the scanning direction is faster than that in the lateral direction. Furthermore, in the moving laser manufacturing process, the laser center always travels on the sweeping path. Therefore, the hollow will not continuously deepen. When the melt pool evolution enters the quasi-steady state, the shape of the free surface almost has no change and the deformation remains about 0.43 mm.

Fig. 19
The variations of melt pool morphology versus time under the moving laser condition
Fig. 19
The variations of melt pool morphology versus time under the moving laser condition
Close modal

3.3.3 Temperature Variation and Surface Shrink.

Figure 20 shows the temperature evolution of the monitoring points at (0.0035, 0.004, and 0.0036) on the workpiece, which includes the temperature increase process as the laser approaches and the cooling process as the laser gradually moves away. The cooling time (about 25 ms) is much longer than the heating time (about 15 ms) for the same temperature difference, which indicates that the moving distance of the monitoring point from the melt pool front edge to the center is much smaller than that from the center to the melt pool rear edge. This phenomenon is also consistent with the melt pool shape of the moving laser beam presented in the previous study. In this process, the cooling rate representing the micro texture of the product after solidification is also investigated. For the point with a maximum temperature of 3250 K, the maximum and average values are 1.4 × 105 K/s and 5.0 × 104 K/s, respectively, which are much higher than that compared to the traditional manufacturing of 102–104 K/s [13]. The laser-aided 3D printing can significantly improve the microstructure and product quality of the products, and it has a bright future in different industrial applications.

Fig. 20
The temperature evolution and cooling rate at the monitoring points of (0.0035, 0.004, and 0.0036)
Fig. 20
The temperature evolution and cooling rate at the monitoring points of (0.0035, 0.004, and 0.0036)
Close modal

The free surface shrinkage also exists under the moving laser condition after quenching as shown in Fig. 21. The interface shrinks rapidly within 4 ms (about 0.14 mm) due to the existence of a formed melt pool, and then shrinkage becomes weaker and gradually disappears. However, due to the asymmetrical convection of the front and rear edges under a moving heating source, the surface shrinkage is also asymmetric. Generally speaking, the transport in the rear edge region is stronger than that in the front edge region. Therefore, the surface shrinkage in the rear edge is faster than that in the front edge, and the final formed rear edge slope is smaller than the front edge slope as shown in Fig. 21.

Fig. 21
The free surface shrinkage under the moving laser condition
Fig. 21
The free surface shrinkage under the moving laser condition
Close modal

4 Conclusion

In this study, a 3D numerical model of metal melt pool based on the VOSET interface capture method is developed and validated. Then, the significant evolution phenomena of metal melt pool under the fixed or moving laser beam conditions are studied, and the formation mechanism is further explored. The main conclusions are drawn as follows:

  1. The evolution morphology and temperature distribution of melt pool obtained by the numerical model are basically consistent with the experimental study, which demonstrates that the VOSET method could provide a good prediction and capture tracking effect in the melt pool evolution process.

  2. In the energy density deposition process, the temperature increases sharply and a large temperature gradient is formed, which induces the formation of Marangoni convection. The convection effect increases rapidly and dominates the melt pool evolution. In the fixed laser condition, the melt pool evolution exhibits a central symmetry. For moving laser conditions, the melt pool evolution presents a plane symmetry.

  3. The melt pool dimension and its free surface deformation increase gradually, and the tangential evolution is more vigorous. Furthermore, for moving laser conditions, under the effect of the increasing asymmetry in the scanning direction, the melt pool is narrow on the front edge and wide on the rear edge. A continuous, smooth, equal width and uniform height bulge is formed on the sweep path, and the evolution in the length direction is also faster than that in the width direction.

  4. In the melt pool solidification process, the free surface shrinkage appears due to the rapid decrease of surface temperature, surface tension, and gravity dominated the evolution process of the melt pool. The surface shrinkage rate rapidly decreases and vanishes as the melt pool gradually disappears. The cooling rate approaches 1.4 × 105 K/s, which indicates the microstructure quality of the product, and it is much higher than that compared to the traditional fabrication technique.

  5. With the laser continuously scanning, the melt pool evolution enters a quasi-steady state, and the heat deposition and dissipation are dynamically balanced. Thus, the variations of the temperature, velocity, surface deformation, and melt pool dimension tend to be gentle and stable.

Acknowledgment

This present study is financially supported by the National Natural Science Foundation of China (Grant No. 51776157) and the Basic Science Research Project (Natural Science) of Colleges and Universities of Jiangsu (Grant No. 21KJB470002).

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper. Data provided by a third party listed in Acknowledgment. No data, models, or code were generated or used for this paper.

Nomenclature

     
  • d =

    distance from the grid to the interface, m

  •  
  • g =

    gravity, m/s2

  •  
  • h =

    enthalpy, J/kg

  •  
  • t =

    time, s

  •  
  • C =

    volume fraction function

  •  
  • P =

    pressure, Pa

  •  
  • Q =

    the energy source term, W/m3

  •  
  • R =

    effective laser radius, m

  •  
  • T =

    temperature, K

  •  
  • fl =

    liquid fraction in the melt pool

  •  
  • ui =

    velocity, m/s

  •  
  • K0 =

    permeability coefficient

  •  
  • T0 =

    ambient temperature, K

  •  
  • Tm =

    melting temperature, K

  •  
  • Ts =

    solidification temperature, K

  •  
  • Tsurf =

    surface temperature of melt pool, K

  •  
  • V0 =

    sound velocity in the workpiece, m/s

  •  
  • x, y, z =

    coordinate directions, m

  •  
  • δx =

    distance between the adjacent grid point

  •  
  • ΔH =

    latent heat of melting, J/kg

Greek Symbols

     
  • β =

    coefficient of volume expansion

  •  
  • ε =

    emissivity

  •  
  •  ε0 =

    Transition region thickness

  •  
  • ζ =

    small number

  •  
  • η =

    absorptivity coefficient

  •  
  • λ =

    thermal conductivity, W/(m·K)

  •  
  • µ =

    dynamic viscosity coefficient, Pa·s

  •  
  • ρ =

    density, kg/m3

  •  
  • ϕ =

    level set function

Subscripts

     
  • i, j, k =

    index of point

  •  
  • L/G =

    liquid/gas interface

  •  
  • surf =

    surface

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