Finite element analysis of thermal behavior in maraging steel during SLM process

Journal Pre-proof Finite Element analysis of thermal behavior in maraging steel during SLM process Mobin Majeed, Murat Vural, Sufian Raja, M. Bilal Naim Shaikh

PII:

S0030-4026(19)32027-3

DOI:

https://doi.org/10.1016/j.ijleo.2019.164128

Reference:

IJLEO 164128

To appear in:

Optik

Received Date:

25 November 2019

Accepted Date:

23 December 2019

Please cite this article as: Majeed M, Vural M, Raja S, Bilal Naim Shaikh M, Finite Element analysis of thermal behavior in maraging steel during SLM process, Optik (2019), doi: https://doi.org/10.1016/j.ijleo.2019.164128

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Finite Element analysis of thermal behavior in maraging steel during SLM process Mobin Majeeda, Murat Vuralb,Sufian Rajac, M. Bilal Naim Shaikhd, a,b

Faculty of Mechanical Engineering, Istanbul Technical University, Gumuşsuyu,Istanbul, Turkey Departmnet of Mechanical Engineering, University of Malaya, Kuala Lumpur, Malaysia d Departmnet of Mechanical Engineering, Aligarh Muslim University, Aligarh, India c

*

Corresponding Author: Mobin Majeed Email addresses: [email protected] (M. Majeed),

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Highlights  

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Temperature and melt pool depth, 2 important parameters in selective laser melting are evaluated. Temperature variation of a single node with respect to the time is studied and plotted. Same is done with melt pool depth. Variation of thermal behavior with respect to processing parameters is studied and plotted. ANSYS simulation study is used to evaluate the melt pool behavior with respect to the laser movement. Behavior in variation in temperature and melt pool depth in 3 perpendicular directions is measured. Melt pool depth and maximum nodal temperature increases with layer addition. The simulated model is validated with experimental results. And the errors are in the acceptable ranges.

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Abstract

Maraging steel founds in a wide application in automotive and aerospace industries owing to its high strength, low weight, and high toughness. In this study, an effort has been made to successfully predict the temperature and melt pool characteristics of Maraging steel during laser scanning of the powder bed as observed in the additive manufacturing process. In additive manufacturing of metals, cooling

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and solidification rates are very high, leaving no time for observations and analysis. The temperature distribution governs the thermal behavior, grain size, morphology, and orientation. Variation of temperature and melt pool dimension is investigated with the speed and power of the laser, which is crucial to achieving the targeted properties. The rise in temperature and melt pool dimensions with subsequent layers is evident in the simulation results and agrees with the experimental work carried out for confirmation. Temperaturedependent properties for both powder and bulk material are used to closely model the analysis in ANSYS APDL to depict the real

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scenario.

Keywords : Selective laser melting, Finite element analysis, maraging steel, melt pool, temperature.

1. Introduction

Additive manufacturing (AM) has gained popularity in the past few decades in the manufacturing sector primarily due to its flexibility in the design of complex structures that are otherwise either impossible to achieve or expensive with conventional methods[1]. The AM process has emerged from the original conception of prototype modeling to an all-inclusive production of end-products and it is widely expanding in the commercial sector[2]. A blade spreader deposits the metal powders of pre-define thickness on a building platform which is then subsequently scanned by a high-powered laser source to fuse the powder particles within a layer and eventually consolidate the subsequently added layers as per

the 3D geometry realized through a pre-determined computer model[3]. The whole process is conducted under a protective environment to avoid oxidation and prevent the ingression of impurities[4][5]. Moreover, in order to attain unblemished surface and bulk mechanical and microstructural features, and optimization of the intrinsic processing parameters is essential[6]. Therefore, several empirical trials are formulated and implemented to attain the desired features which are not only expensive but time-consuming since a single production takes several hours from the preparation to the final evaluation of the finished parts. There are various variables (laser power, scanning speed, scan distance, layer thickness, beam size, scan pattern, etc.) needed to be regulated that simply expands the working window to exceedingly high numbers. It is, therefore, essential to address the parameters optimization problems, in turn, through numerical methods that are not only inexpensive but close enough to experimental findings [7][8]. The scientific society is emphasizing heavily on numerical analysis for economical solutions and this study is an attempt to fill the missing gaps related to the melt pool behavior of laser scanning of powder particles in selective laser melting (SLM) built maraging steels case which is yet to be added in the scientific literature. So far, several attempts have been made for other materials to evaluate the AM process closely which is otherwise difficult even with

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sophisticated cameras. Some of the published reports include the measurements of the melt pool and temperature assessment and evaluation of thermal parameters such as cooling rate, thermal gradient, solidification rate for single laser track, multi-laser-track as well

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as multi-layer cases[9][10].

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2. Modeling 2.1 Thermal modeling

The final part properties are dependent on the processing parameters. Poor optimization of processing parameters either having

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excessively high energy input in the form of high laser power and slow scanning speed or poor energy input through low laser power and high scanning speed results in defects such as balling, partial fusion of powder particles to the geometry, excessive melting of powder as well as large porosity volume, metal oxidation forming tenacious layer on the surface of the processed layers[11][11][12].

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The other factors in the form of hatching, the layer thickness is also important that can alter the incident energy density but those are not undertaken in this study. At most, laser power and scanning speeds are the two most important and critical parameters that are excessively adjusted in the production of SLM parts. The incident energy defined as energy input per unit volume (VED) can be expressed

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mathematically as follows[13];

𝑉𝐸𝐷 =

𝑃 𝐽 [ ] 𝑣𝜎𝑡 𝑚𝑚3

Here 𝑃 is laser power in watts, 𝑣 represents scan speed of the laser, 𝑡 stands for layer thickness in mm, 𝜎 is spot size of the laser.

2.2 Heat source

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The laser scanning of the powder bed represents a Gaussian heat source when modeled in three-dimension. The center of the source is at high temperature representing the maximum energy input which reduces towards the source edge. This can be expressed in the form of the equation as follows[14]. 𝑞=

2Ꜫ𝑃 𝜋𝑅 2 𝑆

𝑒𝑥𝑝 (

2((𝑦−𝑦0 −𝑉𝑡)2 +(𝑥−𝑥0 )2 ) 𝑅2

) 𝑒𝑥𝑝 (−

|𝑧−𝑧0 | 𝑆

)

(1)

Here, 𝑥, 𝑦, 𝑧 are the coordinate system directions with respect to the origin. 𝑉 is scan speed of laser in 𝑦 direction and 𝑧 is built direction. 𝑅 = 100µ𝑚 is the spot radius in this case. Ꜫ is absorptivity of maraging steel. 𝑆 is the penetration depth of the laser. The equation of temperature distribution in 𝑥, 𝑦, 𝑧 in a 3-dimensional model when a heat 𝑞 is added to it can be expressed as follows[15]

𝜌𝑐

𝜕𝑇 𝜕𝑡

=𝑞+

𝜕 𝜕𝑥

(𝑘

𝜕𝑇 𝜕𝑥

)+

𝜕 𝜕𝑦

(𝑘

𝜕𝑇 𝜕𝑦

)+

𝜕 𝜕𝑧

(𝑘

𝜕𝑇 𝜕𝑧

)

(2)

Here 𝜌 is the density of maraging steel in kg/m3, 𝑐 is specific heat of material in J/ kgK. T is a temperature at any location within the model. K is thermal conductivity and t is the time of laser interacted with powder. However, the heat supplied by the laser is not fully absorbed by the powders as there are losses due to convection and radiation at the boundary of the model. Considering the losses, heat supplied and temperature distribution, the equation can be re-written as[16] 𝜕𝑇

𝑘 ( ) = 𝑞 − ℎ𝑐 (𝑇 − 𝑇𝑂 ) − 𝜎Ꜫ(𝑇 4 − 𝑇𝑂4 ) 𝜕𝜂

(3) Where T is the temperature at any location at time t. q is heat supplied by laser to the powder and k is thermal conductivity of maraging

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steel. ℎ𝑐 is convective heat coefficient, 𝜎 is Stefan Boltzmann constant and Ꜫ is emissivity at the surface of bulk. 𝑇0 = 303 𝐾

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𝑇0 is ambient temperature.

The building platform is a mixture of powder and solidified metal. The thermal conductivity of loosely spaced powder in terms of solid

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is given by 𝑘𝑝 = 𝑘𝑠 (1 − Ø)

(4)

powder (density𝜌𝑝 ) and solidified metal (density𝜌𝑠 )[15].

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Where Ø is the porosity of loosely spaced powder and can be obtained from the following equation. Considering the proportion of

2.3 Finite element model

𝜌𝑠 −𝜌𝑝

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Ø=

𝜌𝑠

(5)

In the current study, a prismatic model of size 1500mm x 400 mm x 350 mm is chosen with a mesh size of 5µm as demonstrated in

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Figure 1. The whole model is divided into two sections. The lower portion is assigned the properties of solid geometry while the upper part is designated the properties of powder particles in order to replicate the real environment. The symmetry of the model along the Xaxis is utilized in order to reduce the size of the model and computational time. The study is conducted using 4 layers and element birth and death technique is used. A dwell time of 1 second is practiced between the deposition of the consecutive layers, thereby, allowing

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some cooling between the successive layers.

Figure 1: Meshed model of maraging steel for analysis in ANSYS APDL.

3. Results and discussions 3.1 Experimental Procedure For the validation of analysis, the maraging steel samples were produced on M 290, EOS GmbH makes SLM machine equipped with Yttrium fiber laser source. The spot size of the laser during the process is fixed at 100µm. Fine powder particles of maraging steel are spread by recoater on the building platform inside the manufacturing airtight chamber. In order to avoid the oxidation during the melting, the chamber is supplied with nitrogen gas. The laser then selectively melts and consolidates the powder along the track. The gap between the successive tracks is maintained to overlap a considerable portion, which ensures significant fusion and binding of tracks. Maraging steel is known for its high strength, toughness and good dimensional tolerance, which make it a suitable material for the aerospace industry [17]. Comparatively to other steels, it has low carbon content and the presence of nickel makes it better corrosion resistant. The high strength and toughness of maraging steel are achieved by the ageing of soft martensite at a temperature range of 400-

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450oC. The aging produces the Ni3Ti, Ni3Mo, Ni3V phases[17]. Due to its good ductility and welding properties, it can be easily manufactured. Most of its applications include landing gears, rocket motors, and other tooling applications. The composition of the

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maraging steel is given in Table 1.

Process parameters are adjusted for achieving the desired quality of the final component. The impact of the final part properties even after post processing[13]. Common defects of SLM can be considerably reduced by adjusting processing parameters (scan speed, laser

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power, hatching, layer thickness, etc.)[13]. However, overall energy density (P/V) should be taken into account for the evaluation of parameters. Table 3 lists the standard parameter chosen for the analysis, their associated energy density and results.

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3.2 Temperature and melt pool depth

The laser starts scanning in the y-direction from Y = 150 µm and continues scanning covering the length of 1200 µm of powder in all the four layers, leaving some unmelted powder at the edges of the track. At first, when the laser hits the metal powder the size of the

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melt pool is comparatively small and the temperature is low as shown in Figure 2 a,c. The reason behind this is the low thermal conductivity at ambient temperature thermal history. As the laser traverse along the scanning direction its temperature, as well as melt pool size, continue to grow until a certain time, and the melt pool shape resembles the fishtail. Figure 2 shows the temperature and melt

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pool depth of 1st and 4th layer at power, p =285W and scan speed, V 960 mm/s.

a)

Start of laser

b) End of first track

c)

Start of fourth track

d) End of fourth track

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Figure 2: Temperature attained in first (a & b) and last layers (c &d) at p = 285 W and V = 960 mm/s The temperature and melt pool depth is found to be increasing linearly with energy density as expressed in Figure 3. Analysis no 5 with P/V = 300 had a higher final temperature than analysis no 4 with P/V = 296. Therefore, even a low variation in energy density can

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make a difference. However, the discussion is incomplete without taking actual power and scanning speed into consideration. Identical is the case with melt pool depth, which also increases almost linearly with energy density. In addition, melt pool depth is also associated

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speed, the laser won’t be able to penetrate deeper into the powder bed.

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with scanning speed. Higher is the speed, lower will be the depth, even if the energy density is the same[8][20]. As in case of high

Figure 3: a) Temperature versus energy b) Melt pool depth versus energy

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3.3 Behavior of temperature and melt pool depth with a laser pass At the beginning of every track, the temperature of the melt pool is low and the size is small. As the laser traverse, the melt pool size grows gradually and reaches a nearly constant value termed as a pseudo steady state. Similar is the case with temperature, which is 1256 O

C at the incident and after gradual increment reaches a nearly steady-state value of 1890 OC along the scanning direction as evident in

Figure 4. In addition, the melt pool depth, as well as its width, increases with the addition of subsequent layers. However, this difference in consecutive layers is maximum in the beginning and reduces further with the addition of newly deposited layers. The trend is evident in the studies conducted in the past[10][21].

3.4 Variation of thermal variables along with different directions Investigation of variation in parameters within a melt pool, after it has reached a pseudo-state has shown some interesting results. The temperature is maximum at the center of the melt pool (1883 OC) and reduces gradually up to a certain point as we move away from the

center. As we move further, temperature reduction becomes exponential. At last, it follows the trend similar to the beginning and becomes nearly constant at 373 OC. However, the temperature variation trend along depth and width direction is nearly parallel as shown in Figure 5a. The difference in temperature at scanning direction and width direction is attributed to different boundary conditions of

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the respective surfaces.

Figure 4: a) Temperature variation along scanning direction b) melt pool depth and width variation along with the layers.

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Similarly, as we proceed from the trailing edge of the melt pool in the scanning direction, its depth and widths were found decreasing gradually. In Figure 6, the value of melt pool depth = 90 µm and width = 120 µm were maximum at the left. Moving away from the center of melt pool a gradual decline in the depth and width is observed until the melt pool depth = 10 µm and width = 30 µm is reached.

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After this point there was no further decline is observed. The result is evident in Figure 5 b. and Figure 6. However, in the leading

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direction, the drop in the value of depth and width is much faster as compared to the trailing edge.

Figure 5: a) Variation of temperature b) Melt pool variation within a melt pool.

Figure 6: Melt pool shape attained at the 4th layer

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3.5 Thermal gradient

Similar to temperature, the thermal gradient quickly attained a steady-state and almost remain constant throughout the scanning for

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X(TGx) and Z(TGz) direction .But there is slightly drop in value in TGx direction and slight increment for TGz. In case of Y(TGy) direction, the thermal gradient first increases slightly and then starts declining. This behavior is continued until the end of the scanning, but as the laser proceeds the drop in value becomes slower. Among all, the magnitude of TGz is maximum, TGy and TGz were equal

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in the beigening but the difference in them increases continuously. Thermal gradient also found to be increasing along with the addition of layers. And similar to temperature, it becomes nearly constant with the addition of subsequent layers. Its behavior is evident in Figure

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7 below.

Figure 7: Thermal gradient variation along with the layers.

4. Experimental validation In the previous similar works, it has been noted that the thermal variables don’t show significant variation in values after the fourth layer[9]. Therefore, the experimental validation is restricted to the modeling with the fourth layer considering the computational time. Analysis number 5 with power = 285 W and speed = 960 mm/s is chosen for experimental validation. In the experimental analysis, samples were produced with constant hatching. Data from more than 20 locations are collected for the model validation. It is worth noting from Table 4 and Figure 8 that there is less than a 5% error in melt pool depth in model prediction and experimental validation. Neglecting the convective heat flow inside the model is one of the reasons for this error.

As opposed to the depth, the model overestimated the melt pool width. The analysis is conducted using a single track. Therefore, the model did not experience thermal effects on the subsequently added layers. As a result, each time layer is deposited the thermal conductivity in the width direction is not affected by the thermal history. The opposite is the case with the depth, where the high

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temperature of the previously deposited layer increases its thermal conductivity and stabilizes the depth of the melt pool.

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5. Variation of temperature with a laser pass

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Figure 8: SEM image of melt pool depth and width attained at analysis no 4.w

The data for the temperature attained at a particular node in the first layer from the beginning point of time until the addition of the last layer is plotted against time in Figure 9. The behavior of temperature shows 4 peaks attained for first layer and the difference of time between these peaks is constant. The reason for the peak is the incident laser directly above the node. During scanning of the first

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layer, the first peak is attained and subsequent scanning of top layers again raises the temperature of that node rapidly. However, the effect of further addition of layers reduces on the node. As the laser approaches the node, the rise in temperature of the node is much

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faster. The reason for this behavior is the steep reduction in the effect of a laser at the trailing edge as compared to the leading direction.

Figure 9: Temperature variation in a single node with time for 1st (left) and 2nd (right) layers.

6. Conclusion

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The melt pool size at the incident laser is relatively small and grow in size gradually until a steady state is reached. The shape of melt pool is similar to fish tail. Same is the case with temperature which is low in the beigning and after gradual increment becomes stable. The temperature and melt pool depth increases almost linearly with laser energy density. However, the discussion is incomplete without taking actual power and scanning speed into consideration. In addition, the temperature and melt pool depth increases with the addition of layers and becomes steady gradually. The temperature and melt pool depth are maximum at the centre of the pool. The temperature reduces exponentially as we move away from the centre. In addition, the melt pool decay becomes parabolic while moving away from centre in any direction. Thermal gradient for all the directions rises in the beigining. It becomes almost constant for X, Z directions and shown slight variation until the end. In Y direction the behavior is different, its drop is faster in the beigining and then becomes slower. In the model the percentage error for estimating the melt pool depth is 5 % and for width it is almost 13 %. The model over estimates the melt pool width due to in sufficient heat transfer in the model. And neglecting convective heat transfer is one of the reason for the error. The temperature time data for the single node shows sharp peaks at every pass of laser. There is sudden rise in temperature as the laser hits the location. However, upon the disengagement of laser the fall in temperature is slower due to slower heat disscipation.

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[12]

Table 1: Below shows the other important parameters chosen for this study[17][18][19]. Value 100µm

Penetration depth

100µm

Track length

100µm

Scanning strategy

Singletrack

Density

8 g/cm3

Thermal conductivity

25W/mk

Melting temperature

1413oC

Specific heat

0.5 J/g/oC

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Properties Spot size

Ni 18.8

Mo 4.2

Co 10.2

Ti 0.88

C 0.02

Fe Rest

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Powder constituents Weight in percentage

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Table 2: Chemical composition of maraging steel supplied

Table 3: Process parameters for FE Analysis.

Energy density (P/V) (W/m. s-1)

Max Temperature (K)

Melt pool depth

(W)

(mm/s)

1

200

800

250

1759

80

2

220

850

258

1788

84

3

250

900

277

1839

87

4

285

960

296

1890

90

5

300

1000

300

1900

90

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Scan Rate(V)

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Power(P)

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Analysis No.

(mm)

Table 4: Melt pool dimensions of experimental and FE model results.

FE model Experimental Percentage error %

Power (W) 285 285

Speed (mm/s) 960 960

Meltpool depth (µm) 90 95.52 5%

Meltpool Width (µm) 120 106.07 13 %