Finite Element Simulation of Selective Laser Melting process considering Optical Penetration Depth of laser in powder bed

    Finite element simulation of selective laser melting process considering optical penetration depth of laser in powder bed Ali Foroozmehr, Mohsen Badrossamay, Ehsan Foroozmehr, Sa’id Golabi PII: DOI: Reference:

S0264-1275(15)30580-3 doi: 10.1016/j.matdes.2015.10.002 JMADE 741

To appear in: Received date: Revised date: Accepted date:

29 July 2015 30 September 2015 1 October 2015

Please cite this article as: Ali Foroozmehr, Mohsen Badrossamay, Ehsan Foroozmehr, Sa’id Golabi, Finite element simulation of selective laser melting process considering optical penetration depth of laser in powder bed, (2015), doi: 10.1016/j.matdes.2015.10.002

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Finite Element Simulation of Selective Laser Melting Process Considering Optical Penetration Depth of Laser in Powder Bed

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Ali Foroozmehra, Mohsen Badrossamayb, Ehsan Foroozmehr1b, Sa’id Golabia a

Mechanical Engineering Department, Kashan University, Iran Mechanical Engineering Department, Isfahan University of Technology, Isfahan, Iran

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b

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Abstract

A three dimensional finite element model (FEM) is introduced in this work in order to simulate

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the melt pool size during the Selective Laser Melting (SLM) process. The model adopts the Optical Penetration Depth (OPD) of laser beam into the powder bed and its dependency on the

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powder size in definition of the heat source. The model is used to simulate laser melting of a single layer of stainless steel 316L on a thick powder bed. The results of the model for the melt pool depth are validated with the experimental results. The model is then used to predict the

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effect of different scanning speeds on the melt pool depth, width, and length. The results showed

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that the melt pool size varies from the beginning of a track to its end and from the first track to the next. The melt pool size, however, reaches a stable condition after a few tracks. This concept

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was used to simplify the process modeling in which reduces the computational costs. Keywords: Selective Laser Melting, Finite Element Simulation, Optical Penetration Depth, Melt pool size, AISI 316L

1. Introduction

Additive Manufacturing (AM) is referred to technologies that fabricate directly threedimensional objects in layer-by-layer fashion. Selective Laser Melting (SLM), as one of the powder bed fusion (PBF) AM processes, enables production of complex metallic parts from a CAD model. A schematic of a typical SLM process is depicted in Fig. 1. In this process, in order to deposit powder layers with predefined thickness, an amount of powder comes up to the build table and a roller or blade spreads powder at the build platform. Full dense parts created by scanning a high intensity laser beam in a special pattern and local consolidation of the powder bed in successive layers. A neutral gas flow, usually nitrogen or argon gas, protects molten pool *

Corresponding Author; Tel: (+98) 31 3391 5238, Fax: (+98) 31 3391 2628, E-mail address: [email protected] 1

ACCEPTED MANUSCRIPT from oxidation. Nowadays, the flexibility of SLM process in manufacturing complex parts with high quality has led to an increase in its applications in many industries such as aerospace, medical, automotive and even jewelry. Nonetheless, this process still faces challenges including

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relative density, dimensional accuracy, surface quality, and thermal residual stresses. Moving a large energy density of laser beam on powder bed causes a high thermal gradient in the part,

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which may results in residual stress and thermal cracking in the part [1].

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Normally for fabrication of each component from the desired material, choosing a set of appropriate process parameters such as laser power, scan speed, hatch distance, and scanning

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pattern is necessary to produce a part with acceptable dimensional accuracy and density [2]. On the other hand, geometry of the components has a decisive role in dimensional accuracy. In other

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words, because of different heat transfer conditions in each layer of the part as well as negligibly of heat transfer through the powder bed [3], geometry of the part affects the melt pool size significantly [2]. In addition, the melt pool size may increase considerably in some regions of

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each layer such as, the first track or U-turns in zigzag pattern [4]. Accordingly predicting the

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melt pool size is necessary to improve dimensional accuracy of SLM parts.

Figure 1: Selective Laser Melting (SLM) process overview [5]

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ACCEPTED MANUSCRIPT In recent years, numerous numerical models have been used considerably in predicting the effect of different process parameters on the temperature and stress distribution as well as the melt pool size of SLM. For instance, Matsumoto et al., proposed a two dimensional finite element method

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for predicting temperature and stress distribution within a single layer [6]. Yin et al. have used element birth and death method to obtain the temperature distribution in a single layer [7].

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There are, however, many challenges in modeling a complex process such as SLM. The laser

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beam with uneven distribution of energy strikes a surface covered with metal particles with different shape and size. There are inevitable gaps among particles that let the laser beam

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penetrates through the powder bed. Consequently, the absorption of the laser beam by the particles as well as the multiple reflections from the surface of the particles causes the energy of

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the beam to be attenuated within the powder bed. The powder shape and size, of course, has dramatic effect on the actual absorption of the laser energy by the powder and the amount of penetration depth. Considering all these features makes the simulation very tough or even

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impossible. Therefore, simplifying assumptions have been applied in many SLM modeling

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efforts. Ma et al. and Dai et al. used constant temperature to simulate the laser spot in order to analyze the temperature and stress fields [8, 9]. Xiao et al. and Antony et al. used a constant heat

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flux to analyze the melting of the powder bed [10, 11]. An average uniform heat generation was used by Contuzzi et al. [12] and Song et al. [13] to represent the heat source. More accurate results were reported by Hussein et al. that supposed a Gaussian volumetric heat generation to simulate the process in order to obtain the melt pool size [14]. Ilin et al. used Goldak heat source in a 2D analysis to predict the melt pool size and the temperature distribution [15]. The effect of powder size and distribution has been neglected in the mentioned references. A number of experimental based investigations have studied the effect of powder size and scanning speed on the actual laser absorption by the powder. A ray tracing algorithm has been developed to describe laser power dissipation in depth of the powder in laser micro sintering process [16]. Badrossamay et al. developed a model to predict the absorption coefficient of the powder by considering the effect of scanning speed on the absorption coefficient of three types of steel powder [17]. Energy distribution and thermal and optical penetration of the laser beam in nickel and titanium powder bed were evaluated by Fischer et al. [18].

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ACCEPTED MANUSCRIPT In this paper, a 3D non-linear transient finite element model is presented to predict the temperature distribution and melt pool dimensions in a multi-tracks pattern on powder substrate. In order to improve the accuracy of the model, a practical method is introduced to estimate the

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optical penetration depth (OPD) into the powder bed. The model is compared with the experimental results for validation. In addition, the effect of three different scanning speeds on

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the melt pool dimensions in various regions of a layer is discussed.

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2. Finite Element Modelling

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ANSYS® was used to simulate the heat transfer within the metal powder during the SLM process. Fig. 2 shows geometry of the model, mesh structure, and scanning strategy. A

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volumetric heat generation with uniform distribution was introduced to represent the laser spot (the top view can be seen in the detailed view of Fig. 2). The dimensions of the square region were chosen so that the area of the laser spot in the model is the same as the one with circular

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spot. A subroutine was written based on APDL (ANSYS parametric design language) to simulate

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the moving laser spot over the surface. The continuous movement of the laser was simplified as incremental movement of the heat source at each time-step. In each time-step, a certain number

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of elements were selected with heat generation boundary condition. Once the solution of each time-step was done, the nodes that has exceeded the melting point were selected, and then the material properties of the elements attached to the node was switched from “powder” to “solid.” The criterion for this change was the solidus temperature of the material. The process continued until the whole length of the track was treated. Then, the spot was moved toward Y direction and a new track began.

The incremental nature of the simulation process can affect the melt pool depth prediction. In practice, once the laser hits the powder bed, a thin layer of molten material is formed. The molten material then, transfers the heat to the beneath layer and causes deeper molten pool. In the simulation process, if the solution is considered only for one time-step, the calculated molten pool depth is less than the actual one due to the low conductivity of the powder. To overcome this problem, each time-step is divided into some smaller sub-steps in which the change in the material properties from “powder” to “solid” occurs. Primary investigations showed that two time increments (

in Eq. 1) would be accurate enough for the prediction of the melt pool

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ACCEPTED MANUSCRIPT depth. Eq. 1 shows the relation between the time of each step, number of step divisions (n), time) and the scanning speed (V).

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increment, the amount of movement along X direction (

has two region (Fig. 2): a region where

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The 3D meshed part by dimensions of

(1)

laser scans the powder bed with dimension of

(the scan region) containing

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element size equal to 66 micron from SOLID70, and the region that represents the powder substrate filled with coarser free mesh from the same element type. The layer is scanned with

).

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consists of 64 elements (

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four tracks and raster pattern (Fig. 2). The process parameters are listed in Table 1. The laser spot

Figure 2: a) 3D Finite Element Model and scan strategy (H s is the Hatch Space), b) the modeled laser spot

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ACCEPTED MANUSCRIPT 2.1.Thermal modeling The thermal equilibrium equation for three-dimensional heat transfer in a material with isotropic

Where,

(2)

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thermal properties can be described by:

is material density (kg/m3); c is specific heat capacity (J/kg K); T is temperature (K); t

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is interaction time of powder and heat source (s); Q(x,y,z,t) is heat generation per unit volume (W/m3) and k is thermal conductivity (W/m K).

) throughout the powder bed considered as the

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Uniform temperature distribution of 293 K (20

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initial condition:

(3)

Because of the thick powder bed and low conductivity of the powder, and in order to decrease

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described by:

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the solution time, the base plate was not modeled. The top surface boundary condition is

(4)

Where, h is convective heat transfer coefficient (W/m2K) supposed to be 10 for the top surface as a natural convection [14], and

is surface temperature (K). As Refs. [16, 18] suggested,

radiation heat transfer is ignored in this model. Vaporization and melt pool phenomenon such as Marangoni convection is also ignored in this model. Table 1: FEM Parameters

Material and Process Parameters Laser Power, P (W) Spot Diameter, D (mm) Layer Thickness, T (mm) Scan Speed, V mm/s Track Length (mm) Overlap Material Powder size (μm) [17] Absorption Rate of powder, A [17] Latent Heat of Fusion (KJ/Kg) [20]

Values 110 0.6 1 80, 100, 150 4.5 50% AISI 316L -45 0.52 300

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2.2.AISI 316L material properties As mentioned before, in this model two phases of powder and solid considered. Thermal material

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properties in solid phase were used from Ref. [20]. The conductivity of powder is supposed to be 1% of the solid thermal conductivity in this model based on the results reported by Refs. [4, 21]

(5)

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(Eq. 5).

As the powder bed is considered to be a mixture of solid (AISI 316L particles) and gas (air)

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phases, the density of loose powder could be written as [22]:

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is the ratio of the cross-sectional area occupied by the gas to the total cross-sectional

area of the medium;

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Where,

(6)

is the density of gas phase and

is the density of solid phase.

for

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tapped powder bed is assumed to be 0.4 [23]. The volumetric heat capacity of powder bed in terms of two phases, solid and gas, could be written as [22]:

Where,

and

and

(7)

(J/kg K) are heat capacity of powder bed, gas phase (air) and solid

phase (316L), respectively. According to Eq. (7), heat capacity of metal powder is almost equal to heat capacity of solid phase. Experiments also confirm this result [24]. The temperature dependent material properties of the powder and solid are depicted in Fig. 3, according to Eq. (3) and (4). The abrupt change in material properties of powder and solid at melting temperature shows the transition of powder to liquid state.

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Figure 3: Thermal Material Properties of AISI 316L powder and solid: a) Conductivity, b) Density; c) Specific heat capacity for powder and solid phase

2.3.Heat source modeling When the Gaussian laser beam is exposed to the powder bed, it experiences multiple reflections through the powder layers. Such phenomenon causes drastic deviation from the Gaussian distribution of energy beneath the top surface. Based on the reports of Ref. [18], a uniform energy distribution could be assumed for the heat source. On the other hand, the porous powder 8

ACCEPTED MANUSCRIPT medium causes a penetration depth of the energy into the powder layers [18]. Fig. 4 shows a scheme of laser beam scattering through the powder bed. Estimating correct value for the OPD is very important for the numerical simulation of the process. Generally, scattering of the laser

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beam in powder bed may be occurred in four ways during interaction of laser beam and powder bed: transmission, forward scattering, backward scattering, and entirely absorption of the laser

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beam [16]. All these phenomena take part during the melting process. The probability of

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occurring each of these phenomena depends on powder size, powder bed density, and material

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properties [16].

Figure 4: interaction of Laser and powder bed in SLM process [1]

The OPD is defined as the depth where the intensity of the laser energy reduces to 1/e ( 37%) of the intensity of the absorbed laser beam at the powder bed surface [25]. It has been shown that for materials with similar absorption value the OPD of powder bed is highly affected by granulometric properties such as powder size and shape [18]. For instance, according to experimental investigations of Ref. [18], the OPD in spherical Ni powder with size of -20 measured to be 20

, while it is 200

for powder size of 50-75

is

. In addition, the

absorption of Ni and Fe is in a same range [26]. Therefore, for the current spherical powder of AISI 316L with particle size of -45 mentioned results that is about 170

, the OPD can be estimated by interpolating the

.

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ACCEPTED MANUSCRIPT The power intensity decreases as the beam penetrates through the powder bed. In order to consider such effect, and at the same time for simplifying the model, a uniform heat generation is applied down to an effective depth of penetration, which is a fraction of the considered OPD.

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The ratio of the effective penetration depth to the OPD is defined by . The effective penetration depth that is determined by trial and error and comparison with average thickness of the

to be

. Therefore, the heat generation amount used in the

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that leads

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experimental sample in scan speed of 100 mm/s (the model calibration step) is defined to be

model is described by Eq. (8):

(8)

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,

Where, A is absorption coefficient, P is laser power (W), V is the volume exposed by laser beam is correction factor for assuming uniform heat generation.

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(m3), S is area of laser spot (m2), and

It is clear that the absorption coefficient depends on the material properties and the laser beam

exposed to a CO2 laser was found to be 0.52. In order to determine the value of

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size of

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wavelength [27]. Based on the earlier study in [17], the absorption coefficient for 316L powder

, a calibration procedure is defined. In the next section, this procedure and the method of its

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verification are explained in details.

2.4.Model calibration and validation The FE model were calibrated and the results were verified using the earlier conducted experimental results reported in [24]. AISI 316L stainless steel gas-atomized powder with particle diameter of -45 m, supplied by Osprey Metals Ltd, UK, was used to prepare powder beds of area 120mm x 150mm and 5 mm depth. Square areas 15mm x 15mm were melted in the beds’ surface by a raster-scanning CO2 laser, focused to a beam diameter of 0.6 mm, with the experimental home-made SLM apparatus under an argon atmosphere. The SLM machine has been described in Refs. [27, 28]. Laser power of 110 W was used, with scan speeds from 0.5 to 300 mm/s. The raster scans were parallel to a side of the square area, with scan spacing of 0.30 mm (half of the beam diameter that means 50% overlap). The length and number of the modeled tracks should ideally be the same as that of the fabricated specimens. However, such model imposes high computational costs. As a result, a series of investigations have been carried out in order to scale down the size of modeled tracks. Based on 10

ACCEPTED MANUSCRIPT the cross section images of the produced tracks, after the fourth track, the layer thickness does not show significant changes. In addition, it has been found that the predicted temperature at the beginning of the tracks stays almost constant after the fourth track (results are presented in the

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next section). Therefore, it seems that modeling four tracks may provide adequate information

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about the melt pool size and temperature distribution.

In order to investigate the influence of decreased modeled track length on the results, two models

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with different boundary conditions were compared. Both models assume a track length of 4.5 mm (10.5 mm shorter than the actual experiments), and scanning speed of 100 mm/s. In order to

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consider the temperature history effects of the trimmed section, two extreme conditions were compared. In the first case, the laser stays on for 0.105 sec. at the end of the track (equivalent

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time needed the laser to scan the 10.5 mm). Right after that, the laser heat source jumps to the next track. In the second case, the laser goes off for 0.105 sec. at the end of the track (similar

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equivalent time). Then it jumps to the next track. The temperature history at the beginning and

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the middle of the track are compared for these two cases. The results show that the temperature has less than 2% difference for the two cases. This observation implies that due to the low

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conductivity of the powder and very small cross section of the melted material, the heat from processing the 10.5 mm of the end of the track has almost no effect on the temperature of the first 4.5 mm of the track. Therefore, it was concluded that a model with 4.5 mm could be accurate enough to model the full-scale experiment. The sample made at 100 mm/s scanning speed is shown in Fig. 5-b. As can be seen, it is relatively rough and the tracks can be distinguished. In order to measure the thickness of the produced layer accurately, the cross section of the sample was analyzed. Fig. 5-a shows a portion of the cross section. Over 50 data was collected from the thickness of the sample throughout the section. The average was considered as the “experiment layer thickness”. In order to calibrate the model, the melt pool depth in the model was compared with the measured thickness. A view of the predicted melt pool depth can be seen in Fig. 5-c. The average of the melt pool depth at the end of tracks in the FE model was considered as the “model layer thickness”. As can be seen in Table 2, less than 2% is the deviation of the model from the experiment. It is worth noting that this result is achieved by considering

to be 0.706. This value is considered the same for other

scanning speeds. 11

ACCEPTED MANUSCRIPT Table 2: Comparison of experimental and FE model results in scan speed of 100 mm/s

Average layer thickness of the experimental sample (μm) Average molten pool depth of the FE model (μm) Error

230.6 234.3 1.6%

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The validation of the model was performed by comparing the modeling results of 80 and 150 mm/s with the experiments. Measurements showed the layer thickness of the experiments was

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between 325 and 385 μm for scan speed of 80 mm/s, and between 171 and 231 μm for 150 mm/s. Table 3 shows the comparison of the average thickness of the experiments and the model

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for two speeds of 80 and 150 mm/s.

80 mm/s 355 306.3 13.7 %

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Scan Speed Experiment (μm) FE model (μm) Error

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Table 3: Comparison between average values of the samples layer thickness and the model melt pool depth, in scan speeds of 80 and 150 mm/s

150 mm/s 200.4 178.5 10.8 %

As can be seen, the model has a noticeable, yet acceptable, error from the experiments. Further

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investigations showed that if in calculation of the layer thickness in the FE model the first track

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is ignored, the error is reduced to 3.9 and 1.2% for 80 and 150 mm/s, respectively. In other words, the melt pool depth prediction of the first track has the maximum deviation from the

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experiment. To better understanding the reason of such phenomenon, one should consider the fact that during melting the first track, powder presents on both sides of the track, while for other tracks, one side is powder and the other side is melted material. The convective flows of the molten pool, which is ignored in the current FE model, causes powder particles to be grabbed into the molten pool. The first track behaves differently because powder particles are on both sides of the track, and therefore, deeper and wider melt pool is generated. More details about melt pool size would be discussed in the next section.

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Figure 5: Calculation of layer thickness in experiment sample and model results for depth in velocity of 100 mm/s: A) a part of sample cross section; B) overview of back surface of the sample layer and the section location; C) Temperature distribution in cross section at end of the 4th track

3. Results and discussion

3.1.Temperature distribution As a result of applying laser power to the powder bed, a very high temperature gradient occurs. Fig. 6 shows the temperature distribution at the end of the forth track for three cases of 80, 100, 150 mm/s scanning speed. The color code is set so that the temperature higher than the melting point is in gray color. Therefore, the difference in the melting zone can be distinguished at the end of the forth track. The maximum temperatures at the end of the process are predicted to be 2170, 2123, and 1902 K for scan speeds of 80, 100, and 150 mm/s, respectively. Increasing the scanning speed reduces the maximum temperatures. This temperature is well above the melting temperature. Similar observation had been reported in former studies in which the temperature distribution and densification process of SLM was modeled [14,30]. Similar to SLM process, the temperature beneath the heat source can go over the melting point as reported for electron beam 13

ACCEPTED MANUSCRIPT melting (EBM) [31] and laser metal powder deposition (LMPD) [32]. The melt pool size, also, gets smaller as the scanning speed increases. This effect is illustrated in Fig. 6 by setting the color code at 1648 K. The width and length of the melt pool are analyzed in more details in the

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next section.

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Fig. 7 shows the temperature vs. time for the middle point at the beginning of each track during the process in scan speed of 150 mm/s. Each point experiences a peak temperature of over

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1700 K. Because of the 50% overlap between each two adjacent tracks, after the first two tracks, during scanning of each track, temperature of start point of the previous track exceeds melt

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temperature. Short time of the scanning process and low conductivity of powder bed cause the temperature of about 1400 K at the end of the process. One of the important points shown in Fig.

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7 is that after the fourth track almost no deference observed in maximum reached temperatures. According to this diagram, maximum temperature occurred at the start of the first track. This is

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due to the fact that the first track has the minimum heat sink [4].

Figure 6: Temperature distribution at end of the process in: a) velocity of 80 mm/s; b) velocity of 100 mm/s; c) and velocity of 150 mm/s.

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Figure 7: Heating and cooling cycle during the scanning process of six tracks in scan speed of 150 mm/s; (1)-(6) Start of first to sixth track

3.2.Melt pool size

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Fig. 8 shows the depth, width, and length of molten pool at start, middle and end of each track in

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various scan speeds (Fig. 8-a). As indicated in Fig. 8-b, the depth of the melt pool varies depending on the location on each track and the track number, because of different heat transfer

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conditions. Considering the lowest scanning speed, the melt pool depth increases from location 1 to 2 due to heat accumulation. But, from 2 to 3 it reaches a steady state condition. The beginning of the second track shows an increase in the depth (location 4) that continues to a higher value at location 5. The heating effect of the first track causes this increase in the melt pool depth. Similar to the first track, the middle and the end of the second track also show almost constant values. The beginning of the third track, however, experiences a drop in the depth. This can be explained by the heat sink effect of the formed tracks. The mass of the first two tracks is large enough to extract the heat effectively and cause a reduction in the melt pool depth at location 7. By moving the laser forward on the third track, the melt pool gets deeper. Similar observation presents for the fourth track. The heat sink effect for location 10 makes the depth at this point to be even a little smaller than 7. The rest of the fourth track shows similar depth as the third one. The energy balance between the heat input and the heat sink determines the dimensions of the melt pool. The moving nature of the heat source makes the temperature history to play an important role in the properties of the melt pool. Well understanding the energy balance in the process helps finding proper parameters for making sound parts. Therefore, the depth, width, and 15

ACCEPTED MANUSCRIPT length for each track and three locations of the beginning, middle, and end of the track is

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discussed.

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Figure 8: Melt pool size in different points of powder bed and in various scan speeds; a) Position of the points on powder bed; b) Melt pool depth in various scan speeds and positions; c) Melt pool width in various scan speeds and positions; d) Melt pool length in various scan speeds and positions

The melt pool width shows a similar trend as the melt pool depth (Fig. 8-c). By increasing the scanning speed, the width of the melt pool decreases. The minimum width is located at the beginning of each track (locations 1, 4, 7, and 10). The middle and the end of each track show larger width than the beginning. The width of the track increases for about 200 μm from the first track to the second one, and about 100 μm from second to the third, and about 50 μm from third to the fourth. It can be concluded that the width is reached to its steady state condition at the fourth or fifth track. The length of the melt pool on each track is shown in Fig. 8-d. The beginning of every track has a small length. As the beam progresses, the length increases in all speeds. The length of the melt pool from the first track up to track three shows an increasing trend. The third and fourth track, however, behave similarly. As indicated in analysis of the depth, width, and length of the melt pool, the fourth track follows the properties of the third track. Therefore, the assumption of considering only four tracks out of 17

ACCEPTED MANUSCRIPT 25 in order to reduce the computational costs, and yet obtaining an accurate model is confirmed. In spite of considering the thermal effects of the heat input on the powder bed, the fluid flow in the melt pool has been neglected. Such simplification causes some deviations from the

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experiments. As indicated by Ref. [33], instabilities in the melt pool due to surface tension gradient would cause unevenness of the surface. In higher velocities, such effects are more sever

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that may even lead to discontinuity and making individual droplets (balling effect).

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Based on the presented results, the melt pool depth and width varies over time during the process. In order to increase the accuracy of the part and minimizing the variations of the melt

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pool dimensions, online monitoring and controlling the process have been adopted. Mercelis reported two methods of using camera and photo diode to monitor the melt pool size [21]. While

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the mentioned methods capture the data from the top surface of the melt pool, the main goal is to control the depth of the melt pool (layer thickness). The modeling results imply that the rate of change in the width of the melt pool by altering the speed is not the same as that of the depth.

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4. Conclusions

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to determine the proper relationship between process parameters and the depth of the melt pool.

In this paper, a finite element model of the SLM process was developed. The optical penetration depth of the laser beam in powder bed was considered in defining the heat source. The model was used to predict the melt pool dimensions of a single layer on powder bed of material stainless steel 316L. Experimental data were used to calibrate the effective optical penetration depth. The calibrated model, then, was validated by further experiments. The modeling results indicated good agreement with experiments. Temperature distribution and depth, width, and length of the melt pool were evaluated in each track and the results were analyzed for scan speeds of 80, 100, and 150 mm/s. The results showed that the melt pool dimensions reached a steady condition after the third track. In addition, the melt pool depth of each track stayed almost constant after about 2 mm from the beginning of the track. More experimental investigations, are needed to see the effects of process parameters such as power and scan speed on OPD and absorption rate simultaneously and for various powder materials.

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ACCEPTED MANUSCRIPT Acknowledgments The experimentation of this work had been carried out at University of Leeds, UK, during PhD

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studying of one of authors (MB) who is grateful to the support of Prof. TH.C. Childs as his supervisor, as well as the Iranian Ministry of Research, Science and Education for a scholarship.

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ACCEPTED MANUSCRIPT [11] Antony K, Arivazhagan N, Senthilkumaran K. Numerical and experimental investigations on laser melting of stainless steel 316L metal powders. J Manuf Process 2014;16:345–55. doi:10.1016/j.jmapro.2014.04.001.

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[14] Hussein A, Hao L, Yan C, Everson R. Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Mater Des 2013;52:638–47. doi:10.1016/j.matdes.2013.05.070.

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ACCEPTED MANUSCRIPT [23] Spierings AB, Herres N, Levy G. Influence of the particle size distribution on surface quality and mechanical properties in AM steel parts. Rapid Prototyp J 2011;17:195–202. doi:10.1108/13552541111124770.

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Graphical abstract

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Highlights The developed Finite Element model is able to predict the melt pool size accurately in the

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SLM process.

The rate of change in the width of the melt pool by altering the speed is not the same as

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that of the depth.

The melt pool dimensions reached a steady condition after the third track.

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The melt pool depth of each track stayed almost constant after about 2 mm from the

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beginning of the track.

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