Numerical simulation for the effect of scanning speed and in situ laser shock peening on molten pool and solidification characteristics

The unique thermal cycle of selective laser melting (SLM) significantly affects the undesirable formability and mechanical properties of the deposited parts, especially for materials with complex compositions. Laser shock peening (LSP) is a strengthening technology that can refine grain, convert tensile stress to compressive stress, and improve fatigue strength. In situ LSP is a technology that combines LSP and SLM without ablative coating. The combination can strengthen the additive manufacturing microstructure layer by layer. Some literature has verified the feasibility of no absorption layer and pressure confining layer LSP. However, little research reported the effects of the in situ combination on the molten pool. In this work, the finite element method (FEM) has systematically investigated the impact of scanning speed and in situ LSP on fluid flow behavior, heat transfer, and the solidification process of the molten pool. The flow velocity and the size of the molten pool decrease as the scanning speed increases. The solidification rate shows an increasing-decreasing-increasing process at low scanning speed during the solidification process. Moreover, the value of R is consistently stable at high scanning speeds. The temperature gradient increases gradually and decreases sharply with the scanning speed increase. The in situ LSP reduces the temperature and the fluid flow of the molten pool, which decreases the heat convection and the value of Peclet number, but has little effect on the solidification process of the molten pool.


Introduction
Selective laser melting (SLM) is additive manufacturing that melts metal powder by the laser beam, which has the advantage of high forming accuracy and high density and is widely used in processing parts with complex shapes and high precision [1][2][3][4]. Due to the high scanning speed and small melting regions, SLM has a very short melting and solidification time. Such a phenomenon has certain limitations for forming materials with complex compositions and wide solidification temperatures. Optimizing the SLM process becomes an important method to improve the forming structure and performance because the design of materials cannot be changed. Xu Wei, Laiqi Zhang, and Qinggong Lv contributed equally to this work.
Laiqi Zhang zhanglq@ustb.edu.cn Extended author information available on the last page of the article.
Due to the unique heating process of SLM, the molten pool is formed and solidified very quickly. It is challenging to analyze flow characteristics, heat transfer, and solidification conditions of the molten pool by experimental methods. The experimental approach to the above study is time-consuming and labor-intensive, and the experimental parameters cannot be easily adjusted to draw systematic and regular conclusions. The finite element method (FEM) can freely adjust the simulation parameters and obtain the results of the system, which are less timeconsuming and less expensive. The advantages of FEM in saving a lot of time and effort in transient and difficult-toobserve areas are more pronounced. Simulation is also more helpful for prospective studies, where conclusions can be drawn quickly about significant or non-significant effects, avoiding the waste of extensive experiments and avoiding detours for the researchers.
Many scholars have researched FEM for different materials and processing methods [5][6][7], and the parameters involve laser power, layer thickness, scanning speed, etc. The contents include the relationship between molten pool morphology and flow, solidification behavior, and microstructure. Huang et al. [8] regulated the impact of the process parameters on the thermal behavior, molten pool configuration, and microstructural evolution of the SLM. Chen et al. [5] simulated the influence of electron beam temperature gradient, cooling rate, and solidification rate on solidification behavior and characteristics at the molten pool boundary and predicted the solidification microstructure at different positions of the molten pool. Meng et al. [9] investigated the processing of alloy powders with highthroughput pulsed lasers, and the effect of cooling rate on the molten pool was studied by controlling the cooling water flow rate. Scanning speed is the significant parameter to focus on and determines the microstructure of the deposited layers. The existing simulation studies generally only describe the molten pool or solidification process and have not been further studied.
LSP [10,11] is an effective surface reinforcement technique with high pressure, super-fast, and super-high strain rates, which can improve the stress distribution and microstructure of SLM. Some researchers apply LSP during the SLM process. Lu et al. [12] designed LSP used for every five layers of SLM. It was shown that the LSP treatment of Ti6Al4V improved the hardness, refined the grain size, and converted the residual tensile stress to compressive stress. Kalentics et al. [13] designed a 3D-LSP method to integrate LSP with SLM. The effect law of different LSP power, number of spacer layers, and overlap rate on residual stress were studied, and the parameters of LSP were optimized and compared. However, these studies have focused primarily on conventional LSP strengthening of materials after additive manufacturing. The in situ LSP without absorption layer and pressure confining layer (e.g., paint, tape, or water) are less studied, and the in situ LSP strengthening process moving with SLM heat source is even less. Some literature has successfully performed LSP for unconfining layers using appropriate laser wavelength, energy density, pulse width, and spot area. Yella et al. [14] investigated the variation pattern of surface roughness and residual stress of LSP under the action of different absorption layers using the SS316LN plate as the material. The study confirmed the feasibility of strengthening the material by LSP without an absorption layer. Prabhakaran et al. [15] investigated the strengthening of material properties LSP without an absorption layer. LSP improved the roughness of the material, increased the microhardness by about 65.84%, and increased the fatigue life of the material by 26 times after impact, demonstrating the feasibility of LSP without an absorption layer. [16,17], and [18] investigated LSP without an absorption layer and confining layers using a femtosecond pulsed laser. Such research successfully improved the surface morphology, microstructure, residual stress, and microhardness. The feasibility of LSP in an air environment was verified, making a new field of in situ LSP-SLM applications possible. The in situ LSP-SLM process in such literature mainly focuses on the study of properties and deformation. The in situ LSP may affect the molten pool when the in situ LSP follows the movement of the SLM heat source and acts in the vicinity of the molten pool. The effect of in situ LSP on the molten pool following the movement of the SLM laser beam has not been reported.
This paper studied the effect of scanning speed and in situ LSP on the molten pool. The numerical simulation of the SLM process with different scanning speeds and the SLM process assisted by in situ LSP were carried out using Fluent. The effects of various process conditions on fluid flow behavior, heat transfer, and solidification conditions in the molten pool were studied. The obtained results in this paper can provide theoretical support for SLM process formulation, structure control, and performance improvement. process mainly contains convection, radiation, molten pool formation, and solidification. The simulation model is divided into three parts: the substrate (Z-coordinate 0-0.2 mm), powder layer (Z-coordinate 0.2-0.24 mm), and protective gas (Z-coordinate 0.24-0.34 mm). The sizes of the three parts are 1 mm×0.5 mm×0.2 mm, 1 mm×0.5 mm×0.04 mm, and 1 mm×0.5 mm×0.1 mm, respectively.

Numerical simulation methods
The sparse powder layer was considered a dense solid material in the simulation. Several assumptions were made to simplify the model: (1) The fluid in the simulation model is a Newtonian fluid. (2) Fluid flow is considered laminar.
(3) Buoyancy adopts the Boussinesq assumption, and the density of the rest is regarded as a constant. (4) The mushy zone at the temperature between the solidus and liquidus is a porous medium with isotropic permeability. (5) Mass loss caused by liquid vaporization is ignored.
The simulation results were calculated with models of Multi-phase Volume of Fluid (VOF), Energy, Viscous (Laminar), and Solidification&Melting. Finally, the postprocessing software CFD-Post was used to post-process the calculation results. Extensive literature has described the mass conservation equation [19] and the momentum conservation equation [20] involved in the simulation process and will not be repeated in this paper. This work presents only the critical boundary conditions and the energy conservation equations associated with the heat source. Marangoni convection is a liquid convection phenomenon associated with surface tension changes [19]: where σ T is the Marangoni force, σ 0 is the surface tension, dσ dT is the temperature coefficient of surface tension, T is the temperature of the gas-liquid interface, T m is the melting temperature, σ (T ) is the temperature-dependent surface tension, and T 0 is the reference temperature. The differential equation governing energy conservation can be derived from the first law of thermodynamics [20]. If the flow is incompressible, the governing energy conservation equation can be summarized as Eq. 3.
herein ρ is the density of the material, h is the enthalpy of the fluid, u is the velocity vector, λ is the thermal conductivity coefficient, T is the temperature of the fluid, and Q H is the energy source, including laser heat source and heat lost as Eq. 4.
where Q laser is the Gaussian body heat source used in the model, which expression is shown in Eq. 5 [21,22], and Q lost is the heat loss during the SLM process shown in Eq. 11.
where ξ is the energy distribution factor; η is the effective absorption; W is the laser power; χ is the ratio of the peak energy of the lower surface to the upper surface; z e , z i , r e , and r i are the Z-coordinates and radii of the upper and lower surface for the laser energy distribution area, respectively; r 0 is the radius at the Z-coordinates; and s, w, E, F are the intermediate variable.
herein q con is heat loss due to convection, q rad is the heat loss due to radiation, h c is the convection heat transfer coefficient, σ is the emissivity of alloy, ε is the Stefan-Boltzmann constant, T is the temperature of the gas-liquid interface, and T m is the melting temperature. Figure 2 illustrates the schematic diagram of in situ LSP coupled with SLM. The LSP acts close to the molten pool and moves synchronously with the laser heat source. Since  the in situ LSP is applied near the molten pool, the shock wave conducted near the molten pool may have an agitating and oscillating effect on the molten pool. The laser shock wave generated by the LSP during the impact may affect the temperature, flow field, and the solidification of the molten pool to different degrees. In order to verify the effect of laser shock on the molten pool, the laser shock force is converted into a continuous volume force acting directly on the molten pool as a momentum source term [23]: where P max is the peak pressure of LSP, P t is the normalized pressure in time, r is the distance from the center of the laser spot, α l is the volume fraction of the liquid phase metal, ρ l is the average density for the liquid metal, and ρ s is the average density for the solid metal.
The P max is a parameter related to the laser power and radius, and a suitable pressure value can be obtained by appropriate parameter adjustment. The value of the pressure will be directly used for calculation in the later simulation. According to the available literature, the P max of LSP without a pressure confining layer can reach 754 MPa [24]. Different P max can be obtained by adjusting the LSP parameters. In this paper, the P max was set to 0, 500, 700, and 900 MPa, corresponding to Case 1, Case 2, Case 3, and Case 4. Inconel 718, a nickel-based superalloy, was used as the simulation material in this paper. Table 1 lists the chemical composition of the material, and Table 2 shows the parameters with fixed values used in the simulation calculation. The temperature-dependent parameters (e.g., thermal conductivity, specific heat, viscosity, and surface tension) calculated using J-MatPro are shown in Fig. 3. Figure 4 shows the temperature field and morphology characteristics at different times during the SLM without LSP. Figure 5 indicates the flow field in the molten pool for four scanning speeds (10, 30, 50, and 70 cm/s) at t = 1.5 ms. The increase in scanning speed reduces the heat flow density, which makes the Marangoni convection gradually weaken, resulting in the maximum velocity in the molten pool decreasing from 1.87 to 0.85 m/s. Meanwhile, it gradually caused the molten pool to change from short and wide to narrow and long. Figure 6 shows the molten pool size at t = 1.5 ms, the molten pool area, and the liquid zone ratio at z = 0.23 mm. The molten pool width decreases from 173 to 110.8 μm, and depth decreases from 54 to 47.7 μm as the scanning speed increases, while the length increases gradually with the scanning speed. The width and depth of the molten pool at v s = 70 cm/s and the trends of the molten pool with the scanning speed are consistent with the research of Andreotta et al. [27]. The correctness of the model in this paper can be demonstrated, and the trends of the subsequent studies based on the SLM model are also credible. As shown in Fig. 6(c), the area of the molten pool shows a decreasing trend with the increased scanning speed. Combining Fig. 6(b) and (c), it can be seen that the trend of the molten pool area is more related to the width and depth of the molten pool and less to the length. As the scanning speed increases, the proportion of liquid zone in the molten pool shows an increasing trend. The main reason is that the weakened Marangoni convection cannot transport enough  heat to the edge of the molten pool, which decreases the mushy zone area more than the liquid zone area.

Effect of scanning speed on heat transfer and solidification process
The heat transfer in the molten pool includes heat conduction and convection, determined by the fluid flow. The value of P e can express the degree of heat transfer [19]. A high P e indicates that the heat transfer is intense, and the solidification rate is fast. P e is calculated as follows [28,29]: where v is the fluid velocity, ρ is the density of the metal (kg/m 3 ), C is the specific heat of metal (J/kg-K), and L R is the length of the molten pool. According to Eq. 13, P e is the  ratio of heat convection and conduction. The molten pool flow is mainly heat transfer when P e > 1, and the larger the value of P e, the more intense heat transfer. Figure 8 displays the fluid flow and P e. The taking path of data in Fig. 8 is shown in Fig. 7(a), where the crosssection in the Y-axis is Y = 0.25 mm (i.e., the central position of the molten pool). When v s = 10 cm/s, the molten pool has the fastest fluid velocity, 1.74 m/s. As the scanning speed increases, the peak velocity of the molten pool gradually decreases to 1.17, 0.77, and 0.85 m/s ( Fig. 8  (a)). When v s = 10 cm/s, the value of P e is 85.4, which is significate higher than others. As the scanning speed increases, the value of P e gradually decreases to 54.9, 38.0, and 44.1 (Fig. 8(b)). The high value of P e caused by low scanning speed is also the reason for the wider molten pool than others.
In Fig. 8, the origin of coordinates represents the position of the laser beam, and the position with the lowest velocity represents the highest temperature and the deepest molten pool. The laser beam and deepest position do not coincide because the molten pool needs a warming process. As the speed increases, the distance of the deepest region lagging behind the laser beam increases. When v s = 70 cm/s, the backward distance is 84 μm, resulting from combined scanning speed and heat transfer.
Temperature gradient (G) and solidification rate (R) are essential parameters in the solidification process of molten pools [30]. The temperature gradient and solidification rate can be calculated by formulas [19,31]: R = v s cos θ (15) where G u , G v , and G w are the temperature gradient components, v s is the scanning speed, and θ is the acute angle between the scanning direction and solid-liquid boundary. Figure 9(a) and (b) show the temperature gradient distribution and solidification rate of the molten pool at v s = 70 cm/s and t s = 1.5 ms. The molten pool boundary has the largest temperature gradient due to its proximity to the cold solid metal, reaching 3.497 × 10 7 K/m. The temperature gradient gradually decreases on the molten pool surface, reaching 1.18×10 7 K/m. As shown in Fig. 9(b), the maximum and minimum values of the solidification rate are respectively on the molten pool surface and the solid-liquid boundary. Figure 10 shows the solidification rate of the molten pool boundary during the solidification process. The taking points of data in Fig. 10 are shown in Fig. 7(b) for the solid-liquid boundary of the molten pool at different times. In Fig. 10(a) and (b), the solidification rate shows an increasing-decreasing-increasing change law at v s = 10 and 30 cm/s. When v s = 50 and 70 cm/s, the solidification rate remains stable and increases slowly. Figure 10  no significant increase at the end of the solidification process. This phenomenon is mainly due to the short solidification time and the slight acute angle between the scanning direction and the solid-liquid boundary [19]. Figure 11 illustrates the variation trend of the temperature gradient. The taking points of data in Fig. 11 are shown in Fig. 7(b) for the solid-liquid boundary of the molten pool at different times. According to Fig. 11, the decrease rate of the temperature gradient rapidly increased with the scanning speed increase. At v s = 10 cm/s, the slope of the temperature gradient decreases gently due to the longer solidification time. With the scanning speed increase, the heat transfer in the molten pool is insufficient, and the initial temperature gradient at the molten pool boundary gradually increases.
When v s = 70 cm/s, the maximum temperature gradient is 9.96 × 10 7 K/m. The value of G/R and G×R can reflect the trend of microstructure and grain size of solidified microstructure [5]. The decrease in G/R will lead to the gradual microstructure transition to columnar and equiaxed crystals. G×R is the cooling rate, and the increase in its value means that the microstructure becomes minor, but the cracking tendency also increases [32]. Figure 12 shows the curves of G/R and G×R. When v s = 10 and 30 cm/s, the maximum value of G×R is significantly higher than the others. During solidification, the G×R values at low scanning speeds decrease rapidly and rapidly fall below the values at v s = 50 and 70 cm/s. The reason is the low speed of solidification and sufficient heat transfer of the molten pool. The values of G/R at low speeds are small, and the values of G/R at different speeds tend to be similar as the solidification progresses ( Fig. 12  (b)). As shown in Fig. 12, the molten pools at low speed have high G×R and low G/R, which is more favorable for forming refined equiaxed grains. At high speeds, the molten pools have low G×R and high G/R, which is more potent for forming columnar crystals. In practice, different grain types are required for different locations of the part. Based on the simulation results, different scanning speeds can be used according to grain shape requirements.

Effect of in situ LSP on molten pool
In practice, different scanning speeds are selected depending on the desired organization of the part. At a faster scanning speed, the cracking tendency of the deposition layer is slight. It is an excellent choice to improve further the heat transfer and solidification characteristics of the molten pool using in situ LSP. In this paper, v s = 70 cm/s was chosen to study the effect of in situ LSP on the molten pool. Figure 13 shows the temperature and flow fields of the molten pool in the Y-direction at t = 1.5 ms. The molten pool surface has a distinct concave surface due to the Marangoni convection caused by the fluid flowing from the center to the surroundings. As shown in Fig. 13, the molten pool fluid flows from the center to the surrounding area along the Y-direction. The rapid flow of the molten pool causes insufficient recharge at the bottom of the molten pool and a depressed molten pool surface. Figure 14 shows the temperature trend in the center of the molten pool for the four cases. At t = 0.5 ms, the molten pool temperature tends to stabilize. In Fig. 14, the maximum average temperatures of four cases are 3290, 3190, 3220, and 3250 K. It can be seen that the maximum temperature at the center of the molten pool increases sequentially as the P max increases but is still lower than the case without LSP. Such a phenomenon indicates that the temperature field of the molten pool decreases due to the in situ LSP, and the maximum temperature gradually increases with the increase of the P max .  Figure 15 shows the temperature and flow field of the molten pool at t = 1.5 ms in the Z direction. The molten pool without LSP has the maximum area and the fastest flow velocity, reaching 0.85 m/s. Compared with Case 1, the velocity of the molten pool after laser shock processing reduced to 0.71 m/s. As the P max increase, the flow velocity gradually increases to 0.72 and 0.73 m/s. The trend of velocity variation is consistent with the temperature variation trend in different cases. The trend is because the temperature gradient of the molten pool becomes larger when the temperature is higher, which enhances the Marangoni convection and improves the fluid flow in the molten pool, resulting in the flow velocity increase. Figure 16 shows the length and width of the molten pool in the four cases. The length and width of the molten pool Fig. 14 The maximum temperature of the molten pool at different times without LSP are 219 and 110.8 μm, which are slightly larger than in other cases. As the P max increase, the length and width increase slightly; by comparing Case 2, Case 3, and Case 4, the width and length of the molten pool increase from 212.6 to 213.8 μm and 106.7 to 108.8 μm. The effect of LSP has a more significant impact on the width of the molten pool than the length. The phenomenon is due to the change in molten pool shape being largely dependent on the fluid transferring heat from the high-temperature region to the low-temperature region. The width of the molten pool is smaller than the length, and thermal convection is more likely to transfer heat to the solid-liquid boundary of the molten pool, so the increase in width is more significant than the increase in length. Figure 17(a) and (b) show the area of the molten pool and the liquid zone ratio, respectively. Comparing the four cases, Case 1 has the maximum area of the liquid and mushy zones, 11178 and 4964 μm 2 , respectively. Case 3 has the minimum area of the liquid zone, 10640 μm 2 , and Case 2 has the minimum area of the mushy zone, 4802 μm 2 . With the increase of P max , the area of the liquid zone and mushy zone increases slightly, leading to the area of the molten pool increasing; however, the change between Case 2 and Case 4 was just 65 μm 2 ( Fig. 17(b)). The proportion of liquid zone to the molten pool is the largest in Case 1 and is smallest in Case 3. Although the effect of LSP can reduce the proportion of the liquid zone, the minimum proportion of the liquid phase remains above 68%. In conclusion, LSP can reduce the molten pool area, but the effect is minimal.  Figure 18 shows that LSP decreases the flow velocity and the P e value. The taking path of data in Fig. 18 is shown in Fig. 7(a), where the cross-section in the Y-axis is Y = 0.25 mm (i.e., the central position of the molten pool). Case 1 has the highest value of P e during the solidification process ( Fig. 18(b)). In all cases, the values of P e are close, and the curves highly overlap, but the increasing rate of P e is significantly higher than that of Case 1. P e value corresponds to the heat transfer of the molten pool [19]. The results show that LSP can promote the rapid growth of heat transfer in the molten pool during the initial stage of solidification. However, the P e value in Case 1 is obviously higher than that in other cases, which indicates that the heat transfer in the molten pool is weakened by LSP, leading to a decrease in the molten pool size. Comparing Case 2, Case 3, and Case 4, the curves of P e and the molten pool size are very close. At the end of the solidification process, the slopes of curves are close, meaning that the influence of LSP tends to disappear.   Figure 19 displays the solidification rate, temperature gradient, G×R, and G/R during the solidification process at x = 1.15 mm. The taking points of data in Fig. 19(a) and (b) are shown in Fig. 7(b) for the solid-liquid boundary of the molten pool at different times. As shown in Fig. 19, the curves of Case 1, Case 2, and Case 4 are highly overlapping, except for the solidification rate in Fig. 19(a). The acute angle between the solid-liquid boundary and the laser scanning direction causes such a difference [19]. The difference in temperature gradient reflected in the initial solidification is caused by the difference in the initial temperature of the molten pool. Case 3 shows more differences in temperature gradients. However, these differences gradually disappear as the solidification process progresses. The curves of G×R and G/R are also highly overlapped due to the G and R for different cases being very close, so it can be inferred that LSP will not affect the microstructure. According to Fig. 19, LSP has little influence on the solidification process of the molten pool. Compared with Case 1, the effect of LSP also has little effect on the solidification time, except that the solidification time of Case 4 is increased by just 0.02 ms.

Conclusion
In order to understand the effects of in situ LSP on the molten pool, the flow behavior, heat transfer, and solidification conditions were investigated by simulating the in situ LSP-assisted SLM process with different speeds and different P max . The following conclusions can be drawn: (1) The flow velocity of the molten pool decreases with the increase in scanning speed. As the scanning speed increases, the width of the molten pool decreases rapidly, the length of the molten pool increases slightly, and the area of the molten pool decreases gradually.
(2) When v s = 10 and 30 cm/s, the solidification rate shows an increasing-decreasing-increasing process. The high simulated value of G×R and the low value of G/R is favorable for forming fine equiaxed crystals.
When v s = 50 and 70 cm/s, the solidification rate is stable and is favorable to the formation of columnar crystals. (3) The LSP reduces the temperature and fluid flow of the molten pool, which decreases the heat convection and the value of P e. As a result, the length and width of the molten pool decrease, and the LSP power has a more significant effect on the length than the width. (4) The LSP will somewhat affect the temperature and fluid flow of the molten pool. However, LSP has little effect on the solidification process of the molten pool due to its short solidification time.