Research on the temperature control strategy of thin-wall parts fabricated by laser direct metal deposition

To solve the problem that the macro-size, microhardness, and mechanical properties of the laser direct metal deposition (DMD) of thin-walled parts are inconsistent due to the heat accumulation, an improved three-dimensional finite element heat propagation model was developed to simulate the temperature evolution of the single-pass multi-layer thin-walled parts. The results show that the heat accumulation is contributed to the transformation of the heat dissipation mechanism from three-dimensional to two-dimensional, while the residual heat of the former layer has no significant effect on the heat accumulation of the current layer. The optimized strategy of decreasing laser power gradually is more effective than the optimized strategy of increasing the time interval between layers in maintaining the stability of the molten pool. The integrated optimized strategy of parabolic-shape laser power decreasing and time interval of 5 s is the most effective method to reduce the heat accumulation in the DMD of thin-walled parts. The thin-walled parts with an optimized deposition process have a more uniform width, finer microstructure, and higher microhardness. This work provides theoretical guidance for reducing the heat accumulation during DMD thin-walled parts and is beneficial to improving the uniformity of mechanical properties of thin-walled parts.


Introduction
Laser direct metal deposition (DMD), as one of the advanced additive manufacturing (AM) technology, has been widely used in the manufacture of parts with complex and thinwalled structures due to its design flexibility, dieless manufacturing, and rapid response to market demand and other advantages [1][2][3]. Since the DMD has the characteristics of rapid melting and cooling, the thermal behavior during the deposition process has a significant impact on the microstructure and mechanical properties after solidification [4,5]. Especially in the process of DMD of thin-walled parts, it is of great interest to analyze the thermal histories for manufacturing parts with desired microstructure and mechanical properties.
In the process of DMD of thin-walled parts, with the gradual increase of deposition layers, the heat dissipation mode of the molten pool would gradually change from threedimensional to two-dimensional [6,7]. This phenomenon would worsen the heat dissipation of the molten pool, and then affect macro-morphology by the shape of stable molten pool and microstructure by solidification parameters (temperature gradient and solidification rate), and finally results in the uniformity of mechanical properties of thin-walled parts. To solve the problem of instability of thermal behavior in DMD of thin-walled parts, some researches on molten pool monitoring and numerical simulation have been carried out. In the process of fabricating 316LSi thin-walled parts with a robotized laser/wire direct metal deposition system, Akbari and Kovacevic [8] monitored the molten pool in real-time with a CMOS camera and obtained an empirical correlation between the molten pool area and the cooling rate. This study also found that the molten pool area gradually increases with the increase of the number of layers of thin-walled parts. To ensure the stability of the molten pool size in the process of DMD of thin-walled parts, Zhu et al. [7] used an infrared thermal imager to record the maximum temperature of the molten pool. According to the measurement results, a control strategy of reducing power layer by layer was proposed to eliminate the change in pool size caused by energy accumulation. Besides, numerical simulation is also another effective method to reveal the thermal history of thin-walled parts during the DMD process. Xiong et al. [9] established a finite element model of heat conduction for the manufacturing of the circular thin-walled part using gas metal arc welding technology. The results indicate that the temperature gradient of the molten pool decreases with the increase of deposition height and the main direction of heat conduction changes from axial to circumferential. In the coupled finite element model of temperature field and flow field of thin-walled parts established by Morville et al. [10], the effects of process parameters on the width and length of the molten pool and the surface finish of the solidified part are discussed in detail. The results also point out that the molten pool size increases from the first layer to the fifth layer, which is attributed to the energy storage in the continuous deposition process. Xia et al. [11] characterized the complex thermal history of thin-walled metal parts fabricated by DMD through numerical simulation and experiments. From the results, the cumulative effect of heat increases the peak temperature of the molten pool, while the decreasing cooling rate reduces nucleation rate at the beginning of solidification, which coarsens austenite grains at the top of the part.
Reviewing the above kinds of literature, it is very important to optimize the thermal behavior of the molten pool during the DMD process for the microstructure and mechanical properties of the parts. The methods to reduce the heat accumulation during the DMD process mainly include improving the heat dissipation ability of the molten pool and controlling the energy input [12][13][14]. For the former method, the parts need to be forced cooled [15], which is difficult to carry out in terms of equipment and deposition process. At the same time, controlling the input of laser energy to slow down or suppress heat accumulation is a convenient and effective method. Besides, the previous researches focus on the temperature change in the building direction, but the temperature change in the scanning direction is often ignored. Therefore, in this study, the temperature evolution on both the building direction and scanning direction during the DMD of the thin-walled part was studied by an established finite element model. And then, different power control strategies and interlayer intervals were selected to ensure the stability of the molten pool during the DMD process. Finally, combined with the results of simulation and experiment, the effects of cooling rate, solidification rate at the solid-liquid interface, and thermal history on the microstructure and microhardness of thin-walled parts were analyzed in detail.

Experimental method
The equipment used in this study is an integrated DMD system, as shown in Fig. 1. The hardware parts of the equipment mainly include a robot arm (KR16-2 with six freedom degrees, KUKA Robotics Corporation), a continuous wave (CW) laser generator (YLP-500, IPG, Germany, the wavelength of 1020 nm), a cladding head with a coaxial powder nozzle (RC52), a water cooler (Tongfei cooling SL400), a controller, and an electric control cabinet. The cladding Fig. 1 The DMD system for experimental, a schematic illustration; b experimental setup head is mounted on the end effector of the robot arm, which ensures the flexible design and implementation of the deposition strategy. The deposition track is programmed, optimized, and simulated by offline programming software (Robot-Art), and then imported into the KUKA controller after post-processing. The program can sensitively control the scanning speed, track spacing, and laser on and off. The laser power and powder feed rate can be adjusted online manually during the DMD process. Argon with a purity of 99.99% is used as the shielding gas and carrier gas to reduce the oxidation of the deposited materials.
The commercial medium carbon steel (45 steel) was selected as the substrate with a size of 100 × 100 × 10 mm 3 . The Fe-based powders were used as the deposition material. The chemical composition of the deposition material and substrate is shown in Table 1. As shown in Fig. 2, the diameter of spherical particles are ranged from 42.31 to 184.67 μm, and more than 99.73% of the particles are around 71.46-140.47 μm. Before the experiment, the surface of the substrate was ground with 800# sand paper and cleaned with alcohol to remove dirt. The powders were dried in a constant temperature drying oven at 80 °C for 3 h. The process parameters for the experiment and simulation are shown in Table 2.
After the experiment, the samples for metallographic examination were cut from by thin-walled parts using the wire cut electrical discharge machining perpendicular to the scanning direction, and then they were ground by different types of sandpaper from 240# to 2000#, mechanically polished through the diamond paste and then corroded with a mixed solution of 50 mL hydrochloric acid (HCl), 25 mL water (H 2 O), and 5 g FeCl 3 . The cross-section morphology and microstructure were obtained by 3D laser microscopy (OLS4000, Japan). The micro-hardness of thin-walled parts was measured by a Vickers microhardness tester (HV-1000, Shanghai, China), with a load of 300gf and a load-dell time of 10 s along the building direction.

Numerical simulation process
Since DMD is a complex physical and chemical process, this study focuses on optimizing the temperature control strategy by simulating the temperature accumulation of thin-walled parts during the deposition process, thus following assumptions and simplification are made to simplify the finite element model: 1. The deposition material is isotropic and homogeneous media; 2. The material vaporization is not considered during the modeling process; 3. Neglecting the influence of shielding gas and carrier gas on temperature distribution; 4. The effect of strain and stress field on temperature field is neglected.

Governing equations
The thermal behavior of the DMD process mainly includes (a) heat conduction between layers, (b) thermal radiation, and convection between deposited parts and the atmosphere [16,17]. The classical nonlinear heat conduction equation can be expressed as Eq. (1) [18],  where k is the thermal conductivity (W/m/K), c p is the specific heat capacity (J/Kg/K), Q int is the input heat and T and t is the temperature (°C) and time (s), respectively. In the boundary conditions, thermal conductivity normal to the surface, thermal radiation and convection, and boundary heat flux of laser beam can be described by where h c is the convective heat transfer coefficient between the air and model (W/m 2 /K), T amb is the ambient temperature (20 °C), ε is the emissivity, σ is the Stefan-Boltzmann constant (5.67 × 10 −8 W/m 2 /K 4 ), and q(x, y, z) represents the input heat flux of the laser beam. During the DMD, the moving laser beam with a double ellipsoidal heat distribution was employed when the penetration depth of laser to the material was considered, as shown in Fig. 3. The input heat flux can be defined as Eq. (3), where P is the laser power (W), η is the laser absorptivity of the molten pool, f f (1.4) and f r (0.6) are factors of the heat flux in the front and rear halves, and a 1 , a 2 , b, and c are characteristic parameters of the heat source model, as shown in Fig. 3. (1)

Thermophysical properties
Previous numerical simulations [1,20,21] have shown that the thermophysical properties of the material have a significant influence on the results. The deposited materials undergo a rapid melting and cooling process (> 10 6 K/s) during the DMD process. Therefore, it is very significant to get more accurate simulation results to regard the physical properties of the deposited materials as changing with temperature. Since the physical parameters of Fe-based powder and substrate have not been calibrated, the thermodynamic calculation based on the widely accepted calculation of phase diagrams (CALPHAD) method was used to evaluate the physical parameters of deposited materials [22][23][24]. The thermal physical properties of deposited materials are represented in Fig. 4. In this study, the arc was used to express the cross-section of the single-pass deposition track, which makes the computed results more consistent with the experimental than the commonly used rectangular section [25][26][27]. The deposition path of the thin-walled part is also shown in Fig. 5a. In the process of simulation, the size of the meshing is often inversely proportional to the computational efficiency and accuracy [18]. The temperature distribution in the deposition region is relatively concentrated, so the grid in this region is refined, and the grid in other regions is gradually coarse. The generated meshing is shown in Fig. 5b.

Finite element model set-up
In the process of the DMD process, the generation and boundary conditions of the signal-pass deposited track are dynamic, so the "element birth and death technique technology" was used to simulate the spatiotemporal growth process of the deposition track [28]. As shown in Fig. 6, the elements in different positions are activated in turn according to the position of the laser beam. Cells within the laser beam range are active, while others are inactive and do not participate in the current calculation. At the same time, according to the building state of the deposited track, the boundary conditions are updated step by step to simulate the real DMD process. The details of setting and solving the finite element model are shown in Fig. 7.  Figure 8 shows the computed temperature distribution of the 20-layer thin-walled part when the heat source is respectively located at the middle points of the different layers. As the heat source moves, the finite element elements are activated gradually along the scanning direction. The temperature of the front of the comet-shaped molten pool is high, while the temperature of the rear is low. Besides, with the increase of the number of deposition layers, the maximum temperature of the molten pool becomes higher and higher. The maximum temperature of the molten pool in the 18th layer is 350 °C higher than that in the 3rd layer. As a result, the melt pool is becoming larger, which significantly increases the powder catchment efficiency and thus destroys the width uniformity. In the process of DMD, the heat dissipation of the molten pool can be divided into two types: (a) heat conduction by the  previously deposited layer and (b) atmospheric convection and radiation [29]. The heat accumulation can be expressed as follow: where Q cum is the heat accumulation, q(x, y, z) is input heat flux of the laser beam (Eq. (3)), h cond is the heat conduction to substate or previously deposited layer, and h conv and h rad are the convection and radiation to the atmosphere, respectively.
To analyze the heat accumulation characteristics of thinwalled parts fabricated by the DMD in detail, the temperature history of the nodes where the laser beam is located (shown in Fig. 8) is obtained, and the results are shown in Fig. 9. The temperature history of points from A 1 to A 6 has a similar trend, and there are some temperature peaks and troughs. It can be found from Fig. 9 that the temperature at the nodes rises very quickly, whereas it does fall very slowly. The compression of the metal liquid in the front of the molten pool led to the rapid temperature rise in the front of the molten pool [30]. The slow dissipation of heat in the tail of the molten pool leads to a slow drop in temperature. As the DMD process, the temperature of the nodes is significantly higher than that of the nodes of the former deposited layer, but the temperature change tends to be stable. Besides, the phenomenon that the temperature peak of each node is higher and higher is mainly due to the gradual heat accumulation.
Since the heat dissipation of the molten pool at both two ends during the DMD thin-walled part is worse, it is of great significance to analyze the thermal history of horizontal nodes [10,31]. As shown in Fig. 10, the temperature of the first peaks at the two endpoints (B 1 and B 5 ) is significantly higher than that at the middle points (B 2 , B 3 , and B 4 ). As the thermal conductivity of air is significantly lower than that of metal, a large amount of heat accumulates at the edges of the thin-walled part as the laser beam moves to the ends. Comparing the thermal cycle curves of other points, two temperature peaks with small-time intervals can be found on the thermal cycling curve at point B 1 at about 60 s. The rapid change of direction as the laser head moves to the edge of the thin-walled part results in the appearance of small temperature peaks. As the heat builds up, these small temperature fluctuations are difficult to detect, as shown in Fig. 10. Besides, the number of temperature peaks at B 1 and B 5 is half of that at B 2 , B 3 , and B 4 , which indicates that the liquid metal at both ends of the thin-walled part has a longer cooling time.   Fig. 10). As shown in Fig. 11a, c, the temperature distribution at the left side and the right side is not strictly consistent. Besides, the material at points B 1 and B 3 is heated by the laser twice in a relatively short time and then is heated again before the heat dissipation, resulting in a large molten pool, which is consistent with the results in Fig. 10. This phenomenon might lead to the difference in the solidified microstructure between layers. The maximum temperature at locations along vertical lines passing through points B 1 , B 3 , and B 5 (see in Fig. 11a-c) of each deposition layer was extracted; the results are shown in Fig. 11d. The temperature curve in the middle region of the thin-walled part presents a parabolic trend with the increase in the number of layers, while the temperature at the two points on the edge of the thin-walled part tends to rise gradually in

Optimized strategies
Gradually reducing the laser power and increasing the time interval between deposition layers can be considered as two effective methods to reduce the heat accumulation in the process of DMD of thin-walled parts. When the necessary bonding ability between layers is considered, the limiting power P lim required can be expressed as follows: where η is the utilization of laser energy, which can be obtained by a previous study [30] and Q lim is the limited energy required to remelting the former layer and can be defined by Eq. (6).
where S is the cross-sectional area of a single track, μ is the ratio of the remelted zone and can be obtained by experimental, T m is the liquids, T 0 is melting point, k is thermal conductivity, A is laser absorption coefficient, and C * p is equivalent specific heat capacity, which can be defined by Eq. (7).
where ΔH is the enthalpy change due to solid-liquid transition, latent, and C p is specific heat capacity (Fig. 4). According to Eqs. (5)−(7), the limited power required for DMD of thin-walled parts is 280 W. Linear, step, and parabolic functions are used as the layer by layer decreasing mode of laser power. Optimized strategies carried out in this study are shown in Table 3.
Since the temperature field at the endpoint generated by the reciprocating scanning method is symmetrical, the computed results of the middle point and the left endpoint of each layer were selected to analyze the effect of the optimized strategies on the maximum temperature. As shown in Fig. 12a, b, reducing laser power can improve the stability of the molten pool. When the 20th layer was built, the maximum temperature of the molten pool obtained by the three laser power optimization strategies (P1-3) is almost the same. The heat absorption and loss of the molten pool have reached a balance, and the heat accumulation of the former layer on the current layer can be ignored. The evolution of the maximum temperature under the strategies of P1 and P2 is almost the same. The temperature of the first 8 layers of the molten pool gradually rises. After that, with the continuous decrease of laser power, the heat absorbed by the former layer is equal to the heat dissipated. Figure 12b also shows that the temperature evolution at the endpoint is still serrated. From the above analysis, the temperature stability of the molten pool is best under the parabolic-shape power optimization, but the "sawtooth effect" still exists. Figure 12c, d show the temperature evolution of the molten pool under the time intervals of 0 s, Fig. 10 Thermal cycle curves of different nodes on the 9th layer 5 s, 10 s, and 15 s. Although the maximum temperature was reduced by time interval optimization, its effect is less than that by the power adjustment. Besides, increasing the time interval would also reduce the deposition rate. This phenomenon shows that the gradual increase of the maximum temperature in the process of DMD thin-walled parts is mainly  due to the transformation of the heat dissipation mechanism from three-dimensional to two-dimensional. The effect of the heat accumulation of the previous deposition on the current temperature field is secondary. Previous studies [12,13] have shown that the time intervals between layers is beneficial to release thermal stress. Compared with Fig. 12b, d, the "sawtooth effect" of temperature evolution at the left end of the deposition layer can be effectively alleviated by optimizing the time interval. From the above analysis, the effect of decreasing the laser power gradually on the temperature stability of the molten pool is obvious. Its effect is not only superior to that of increasing the interlayer time interval but also does not reduce the deposition rate. Notably, it is not obvious to avoid the "sawtooth effect" in the process of deposition of thin-walled parts by optimized strategies of laser power (P1-P3). The time interval between layers can not only avoid the velocity fluctuation but also contribute to the heat loss. Therefore, the integrated optimized strategies of parabolic-like regulation (P3) and time interval (T5) were carried out, and the results are shown in Fig. 13. It can be seen that the temperature of about 2100 °C at the middle point and the endpoint of each layer is stable during the deposition process. In addition, the temperature fluctuation is significantly lower than that of a single optimized strategy. Therefore, the effect of an integrated optimized strategy (P3 and T3) on optimizing the maximum temperature of the molten pool is the most effective. Figure 14 shows the thermal cycle curves of the middle points in the first, fifth, tenth, fifteenth, and twentieth layers. The maximum temperature of the molten pool is almost coincident under the integrated optimization strategy. Four peaks are exceeding the liquids in the thermal cycle curves of all layers except the first layer, which indicates that the remelting times of each layer are two to three. The first layer only experienced two times of remelting because of the good heat dissipation of the substrate. The fifth deposited layer would undergo three remelting processes according to three temperature peaks. This phenomenon can achieve good bonding between layers. The same thermal cycle process is beneficial to improve the uniformity of microstructure and mechanical properties along the building direction.
Due to the layer-by-layer accumulation, and rapid melting and solidification characteristics of the DMD process, the deposited materials would experience complex thermal history, which can lead to complex phase transformation and eventually form a variety of microstructures [5,32,33]. Figure 15 represents the cooling rate of the middle points in the first, fifth, tenth, fifteenth, and twentieth layers under integrated optimized strategies. It can be seen that the changing trend of the cooling rate curve of each layer is almost the same, which gradually decreases and then tends to be stable with the increase of deposition layer. According to Fig. 15, the solidified microstructure of the middle part of the thin-walled part can be inferred to be similar, while the microstructure at the bottom and top of the part is slightly different due to a bigger cooling rate and lack of subsequent heat treatment.

Cross-section morphology
The macro-section morphologies of the thin-walled parts before and after optimization are shown in Fig. 16. It can be found that the width of the thin-walled parts with the integrated optimized strategy is more uniform, and its height is slightly higher than that of the thin-walled parts without optimization. Figure 16 also shows that the width of the unoptimized thin-walled part increases with the deposition height. Besides, the width error band at the bottom and top Fig. 15 The cooling rate of deposition layer under integrated optimized strategies Fig. 16 Cross-section morphologies of thin-walled parts after the 20-layer build-process. a Part 1 optimization before. b Part 2 optimization after of Part 1 is wider than that at the middle. At the beginning of the deposition, the maximum temperature of the first layer is the lowest due to the good heat dissipation of the substrate (Fig. 9). Therefore, a smaller molten pool size would reduce the powder catchment efficiency [34], resulting in a smaller width of thin-walled parts. With the deposition process, the accumulation of heat promotes the increase of the size of the molten pool, which increases powder catchment efficiency, resulting in the bigger width of the solidified part. As shown in Fig. 14, the temperature of the molten pool of the thin-walled parts under an integrated optimized strategy is more stable. This behavior indirectly proves that the size of the molten pool almost does not change with the deposition height, so the mass of powder entering the molten pool is almost the same during the DMD process. Therefore, the width uniformity of the optimized thin-walled parts is better than that of the unoptimized one. Figure 17 shows the typical microstructure of thin-walled parts at different positions before and after optimization. The micromorphology of solidified thin-walled parts has the characteristics of typical rapid solidification microstructure, mainly including dendrite, columnar, and equiaxed grains. As shown in Fig. 17a-c, the microstructure at the bottom of the thin-walled parts without optimization is mainly composed of dendrites and columnar grains. These directional grains are mainly contributed to the large temperature gradient (G), which easily leads to the anisotropy of mechanical properties of the parts, and then reduces the service life of the parts [35]. The microstructure in the middle of the part changes from directional dendrites to isotropic columnar and equiaxed grains. The accumulation of heat reduces the G in the molten pool, and the direction of heat conduction also changes from interlayer to both sides of the thin-walled part. With the increase of deposition height, the main part of heat loss is dominated by heat exchange and convection with the atmosphere, which leads to the increase of the number of equiaxed crystals. This phenomenon is similar to the study of Sun et al. [36]. As shown in Fig. 17d-f, the microstructure at the bottom of the thin-walled parts with optimization is mainly composed of columnar, and equiaxed grains. The anisotropy of the microstructure of these optimized parts is weaker than that of the parts without optimization. As analyzed above, the temperature field of the molten pool becomes stable and the cooling rate decreases gradually. These are beneficial to reduce the G and lead to the generation of a large number of expected equiaxed grains.

Microhardness distribution
The microhardness distribution along the building direction of optimized and unoptimized thin-walled parts is depicted in Fig. 18, which can be divided into four regions: substrate region I, bottom region II, middle region III, and top region IV. The microhardness of the thin-walled parts is larger than that of the substrate. This phenomenon shows that solidified phases of alloy elements in metal powder are beneficial to increase the microhardness of the parts. In region I, the microhardness increases gradually along the building direction. The microhardness of the bonding zone between the thin-walled parts and the substrate increases sharply, which is mainly contributed to the strong convection in the molten pool [20]. This behavior leads to the full mixing of the elements in the alloy powder and the substrate, so the solidified hard phases can increase the microhardness of region I, significantly. In region II, the heat dissipation of the thin-walled Fig. 17 The typical optical microstructure of a-c optimization before and d-f optimization after part changes from three-dimensional to two-dimensional, and the heat dissipation becomes worse. Therefore, the microhardness in this region decreases slightly due to the repeated remelting and tempering heat treatment between the deposited layers. In region III, the fluctuation of microhardness of thin-walled parts is the smallest, which is due to the heat dissipation mechanism and the consistent thermal cycle of the deposition layer. In Region IV, the microhardness of thin-walled parts increases slightly. This is due to the absence of tempering heat treatment and the formation of a large number of equiaxed grains in this region. In addition, the evolution trend of microhardness with or without temperature optimization is almost the same. However, the average microhardness of thin-walled parts under integrated optimized strategies is higher than that without optimization, and the uniformity of microhardness distribution is better.

Conclusions
In this paper, an improved finite element model was first established to simulate the three-dimensional heat dissipation process of thin-walled wall parts by the DMD process. Secondly, the temperature evolution of the molten pool was optimized by reducing the laser power and increasing the time interval. And then, the temperature cycle and cooling rate of thin-walled parts under the optimized strategy were analyzed. Finally, the cross-section morphology, microstructure, and microhardness of thin-walled parts are discussed in detail to verify the effect of the integrated optimized strategies on temperature evolution, geometric dimension, microstructure, and microhardness. The conclusions are as follows: 1. The optimization strategies of decreasing laser power and increasing time intervals can reduce the heat accumulation of the middle and endpoint points of thin-walled parts. The optimized strategy of gradually reducing the laser power is more significant than that of increasing time intervals. 2. During the DMD thin-walled parts, the heat accumulation is contributed to the transformation of heat dissipation from three-dimensional to two-dimensional, and the effect of the residual heat of the former layer on the heat accumulation of the current deposited layer is not significant. 3. The most significant effect is to reduce the heat accumulation in the DMD of thin-walled parts by adopting an integrated optimized strategy of gradually decreasing the laser power of the parabola shape and the time interval of 5 s. 4. The thin-walled parts with an integrated optimized strategy have a more uniform cross-section size, finer microstructure, and higher microhardness.
Author contribution Tianbiao Yu: methodology, modeling, writing and editing, experiment instruction, supervision. Liaoyuan Chen: writing-original draft, review, investigation and experiment. Zhe Liu: investigation and experiment, Simulation, Pengfei Xu: experiment and data curation. Fig. 18 The microhardness of optimized and unoptimized thin-walled parts along the building direction