Molten pool area (mm 2 ) Cp Specific heat capacity (J/kgK) dc
Distance from the consolidation plane to the nozzle outlet (mm) dp
Distance from nozzle outlet to the beam centre (mm) fg
Volumetric flow rate of carrier gas (L/min) hc
Convective heat transfer coefficient (Wm -2 K -1 ) Lm
Latent heat of fusion (kJ/kg)
Energy attenuated by the powders (J) Qconvection Energy loss due to convection (J) Qf Latent heat energy (J) Ql
Laser energy (J) Qp
Energy attenuated by the powders (J) Qradiation
Energy loss due to radiation (J) Qrp
Energy reflected by the powders (J) Qs
Energy absorbed by the substrate (J) ti
Radiation time of the powders within laser beam (s) Tm
Temperature of the molten pool (K) T0
Ambient temperature (K) v
Scanning speed (mm/s) vpz
Vertical velocity of the powders (mm/s) Vp
Volume of the deposited material (cm 3 
Volume of the heat affected zone (cm 3 Molten pool area (mm 2 ) Cp Specific heat capacity (J/kgK) dc
Distance from the consolidation plane to the nozzle outlet (mm) dp
Distance from nozzle outlet to the beam centre (mm) fg
Volumetric flow rate of carrier gas (L/min) hc
Convective heat transfer coefficient (Wm -2 K -1 ) Lm
Latent heat of fusion (kJ/kg)
Energy attenuated by the powders (J) Qconvection Energy loss due to convection (J) Qf Latent heat energy (J) Ql
Laser energy (J) Qp
Energy attenuated by the powders (J) Qradiation
Energy loss due to radiation (J) Qrp
Energy reflected by the powders (J) Qs
Energy absorbed by the substrate (J) ti
Radiation time of the powders within laser beam (s) Tm
Temperature of the molten pool (K) T0
Ambient temperature (K) v
Scanning speed (mm/s) vpz
Vertical velocity of the powders (mm/s) Vp
Volume of the deposited material (cm 3 
Volume of the heat affected zone (cm 3 ) α Energy attenuation coefficient (%) β
Energy efficiency (%) 
Laser based direct energy deposition (DED) has been developed into a promising technology for metallic coating [1] [2] [3] , free-form fabrication [4] [5] [6] and component repair [7] [8] [9] [10] . Additionally, the high flexibility and outstanding mechanical properties have enabled the application of DED to new materials development, such as hard matrix components [11, 12] , ceramic materials [13] and hard-to-machine alloys [14] [15] [16] . DED offers unique capabilities with tremendous applications potentials that cannot be matched by traditional processes. However, low part quality assurance and process reliability continue to hamper the widespread adoption of DED as a viable manufacturing process [17] .
To achieve the desired material properties, extensive experimentation and testing have been employed to determine optimal parameter settings in DED [18] [19] [20] [21] [22] . Typically, these parameters are kept fixed throughout the fabrication process. However, optimizing input variables alone is insufficient to ensure the part quality due to the complexities of DED. In practice, the material properties very much depend on dynamic processes during material deposition, are shown in Figure 1 . Among these dynamic processes, laser-material interaction is most important because it forms a link between the preceding and following processes. In laser-material interaction an amount of energy is released when the laser beam, with high energy electrons, hit the powder stream. The powders absorb energy, till melted, through electron-ion collision when laser energy is transformed into plasma [24, 25] . The study of the energy attenuation by the powders is essential for understanding of the laser-material interaction behaviors under short and intense electromagnetic radiation in DED. Stepwise heating method has been applied to measure the energy absorption in laser additive manufacturing, assuming the absorbed energy is transferred to the heat of the powders [26] . This approach, however, assumes that the pre-deposited powders are evenly distributed and placed on the powder bed. Further, it neglected the variation of thermophysical property of the particles under a high temperature environment.
There are lot of challenges to explore the energy attenuation and partitioning due to multitude of factors, such as the high complexity of the underlying physical phenomena and transformations that happen during material deposition. On the other hand, the study of energy attenuation is of interest, because it can help to interpret the property variations under different experimental conditions, therefore allowing to determine the accurate processing window for deposition process without need for extensive testing given a newly developed powder material. An energy distribution model proposed in [27] suggests that more than 50 % of the laser energy was reflected by the substrate and about 30 % of energy was absorbed by the substrate when processing 316L stainless steel with YAG laser. This research simplified the modeling process by assuming that the molten pool width is equal to that of the laser beam and ignored the heat loss due to convection and radiation. Lia et al., investigated the energy distribution when processing different kinds of materials with a fiber laser [28] . However, the measured energy absorption by the substrate is lower due to the heat loss during energy transfer and the error in temperature measurement with thermocouples [29] .
This paper tries to analyze the energy attenuation and partitioning in DED through a simplified lumped capacity model. Energy absorption and reflection by substrate and powders, energy loss due to radiation and convection as well as latent heat of fusion were quantified based on experimental analysis. High-resolution infrared camera was used to measure the temperature of the molten pool. The outcomes, complemented with earlier investigations, can help to better understand and clarify the energy attenuation and partitioning in DED.
When a high-density powder stream is irradiated by a laser beam, part of the energy of the laser beam is absorbed and reflected by the powders [28] . The leftover energy pass through the powder stream and hits the substrate. Meanwhile, the powders, carried with irradiated energy, are delivered into the molten pool [30] . Then, the substrate's temperature raises due to heat conduction, and at the same time, part of the energy is lost due to heat sinking effect, such as radiation and convection [31] . The energy distribution during DED is show in Figure 2 . Lumped capacity modeling is a simple but practical method for solving heat transfer problems. In this model, the temperature of the solid body is considered a function of the time only, assuming the temperature is spatially independent and uniformly distributed. This model ignores the spatial variables, such as temperature gradients within the solid, and time is the only independent variable. The transient
• Type, power, frequency; • Beam profile, diameter; • Laser-substrate speed.
• Powder feed rate, efficiency; • Particle-gas interaction; • power-powder interaction.
• Molten pool-substrate interaction; • Heat affected zone; • Temperature distribution; • Radiation and conduction. 
Where, Ql is the laser energy (J), Qrs is the energy reflected by the substrate (J), Qf is the latent heat energy (J), Qa is the energy absorbed by the powders (J), η is the powder catchment efficiency, expressing the ratio of the part weight to the total mass of powder fed into the chamber, Qrs = (1w β )× (Ql -Qa), w β is the absorptivity of workpiece. Qrp is the energy reflected by the powders (J), Qradiation is the energy loss due to radiation (J), Qconvection is the energy loss due to convection (J).
The amount of laser energy (Ql, J) input depends on the laser power (P, W) and the radiation time of the powders within laser beam (ti, s), and it can be calculated by Equation (2) and (3) [32]:
Where, P is the laser power (W), vpz is the vertical velocity of the powders (mm/s), dc is the distance from the consolidation plane to the nozzle outlet (mm), dp is the distance from nozzle outlet to the beam centre (mm), r0 is the radius of powder nozzle outlet (mm), fg is the carrier gas volumetric flow rate (L/min).
Latent heat of fusion (Lm, kJ/kg) is the heat supplied to a solid body at the melting point when it changes state from solid to liquid [33] . Latent heat energy (Qf, J) can be calculated with Equation (4):
Where, Lmp is the latent heat of fusion of the powders (J/kg), p ρ is the density of the powders (g/cm 3 ), p V is the volume of the deposited material (cm 3 ). Ignoring the dilution effect, p V can be calculated by:
Based on Stefan-Boltzmann Law, the energy loss due to radiation can be expressed as:
Where, Am is the molten pool area (mm 2 ), ε is the emissivity of the material ( ε <1), σ is the Stefan-Boltzmann constant (Wm -2 K -4 ), Tm is the temperature of the molten pool (K), T0 is the ambient temperature (K). Convection involves the heat transfer by the motion of the molten pool. The energy loss due to convection can be expressed as:
Where, hc is the convective heat transfer coefficient (Wm -2 K -1 ). Considering the energy absorbed by the substrate as effective energy, the overall efficiency ( β ) during material deposition in DED can be expressed as Equation (8):
Nickel-based superalloys are widely used in industrial gas turbines and jet/rocket engines because of their high strength and fatigue endurance as well as good resistance to oxidation and creep at high temperature [34] . Precipitation-hardened Inconel 718 nickel-based alloy (IN 718) was used as powder materials, it has a melting temperature of 1260~1336 o C. The particle morphology of IN 718 is shown in Figure 3 , and its average chemical composition is summarized in Table 1 . Low carbon steel was used as the substrate. 
The DED was performed with Optomec laser engineered net shaping (LENS) 450 Workstation with a chamber size of 254 × 254 × 254 (mm). A fiber laser (wavelength: 1064 nm) with maximum power output of 400 W is transmitted to the substrate through lens reflector. A pneumatic powder delivery system and a computer-controlled motion system are integrated with the LENS system. Four-jet exit nozzles are placed around z axis and targeted to the molten pool. Argon was used as a protective and carrier gas. The schematic diagram of the LENS system is illustrated in Figure 4 . 
To investigate the energy efficiency and distribution during material deposition, laser power of 250 W and scanning speed of 7 mm/s were selected based on preliminary results [35] . The hatch space and layer thickness were set as constant values. Thin wall specimen (four layers) was designed and fabricated based on the experimental variables in Table 2 . The scanning strategy of the designed specimen is shown in Figure 5 . Based on an analytical model proposed by the author, η equals to 10 .88% when IN 718 is processed with DED using the same experimental condition [32] . Other known parameters in this study are presented in Table 3 . 
The molten pool temperature was measured with a highresolution infrared (IR) camera (Pyroview 768N, DIAS Inc, Dresden, Germany). The spectral range of the camera is 0.8 to 1.1 µm, and it has a measurement range from 1000 to 3000 °C with a resolution of 768 × 576 pixels. The camera was fixed inside the chamber heading to the molten pool, as shown in Figure 6 . To protect the camera from the laser radiation and prevent particles from damaging the optical lens, a laser blocking filter (wavelength: 1064 nm) was mounted in front of the lens. The real-time temperature was recorded with a professional software (Pyrosoft 3.22, DIAS Inc, Dresden, Germany). The sampling rate is 25 Hz with a response time of 40 ms. 
A power meter (FL400A-BB-50, Ophir, North Logan, USA) was used to measure the actual power output before and after the powder injection, to measure the energy attenuation by the powder stream. The power meter was placed under the four-jet exit nozzle, the distance between the power meter and nozzle outlet was set as 25 mm. An anti-reflection BK 7 class was placed upper the meter to protect the sensor against the injected powders. Also, an air filter was used to wrap the meter to protect the sensor from damaging by surrounding powders. The power output, with and without the powder injection was measured and recorded by starlab software (v3.31, Ophir, North Logan, USA). The experimental set up is shown in Figure 7 . 
Given the input parameters in Table 2 , the molten pool temperature profile for the first layer deposition is shown in Figure 8 . The temperature profile of the first layer, shown in Figure 8 (a) , indicates a good consistency with an average of 1593.7 °C and the fluctuation is within 96.88 °C. The average temperature and fluctuations for different layers are summarized in Table 4 . Figure 8 (b) suggests that the molten pool temperature increases nonlinearly with increasing of the layer numbers. This is because the heat accumulated in previous layers cannot be dissipated completely, causing the increase of the molten pool temperature. The temperature of the intervals between the consecutive layers is about 1150 °C due to the shutter off of the laser power.
A typical thermal image of the molten pool temperature for the eighth layer of thin wall (P = 250 W, v =7 mm/s) is shown in Figure 9 . The maximum temperature occurs at the center of the molten pool, reaching up to 2000 °C. The shape of the molten pool is an approximately circle with a diameter of 1.5 mm, taking 1650 °C as the molten pool boundary. 
Given the input parameters in Table 2 , the power output under the laser power of 250 W is shown in Figure 10 . The actual power output (P0) is 183 W without the powder feeding. The powder injection starts at point A, then the real-time power decreases until stabilized at P1 = 171.5 W. The difference between P0 and P1 is the energy attenuated (absorbed or reflected) by the powders (Qp, Qp = Qa + Qrp), and the energy attenuation coefficient (α ) of IN 718 is calculated to be 6.13 % based on Equation (9) 
Substitution of the molten pool temperature, diameter and energy absorption coefficient in Equation (6) -(7) yields the energy loss by radiation and convection. The energy partitioning of DED when processing IN 718 is shown in Figure 11 . Being similar with the previous investigations in [27, 28] , about 36 % of the laser energy is absorbed by the substrate, while more than 57 % of laser energy is reflected. It can be attributed to two reasons. First, the molten pool area is much higher than that of the laser beam, making it easier to absorb/reflect the energy; Second, instead of considering a long track deposition, this study analyzed heat transfer within molten pool area, and because of the short interaction time between laser and material, only a small amount of energy (less than 1 %) is lost due to radiation and convection. Unlike the radiation and convection, the latent heat energy is always considered as a hidden form when analyzing the energy efficiency in DED. It refers to the energy that is required to make room for the change of volume of material when it is changing from solid to a liquid, and no temperature change occurs during this phase transition. The latent heat of fusion accounts for 0.59 % of laser energy. It can be expected that Qf increases with increasing of the powder feeding rate and decreasing of the scanning speed based on Equation (3) and (4).
Energy loss due to convection is always excluded when modeling the energy distribution in DED [28] . This is partly because the negligible amount of energy loss due to short reaction time, another reason is that the convective heat transfer coefficient is difficult to obtain during material deposition. At the solid-fluid interface, the convective heat transfer coefficient depends on the thermal conductivity of the fluid, temperature gradient at the interface and temperature difference between the molten pool and the air.
The overall energy efficiency ( β ) in DED for IN 718 fabrication is calculated to be 37.58 % based on Equation (8), indicating that the power efficiency is relatively low, and a large proportion of laser energy has been reflected by substrate. Energy partitioning during thin wall/multi layers fabrication is complex due to the complicated heat accumulation effect. In general, energy absorption is a function of laser wavelength and temperature, and the energy absorption increases with increasing temperature in metals [39] . When considering multilayers deposition, the molten pool temperature increases with increasing number of layers, as shown in Figure 8 . Ignoring the variation of thermal property of powders under high temperature, the energy loss due to convection and radiation increases based on Equation (7) and (8) . During multi-layers fabrication, energy absorption by the pre-deposited layers tends to increase due to the initiated high temperature. In addition, the energy loss due to energy convection and radiation decrease because of the heat accumulation, therefore, the overall energy efficiency tends to increase for successive layers fabrication.
Energy partitioning and efficiency is high related with the material thermal properties. According to the Equations from (2) to (6) , it can be expected β will decrease with increasing of latent heat of fusion, emissivity and reflectivity. Also, it needs to be mentioned that α measured experimentally in section 3.2 is essential when analyzing the overall energy efficiency during material deposition. Also, part of the laser energy is reflected by protective glass, resulting in the measurement α is relatively smaller that the true value. It is plausible to suppose that β should be even larger under ideal condition. The energy absorbed by the substrate (Qs) can be expressed as integral form: 
Plugging the derived expression for in Qs Equation (1) into Equation (10) leads to a differential equation that presents the lumped model, which can be solved by different numerical approaches. The energy absorption ability varies with the change of powder materials, power density and powder stream distribution [40] . therefore, the future research should focus on the relationship of the energy absorption with spreading behavior, power density as well as characteristics of powder materials.
It is evident that the metallurgical behaviors vary under different molten pool temperature, which depends on the energy absorption by the substrate. The clarification of the energy absorption and partitioning can help to interpret the property variations under different experimental conditions and therefore allowing one to determine the accurate processing window for deposition process without need for extensive testing given a powder material. In this study, the energy attenuation and partitioning in DED were investigated based on lumped capacity modeling. Experimental method was applied to measure the molten pool temperature and energy absorption by the powders. The main findings can be drawn as follows.
(1) The molten pool temperature increases nonlinearly with increasing of the layer numbers. When the laser power is 250 W, scanning speed is 7 mm/s, the average molten pool temperature of the first layer is 1593.7 °C in DED of IN 718.
(2) When the laser power is 250 W, scanning speed is 7 mm/s, the energy attenuation coefficient of IN 718 in DED is 6.13 %.
(3) About 36.3 % of the laser energy is absorbed by the substrate, only a small amount of energy is lost due to the reflection, radiation and convection.
It has been proposed that the energy absorption by the powders in DED relies on the velocity and concentration of the uniformly distributed powders; Also, inverse bremsstrahlung absorption mechanism suggests that energy absorption by high dense particles is not constant, it varies with different distribution of plasma caused by different power input. Therefore, the next step of this research is to study the relationship of input parameters, plasma characteristics and energy absorption by the powders and their effects on the overall energy efficiency in DED. 