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Simulation of temperature distribution in single metallic powder layer for laser micro-sintering
Computational Materials Science 53 (2012) 333–339
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Simulation of temperature distribution in single metallic powder layer for laser micro-sintering Jie Yin, Haihong Zhu ⇑, Linda Ke, Wenjuan Lei, Cheng Dai, Duluo Zuo Division of Laser Science and Technology, Wuhan National Laboratory for Optoelectronics, Institute of Optoelectronics Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China
a r t i c l e
i n f o
Article history: Received 24 June 2011 Received in revised form 5 August 2011 Accepted 8 September 2011 Available online 22 October 2011 Keywords: Laser micro-sintering Simulation Process parameter Temperature distribution Dimensions of molten pool
a b s t r a c t Simulation of temperature distribution in single metallic powder layer for laser micro-sintering (LMS) using finite element analysis (FEA) has been proposed, taking into account the adoption of ANSYS lMKS system of units, the transition from powder to solid and the utilization of moving laser beam power with a Gaussian distribution. By exploiting these characteristics a more accurate model could be achieved. The effects of the process parameters, such as laser beam diameter, laser power and laser scan speed on the temperature distribution and molten pool dimensions have been preliminarily investigated. It is shown that temperature increases with the laser power and decreases with the scan speed monotonously. For the laser beam diameter during single-track, the maximum temperature of the powder bed increases with the decrease in the laser beam diameter, but far from the center of the laser beam area, the temperature increases with the laser beam diameter. The molten pool dimensions in LMS are much less than that in classical selective laser sintering (SLS) process. Both molten pool length and width decrease with the laser beam diameter and the laser scan speed, but increase with the laser power. The molten pool length is always larger than the molten pool width. Furthermore, the center of molten pool is slightly shifted for the laser multi-track. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The development of selective laser sintering (SLS) described as ‘‘laser micro-sintering (LMS)’’ was put forward by laserinstitut Mittelsachsen e.V. in May 2003 [1]. LMS can fabricate complex microthree-dimensional parts from powder material. The resolution and surface roughness obtained by this new technology was more than one order of magnitude better than those fabricated by conventional SLS process [2]. Therefore, LMS attracted more and more attention in these years [3,4]. During the LMS process, a powder layer thin as tens of micrometers is laser-scanned to fuse the two-dimensional slice to an underlying solid piece, which consists of a series of stacked and fused two-dimensional slices. After laser scanning, a fresh powder layer is spread and the scanning process is repeated. LMS is a complex process that requires further understanding of the physical mechanisms. Temperature distribution plays a significant role in final properties of the sintered parts; therefore, the simulation of LMS is very important. The analytical approach and finite element analysis (FEA) are methods to solve these problems.
⇑ Corresponding author. Tel.: +86 027 87544774; fax: +86 027 87792355. E-mail address: [email protected] (H. Zhu). 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.09.012
However, FEA is a usual method to simulate temperature distribution for laser process due to its high accuracy. In fact, some heat conduction models have been developed to reveal the influence of processing conditions for SLS in the past. A series of researches on prediction of the density, temperature distribution and molten pool dimensions taking account of single-track, thermophysical properties and Gaussian distribution of laser spot using a two-dimensional model were investigated by Childs. In these researches, the concerning materials included amorphous polymer [5], crystalline polymer [6] and metallic powder [7]. Similarly, Shiomi et al. [8] developed a finite element heat condition model to calculate the weight of the solidified part made of metallic powder. They reconstructed meshes after each heating cycle by several laser pulses and assumed the physical properties to be independent of temperature. Their experimental and simulated results showed that the amount of the solidified part after a pulse was affected by the peak power of the laser rather than the duration of laser irradiation. Kolossov et al. [9] established a three-dimensional model based on continuous media theory to predict temperature distribution on surface of titanium powder layer during SLS, considering nonlinear behavior of thermal conductivity and specific heat due to temperature change and phase transformation. The results demonstrated that the simulated temperature field distribution using temperature-dependent thermal conductivity fitted the experimental
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results better than that using constant thermal conductivity. This conclusion [9,10] was also later confirmed by Patil and Yadava [11]. They found that the peak temperature during the laser multi-track was observed not exactly at the center of the laser beam but slightly toward decreasing X-axis (perpendicular to the laser scan direction) and increasing Y-axis, but the situation in the laser single-track was not detailedly reported. A three-dimensional thermomechanical finite element model encompassing effect of the powder-to-solid transition as well as the moving Gaussian power distribution has been developed by Dai and Shaw [12,13]. They studied the relationship between processing parameters, physical granularity of metallic powder and temperature distribution on ceramic and metal powder. Afterwards, grounded on the phase transformation from the powder phase to the solid phase during the sintering phenomenon of polycarbonate powder, Dong et al. [14,15] further demonstrated density evolution and temperature development by establishing a transient three-dimensional finite element model. The predicted results indicated that higher laser power, lower laser scan speed and smaller laser beam diameter could induce higher heat diffusion. Furthermore, with substrate structure, based on temperaturedependent thermophysical parameters and nonlinear phase transformation, Li et al. [16] and Zhang et al. [17] developed a threedimensional selective laser melting (SLM) finite element model on 316L stainless steel powder and W–Ni–Fe powder respectively. Their simulated results also showed that a lower scan speed, higher laser power and lower scan interval enabled much higher maximum temperature and wider track width. Although there are many numerical simulations of SLS/SLM process have been carried out to investigate the temperature distribution, there are few simulation researches on the temperature field of LMS. Yue et al. [18] have established a two-dimensional numerical model to predict the width and depth of sintered line for laser micro-fabrication. Meanwhile, these previous studies [5–20] may not be appropriate for the LMS process which requires the simulation to involve the microscale both in laser beam spot and powder granularity as well as the effects of the transition from powder to solid. Consequently, in this study we have developed a model that includes the adoption of ANSYS lMKS system of units, the transition from powder to solid and the utilization of moving laser beam power with a Gaussian distribution. The effects of laser beam diameter, laser power and laser scan speed on the temperature distribution and molten pool length and width were thoroughly analyzed.
difficult to estimate the penetration depth precisely [9], the laser moving source is considered as Gaussian distributed surface heat flux load input. The scale of the LMS is in the tens of micrometers, which is much larger than the characteristic dimension of the thermal conduction. For metal, the thermal conduct is mainly caused by free electron, the characteristic dimensions of the electrons are the length of the average free path which is only about 10 nm. Therefore, the governing energy balance equation of three-dimensional heat conduction can still utilize Fourier’s law:
fqg ¼ ½DrT
ð1Þ
where {q} defines heat flux vector; T is the temperature and
2
kx
0
6 ½D ¼ 4 0
ky
0
0
0
3
7 05 kz
represents heat conduct matrix and the material is assumed to be isotropic in all directions, so there is kx = ky = kz = k. The first law of thermodynamics states that thermal energy is conserved. For a differential control volume associated with LMS, the heat transfer problem can be mathematically described as:
qC
v @T þ fmgrT þ r fqg ¼ q @t
where q is the material density; C is the specific heat capacity; t is the interaction time between laser and the powder bed; m is velocity v vector for mass transport of heat; and q is heat generation rate per unit volume. In this hypothetical scenario, according to assumptions above, the heat transfer during sintering can be remodeled by combining Eqs. (1) and (2):
qðTÞCðTÞ
@T @ @T @ @T @ @T ¼ kðTÞ þ kðTÞ þ kðTÞ @t @x @x @y @y @z @z
In modeling the heat transmission during LMS process, a theoretical model is established to predict the thermal time history of the Heat Affected Zone (HAZ). The following assumption can be made: The whole powder bed is considered to be homogeneous and continuous media. The thermal history of HAZ is made by the effects of conduction and convection only, the effect of radiation is ignored. In addition, the coefficient of convection between powder bed and the environment is assumed to be a constant. During the sintering process, the powder’s thermal parameters such as thermal conductivity, specific heat capacity and enthalpy are varied with temperatures. The only source acting on the powder bed is that provided by the laser source. Moreover, since the magnitude of optical penetration depth is several micros for mono-sized powder and it is
ð3Þ
To obtain the solution from the differential equation of heat conduction [21], the initial condition and boundary condition are needed. Initial condition
Tðx; y; z; 0Þ ¼ T 0 ðx; y; zÞ
ð4Þ
Boundary condition of the third kind
fqgT fgg ¼ hf ðT T surf Þ 2. Physical description of LMS
ð2Þ
ð5Þ
where T0 denotes the initial temperature; {g} is the unit outward normal vector; hf is the coefficient of heat convection; and Tsurf is the temperature at the surface of the powder bed. The laser beam radius is defined as the radius in which the power density reduces from the peak value by a factor of e2. What’s more, the thermal flux density of laser beam obeys Gaussian distribution [22]:
I¼
2r 2 exp pR2 R2
2AP
ð6Þ
where A denotes the heat absorptivity of laser beam on metal surface; P is the laser power; R is the effective laser beam radius and r is the radial distance from the center of the laser beam. Latent heat is taken into consideration for the phase change problem such as LMS process. To account for the latent heat, the enthalpy of the material is defined as a function of temperature:
HðTÞ ¼
Z
qðTÞCðTÞdT
ð7Þ
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In our FEA model, the porosity is assumed to change from
3. Finite element model description
u0 = 0.45 (initial powder bed) to the minimum value u = 0 (bulklike material), linearly with temperature when the temperature is above sintering temperature Ts and below the melting temperature Tm. Therefore the density of the powder bed q is defined as:
A three-dimensional model was developed and the commercial FEA software ANSYS was utilized. In comparison with the modeling of the SLS processing, owing to the tens of micrometers of the laser spot diameter as well as the sintering specimen during the modeling of the LMS processing, the element size should be even smaller (the element edge length of hexahedrons in our model was 7.5 lm). Meanwhile, for the models of the same dimensions, the decrease of the element size will lead to the sharply increase in the magnitude of the element and node number, consequently, the computational time cost will increase. Furthermore, inspired by the solution of the MEMS problem, the lMKS (termed as lm, kg, s) units system was adopted for the micro-scale modeling and has proven to be efficient. The dimensions of model are 30 lm in height and 900 lm in both length and width. Taking account of the computational precision as well as the elapsed time cost of iterations, the finite element meshes with 57,600 hexahedral elements and about 276,969 nodes have been used for the simulation, which is shown in Fig. 1. In the simulation, the utilized powder is pure iron powder and the thermal material properties used in the model are summarized in Table 1.
8 > < q0 ðTÞ; T 0 6 T 6 T s Þq0 ðT s Þ q ¼ qbulk ðTT mmT ðT T s Þ þ q0 ðT s Þ; T s < T < T m s > : qbulk ðTÞ; T P T m
where q0 denotes the initial powder density. Furthermore, the initial powder state elements are irreversibly changed to the solid state elements when temperature exceeds Tm. Consequently, the thermal properties such as thermal conductivity of the powder bed are treated as a function of temperature and the initial porosity. 3.2. Thermal conductivity of the powder bed Since effective heat conductivity plays an important role in the micro-sintering process. Meanwhile, because of the insufficiency of data on molten metals as well as the complication of sintering model, a piecewise model for thermal conductivity was proposed:
3.1. Powder density
keff
The fractional porosity u is a function of the local density of the porous material q and the density of the solid material qbulk [14]:
u¼
qbulk q qbulk
ð9Þ
8 ðTÞ; T 0 6 T 6 T s k > < powder ¼ kbulk ðT mTÞkTpowder ðT s Þ ðT T s Þ þ kpowder ðT s Þ; T s < T < T m m s > : kbulk ðTÞ; T P T m
ð10Þ
where Ts = 1000 °C denotes the initial sintering temperature representing that the sintering process only starts above the threshold temperature; Tm = 1537 °C is the melting point of the specimen;
ð8Þ
Fig. 1. The established three-dimensional FE model and schematic of (a) laser single-track, (b) laser multi-track.
Table 1 Summary of material properties of solid iron [23]. Temperature, T (°C) Thermal conductivity, k (W/m °C) Specific heat, C (J/Kg °C) Initial powder density, q0 (kg/m3) Initial powder porosity, u0 Initial sintering temperature, Ts (°C) Melting point, Tm (°C) Absorptivity of YAG laser energy, A Initial temperature of powder, T0 (°C) Heat transfer coefficient, h (W/m2 °C) Ambient air temperature, Ts (°C)
20 81.1 460 4325 0.45 1000 1537 0.64 20 20 20
250 72.1 480
500 63.5 530
750 50.3 675
1000 39.4 670
1500 29.6 660
1700 29.4 780
2500 31.6 820
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Fig. 2. Effective thermal conductivity keff versus temperature during heating stage.
kbulk is the thermal conductivity of the solid; kpowder is thermal conductivity of the iron powder and is equal to [23]:
kpowder ¼ kbulk ð1 uÞn
ð11Þ
where n is an empirical parameter which is taken as 4 in this simulation. Each element in the model is assumed to be initially powder material, so the effective thermal conductivity of the powder bed keff equals to kpowder. During the heating stage, when the temperature is above sintering temperature Ts and below the melting temperature Tm, keff coupling with sintering material transformation from powder phase to bulk phase increases linearly. Moreover, the effective thermal conductivity k takes as kbulk when the temperature exceeds Tm. Namely, the keff versus temperature during the heating stage follows curve ABCD shown in Fig. 2. Furthermore, at the end of heating stage, the elements heated by laser exposure result in bulk-like material, thus the initial powder state elements are irreversibly changed to the solid state elements with thermal conductivity of kbulk under this condition. This transformation is carried out by the function of changing the material number attribute in ANSYS. 4. Simulation results and discussion 4.1. Effect of laser beam diameter Fig. 3a shows the temperature distribution of the powder surface along X-axis at Y = 450 lm distance with different laser beam diameters during the laser single-track. The utilized diameter ranges from 30 lm to 60 lm with the same laser power of 4 W, scan speed of 200 mm/s and hatching space of 20 lm. From Fig. 3a, it can be found that the maximum temperature increases with the decrease of the laser beam diameter. However, the relationship is not proportional. The maximum temperatures of the specimen fabricated by D1 = 30 lm, D3 = 45 lm and D3 = 60 lm are 2278.1 °C, 1817.3 °C and 1596.6 °C, respectively. Furthermore, the curve slope is also different when different laser beam diameters are utilized, suggesting the temperature gradient changes with the laser beam diameter. In general, the smaller the laser beam diameter, the higher the temperature gradient. The maximum temperature gradient (76.6 °C/lm) during processing at D1 = 30 lm is almost two times larger than that at D3 = 60 lm (41.9 °C/lm). From Fig. 3a, it can also be found that the temperature does not always decrease with the increase of the laser beam diameter. In
Fig. 3. Temperature distribution with different laser beam diameter mapping on to path along (a) X-axis at Y = 450 lm (b) Y-axis at X = 450 lm (laser power: 4 W, scan speed: 200 mm/s, hatching space: 20 lm, scan track: 1).
the range of 300–468.75 lm of X-axis, the temperature decreases with the increase in diameter, but if in the other range from 476.25 lm to 600 lm of X-axis, the situation is different, the temperature increases as increasing the beam diameter. For the same position, e.g., X = 487.5 lm, the temperature at D3 = 60 lm (682.1 °C) is higher than that at D1 = 30 lm (391.7 °C). In addition, according to the melting point of sintering specimen, the center of the molten pool is observed slightly shift toward decreasing X-axis. This phenomenon can be ascribed to the thermal accumulation effect reasonably. Fig. 3b shows the effect of laser beam diameter on temperature distribution along Y-axis at X = 450 lm distance in the powder layer. Similar to Fig. 3a, the temperature increases with decrease in beam diameter from 427.5 lm to 472.5 lm of Y-axis, but in the other range (i.e., from 300 lm to 416.25 lm) the temperature increases as increasing the beam diameter. Moreover, the molten pool along Y-axis is symmetric concerning the center of laser beam area. This is the case because the elements outside the region irradiated by laser beam are still the powder phase. Therefore during the single-track scan, the thermal conductivities of both increasing and decreasing Y-axis from the center of laser beam area are almost the same. Consequently, no shift in the center of molten pool could be observed along the Y-axis. Fig. 4 shows that the molten pool length (along X-axis) and width (along Y-axis) versus laser beam diameter. The molten pool
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Fig. 4. The molten pool dimensions versus laser beam diameter.
length and width were extracted from isotherms that approximately represent the size of the molten pool. From Fig. 4, it can be found that the molten pool dimensions of LMS change with the laser beam diameter and are in size of tens of micrometers, which are much smaller than conventional SLS process. Both molten pool length and width decrease with the increase in laser beam diameter, but the decrease rate is not the same. Molten pool width at D1 = 30 lm is 41.3 lm and at D2 = 45 lm is 38 lm, but the molten pool width at D3 = 60 lm is only 19.9 lm. The same rule is for the molten pool length. This is because the input heat flux is inversely proportional to the squared laser beam diameter and hence the molten pool dimensions decrease steeply with increase in laser diameter. What’s more, for the same laser diameter (i.e., for D2 = 45 lm), the molten pool length (42.8 lm) is larger than molten pool width (37.5 lm). This phenomenon is because the laser beam is moving along X-axis and some elements on the laser path are repeatedly heated, therefore the temperature is higher at Xaxis than that at Y-axis if the distance (within the laser beam area) from the beam center is the same. 4.2. Effect of laser power Different to Fig. 3 with single-track, in order to investigate the influence of track to track on temperature distribution and the dimensions of the molten pool for different laser power values, the multi-track scan along X-axis was performed. Fig. 5a shows the temperature distribution along X-axis at Y = 450 lm distance in the powder bed due to irradiation of laser beam on the third track. Laser power is varying from 2 W to 4 W with 1 W increment and the other sintering parameters such as the scan speed, laser diameters and hatch spacing are held as constants. The nature of temperature distribution shows that there is an increase in temperature with increase in laser power of the entire X-axis. When laser power surpasses 4 W, the maximum temperature in powder bed is 2465.8 °C, which is close to the boiling point of iron. Under this condition, the high laser power may not be suitable for laser rapid prototyping because the boiled liquid splashes and final dense parts cannot be made. Whereas the top temperature attains only 1596.9 °C when laser power is decreased to 2 W, the inadequate energy input may give rise to poor sintering parts. Fig. 5b shows the effect of laser power on temperature distribution along Y-axis at X = 450 lm distance in the powder layer. It can be seen that the increase of laser power could induce high temperature of the specimen for the whole Y-axis. The maximum temperature gradient (53.6 °C/lm) during fabrication process at
Fig. 5. Temperature distribution for different laser power mapping on to path along (a) X-axis at Y = 450 lm (b) Y-axis at X = 450 lm (scan speed: 200 mm/s, beam diameter: 60 lm, hatching space: 20 lm, scan tracks: 3).
P1 = 4 W is larger than that at P3 = 2 W (47.0 °C/lm). The high thermal gradient along Y-axis may cause large thermal stresses in the powder layer. Figs. 5a and 5b show that in three curves, the molten pool is asymmetric with respect to the laser beam area. Namely, the center of the molten pool is not observed at the center of laser beam, but slightly shifted toward the side of increasing Y-axis and decreasing X-axis. The phenomenon has reported by former researchers [11,12] and can be attributed to the fact that the combined actions of the thermal accumulation effect and the thermal conductivity change due to the transition from powder to solid. On the one hand, comparing the location of the adjacent laser spot, about 86.4% elements are sited in the intersection of both two laser spot regions, so the elements lying on the laser scan path are getting heated frequently. Therefore, the center of laser beam along Xaxis is observed slightly toward the previous sintered zone (Fig. 5a). On the other hand, because during the fabrication of the third scan track, the powder-phase elements in previous track which has been laser heated are now solid-phase elements, they conduct heat quickly when the adjacent elements are under the laser exposure. Hence for the laser beam area along Y-axis, the temperature on the solid-phase side may be smaller than that on the powder-phase side (Fig. 5b). Fig. 6 shows that both molten pool length and width are proportional to the laser power. Molten pool length and width at P1 = 4 W are 70.9 lm and 53.2 lm, whereas at P3 = 2 W are 15.2 lm and
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Fig. 6. The molten pool dimensions versus laser power.
13.0 lm, respectively. This observation implies that the increase of laser power increases the heat flux intensity of the laser beam, which in turn leads to increase of the molten pool dimensions. Moreover, for the same laser power (i.e., for P2 = 3 W), the molten pool length (40.8 lm) is larger than molten pool width (36.5 lm). This phenomenon can also be ascribed to the fact that temperature gradient along X-axis is less than that along Y-axis for the molten pool region. Furthermore, as the laser power increases, the difference between the molten pool length and the molten pool width increases, indicating more significant thermal accumulation effect for the higher laser power.
when sample point temperature rise to the first peak temperature at V3 = 225 mm/s is less than that at V1 = 180 mm/s (2.26 ms). The finish time (4 ms) of former speed is shorter than that of latter one (5 ms). It informs us that there is an increase in response time when the sample point temperature rise to the maximum of each track with decrease in laser scan speed. Fig. 8a shows the effect of laser scan speed on temperature distribution along X-axis at Y = 450 lm distance in the powder layer. The simulated temperature distribution shows that there is an increase in temperature with decrease in laser scan speed for the whole X-axis. This phenomenon can be ascribed to the fact that if we increase laser scan speed, the interaction time of the input heat flux due to laser irradiation with powder layer decreases and therefore decreases in maximum temperature. In addition, the center of molten pool is observed slightly shifted toward the side of decreasing X-axis. The shift in the center of molten pool (toward increasing Y-axis side) is also observed in Fig. 8b, which shows the effect of laser scan speed on temperature distribution along Y-axis at X = 450 lm distance in the powder layer. It can be seen that the decrease of the scan speed could induce low temperature gradient of the specimen. The maximum temperature gradient (42.3 °C/lm) which derives from temperature change at V3 = 225 mm/s is somewhat larger than that at V1 = 180 mm/s (41.6 °C/lm).
4.3. Effect of laser scan speed Fig. 7 shows that the temperature change versus the laser exposure time with fixed laser power of 3 W, laser beam diameter of 30 lm, hatching spacing of 20 lm, but different laser scan speed of 180 mm/s, 200 mm/s and 225 mm/s, respectively. According to the graph, we can observe from the fluctuating temperature distribution that the maximum temperature of each track at the sampling point (face centered in the powder bed) increases when laser beam spot approaches and decreases when departures. However, the minimum temperature of each scan track monotonously increases with time elapse. What’s more, the time (1.85 ms)
Fig. 7. Temperature versus time at the face-centered sampling point with different laser scan speed (laser power: 3 W, laser beam diameter: 30 lm, hatching space: 20 lm, scan tracks: 5).
Fig. 8. Temperature distribution for different laser scan speed mapping on to path along (a) X-axis at Y = 450 lm (b) Y-axis at X = 450 lm (power: 3 W, laser beam diameter: 30 lm, scan tracks: 3).
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during the single-track, no shift is observed along the Y-axis. These phenomena happen because the thermal accumulation effect and the thermal conductivity change because of the transition from powder to solid. There is an increase in response time when the sample point temperature rises to the maximum of each track with the decrease in laser scan speed. The transition from powder to solid has not been taken into consideration in the previous laser micro-fabrication model; hence the present model involving the characteristics is more accurate. Acknowledgements
Fig. 9. The molten pool dimensions versus laser scan speed.
This work is supported by the National Natural Science Foundation of China (60878022), the fund of Key Laboratory of Chemical Laser (KLCL-HT-200907) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. References
Fig. 9 shows that both molten pool length and width decrease with the laser scan speed. Molten pool width at V1 = 180 mm/s is 39.6 lm whereas molten pool width at V2 = 180 mm/s is 36.5 lm. Again for different speed values (e.g., for V3 = 225 mm/ s), the molten pool length (38.1 lm) is always larger than molten pool width (33.8 lm) due to the temperature gradient along Xaxis is less comparing to that along Y-axis for the molten pool region. 5. Conclusions Although there are many numerical simulations for SLS/SLM, reports of simulation research for LMS on the temperature evolution are few. Furthermore, to the best of our knowledge, the finite element model for LMS has not been discussed previously. In this paper, a three-dimensional finite element model for LMS that encompasses the adoption of ANSYS lMKS system of units, the transition from powder to solid and the utilization of moving laser beam power with a Gaussian distribution in the single powder layer has been proposed. The effects of process parameters, such as laser beam diameter, laser power and laser scan speed, on the temperature distribution and molten pool length and width have been preliminarily investigated. Based on these numerical simulations, the following conclusions can be drawn. The temperature increases with the laser power and decreases with the scan speed monotonously. However, complex relationship can be found between the temperature and laser spot diameter during the laser single-track. The maximum temperature of powder bed decreases with the laser beam diameter, but far from the center of the laser beam area, the temperature increases with the laser beam diameter. In the model, the dimensions of molten pool in LMS process are several tens of micrometers which are about one order of magnitude smaller than that in SLS process. This phenomenon is due to the small laser beam diameter and molten pool dimensions of LMS in comparison with that of SLS. Both molten pool length and width decrease with the laser beam diameter and the laser scan speed, but increase with the laser power. Furthermore, the molten pool length is always larger than the molten pool width due to the temperature gradient along X-axis is less than that along Y-axis for the molten pool region. The center of molten pool is observed slightly toward decreasing X-axis and increasing Y-axis for the laser multi-track. However,
[1] P. Regenfuss, L. Hartwig, S. Klotzer, R. Ebert, T. Brabant, T. Petsch, H. Exner, Rapid Prototyping Journal 11 (2005) 18–25. [2] P. Regenfuss, A. Streek, L. Hartwig, S. Klotzer, T. Brabant, M. Horn, R. Ebert, H. Exner, Rapid Prototyping Journal 13 (2007) 204–212. [3] H. Exner, P. Regenfuss, L. Hartwig, S. Klotzer, R. Ebert, Selective laser microsintering with a novel process, in: I. Miyamoto, A. Ostendorf, K. Sugioka, H. Helvajian (Eds.) Fourth International Symposium on Laser Precision Microfabrication, 2003, pp. 145–151. [4] H. Exner, M. Horn, A. Streek, P. Regenfuss, F. Ullmann, R. Ebert, Laser microsintering – a new method to generate metal and ceramic parts of high resolution with sub-micrometer powder, in: P.J. Bartolo, A.J. Mateus, F.D.C. Batista, H.A. Almeida, J.M. Matias, J.C. Vasco, J.B. Gaspar, M.A. Correia, N.C. Andre, N.F. Alves, P.P. Novo, P.G. Martinho, R.A. Carvalho (Eds.) Virtual and Rapid Manufacturing – Advanced Research in Virtual and Rapid Prototyping, Routledge, London, UK, 2008, pp. 491–499. [5] T.H.C. Childs, M. Berzins, G.R. Ryder, A. Tontowi, Proceedings of the Institution of Mechanical Engineers Part B-Journal of Engineering Manufacture 213 (1999) 333–349. [6] T.H.C. Childs, A.E. Tontowi, Proceedings of the Institution of Mechanical Engineers Part B-Journal of Engineering Manufacture 215 (2001) 1481–1495. [7] T.H.C. Childs, C. Hauser, M. Badrossamay, Proceedings of the Institution of Mechanical Engineers Part B-Journal of Engineering Manufacture 219 (2005) 339–357. [8] M. Shiomi, A. Yoshidome, F. Abe, K. Osakada, International Journal of Machine Tools & Manufacture 39 (1999) 237–252. [9] S. Kolossov, E. Boillat, R. Glardon, P. Fischer, M. Locher, International Journal of Machine Tools & Manufacture 44 (2004) 117–123. [10] P. Fischer, M. Locher, V. Romano, H.P. Weber, S. Kolossov, R. Glardon, International Journal of Machine Tools & Manufacture 44 (2004) 1293–1296. [11] R.B. Patil, V. Yadava, International Journal of Machine Tools & Manufacture 47 (2007) 1069–1080. [12] K. Dai, L. Shaw, Acta Materialia 52 (2004) 69–80. [13] K. Dai, X. Li, L. Shaw, Journal of Heat Transfer-Transactions of the ASME 126 (2004) 818–825. [14] L. Dong, A. Makradi, S. Ahzi, Y. Remond, Journal of Materials Processing Technology 209 (2009) 700–706. [15] L. Dong, A. Makradi, S. Ahzi, Y. Remond, Finite element analysis of temperature and density distributions in selective laser sintering process, in: A. Ochsner, J. Gracio (Eds.), Diffusion in Solids and Liquids: Heat Transfer – Microstructure & Properties, Trans Tech Publications Ltd., Stafa-Zurich, 2007, pp. 75–80. [16] R.D. Li, Y.S. Shi, J.H. Liu, H.S. Yao, W.X. Zhang, Powder Metallurgy and Metal Ceramics 48 (2009) 186–195. [17] D.Q. Zhang, Q.Z. Cai, J.H. Liu, L. Zhang, R.D. Li, International Journal of Advanced Manufacturing Technology 51 (2010) 649–658. [18] C.F. Yue, J.M. Chen, T.C. Zuo, A model for the micro-fabrication with selective laser sintering metal powders, in: Z. Ma, G. Jin, X. Chen (Eds.) Mems/Moems Technologies and Applications Ii, Spie-Int Soc Optical Engineering, Bellingham, 2004, pp. 354–361. [19] K. Dai, L. Shaw, Acta Materialia 49 (2001) 4171–4181. [20] K. Dai, L. Shaw, Rapid Prototyping Journal 8 (2002) 270–276. [21] M.N. Özısık, Heat Conduction, 2nd ed., Wiley and Sons, New York, 1993. [22] M. Labudovic, D. Hu, R. Kovacevic, Journal of Materials Science 38 (2003) 35– 49. [23] I.V. Shishkovsky, Proceedings of the SPIE – The International Society for Optical Engineering 4644 (2002) 446–449.
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Simulation of temperature distribution in single metallic powder layer for laser micro-sintering Jie Yin, Haihong Zhu ⇑, Linda Ke, Wenjuan Lei, Cheng Dai, Duluo Zuo Division of Laser Science and Technology, Wuhan National Laboratory for Optoelectronics, Institute of Optoelectronics Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China
a r t i c l e
i n f o
Article history: Received 24 June 2011 Received in revised form 5 August 2011 Accepted 8 September 2011 Available online 22 October 2011 Keywords: Laser micro-sintering Simulation Process parameter Temperature distribution Dimensions of molten pool
a b s t r a c t Simulation of temperature distribution in single metallic powder layer for laser micro-sintering (LMS) using finite element analysis (FEA) has been proposed, taking into account the adoption of ANSYS lMKS system of units, the transition from powder to solid and the utilization of moving laser beam power with a Gaussian distribution. By exploiting these characteristics a more accurate model could be achieved. The effects of the process parameters, such as laser beam diameter, laser power and laser scan speed on the temperature distribution and molten pool dimensions have been preliminarily investigated. It is shown that temperature increases with the laser power and decreases with the scan speed monotonously. For the laser beam diameter during single-track, the maximum temperature of the powder bed increases with the decrease in the laser beam diameter, but far from the center of the laser beam area, the temperature increases with the laser beam diameter. The molten pool dimensions in LMS are much less than that in classical selective laser sintering (SLS) process. Both molten pool length and width decrease with the laser beam diameter and the laser scan speed, but increase with the laser power. The molten pool length is always larger than the molten pool width. Furthermore, the center of molten pool is slightly shifted for the laser multi-track. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The development of selective laser sintering (SLS) described as ‘‘laser micro-sintering (LMS)’’ was put forward by laserinstitut Mittelsachsen e.V. in May 2003 [1]. LMS can fabricate complex microthree-dimensional parts from powder material. The resolution and surface roughness obtained by this new technology was more than one order of magnitude better than those fabricated by conventional SLS process [2]. Therefore, LMS attracted more and more attention in these years [3,4]. During the LMS process, a powder layer thin as tens of micrometers is laser-scanned to fuse the two-dimensional slice to an underlying solid piece, which consists of a series of stacked and fused two-dimensional slices. After laser scanning, a fresh powder layer is spread and the scanning process is repeated. LMS is a complex process that requires further understanding of the physical mechanisms. Temperature distribution plays a significant role in final properties of the sintered parts; therefore, the simulation of LMS is very important. The analytical approach and finite element analysis (FEA) are methods to solve these problems.
⇑ Corresponding author. Tel.: +86 027 87544774; fax: +86 027 87792355. E-mail address: [email protected] (H. Zhu). 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.09.012
However, FEA is a usual method to simulate temperature distribution for laser process due to its high accuracy. In fact, some heat conduction models have been developed to reveal the influence of processing conditions for SLS in the past. A series of researches on prediction of the density, temperature distribution and molten pool dimensions taking account of single-track, thermophysical properties and Gaussian distribution of laser spot using a two-dimensional model were investigated by Childs. In these researches, the concerning materials included amorphous polymer [5], crystalline polymer [6] and metallic powder [7]. Similarly, Shiomi et al. [8] developed a finite element heat condition model to calculate the weight of the solidified part made of metallic powder. They reconstructed meshes after each heating cycle by several laser pulses and assumed the physical properties to be independent of temperature. Their experimental and simulated results showed that the amount of the solidified part after a pulse was affected by the peak power of the laser rather than the duration of laser irradiation. Kolossov et al. [9] established a three-dimensional model based on continuous media theory to predict temperature distribution on surface of titanium powder layer during SLS, considering nonlinear behavior of thermal conductivity and specific heat due to temperature change and phase transformation. The results demonstrated that the simulated temperature field distribution using temperature-dependent thermal conductivity fitted the experimental
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results better than that using constant thermal conductivity. This conclusion [9,10] was also later confirmed by Patil and Yadava [11]. They found that the peak temperature during the laser multi-track was observed not exactly at the center of the laser beam but slightly toward decreasing X-axis (perpendicular to the laser scan direction) and increasing Y-axis, but the situation in the laser single-track was not detailedly reported. A three-dimensional thermomechanical finite element model encompassing effect of the powder-to-solid transition as well as the moving Gaussian power distribution has been developed by Dai and Shaw [12,13]. They studied the relationship between processing parameters, physical granularity of metallic powder and temperature distribution on ceramic and metal powder. Afterwards, grounded on the phase transformation from the powder phase to the solid phase during the sintering phenomenon of polycarbonate powder, Dong et al. [14,15] further demonstrated density evolution and temperature development by establishing a transient three-dimensional finite element model. The predicted results indicated that higher laser power, lower laser scan speed and smaller laser beam diameter could induce higher heat diffusion. Furthermore, with substrate structure, based on temperaturedependent thermophysical parameters and nonlinear phase transformation, Li et al. [16] and Zhang et al. [17] developed a threedimensional selective laser melting (SLM) finite element model on 316L stainless steel powder and W–Ni–Fe powder respectively. Their simulated results also showed that a lower scan speed, higher laser power and lower scan interval enabled much higher maximum temperature and wider track width. Although there are many numerical simulations of SLS/SLM process have been carried out to investigate the temperature distribution, there are few simulation researches on the temperature field of LMS. Yue et al. [18] have established a two-dimensional numerical model to predict the width and depth of sintered line for laser micro-fabrication. Meanwhile, these previous studies [5–20] may not be appropriate for the LMS process which requires the simulation to involve the microscale both in laser beam spot and powder granularity as well as the effects of the transition from powder to solid. Consequently, in this study we have developed a model that includes the adoption of ANSYS lMKS system of units, the transition from powder to solid and the utilization of moving laser beam power with a Gaussian distribution. The effects of laser beam diameter, laser power and laser scan speed on the temperature distribution and molten pool length and width were thoroughly analyzed.
difficult to estimate the penetration depth precisely [9], the laser moving source is considered as Gaussian distributed surface heat flux load input. The scale of the LMS is in the tens of micrometers, which is much larger than the characteristic dimension of the thermal conduction. For metal, the thermal conduct is mainly caused by free electron, the characteristic dimensions of the electrons are the length of the average free path which is only about 10 nm. Therefore, the governing energy balance equation of three-dimensional heat conduction can still utilize Fourier’s law:
fqg ¼ ½DrT
ð1Þ
where {q} defines heat flux vector; T is the temperature and
2
kx
0
6 ½D ¼ 4 0
ky
0
0
0
3
7 05 kz
represents heat conduct matrix and the material is assumed to be isotropic in all directions, so there is kx = ky = kz = k. The first law of thermodynamics states that thermal energy is conserved. For a differential control volume associated with LMS, the heat transfer problem can be mathematically described as:
qC
v @T þ fmgrT þ r fqg ¼ q @t
where q is the material density; C is the specific heat capacity; t is the interaction time between laser and the powder bed; m is velocity v vector for mass transport of heat; and q is heat generation rate per unit volume. In this hypothetical scenario, according to assumptions above, the heat transfer during sintering can be remodeled by combining Eqs. (1) and (2):
qðTÞCðTÞ
@T @ @T @ @T @ @T ¼ kðTÞ þ kðTÞ þ kðTÞ @t @x @x @y @y @z @z
In modeling the heat transmission during LMS process, a theoretical model is established to predict the thermal time history of the Heat Affected Zone (HAZ). The following assumption can be made: The whole powder bed is considered to be homogeneous and continuous media. The thermal history of HAZ is made by the effects of conduction and convection only, the effect of radiation is ignored. In addition, the coefficient of convection between powder bed and the environment is assumed to be a constant. During the sintering process, the powder’s thermal parameters such as thermal conductivity, specific heat capacity and enthalpy are varied with temperatures. The only source acting on the powder bed is that provided by the laser source. Moreover, since the magnitude of optical penetration depth is several micros for mono-sized powder and it is
ð3Þ
To obtain the solution from the differential equation of heat conduction [21], the initial condition and boundary condition are needed. Initial condition
Tðx; y; z; 0Þ ¼ T 0 ðx; y; zÞ
ð4Þ
Boundary condition of the third kind
fqgT fgg ¼ hf ðT T surf Þ 2. Physical description of LMS
ð2Þ
ð5Þ
where T0 denotes the initial temperature; {g} is the unit outward normal vector; hf is the coefficient of heat convection; and Tsurf is the temperature at the surface of the powder bed. The laser beam radius is defined as the radius in which the power density reduces from the peak value by a factor of e2. What’s more, the thermal flux density of laser beam obeys Gaussian distribution [22]:
I¼
2r 2 exp pR2 R2
2AP
ð6Þ
where A denotes the heat absorptivity of laser beam on metal surface; P is the laser power; R is the effective laser beam radius and r is the radial distance from the center of the laser beam. Latent heat is taken into consideration for the phase change problem such as LMS process. To account for the latent heat, the enthalpy of the material is defined as a function of temperature:
HðTÞ ¼
Z
qðTÞCðTÞdT
ð7Þ
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In our FEA model, the porosity is assumed to change from
3. Finite element model description
u0 = 0.45 (initial powder bed) to the minimum value u = 0 (bulklike material), linearly with temperature when the temperature is above sintering temperature Ts and below the melting temperature Tm. Therefore the density of the powder bed q is defined as:
A three-dimensional model was developed and the commercial FEA software ANSYS was utilized. In comparison with the modeling of the SLS processing, owing to the tens of micrometers of the laser spot diameter as well as the sintering specimen during the modeling of the LMS processing, the element size should be even smaller (the element edge length of hexahedrons in our model was 7.5 lm). Meanwhile, for the models of the same dimensions, the decrease of the element size will lead to the sharply increase in the magnitude of the element and node number, consequently, the computational time cost will increase. Furthermore, inspired by the solution of the MEMS problem, the lMKS (termed as lm, kg, s) units system was adopted for the micro-scale modeling and has proven to be efficient. The dimensions of model are 30 lm in height and 900 lm in both length and width. Taking account of the computational precision as well as the elapsed time cost of iterations, the finite element meshes with 57,600 hexahedral elements and about 276,969 nodes have been used for the simulation, which is shown in Fig. 1. In the simulation, the utilized powder is pure iron powder and the thermal material properties used in the model are summarized in Table 1.
8 > < q0 ðTÞ; T 0 6 T 6 T s Þq0 ðT s Þ q ¼ qbulk ðTT mmT ðT T s Þ þ q0 ðT s Þ; T s < T < T m s > : qbulk ðTÞ; T P T m
where q0 denotes the initial powder density. Furthermore, the initial powder state elements are irreversibly changed to the solid state elements when temperature exceeds Tm. Consequently, the thermal properties such as thermal conductivity of the powder bed are treated as a function of temperature and the initial porosity. 3.2. Thermal conductivity of the powder bed Since effective heat conductivity plays an important role in the micro-sintering process. Meanwhile, because of the insufficiency of data on molten metals as well as the complication of sintering model, a piecewise model for thermal conductivity was proposed:
3.1. Powder density
keff
The fractional porosity u is a function of the local density of the porous material q and the density of the solid material qbulk [14]:
u¼
qbulk q qbulk
ð9Þ
8 ðTÞ; T 0 6 T 6 T s k > < powder ¼ kbulk ðT mTÞkTpowder ðT s Þ ðT T s Þ þ kpowder ðT s Þ; T s < T < T m m s > : kbulk ðTÞ; T P T m
ð10Þ
where Ts = 1000 °C denotes the initial sintering temperature representing that the sintering process only starts above the threshold temperature; Tm = 1537 °C is the melting point of the specimen;
ð8Þ
Fig. 1. The established three-dimensional FE model and schematic of (a) laser single-track, (b) laser multi-track.
Table 1 Summary of material properties of solid iron [23]. Temperature, T (°C) Thermal conductivity, k (W/m °C) Specific heat, C (J/Kg °C) Initial powder density, q0 (kg/m3) Initial powder porosity, u0 Initial sintering temperature, Ts (°C) Melting point, Tm (°C) Absorptivity of YAG laser energy, A Initial temperature of powder, T0 (°C) Heat transfer coefficient, h (W/m2 °C) Ambient air temperature, Ts (°C)
20 81.1 460 4325 0.45 1000 1537 0.64 20 20 20
250 72.1 480
500 63.5 530
750 50.3 675
1000 39.4 670
1500 29.6 660
1700 29.4 780
2500 31.6 820
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Fig. 2. Effective thermal conductivity keff versus temperature during heating stage.
kbulk is the thermal conductivity of the solid; kpowder is thermal conductivity of the iron powder and is equal to [23]:
kpowder ¼ kbulk ð1 uÞn
ð11Þ
where n is an empirical parameter which is taken as 4 in this simulation. Each element in the model is assumed to be initially powder material, so the effective thermal conductivity of the powder bed keff equals to kpowder. During the heating stage, when the temperature is above sintering temperature Ts and below the melting temperature Tm, keff coupling with sintering material transformation from powder phase to bulk phase increases linearly. Moreover, the effective thermal conductivity k takes as kbulk when the temperature exceeds Tm. Namely, the keff versus temperature during the heating stage follows curve ABCD shown in Fig. 2. Furthermore, at the end of heating stage, the elements heated by laser exposure result in bulk-like material, thus the initial powder state elements are irreversibly changed to the solid state elements with thermal conductivity of kbulk under this condition. This transformation is carried out by the function of changing the material number attribute in ANSYS. 4. Simulation results and discussion 4.1. Effect of laser beam diameter Fig. 3a shows the temperature distribution of the powder surface along X-axis at Y = 450 lm distance with different laser beam diameters during the laser single-track. The utilized diameter ranges from 30 lm to 60 lm with the same laser power of 4 W, scan speed of 200 mm/s and hatching space of 20 lm. From Fig. 3a, it can be found that the maximum temperature increases with the decrease of the laser beam diameter. However, the relationship is not proportional. The maximum temperatures of the specimen fabricated by D1 = 30 lm, D3 = 45 lm and D3 = 60 lm are 2278.1 °C, 1817.3 °C and 1596.6 °C, respectively. Furthermore, the curve slope is also different when different laser beam diameters are utilized, suggesting the temperature gradient changes with the laser beam diameter. In general, the smaller the laser beam diameter, the higher the temperature gradient. The maximum temperature gradient (76.6 °C/lm) during processing at D1 = 30 lm is almost two times larger than that at D3 = 60 lm (41.9 °C/lm). From Fig. 3a, it can also be found that the temperature does not always decrease with the increase of the laser beam diameter. In
Fig. 3. Temperature distribution with different laser beam diameter mapping on to path along (a) X-axis at Y = 450 lm (b) Y-axis at X = 450 lm (laser power: 4 W, scan speed: 200 mm/s, hatching space: 20 lm, scan track: 1).
the range of 300–468.75 lm of X-axis, the temperature decreases with the increase in diameter, but if in the other range from 476.25 lm to 600 lm of X-axis, the situation is different, the temperature increases as increasing the beam diameter. For the same position, e.g., X = 487.5 lm, the temperature at D3 = 60 lm (682.1 °C) is higher than that at D1 = 30 lm (391.7 °C). In addition, according to the melting point of sintering specimen, the center of the molten pool is observed slightly shift toward decreasing X-axis. This phenomenon can be ascribed to the thermal accumulation effect reasonably. Fig. 3b shows the effect of laser beam diameter on temperature distribution along Y-axis at X = 450 lm distance in the powder layer. Similar to Fig. 3a, the temperature increases with decrease in beam diameter from 427.5 lm to 472.5 lm of Y-axis, but in the other range (i.e., from 300 lm to 416.25 lm) the temperature increases as increasing the beam diameter. Moreover, the molten pool along Y-axis is symmetric concerning the center of laser beam area. This is the case because the elements outside the region irradiated by laser beam are still the powder phase. Therefore during the single-track scan, the thermal conductivities of both increasing and decreasing Y-axis from the center of laser beam area are almost the same. Consequently, no shift in the center of molten pool could be observed along the Y-axis. Fig. 4 shows that the molten pool length (along X-axis) and width (along Y-axis) versus laser beam diameter. The molten pool
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337
Fig. 4. The molten pool dimensions versus laser beam diameter.
length and width were extracted from isotherms that approximately represent the size of the molten pool. From Fig. 4, it can be found that the molten pool dimensions of LMS change with the laser beam diameter and are in size of tens of micrometers, which are much smaller than conventional SLS process. Both molten pool length and width decrease with the increase in laser beam diameter, but the decrease rate is not the same. Molten pool width at D1 = 30 lm is 41.3 lm and at D2 = 45 lm is 38 lm, but the molten pool width at D3 = 60 lm is only 19.9 lm. The same rule is for the molten pool length. This is because the input heat flux is inversely proportional to the squared laser beam diameter and hence the molten pool dimensions decrease steeply with increase in laser diameter. What’s more, for the same laser diameter (i.e., for D2 = 45 lm), the molten pool length (42.8 lm) is larger than molten pool width (37.5 lm). This phenomenon is because the laser beam is moving along X-axis and some elements on the laser path are repeatedly heated, therefore the temperature is higher at Xaxis than that at Y-axis if the distance (within the laser beam area) from the beam center is the same. 4.2. Effect of laser power Different to Fig. 3 with single-track, in order to investigate the influence of track to track on temperature distribution and the dimensions of the molten pool for different laser power values, the multi-track scan along X-axis was performed. Fig. 5a shows the temperature distribution along X-axis at Y = 450 lm distance in the powder bed due to irradiation of laser beam on the third track. Laser power is varying from 2 W to 4 W with 1 W increment and the other sintering parameters such as the scan speed, laser diameters and hatch spacing are held as constants. The nature of temperature distribution shows that there is an increase in temperature with increase in laser power of the entire X-axis. When laser power surpasses 4 W, the maximum temperature in powder bed is 2465.8 °C, which is close to the boiling point of iron. Under this condition, the high laser power may not be suitable for laser rapid prototyping because the boiled liquid splashes and final dense parts cannot be made. Whereas the top temperature attains only 1596.9 °C when laser power is decreased to 2 W, the inadequate energy input may give rise to poor sintering parts. Fig. 5b shows the effect of laser power on temperature distribution along Y-axis at X = 450 lm distance in the powder layer. It can be seen that the increase of laser power could induce high temperature of the specimen for the whole Y-axis. The maximum temperature gradient (53.6 °C/lm) during fabrication process at
Fig. 5. Temperature distribution for different laser power mapping on to path along (a) X-axis at Y = 450 lm (b) Y-axis at X = 450 lm (scan speed: 200 mm/s, beam diameter: 60 lm, hatching space: 20 lm, scan tracks: 3).
P1 = 4 W is larger than that at P3 = 2 W (47.0 °C/lm). The high thermal gradient along Y-axis may cause large thermal stresses in the powder layer. Figs. 5a and 5b show that in three curves, the molten pool is asymmetric with respect to the laser beam area. Namely, the center of the molten pool is not observed at the center of laser beam, but slightly shifted toward the side of increasing Y-axis and decreasing X-axis. The phenomenon has reported by former researchers [11,12] and can be attributed to the fact that the combined actions of the thermal accumulation effect and the thermal conductivity change due to the transition from powder to solid. On the one hand, comparing the location of the adjacent laser spot, about 86.4% elements are sited in the intersection of both two laser spot regions, so the elements lying on the laser scan path are getting heated frequently. Therefore, the center of laser beam along Xaxis is observed slightly toward the previous sintered zone (Fig. 5a). On the other hand, because during the fabrication of the third scan track, the powder-phase elements in previous track which has been laser heated are now solid-phase elements, they conduct heat quickly when the adjacent elements are under the laser exposure. Hence for the laser beam area along Y-axis, the temperature on the solid-phase side may be smaller than that on the powder-phase side (Fig. 5b). Fig. 6 shows that both molten pool length and width are proportional to the laser power. Molten pool length and width at P1 = 4 W are 70.9 lm and 53.2 lm, whereas at P3 = 2 W are 15.2 lm and
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Fig. 6. The molten pool dimensions versus laser power.
13.0 lm, respectively. This observation implies that the increase of laser power increases the heat flux intensity of the laser beam, which in turn leads to increase of the molten pool dimensions. Moreover, for the same laser power (i.e., for P2 = 3 W), the molten pool length (40.8 lm) is larger than molten pool width (36.5 lm). This phenomenon can also be ascribed to the fact that temperature gradient along X-axis is less than that along Y-axis for the molten pool region. Furthermore, as the laser power increases, the difference between the molten pool length and the molten pool width increases, indicating more significant thermal accumulation effect for the higher laser power.
when sample point temperature rise to the first peak temperature at V3 = 225 mm/s is less than that at V1 = 180 mm/s (2.26 ms). The finish time (4 ms) of former speed is shorter than that of latter one (5 ms). It informs us that there is an increase in response time when the sample point temperature rise to the maximum of each track with decrease in laser scan speed. Fig. 8a shows the effect of laser scan speed on temperature distribution along X-axis at Y = 450 lm distance in the powder layer. The simulated temperature distribution shows that there is an increase in temperature with decrease in laser scan speed for the whole X-axis. This phenomenon can be ascribed to the fact that if we increase laser scan speed, the interaction time of the input heat flux due to laser irradiation with powder layer decreases and therefore decreases in maximum temperature. In addition, the center of molten pool is observed slightly shifted toward the side of decreasing X-axis. The shift in the center of molten pool (toward increasing Y-axis side) is also observed in Fig. 8b, which shows the effect of laser scan speed on temperature distribution along Y-axis at X = 450 lm distance in the powder layer. It can be seen that the decrease of the scan speed could induce low temperature gradient of the specimen. The maximum temperature gradient (42.3 °C/lm) which derives from temperature change at V3 = 225 mm/s is somewhat larger than that at V1 = 180 mm/s (41.6 °C/lm).
4.3. Effect of laser scan speed Fig. 7 shows that the temperature change versus the laser exposure time with fixed laser power of 3 W, laser beam diameter of 30 lm, hatching spacing of 20 lm, but different laser scan speed of 180 mm/s, 200 mm/s and 225 mm/s, respectively. According to the graph, we can observe from the fluctuating temperature distribution that the maximum temperature of each track at the sampling point (face centered in the powder bed) increases when laser beam spot approaches and decreases when departures. However, the minimum temperature of each scan track monotonously increases with time elapse. What’s more, the time (1.85 ms)
Fig. 7. Temperature versus time at the face-centered sampling point with different laser scan speed (laser power: 3 W, laser beam diameter: 30 lm, hatching space: 20 lm, scan tracks: 5).
Fig. 8. Temperature distribution for different laser scan speed mapping on to path along (a) X-axis at Y = 450 lm (b) Y-axis at X = 450 lm (power: 3 W, laser beam diameter: 30 lm, scan tracks: 3).
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during the single-track, no shift is observed along the Y-axis. These phenomena happen because the thermal accumulation effect and the thermal conductivity change because of the transition from powder to solid. There is an increase in response time when the sample point temperature rises to the maximum of each track with the decrease in laser scan speed. The transition from powder to solid has not been taken into consideration in the previous laser micro-fabrication model; hence the present model involving the characteristics is more accurate. Acknowledgements
Fig. 9. The molten pool dimensions versus laser scan speed.
This work is supported by the National Natural Science Foundation of China (60878022), the fund of Key Laboratory of Chemical Laser (KLCL-HT-200907) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. References
Fig. 9 shows that both molten pool length and width decrease with the laser scan speed. Molten pool width at V1 = 180 mm/s is 39.6 lm whereas molten pool width at V2 = 180 mm/s is 36.5 lm. Again for different speed values (e.g., for V3 = 225 mm/ s), the molten pool length (38.1 lm) is always larger than molten pool width (33.8 lm) due to the temperature gradient along Xaxis is less comparing to that along Y-axis for the molten pool region. 5. Conclusions Although there are many numerical simulations for SLS/SLM, reports of simulation research for LMS on the temperature evolution are few. Furthermore, to the best of our knowledge, the finite element model for LMS has not been discussed previously. In this paper, a three-dimensional finite element model for LMS that encompasses the adoption of ANSYS lMKS system of units, the transition from powder to solid and the utilization of moving laser beam power with a Gaussian distribution in the single powder layer has been proposed. The effects of process parameters, such as laser beam diameter, laser power and laser scan speed, on the temperature distribution and molten pool length and width have been preliminarily investigated. Based on these numerical simulations, the following conclusions can be drawn. The temperature increases with the laser power and decreases with the scan speed monotonously. However, complex relationship can be found between the temperature and laser spot diameter during the laser single-track. The maximum temperature of powder bed decreases with the laser beam diameter, but far from the center of the laser beam area, the temperature increases with the laser beam diameter. In the model, the dimensions of molten pool in LMS process are several tens of micrometers which are about one order of magnitude smaller than that in SLS process. This phenomenon is due to the small laser beam diameter and molten pool dimensions of LMS in comparison with that of SLS. Both molten pool length and width decrease with the laser beam diameter and the laser scan speed, but increase with the laser power. Furthermore, the molten pool length is always larger than the molten pool width due to the temperature gradient along X-axis is less than that along Y-axis for the molten pool region. The center of molten pool is observed slightly toward decreasing X-axis and increasing Y-axis for the laser multi-track. However,
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