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Finite element analysis of thermal behavior and experimental investigation of Ti6Al4V in selective laser melting
Journal Pre-proof Finite element analysis of thermal behavior and experimental investigation of Ti6Al4V in selective laser melting Junfeng Li, Zhengying Wei, Lixiang Yang, Bokang Zhou, Yunxiao Wu, Sheng-Gui Chen, Zhenzhong Sun
PII:
S0030-4026(19)31658-4
DOI:
https://doi.org/10.1016/j.ijleo.2019.163760
Reference:
IJLEO 163760
To appear in:
Optik
Received Date:
23 August 2019
Accepted Date:
7 November 2019
Please cite this article as: Li J, Wei Z, Yang L, Zhou B, Wu Y, Chen S-Gui, Sun Z, Finite element analysis of thermal behavior and experimental investigation of Ti6Al4V in selective laser melting, Optik (2019), doi: https://doi.org/10.1016/j.ijleo.2019.163760
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Finite element analysis of thermal behavior and experimental investigation of Ti6Al4V in selective laser melting
Junfeng Lia*, Zhengying Weia, Lixiang Yanga, Bokang Zhoua, Yunxiao Wua, ShengGui Chenb, Zhenzhong Sunb
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong
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a
University, Xi’an 710049, China. b
School of Mechanical Engineering, Dongguan University of Technology, Dongguan
Corresponding author: Junfeng Li
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Abstract
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E-mail: [email protected]
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*
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523808, China
The selective laser melting (SLM) has always been a challenge due to the
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characteristics of extremely rapid melting and solidification in the micro melt pool. Therefore, a three-dimensional finite element model was developed to investigate the thermal history and solidification parameters in the SLM process. The model presents the temperature distribution, molten region dimensions under different process parameters. The width, depth and length of molten region are inversely proportional to the laser power and scan speed. And then, the variations of solidification
parameters with different laser power and scan speeds was discussed. The temperature gradient is mainly affected by laser power and decreases with the increase of laser power; the solidification rate is proportional to the scan speed. The cooling rate decreases progressively with the increase of the linear energy density while solidification morphology parameter is inversely proportional to laser power and scan speed, but fluctuates with the change of linear energy density. Single-track experiments demonstrate the accuracy and effectiveness of the model. Besides,
range.
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surface quality can be improved with the increase of linear energy input in a certain
Key words: selective laser melting, finite element analysis, Ti6Al4V, temperature
1.Introduction
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distribution, solidification parameters, surface morphology
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Selective laser melting (SLM), as a promising metal additive manufacturing technology, has received much attention in recent years because of its ability to
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fabricate complex components directly. In the SLM process, the metallic powder is melted by a high-energy laser beam track by track and layer by layer according to the
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2D slice data. Thus, the investigations of single track and single layer are of great importance to the microstructure and mechanical properties of SLM final components. Yadroitsev et al. [1] explored the effects of the laser power and scan speed on single tracks formation in SLM and their results showed that distortions and irregularities appeared at low scan speed and excessively high speed gives rise to the balling effect. Yadroitsev et al. [2] also investigated the influences of preheating
temperature and scan speed on the microstructure and geometry of single tracks. They found that the preheating temperature controlled the contact angle and track height, and the scan speed influenced the track width and contact zone characteristics. Wang et al. [3] thought that the regular and thin shape track was the most suitable for selective laser melting by analysis of single-track and multi-track experiments. A large number of single-track experiments under different process parameters were performed by Ciurana et al. [4] and the optimum process parameters were obtained
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for CoCrMo in the SLM process. Aboulkhair et al. [5] studied the effect of scan speed on single tracks and single layer in SLM AlSi10Mg. Furthermore, fine microstructure and high nano-hardness in the single track were obtained according to their results.
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Nie et al. [6] and Shi et al. [7] studied the effects of laser power and scan speed on the geometric characteristics of single scan tracks and obtained the optimized process
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parameters. Similarly, single track, surface morphology and microstructure of single
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track and single layer in SLM Ti6Al4V were investigated by Zhang et al,[8] and Yang et al. [9]. However, it is time-consuming and expensive to perform a lot of experiments due to many factors are involved in SLM [10]. Nowadays, finite element
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simulation has become one of the powerful tools to study the process parameters, thermal behavior, microstructure prediction and control in the process of additive
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manufacturing [11-17].
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In this paper, a three-dimensional finite element model was developed to study the thermal behavior and solidification parameters during SLM Ti6Al4V. Temperature distribution and evolution under different process parameters were studied. The length, width and depth of melt region were defined and the effects of process parameters on the melt region geometrical features were evaluated. And then, solidification parameters including temperature gradient, solidification rate, cooling
rate and solidification morphology parameter were investigated. The investigation of solidification parameters is contributed to further predicting and controlling the microstructure of SLM final components. To verify the accuracy and effectiveness of simulation model, single-track experiments were carried out. Besides, the surface morphologies of the single layer under different process parameters were characterized,
2. Description of Finite Element Model for SLM process
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2.1 Finite element model
A finite element transient thermal behavior model for single track of SLM Ti6Al4V was developed based on Ansys multi-physics package. A schematic simulation model
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is presented in Fig.1. The finite element model consists of Ti6Al4V substrate and
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powder bed with dimensions of 3.2mm×1.2mm×0.5mm and 3mm×0.9mm×0.03mm, respectively. In this simulation, the powder layer thickness is 30μm, which is
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accordance with the actual experimental powder layer. The moving direction of the laser beam is along the x-axis and z-axis is the building direction in SLM process. For
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exact calculation, powder layer was meshed by Solid70 element with dimension of 0.015mm×0.015mm×0.015mm. The Ti6Al4V substrate was meshed with larger non-
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uniform grids for the saving of computational time. Point A, the midpoint of single
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track, would be analyzed and discussed in this paper.
Fig.1. Schematic model of finite element model.
2.2. Theoretical analysis and model establishment Fig.2 depicts the thermophysical phenomena in SLM process. When the laser irradiates the powder, a part of the heat is absorbed by the powder. Then the powder is melted and the micro melt pool is formed. As the laser moves, the melt pool solidifies rapidly and forms a good metallurgical bond with the substrate. In SLM process, a
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large amount of absorbed heat is dissipated through heat conduction, and a small part of absorbed heat is dissipated through heat convection and radiation. The thermal
conditions in the simulation for SLM process would be discussed and described in
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detail.
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Fig.2. Thermophysical phenomenon in the process of SLM.
The governing equation for heat transfer of heat conduction is expressed as
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follows:
c
T t
x
(k
T x
)
y
(k
T y
)
z
(k
T z
) q
where , c and k are density, specific heat and thermal conductivity, respectively. and t are temperature and time respectively.
q
(1)
T
is heat generated by per volume of part.
The initial temperature of process chamber including powder bed at
t 0
can be
applied as follows: T（ x , y , z )
t0
T0 ( x , y , z )
(2)
where T 0 in this work is set to 298.15K, consistent with the experimental condition. Thermal boundary condition can be expressed as follows: T
Q h (T T 0 ) (T
n
4
T0 ) 4
(3)
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k
where n is surface vector. the heat transfer coefficient ( h ) is taken as
and
5 .6 7 1 0 W m -8
is the Stefan-Boltzmann constant and the value is
is the emissivity and the value is set as 0.65[18].
2
-2
K
1
K 4
,
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[18].
1 0W m
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2.3. Heat source model
The Gaussian heat source used in this work is described as [19]: 2 P
R D OPD 2
Q
R
2
2
) exp(
z
(4)
)
D OPD
is efficient energy absorbed by powder,
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where
x y 2
exp( 2
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Q
absorptivity of Ti6Al4V power, which is set as 0.3.
P
is laser power,
D OPD
is laser
is the optical penetration D OPD
is accordance with
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depth of the powder bed to the incident laser. The value of
the thickness of powder layer. R is radius of laser beam, which is taken as 40μm. are coordinate point.
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x, y, z
2.4. Consideration and selection of material thermophysical properties For SLM, powder bed is taken as a combination of powder particle and argon gas. Therefore, the effective density of Ti6Al4V powder can be calculated by [20]:
p o w d e r (1 ) s o lid
(5)
where p o w d e r is powder density. in this work.
s o lid
is porosity of powder particle which is set to 0.4
is solid density of Ti6Al4V. The density of argon gas is neglected
due to a negligible value. Thermal conductivity is expressed as below [20]: k p o w d e r (1 ) k s o lid
k pow der
and k s o lid are thermal conductivity of powder and solid material,
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where
(6)
respectively.
The latent heat for phase transformation was defined by enthalpy. The equation
c ( T )d T
where H is material enthalpy,
c (T )
(7)
is specific heat.
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H
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can be written by:
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According to the analysis mentioned above, thermal physical properties of Ti6Al4V
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powder used in this work were illustrated in Figure 3.
Fig.3. Thermo-physical curve of Ti6Al4V powder at different temperature. (a) Density. (b) Thermal conductivity. (c) Specific heat and enthalpy
3. Experiments. Ti6Al4V spherical powder was used and the particle size distribution of powder
is as follows: D10=21.29μm, D50=32.42μm, D90=49.24μm. Single track and single layer experiment were conducted by self-developed SLM machine, which equipped with a 500W IPG fiber laser. Inert argon gas was used in the process chamber of SLM in order to keep the material from oxidation. Parameters used in the experiment are tabulated in Table 1. The samples were cut off from substrate by electrical discharge wire-cutting machine and cleaned by alcohol. And then, the cross section of melt pool
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was processed according to standard metallographic process. microstructure of melt pool was characterized by using Optical microscope (Nikon MA 200). The surface
S4800 SEM) Table 1: Parameters used in this work.
Value 280,320,360 1800,2200,2600 0.06 0.03
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Parameter Laser power, P/W Scan speed, V/(mm/s) Hatch spacing, H/mm Layer thickness, LT/mm
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morphology of the samples was observed by scanning electron microscope (Hitachi
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4. Results and discussion
4.1. Temperature distribution and evolution The typical temperature distribution is investigated at LP=360W. Fig.4 shows the
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transient temperature distribution under different scan speed. The internal region of
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the isothermal solid line (1923K) indicates the molten region. As shown in Fig.4, the shape of the molten region corresponding to different scan speed has similar characteristics, that is the comet tail profile. It can be found that the forepart isothermal lines of the molten region are more intense than the rear side. It means that the temperature gradient at the front of the molten region is much larger than the area of back-end. This phenomenon can be ascribed to the higher thermal conductivity of
melted powder than un-melted Ti6Al4V powder. The isothermal lines at the front of the molten region are sparser with the increase of scan speed and this is mainly due to different heat input. Fig.5 depicts the temperature evolution of midpoint A under different scan speeds when LP is 360W and the red dashed line indicated melting point (1923K). The temperature changes rapidly with time in the SLM process. The highest temperature of midpoint A decreases from 4270K to 3553K with the increase of scan speed. Also, the residence time of the liquid phase was calculated and it
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decreases from 255μs to 156μs when scan speed increases from 1800mm/s to 2600mm/s. Similarly, the temperature evolution at midpoint A with the variation of laser power was investigated (Fig. 6). As shown in Fig.6, the highest temperature
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ranges from 3291K to 3866K when the laser power increases from 280W to 360W. The liquid residence time corresponding to 280W and 360W are 143μs and 191μs,
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respectively. During the SLM process, high power or low speed means that the unit
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volume of powder absorbs more heat per unit time. Therefore, the temperature rises and the liquid phase residence time is also prolonged at high laser power or low scan speed.
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To quantitatively analyze the relationship between the dimensions of molten region and the process parameters, the length, width and depth of molten region were defined
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(Fig. 7). Fig. 8 depicts the dimensions variation of the molten region under different
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scan speed at LP=360W. It can be noted that the length, width and depth of the molten region decrease with the increase of scan speed. This is mainly attributed to the fact that short residence time of liquid phase and low heat input.
Fig.4. Temperature distribution under different scan speeds at LP=360W. (a) 1800mm/s; (b)
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2200mm/s; (c) 2600mm/s.
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Fig.5. Temperature evolution of midpoint A under different scan speeds at LP=360W.
Fig.6. Temperature evolution of midpoint A under different laser power at SS=2200mm/s.
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Fig.7. Illustration of molten region dimensions.
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Fig. 8. Dimensions variation of molten region under different scan speeds at LP=360W.
4.2. Solidification behavior with different process parameters
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Solidification parameters were investigated based on temperature field. The temperature gradient (G), solidification rate (R), cooling rate (CR, GR) and
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solidification morphology parameter (SMR, G/R) can be obtained according to temperature evolution and distribution information. Thus, the overall information of grains formed in the SLM process can be described according to cooling rate and solidification morphology parameter. Fig. 9 shows the effect of scan speed on the solidification parameters when the laser power was kept at 360W. Fig. 9 (a) illustrates the effect of scan speed on
temperature gradient along X axis (TGX) and solidification rate (R). When the scan speed increases from 1800mm/s to 2600mm/s, the value of TGX increases from 1.31× 106K/m to 1.33×106K/m and then decreases to 1.28×106K/m. The temperature gradient fluctuates slightly with the scan speed, which indicates that the scan speed has little effect on scan speed. This is attributed to the fact that the effective input of heat is fixed when the laser power is constant. In addition, the value of R increases
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from 1.802m/s to 2.609m/s as the increase of scan speed. It is known that the solidification rate can be obtained through the scan speed by means of R
V cos
.
is the angle between R and V. Along the X direction, the value of approaches 0,
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so R and V are approximately equal. With the increase of laser speed, the grain size tends to be finer due to the increase of cooling rate. On the contrary, the value of
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SMR is proportional to scan speed (Fig.9(b)).
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Fig.10 shows the effect of laser power on the solidification parameters when the scan speed was kept at 2200mm/s. The temperature gradient is inversely proportional
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to laser power. In micro melt pool, the low thermal conductivity makes the heat dissipation rate less than the increase of heat input due to the increase of laser power. Therefore, the temperature distribution in melt pool is more homogeneous due to the
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saturated heat in melt pool and thus lowering thermal gradient [21]. The solidification
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rate fluctuates around 2.2mm/s without obvious change (Fig.10(a)). As explained earlier, the solidification rate is mainly influenced by the scan speed. In addition, for CR and SMR, they both decrease with the increase of laser power (Fig.10(b)). These phenomena can be attributed to the high input of heat. The grains tend to coarser with the increase of laser power due to enough residence time of liquid phase.
In order to consider the combined effect of laser power (P) and scan speed (V) on solidification parameters, the linear energy density (LED, P/V ratio) was defined. Fig.11(a) shows the linear energy density on the temperature gradient along X-axis and solidification rate. Both TGX and R presents a fluctuation with the increase of LEDs. However, in general, they all decrease with the increase of LEDs. As shown in Fig.11(b), it can be found that an significantly inverse dependence of the cooling rate with respect to the LED, which indicates that grains in the SLM process tend to be
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coarser with the increase of LEDs. This phenomenon is consistent with the results observed by Hu et al. [13]. For solidification morphology parameter, there is no
obvious relationship between the LEDs. This phenomenon mainly depends on the
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extent to which the line energy density affects the temperature gradient and the
solidification rate. In fact, acicular martensite is the main microstructure in the SLM
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Ti6Al4V samples according to previous studies [22,23]. The solidification
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morphology parameter (SMR) seems to have little effect on the shape of solidification
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microstructure of the final Ti6Al4V samples.
Fig. 9. Effect of scan speed on solidification parameters at LP=360W. (a) Temperature gradient and cooling rate; (b) Solidification rate and solidification morphology parameter.
Fig. 10. Effect of laser power on solidification parameters at V=2200mm/s. (a) Temperature gradient
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and cooling rate; (b) Solidification rate and solidification morphology parameter.
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Fig. 11. Effect of linear energy density on solidification parameters.
4.3. Experimental investigation and simulation validation
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As shown in Fig.12, the cross-sectional profile of melt pool is compared between simulation and experiment at the same process parameter combination. The width and
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depth of melt pool is illustrated in Fig.12 (b). The melt pool width and depth obtained by simulation and experiment are plotted in Fig.13. FEM simulation results have a
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good agreement with the experimental data. For the width and depth of the melt pool prepared at 360W and 1800mm/s, the width and depth of FEM simulation are 102.95μm and 47.27μm, respectively. For experimental results under the same process parameter combination, the width and depth are 123.46μm and 43.45μm, respectively. The simulated melt pool depth is relatively well with experimental result while the melt pool width is not as well. The possible reason is that complicated
factors exist in the SLM process, which cannot be considered comprehensively. The powder particles are randomly distributed on the substrate, it is difficult to obtain an excellent definition of powder bed state. In addition, the absorptivity of material to the laser varies with the input of energy and the change of material state, therefore, a specific value is hard to obtain. Of course, apart from the factors described above, other uncertain factors are difficult to consider accurately in actual process and FE simulation model.
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Microstructure of melt pool was characterized and investigated (Fig.14). The
growth direction of β grains is substantially perpendicular to the melt pool boundaries parallel to the building direction. Moreover, fine α' martensitic formed at the β grain
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boundaries. Fine acicular martensitic tilted at an angle and is parallel distributed
within the β matrix. This mainly attributed to the high temperature gradient(~106K/m)
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and cooling rate(~106K/s) in the process of SLM just as mentioned earlier.
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Figure 12. Melt pool profile at P=360W, SS=1800mm/s. (a) FEM simulation. (b) Experimental result.
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Figure 13. Dimensions of melt pool at 360W in FEM simulation and experimental results.
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Figure 14. Microstructure formed in the melt pool (P=320W, SS=2200mm/s).
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4.4. surface morphology investigation under different process parameters The top surface morphology analysis of the single layer was conducted with SEM.
The relationship of the surface morphology with the linear energy densities was investigated. Fig. 15(a) shows the poor surface with pores fabricated using a low linear energy density of 0.127J/mm. According to SEM observations, surface pores forming because of a lack of fusion and un-melted spherical powder particle can be
found. As shown in Fig.15(b), an increase of linear energy density to 0.145J/mm, improved the surface morphology by eliminating partial surface pores. However, partially sputtered small particles are always visible and adhere to the surface. Fig. 15(c) shows a better surface morphology after using a higher linear energy density of 0.156J/mm. It can be found that noticeable surface pores were eliminated and the number of small spherical adhering particles was reduced. Besides, satellites appear
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on the top surface due to the unavoidable spattering during the process of SLM.
Worse surface morphology was found after applying a higher linear energy density of 0.2J/mm, as shown in Fig.15 (f). Under this linear energy density, the laser scanning
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trace is eliminated and large un-melted powder particles disappeared. However, many
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small particles adhered to the surface leading to poor surface quality. This is mainly attributed to excessive heat input causes an increase in the instability of the melt pool,
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and small droplets are splashed and solidified from the melt pool to form small
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particles adhering to the surface.
Figure 15. Surface morphology of different LED. (a) 0.127J/mm, (b) 0.145J/mm, (c) 0.156J/mm, (d) 0.164J/mm, (e) 0.178J/mm, (f) 0.2J/mm.
5. Conclusions In this work, a 3D single track numerical simulation model was developed to investigate the thermal behavior and solidification parameters under different process parameters. Also, the single-track experiments were carried out to verify the validity
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of the numerical model. In addition, the surface morphology under different process
parameters was investigated. The major conclusions in this work can be summarized as follows:
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(1) The maximum temperature decreases with the increase of scan speed and
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increases when laser power increases. Dimensions of molten region increase with the increase of laser power or decrease of scan speed.
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(2) Temperature gradient along X axis is mainly affected by laser power and is inversely proportional to the laser power. Solidification rate depends on scan
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speed and is proportional to the scan speed. Cooling rate decreases with the increase of laser power or decrease of scan speed. The value of the
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solidification morphology parameter decreases regardless of the increase in laser power or the increase in scan speed.
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(3) The simulation results are in good agreement with the experimental results, which proves that the three-dimensional numerical model is effective. Besides, the cross-sectional microstructure of single track indicates that β grains along the building direction and fine α ' martensitic formed in the SLM due to high temperature gradient and cooling rate.
(4) Surface morphology will deteriorate at low energy density due to the appearance of surface porosity. With the increase of linear energy input, the surface quality of single layer would be improved while deteriorates at a higher linear energy density (0.2J/mm).
Acknowledgments
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This work was supported by Science Challenge Project (TZ2018006-0301-01), Dongguan University of Technology High-level Talents (Innovation Team) Research Project (KCYCXPT2016003) and Guangdong Scientific and Technological Project
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(2017B090911015)
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PII:
S0030-4026(19)31658-4
DOI:
https://doi.org/10.1016/j.ijleo.2019.163760
Reference:
IJLEO 163760
To appear in:
Optik
Received Date:
23 August 2019
Accepted Date:
7 November 2019
Please cite this article as: Li J, Wei Z, Yang L, Zhou B, Wu Y, Chen S-Gui, Sun Z, Finite element analysis of thermal behavior and experimental investigation of Ti6Al4V in selective laser melting, Optik (2019), doi: https://doi.org/10.1016/j.ijleo.2019.163760
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Finite element analysis of thermal behavior and experimental investigation of Ti6Al4V in selective laser melting
Junfeng Lia*, Zhengying Weia, Lixiang Yanga, Bokang Zhoua, Yunxiao Wua, ShengGui Chenb, Zhenzhong Sunb
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong
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a
University, Xi’an 710049, China. b
School of Mechanical Engineering, Dongguan University of Technology, Dongguan
Corresponding author: Junfeng Li
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Abstract
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E-mail: [email protected]
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*
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523808, China
The selective laser melting (SLM) has always been a challenge due to the
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characteristics of extremely rapid melting and solidification in the micro melt pool. Therefore, a three-dimensional finite element model was developed to investigate the thermal history and solidification parameters in the SLM process. The model presents the temperature distribution, molten region dimensions under different process parameters. The width, depth and length of molten region are inversely proportional to the laser power and scan speed. And then, the variations of solidification
parameters with different laser power and scan speeds was discussed. The temperature gradient is mainly affected by laser power and decreases with the increase of laser power; the solidification rate is proportional to the scan speed. The cooling rate decreases progressively with the increase of the linear energy density while solidification morphology parameter is inversely proportional to laser power and scan speed, but fluctuates with the change of linear energy density. Single-track experiments demonstrate the accuracy and effectiveness of the model. Besides,
range.
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surface quality can be improved with the increase of linear energy input in a certain
Key words: selective laser melting, finite element analysis, Ti6Al4V, temperature
1.Introduction
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distribution, solidification parameters, surface morphology
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Selective laser melting (SLM), as a promising metal additive manufacturing technology, has received much attention in recent years because of its ability to
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fabricate complex components directly. In the SLM process, the metallic powder is melted by a high-energy laser beam track by track and layer by layer according to the
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2D slice data. Thus, the investigations of single track and single layer are of great importance to the microstructure and mechanical properties of SLM final components. Yadroitsev et al. [1] explored the effects of the laser power and scan speed on single tracks formation in SLM and their results showed that distortions and irregularities appeared at low scan speed and excessively high speed gives rise to the balling effect. Yadroitsev et al. [2] also investigated the influences of preheating
temperature and scan speed on the microstructure and geometry of single tracks. They found that the preheating temperature controlled the contact angle and track height, and the scan speed influenced the track width and contact zone characteristics. Wang et al. [3] thought that the regular and thin shape track was the most suitable for selective laser melting by analysis of single-track and multi-track experiments. A large number of single-track experiments under different process parameters were performed by Ciurana et al. [4] and the optimum process parameters were obtained
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for CoCrMo in the SLM process. Aboulkhair et al. [5] studied the effect of scan speed on single tracks and single layer in SLM AlSi10Mg. Furthermore, fine microstructure and high nano-hardness in the single track were obtained according to their results.
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Nie et al. [6] and Shi et al. [7] studied the effects of laser power and scan speed on the geometric characteristics of single scan tracks and obtained the optimized process
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parameters. Similarly, single track, surface morphology and microstructure of single
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track and single layer in SLM Ti6Al4V were investigated by Zhang et al,[8] and Yang et al. [9]. However, it is time-consuming and expensive to perform a lot of experiments due to many factors are involved in SLM [10]. Nowadays, finite element
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simulation has become one of the powerful tools to study the process parameters, thermal behavior, microstructure prediction and control in the process of additive
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manufacturing [11-17].
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In this paper, a three-dimensional finite element model was developed to study the thermal behavior and solidification parameters during SLM Ti6Al4V. Temperature distribution and evolution under different process parameters were studied. The length, width and depth of melt region were defined and the effects of process parameters on the melt region geometrical features were evaluated. And then, solidification parameters including temperature gradient, solidification rate, cooling
rate and solidification morphology parameter were investigated. The investigation of solidification parameters is contributed to further predicting and controlling the microstructure of SLM final components. To verify the accuracy and effectiveness of simulation model, single-track experiments were carried out. Besides, the surface morphologies of the single layer under different process parameters were characterized,
2. Description of Finite Element Model for SLM process
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2.1 Finite element model
A finite element transient thermal behavior model for single track of SLM Ti6Al4V was developed based on Ansys multi-physics package. A schematic simulation model
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is presented in Fig.1. The finite element model consists of Ti6Al4V substrate and
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powder bed with dimensions of 3.2mm×1.2mm×0.5mm and 3mm×0.9mm×0.03mm, respectively. In this simulation, the powder layer thickness is 30μm, which is
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accordance with the actual experimental powder layer. The moving direction of the laser beam is along the x-axis and z-axis is the building direction in SLM process. For
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exact calculation, powder layer was meshed by Solid70 element with dimension of 0.015mm×0.015mm×0.015mm. The Ti6Al4V substrate was meshed with larger non-
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uniform grids for the saving of computational time. Point A, the midpoint of single
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track, would be analyzed and discussed in this paper.
Fig.1. Schematic model of finite element model.
2.2. Theoretical analysis and model establishment Fig.2 depicts the thermophysical phenomena in SLM process. When the laser irradiates the powder, a part of the heat is absorbed by the powder. Then the powder is melted and the micro melt pool is formed. As the laser moves, the melt pool solidifies rapidly and forms a good metallurgical bond with the substrate. In SLM process, a
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large amount of absorbed heat is dissipated through heat conduction, and a small part of absorbed heat is dissipated through heat convection and radiation. The thermal
conditions in the simulation for SLM process would be discussed and described in
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detail.
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Fig.2. Thermophysical phenomenon in the process of SLM.
The governing equation for heat transfer of heat conduction is expressed as
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follows:
c
T t
x
(k
T x
)
y
(k
T y
)
z
(k
T z
) q
where , c and k are density, specific heat and thermal conductivity, respectively. and t are temperature and time respectively.
q
(1)
T
is heat generated by per volume of part.
The initial temperature of process chamber including powder bed at
t 0
can be
applied as follows: T（ x , y , z )
t0
T0 ( x , y , z )
(2)
where T 0 in this work is set to 298.15K, consistent with the experimental condition. Thermal boundary condition can be expressed as follows: T
Q h (T T 0 ) (T
n
4
T0 ) 4
(3)
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k
where n is surface vector. the heat transfer coefficient ( h ) is taken as
and
5 .6 7 1 0 W m -8
is the Stefan-Boltzmann constant and the value is
is the emissivity and the value is set as 0.65[18].
2
-2
K
1
K 4
,
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[18].
1 0W m
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2.3. Heat source model
The Gaussian heat source used in this work is described as [19]: 2 P
R D OPD 2
Q
R
2
2
) exp(
z
(4)
)
D OPD
is efficient energy absorbed by powder,
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where
x y 2
exp( 2
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Q
absorptivity of Ti6Al4V power, which is set as 0.3.
P
is laser power,
D OPD
is laser
is the optical penetration D OPD
is accordance with
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depth of the powder bed to the incident laser. The value of
the thickness of powder layer. R is radius of laser beam, which is taken as 40μm. are coordinate point.
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x, y, z
2.4. Consideration and selection of material thermophysical properties For SLM, powder bed is taken as a combination of powder particle and argon gas. Therefore, the effective density of Ti6Al4V powder can be calculated by [20]:
p o w d e r (1 ) s o lid
(5)
where p o w d e r is powder density. in this work.
s o lid
is porosity of powder particle which is set to 0.4
is solid density of Ti6Al4V. The density of argon gas is neglected
due to a negligible value. Thermal conductivity is expressed as below [20]: k p o w d e r (1 ) k s o lid
k pow der
and k s o lid are thermal conductivity of powder and solid material,
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where
(6)
respectively.
The latent heat for phase transformation was defined by enthalpy. The equation
c ( T )d T
where H is material enthalpy,
c (T )
(7)
is specific heat.
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H
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can be written by:
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According to the analysis mentioned above, thermal physical properties of Ti6Al4V
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powder used in this work were illustrated in Figure 3.
Fig.3. Thermo-physical curve of Ti6Al4V powder at different temperature. (a) Density. (b) Thermal conductivity. (c) Specific heat and enthalpy
3. Experiments. Ti6Al4V spherical powder was used and the particle size distribution of powder
is as follows: D10=21.29μm, D50=32.42μm, D90=49.24μm. Single track and single layer experiment were conducted by self-developed SLM machine, which equipped with a 500W IPG fiber laser. Inert argon gas was used in the process chamber of SLM in order to keep the material from oxidation. Parameters used in the experiment are tabulated in Table 1. The samples were cut off from substrate by electrical discharge wire-cutting machine and cleaned by alcohol. And then, the cross section of melt pool
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was processed according to standard metallographic process. microstructure of melt pool was characterized by using Optical microscope (Nikon MA 200). The surface
S4800 SEM) Table 1: Parameters used in this work.
Value 280,320,360 1800,2200,2600 0.06 0.03
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Parameter Laser power, P/W Scan speed, V/(mm/s) Hatch spacing, H/mm Layer thickness, LT/mm
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morphology of the samples was observed by scanning electron microscope (Hitachi
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4. Results and discussion
4.1. Temperature distribution and evolution The typical temperature distribution is investigated at LP=360W. Fig.4 shows the
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transient temperature distribution under different scan speed. The internal region of
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the isothermal solid line (1923K) indicates the molten region. As shown in Fig.4, the shape of the molten region corresponding to different scan speed has similar characteristics, that is the comet tail profile. It can be found that the forepart isothermal lines of the molten region are more intense than the rear side. It means that the temperature gradient at the front of the molten region is much larger than the area of back-end. This phenomenon can be ascribed to the higher thermal conductivity of
melted powder than un-melted Ti6Al4V powder. The isothermal lines at the front of the molten region are sparser with the increase of scan speed and this is mainly due to different heat input. Fig.5 depicts the temperature evolution of midpoint A under different scan speeds when LP is 360W and the red dashed line indicated melting point (1923K). The temperature changes rapidly with time in the SLM process. The highest temperature of midpoint A decreases from 4270K to 3553K with the increase of scan speed. Also, the residence time of the liquid phase was calculated and it
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decreases from 255μs to 156μs when scan speed increases from 1800mm/s to 2600mm/s. Similarly, the temperature evolution at midpoint A with the variation of laser power was investigated (Fig. 6). As shown in Fig.6, the highest temperature
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ranges from 3291K to 3866K when the laser power increases from 280W to 360W. The liquid residence time corresponding to 280W and 360W are 143μs and 191μs,
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respectively. During the SLM process, high power or low speed means that the unit
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volume of powder absorbs more heat per unit time. Therefore, the temperature rises and the liquid phase residence time is also prolonged at high laser power or low scan speed.
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To quantitatively analyze the relationship between the dimensions of molten region and the process parameters, the length, width and depth of molten region were defined
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(Fig. 7). Fig. 8 depicts the dimensions variation of the molten region under different
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scan speed at LP=360W. It can be noted that the length, width and depth of the molten region decrease with the increase of scan speed. This is mainly attributed to the fact that short residence time of liquid phase and low heat input.
Fig.4. Temperature distribution under different scan speeds at LP=360W. (a) 1800mm/s; (b)
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2200mm/s; (c) 2600mm/s.
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Fig.5. Temperature evolution of midpoint A under different scan speeds at LP=360W.
Fig.6. Temperature evolution of midpoint A under different laser power at SS=2200mm/s.
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Fig.7. Illustration of molten region dimensions.
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Fig. 8. Dimensions variation of molten region under different scan speeds at LP=360W.
4.2. Solidification behavior with different process parameters
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Solidification parameters were investigated based on temperature field. The temperature gradient (G), solidification rate (R), cooling rate (CR, GR) and
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solidification morphology parameter (SMR, G/R) can be obtained according to temperature evolution and distribution information. Thus, the overall information of grains formed in the SLM process can be described according to cooling rate and solidification morphology parameter. Fig. 9 shows the effect of scan speed on the solidification parameters when the laser power was kept at 360W. Fig. 9 (a) illustrates the effect of scan speed on
temperature gradient along X axis (TGX) and solidification rate (R). When the scan speed increases from 1800mm/s to 2600mm/s, the value of TGX increases from 1.31× 106K/m to 1.33×106K/m and then decreases to 1.28×106K/m. The temperature gradient fluctuates slightly with the scan speed, which indicates that the scan speed has little effect on scan speed. This is attributed to the fact that the effective input of heat is fixed when the laser power is constant. In addition, the value of R increases
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from 1.802m/s to 2.609m/s as the increase of scan speed. It is known that the solidification rate can be obtained through the scan speed by means of R
V cos
.
is the angle between R and V. Along the X direction, the value of approaches 0,
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so R and V are approximately equal. With the increase of laser speed, the grain size tends to be finer due to the increase of cooling rate. On the contrary, the value of
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SMR is proportional to scan speed (Fig.9(b)).
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Fig.10 shows the effect of laser power on the solidification parameters when the scan speed was kept at 2200mm/s. The temperature gradient is inversely proportional
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to laser power. In micro melt pool, the low thermal conductivity makes the heat dissipation rate less than the increase of heat input due to the increase of laser power. Therefore, the temperature distribution in melt pool is more homogeneous due to the
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saturated heat in melt pool and thus lowering thermal gradient [21]. The solidification
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rate fluctuates around 2.2mm/s without obvious change (Fig.10(a)). As explained earlier, the solidification rate is mainly influenced by the scan speed. In addition, for CR and SMR, they both decrease with the increase of laser power (Fig.10(b)). These phenomena can be attributed to the high input of heat. The grains tend to coarser with the increase of laser power due to enough residence time of liquid phase.
In order to consider the combined effect of laser power (P) and scan speed (V) on solidification parameters, the linear energy density (LED, P/V ratio) was defined. Fig.11(a) shows the linear energy density on the temperature gradient along X-axis and solidification rate. Both TGX and R presents a fluctuation with the increase of LEDs. However, in general, they all decrease with the increase of LEDs. As shown in Fig.11(b), it can be found that an significantly inverse dependence of the cooling rate with respect to the LED, which indicates that grains in the SLM process tend to be
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coarser with the increase of LEDs. This phenomenon is consistent with the results observed by Hu et al. [13]. For solidification morphology parameter, there is no
obvious relationship between the LEDs. This phenomenon mainly depends on the
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extent to which the line energy density affects the temperature gradient and the
solidification rate. In fact, acicular martensite is the main microstructure in the SLM
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Ti6Al4V samples according to previous studies [22,23]. The solidification
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morphology parameter (SMR) seems to have little effect on the shape of solidification
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microstructure of the final Ti6Al4V samples.
Fig. 9. Effect of scan speed on solidification parameters at LP=360W. (a) Temperature gradient and cooling rate; (b) Solidification rate and solidification morphology parameter.
Fig. 10. Effect of laser power on solidification parameters at V=2200mm/s. (a) Temperature gradient
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and cooling rate; (b) Solidification rate and solidification morphology parameter.
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Fig. 11. Effect of linear energy density on solidification parameters.
4.3. Experimental investigation and simulation validation
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As shown in Fig.12, the cross-sectional profile of melt pool is compared between simulation and experiment at the same process parameter combination. The width and
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depth of melt pool is illustrated in Fig.12 (b). The melt pool width and depth obtained by simulation and experiment are plotted in Fig.13. FEM simulation results have a
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good agreement with the experimental data. For the width and depth of the melt pool prepared at 360W and 1800mm/s, the width and depth of FEM simulation are 102.95μm and 47.27μm, respectively. For experimental results under the same process parameter combination, the width and depth are 123.46μm and 43.45μm, respectively. The simulated melt pool depth is relatively well with experimental result while the melt pool width is not as well. The possible reason is that complicated
factors exist in the SLM process, which cannot be considered comprehensively. The powder particles are randomly distributed on the substrate, it is difficult to obtain an excellent definition of powder bed state. In addition, the absorptivity of material to the laser varies with the input of energy and the change of material state, therefore, a specific value is hard to obtain. Of course, apart from the factors described above, other uncertain factors are difficult to consider accurately in actual process and FE simulation model.
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Microstructure of melt pool was characterized and investigated (Fig.14). The
growth direction of β grains is substantially perpendicular to the melt pool boundaries parallel to the building direction. Moreover, fine α' martensitic formed at the β grain
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boundaries. Fine acicular martensitic tilted at an angle and is parallel distributed
within the β matrix. This mainly attributed to the high temperature gradient(~106K/m)
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and cooling rate(~106K/s) in the process of SLM just as mentioned earlier.
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Figure 12. Melt pool profile at P=360W, SS=1800mm/s. (a) FEM simulation. (b) Experimental result.
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Figure 13. Dimensions of melt pool at 360W in FEM simulation and experimental results.
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Figure 14. Microstructure formed in the melt pool (P=320W, SS=2200mm/s).
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4.4. surface morphology investigation under different process parameters The top surface morphology analysis of the single layer was conducted with SEM.
The relationship of the surface morphology with the linear energy densities was investigated. Fig. 15(a) shows the poor surface with pores fabricated using a low linear energy density of 0.127J/mm. According to SEM observations, surface pores forming because of a lack of fusion and un-melted spherical powder particle can be
found. As shown in Fig.15(b), an increase of linear energy density to 0.145J/mm, improved the surface morphology by eliminating partial surface pores. However, partially sputtered small particles are always visible and adhere to the surface. Fig. 15(c) shows a better surface morphology after using a higher linear energy density of 0.156J/mm. It can be found that noticeable surface pores were eliminated and the number of small spherical adhering particles was reduced. Besides, satellites appear
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on the top surface due to the unavoidable spattering during the process of SLM.
Worse surface morphology was found after applying a higher linear energy density of 0.2J/mm, as shown in Fig.15 (f). Under this linear energy density, the laser scanning
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trace is eliminated and large un-melted powder particles disappeared. However, many
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small particles adhered to the surface leading to poor surface quality. This is mainly attributed to excessive heat input causes an increase in the instability of the melt pool,
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and small droplets are splashed and solidified from the melt pool to form small
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particles adhering to the surface.
Figure 15. Surface morphology of different LED. (a) 0.127J/mm, (b) 0.145J/mm, (c) 0.156J/mm, (d) 0.164J/mm, (e) 0.178J/mm, (f) 0.2J/mm.
5. Conclusions In this work, a 3D single track numerical simulation model was developed to investigate the thermal behavior and solidification parameters under different process parameters. Also, the single-track experiments were carried out to verify the validity
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of the numerical model. In addition, the surface morphology under different process
parameters was investigated. The major conclusions in this work can be summarized as follows:
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(1) The maximum temperature decreases with the increase of scan speed and
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increases when laser power increases. Dimensions of molten region increase with the increase of laser power or decrease of scan speed.
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(2) Temperature gradient along X axis is mainly affected by laser power and is inversely proportional to the laser power. Solidification rate depends on scan
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speed and is proportional to the scan speed. Cooling rate decreases with the increase of laser power or decrease of scan speed. The value of the
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solidification morphology parameter decreases regardless of the increase in laser power or the increase in scan speed.
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(3) The simulation results are in good agreement with the experimental results, which proves that the three-dimensional numerical model is effective. Besides, the cross-sectional microstructure of single track indicates that β grains along the building direction and fine α ' martensitic formed in the SLM due to high temperature gradient and cooling rate.
(4) Surface morphology will deteriorate at low energy density due to the appearance of surface porosity. With the increase of linear energy input, the surface quality of single layer would be improved while deteriorates at a higher linear energy density (0.2J/mm).
Acknowledgments
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This work was supported by Science Challenge Project (TZ2018006-0301-01), Dongguan University of Technology High-level Talents (Innovation Team) Research Project (KCYCXPT2016003) and Guangdong Scientific and Technological Project
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(2017B090911015)
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