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FEA simulation of thermal processes during the direct metal laser sintering of Ti64 titanium powder
Accepted Manuscript FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder J. Živč ák, M. Šarik, R. Hudák PII: DOI: Reference:
S0263-2241(16)30439-0 http://dx.doi.org/10.1016/j.measurement.2016.07.072 MEASUR 4259
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
29 May 2016 21 July 2016 25 July 2016
Please cite this article as: J. Živč ák, M. Šarik, R. Hudák, FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder, Measurement (2016), doi: http://dx.doi.org/10.1016/ j.measurement.2016.07.072
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FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder J. Živčák1, M. Šarik, R. Hudák Faculty of machanical engineering, TU Košice, Department of Biomedical engineering and measurement, Letná 9, 042 00 Košice, Slovakia
Abstract: With regard to the fact that laser sintering belongs to the high-temperature processes in which metal particles are sintered by a high-power laser, forming a homogenous structure, it is necessary and important to know the characteristics and the mechanism of these thermal processes. A high-power laser system produces three forms of heat that include convection, conduction, and radiation. These thermal processes affect the formation of internal stresses and tension that lead to deformations and rapidly influence the resulting quality, dimensions, density, micro-structure, and mechanical properties of fabricated parts. In response to this fact, it was important to analyse these heat transfer methods instantly during the direct metal laser sintering (DMLS) process simulation and subsequently monitor the parameters and settings of the sintering equipment in order to obtain acceptable manufacture outputs intended for further use. This work is focused on the creation of a FEA simulation model and the simulation of thermal processes across an object during and after the sintering process in the cooling stage, when it is important to consider a laser beam trajectory, temperatures of individual elements affected by the laser beam, and current laser energy in time. A 3D FEA simulation model was created in order to represent actual behaviour of a part during the sintering process. The simulation model consisted of two sub-models, particularly the building platform model with the dimensions of 250 mm x 250 mm x 22 mm, with stainless steel as the selected material, and the model of individual layers of sintered titanium powder with the dimensions of 10 mm x 10 mm x 0.03 mm. The total number of used layers was 12, which represents the total thickness of 0.36 mm. Applied power was P = 170 W. The simulation as such was carried out using the FEA software, Simulia Abaqus supported on the Windows x86-64 platform, which uses an integrated solver to make thermal and mechanic calculations. The calculations included also the impact of the protective argon atmosphere located in the process chamber. Mutual impact between individual layers was also considered. The simulation results were confronted with the results of already performed experimental studies of other scientific works, with the compliance and confirmation of assumptions being on a very good level.
1
Corresponding author. Tel.: +421 55 6022381, E-mail address: [email protected]
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
Keywords: additive manufacturing;laser sintering; FEM; thermal simulation.
1
Introduction
In the field of fast manufacture of prototypes, laser sintering has become a productive part of 3D object fabrication from metal materials. The laser sintering process is complicated especially due to the laser’s scan rate and material changes occurring in a very short period of time. Thermal fields were assessed as nonhomogenous in many previous researches [1] [2] [3] [4] [5] [6] . High temperature gradients increase the residual stresses and deformations and can lead to the formation of cracks in manufactured parts. Thermal deformations of a manufactured part represent one of the fundamental issues in the field of laser sintering [7] . In the meantime, the development in this area showed that this process has a significant impact on the quality of final parts and large thermal changes can cause gathering of disturbances in the manufactured product. A case study of main characteristics of the temperature distribution during the laser sintering and the effects of the process parameters on the temperature were summarised in [7] . As laser sintering represents a high-temperature process in which individual layers of melted material are gradually solidified, it must be taken into account that internal stresses and tension occur during this process. After products are removed from the building platform, these stresses are demonstrated in form of deformations and shape changes; these shape changes, however, are unacceptable in this type of manufacture, due to high accuracy requirements. Thermal analysis of laser processes can be used to predict thermal loads and micro-structures during the manufacture and in a finished part. Thermal analysis is also the basis for the feedback inspection of laser parameters in the manufacture. For the purpose of the analysis of thermal processes occurring during the DMLS process, the measuring methodology was proposed, using the Abaqus simulation software that operates on the principle of finite element analysis (FEA). The most important step is the determination of boundary conditions, i.e. the input data that are required for the performance of measurements. The quality of parts manufactured using the laser sintering technology largely depends on an appropriate, and thus correct, selection of manufacture parameters, such as laser power, scan rate, laser point size, and material. These parameters significantly affect the temperature distribution in the powder bed. Homogenous thermal field can lead to better product micro-structure and mechanical properties. In number of studies, combinations of experimental methods were used for the detection and verification of thermal conduct during the treatment. The combination of the thermal analysis (thermal experiments) and the FEA analysis was used in many subsequent studies [8] [9] [12] [13] . Analytical solutions were often derived from
the Rosenthal’s solution and other implemented theories. In recent years, some thermal measuring systems were implemented to verify the simulation results.
2
Materials and methods
Thermal field is a scalar function of temperature as the function of spatial coordinates (x, y, z) and time t.
T = T(t, x, y, z)
(1)
Thermal field can be steady or unsteady, depending on whether the temperature is, or is not, the function of time. If the temperature changes in the direction of only one spatial coordinate, the thermal field is unidirectional; if it changes in the direction of several spatial coordinates, it is a multidirectional field, particularly two- or three-directional. We characterise several thermophysical parameters, including thermal conductivity, specific heat capacity, and thermal diffusivity. Thermal conductivity expresses the ability of the given material to conduct heat. In figures, it expresses the amount of heat that is transferred in a steady condition through the unit cross-section of the material in the unit gradient per unit time. A parameter characterizing the ability of the given material to conduct heat is the heat transfer coefficient (thermal conductivity, thermal conductance, specific thermal conductivity) and is defined by the Fourier’s Law[11] : Δ
(2)
where, – is the heating capacity generated in the unit volume of the material, or the unit output of a heat source . . , – is the heat flux density . . , – is the gradient of thermodynamic temperature at the same spot of the material, – is the constant thermal conductivity . . . Heat conduction is the most frequent method of heat distribution in solid objects. Comparison of different materials by their thermal conductivity is possible due to the parameter – heat transfer coefficient. Materials of higher densities are usually better heat conductors; metals are excellent heat conductors. These materials are called heat conductors[11] . Specific heat capacity is the heat necessary for a slight increase in the temperature of the material in , divided by the mass of the material and the temperature increase [11] :
.
(3)
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
In figures, the specific heat capacity equals the heat necessary for heating one kilogram of material in 1 . We distinguish between the specific heat capacity at constant pressure and the specific heat capacity at constant volume . For solid materials and fluids we usually mean the specific heat capacity at constant pressure; for gases there is an evident difference between both specific heat capacities and their ratio represents the so-called Poisson constant. In majority of materials, specific heat capacity increases with increasing temperature. The SI unit is . . [11] . Thermal diffusivity expresses the material’s ability to balance differing temperatures at constant heat conduction in homogenous environment. Thermal conductivity is also referred to as the thermal diffusivity. This parameter indicates how the material conducts heat, i.e. how easily the temperature differences are balanced inside the material. For the simplification purposes, the following parameter is implemented[11] :
.
(4)
It equals the quotient of thermal conductivity . ିଵ . ିଵ . ିଵ and the product of its density . ିଷ and the specific heat capacity at constant pressure [11] . Heat conduction can be divided into: 1. Steady state heat conduction: o the difference in temperatures of individual object parts does not change in time. 2. Transient heat conduction: o temperature differences between individual object parts, between which the heat is transferred, are gradually balanced. 1.
Steady state heat conduction:
Heat transferred through the surface is determined by the so-called heat flux. The quantity of heat transfered through the surface in time is denoted as the heat flux density. If an object (e.g. a board), through which the heat is transferred, consists of layers with various thermal conductivities and thickness of for the layer , then in the steady state the heat flux density in all layers is identical, it means that:
(5)
For the overall difference in temperatures we will then get: . . . ∑
(6)
The heat flux density for such a board can be expressed as:
(7)
∑
The / quotient is called the specific thermal resistance of a layer. 2.
Unsteady state heat conduction:
We are examining the case of heat conduction through a board, occurring at sudden temperature increase on one of the board surfaces. If we divide the board into layers with the thickness of ∆ , the heat flux density in all the layers will not be identical to the one formed in the steady state heat conduction. The reason is that certain proportion of heat entering the layer is consumed to heat up the layer. The flux in the subsequent layer is then lacking this heat proportion. In our case, heat ! "∆# enters the layer with the thickness of ∆ and the surface of " in time ∆# and from the same layer, in the same period of time, the heat ! "∆# exits, while and are heat flux densities on the entering and exiting surfaces. The temperature of the layer is thus increased in the heat representing the difference between these temperatures, i.e.: ! ! "∆# Δ"∆#
(8)
If the specific heat capacity of the layer is $ and its mass is ∆ %"∆ , where % is the layer’s thickness, then: ! ! $Δ∆&
(9)
For the time change of the mean temperature of the layer, we will get the following expression from the calculations of relations above (in the limit for Δ ' 0 and ∆# ' 0) we will get the expression:
(10)
This relation represents a one-dimensional differential equation of heat conduction. This equation can be simply generalised for a three-dimensional case:
)
*
(11)
Conductivity or the heat transfer coefficient: +
∆
(12)
+ – conductivity W. m . K Then the Fourier’s Law can be described as: ∆ ∆
+. / ∆
(13)
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
Reciprocity within the heat conduction means that the conduction is reciprocally connected with the thermal resistance 0, which is determined by: 0
∆
∆ ∆
(14)
∆
It is the resistance which is additive, if several conductive layers are located between hot and cold regions, as / and ! are the same for all layers. In a multilayer section, the overall conductivity relates to the conductivities of individual layers:
(15)
in the solution of a multi-layer section, the following relation is applied:
o ∆
∆
∆
(16)
∆ ∆
Heat transfer from one object to another object by means of moving fluids (gases). A dominant form for fluids and gas. It comprises combined conduction processes, including especially thermal diffusion and heat transfer through a part of the fluid flow. Convective heat transfer coefficientin thermodynamics and in mechanical and chemical engineering, it is used when calculating the heat transfer, typically by convection or phase transfer (the transfer between the fluid and a solid object): 1
(17)
.∆
where, ! – heat flux / , 1 - heat transfer coefficient / , / – heat transfer area , ∆ – difference in temperatures of the solid surface and the surrounding environment. Table 1 Convective Heat Transfer Coefficient Values h 2/3! 4 Gases(no convection) Gases (convection) Fluids (no convection) Fluids (convection) Boiling fluids Condensing steam
15 15 – 250 100 100 – 2000 2000 – 35000 2000 – 25000
1 - is proportional to the coefficient between the heat transfer, i.e. heat flux, through the a unit area !// and the thermodynamic controlling force for the heat flux, i.e. the temperature difference ∆.
Heat transfer coefficient represents the inversion to the thermal insulation resistance (thermal insulation). It is often calculated from the Nusselt number which is dimensionless. Understanding of boundary layers of the flow requires understanding of convective heat transfer between the surface and the fluid flowing through it. Thermal boundary layer is described when the free thermal flux of the fluid and the surface temperature are different. The thermal profile exists with regard to the energy exchange resulting from this thermal difference. Heat transfer can be expressed as: ! 1. /" #
(18)
and as the heat transfer on the surface is carried out by conduction, ! . /.
$ $
" /5 0
(19)
The Newton’s Law that requires the constant heat transfer coefficient states that the heat loss value is proportional to the difference of temperatures between the object and the surroundings. Heat transfer value under these circumstances is derived as follows:
1. /& %& 1. /. Δ&
(20)
where, ! – is the thermal energy . , 1 - is the conductive heat transfer coefficient, / – is the area , – is the temperature of the object’s surface and its interior 6, %& – is the temperature of the environment, for example the temperature corresponding to the distance from the surface. ∆& & %& – is the time – dependent temperature gradient between the environment and the object.1 - dependson physical properties of the fluid and the physical situation in which the convection occurs. Radiation output: o thermal radiation capacity of the black body per a unit spatial angle and per unit frequency ν is determined by the Planck’s Law as: 78,
'(
.
%
(21)
or, 7 ,
)
.
%
(22)
where, : – is a constant The relation is derived as an indefinite sum of all possible frequencies. Energy ; 18 of each photon is multiplied by the number of possible conditions for the given frequency and the probability that each one of these possible conditions will be occupied.
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
By integrating the previous relation through 8, we will get the power determined by the Stefan Boltzmann’s Law as : < =. /. *
(23)
where the proportionality constant = is the Stefan – Boltzmann constant and / – is the radiation surface area. The following wavelength , for which the radiation intensity is the highest, is determined by the Wien’s Law as: + >/
(24)
For surfaces that are not black bodies it is necessary to consider a frequencydependent emission factor ?8. This factor must be multiplied, prior to integration, by the radiation spectrum formula. If the constant is understood as the resulting formula for the output power, it can be written so that it contains ? as a factor. < ?. =. /. *
(25)
This type of theoretical model with frequency-independent emissivity lower than for a perfect black body is often referred to as the grey body.
Methodology of the DMLS Process Simulation Using the Abaqus FEA software. All temperature and heat data are entered as constants or as functions of time. Simulation and analysis of thermal processes in DMLS include three main steps: 1. definition of boundary conditions 2. preparation of the script for the thermal software-assisted analysis 3. modelling of simulation steps. Determination of constants: o temperature of the building platform o temperature of the metal powder in the feeder o temperature in the process chamber Consideration of variables: o various sizes (dimensions) o various thicknesses o various types of supports o various laser settings (power) o various positions (placement) on the platform o laser trajectory (motion trajectory) o laser movement speed During the sintering process, each sintered layer with the thickness of 30 µm is subsequently covered with a following metal powder layer of the same thickness,
which is then sintered on the previous layer, where certain cooling effect occurs, which is followed by the heating process.
The process of analysis and simulation represents: 1. 2. 3. 4.
Preparation of the required input parameters for the simulation. Designing of testing FEA 3D models of parts, selection of dimensions, material composition. Proposal of the script of the laser sintering simulation. Testing of the proposed script, collection of recorded data.
Preparation of input parameters o Analysis of suitable biomaterials, collection of technical parameters of given biomaterials, analysis of their properties and verification of appropriateness of their utilisation. o Analysis of the sintering process using the EOSINT M 280 equipment, study of manuals, practical exams. o Video - analysis of the sintering process during the manufacture of a trial 3D model of a part. o Analysis of the performed studies focused on thermal analysis, heat conduct and flux using the finite element analysis (FEA). o Collection and analysis of input parameters necessary for the designing and execution of the model simulation of thermal processes during the manufacture of parts by laser sintering. Building platform: o dimensions 250 x 250 x 22 mm o preheating temperature: 40 – 100 ˚C o o o o
Direct Base S22 1.1730 tool steel mechanical working 8 mm fixation holes
Figure 1 Building Platform in the DMLS Process Configuration of the EOSINT M 280 sintering equipment: Process chamber of the EOSINT M 280 equipment includes individual operating systems with the following volumes:
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
1. 2. 3. o o o o o
building system: 21B dispenser system: 26B collector system: 13B
volume of the chamber (excluding individual systems) represents: 101B operating volume of the chamber has dimensions: 250 x 250 x 325 mm overall dimensions of the processing chamber are: 350 x 430 x 675 mm minimum thickness of a sintered layer: 0.03 mm laser beam diameter: d = 0.1 – 0.5 mm
Table 2 Material Properties and Parameters as the Input Data for the Simulation
Designing the FEA simulation models Creation of a testing 3D FEA model in the Abaqus environment. The emphasis was put especially on adherence to the required dimensions, simplification of the simulation process, and reduction in the requirements regarding the calculation performance of the system and the time required to perform the analysis.
Jozeef Živččáket al.FEA A Sim mulatioon of Therm T mal Prrocessses duuring the t Direct Metal M Laserr Sinteering oof Ti664 Titaanium Pow wder
Figurre2 FEA F Sim mulattion Moddel of o the Bu uilding P Platfo orm and d Inddividuual Meta M al Poowdeer L rs annd a detaail co Layer ontaiining g thee Reepressentaation n of Indiv I vidu ual L Layerrs. Thee buuildin ng pplatfform m posssessses the t presscrib bed stand s darddizedd dim menssionss 25 50 x 250 0 x 22 2 mm, m ddimeensioons of o thhe faabricatedd mettal powd p der laayerrs aree 10 x 100 x 0.03 0 mm m. Foor th he puurpoose of o more m accu uratee callculaation n, deenserr nettting g waas created in the areea off inddividdual layeers aand also on the layeers them t mselvves. Thee num mbeer off layers is 12. 1 T The messh of o laayerss is form med by orth hogoonal elemennts with w the dim menssionss 0.225 x 0.255 mm m; iit meeans thaat in the x an nd y axees th here are 40 x 40 elem mennts, reprresenntingg 160 00 eelemeents withhin one o layeer. Nettin N ng was w cchossen after a r iniccial pre--sim mulationss wh hich hav ve shhow wn optim o mal net n denssity in the areaa off ind dividdual layer l rs foor geetting g siggnificcantt calcculattion resu ults. Scrript prop posaal foor th he DM MLS S prrocesss simullatio on o
o
Preeparationn off input param meters foor thhe simulaation n. Thhe propo p osal of scrip s pt orr subbrou utinees foor the t simuulatiion of the laseer sinte s ring pro ocesss as a su uch. Coonsid derattion of innputt variiablees annd thheir impa i act on o thhe sim mulaationn couurse. Scrript prooposaal in th he sscrip pt edditorr. The T prop posaal coountss w with grad dual appplicaationn of indiividu ual llayerrs off titaanium m po owd der, i.e. i with w the adddition n off maateriaal annd afffectting prevvious layyers.. Th he propo osal takees intto coonsidderaation varriablle seettinggs off thee equuipm ment paraametters, as well w as other o settting optio ons. It also a couunts w withh a patter p rn, or o a traje t ectorry, of thee lasser beam b m moovem ment andd thee mo ovem ment speeed.
Figgure3 3 Suubrou utinee Preeparaation n andd thee Graaphiic Model M l for the Laseer Siinterring Proccess S ulatio Simu on.
Figuure 4 T Testiing of o prroposedM Methhodo ology y and d scrript in i 2D D.
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
3
Results and disscusion
Upon successful verification of the proposed methodology of the analysis focused on the thermal processes in the DMLS, it was possible to perform the simulation using and applying real values obtained from the expert literature and from experimental measurements. The subroutine of the simulation was supplemented with the values of temperatures of the building platform, protective atmosphere inside the process chamber, with radiation between individual models, i.e. with the values of constants and variables.
Figure5 Simulation of the Heating Process with the Representation of Heat Distribution in the Powder Bed. Based on the performed simulation of heating and cooling of the direct metal laser sintering technological process we can state that the heat distribution in the powder bed during heating, and thus the heat application, is unsteady and nonhomogenous, due to its nature. The sintered layer cooling as such occurred from the edges towards the centre, i.e. the centre of the metal layer. This phenomenon is caused by the higher heat accumulation in the centre of the sintered part where the flow impact in the surrounding environment is not so significant.
Figure 6 Cooling Process Simulation Including the Representation of Heat Distribution in the Metal Layer By analysing the cooling process Figure 6, it was observed that at the completion of the powder layer sintering the temperature in the last heated element is gradually rising. It is a result of the die-away and the heat trace impact. This increase in temperature is of the short-term nature and subsequently the temperature begins to fall due to convection.
Temperature (˚C)
1200
Tmax = 1039,8
1000 800 600
Tmin = 576
400 200 0 0
1
2
3
4
5
6
7
8
Time (s) Figure7 Temperature Development in the Course of Sintering a Single Powder Layer with the Thickness of 0.03 mm
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
Figure 7shows that during the sintering of a single powder layer the maximum achieved temperature was ௫ 1039.8 and the minimum temperature was 576 . The average temperature was ௩ 748.948 . A decisive factor in the heat distribution is the size of sintered parts, their thickness and the resulting number of powder layers. With increasing number of layers, the demonstrations of heat accumulation and more even heat distribution in individual layers begin to occur. At the same time, with a growing number of layers, the heat trace is more significantly demonstrated after the laser beam is applied, but in a relatively short period of time, the cooling and the heat trace reduction occur when the thermal conductivity and heat flux begin in the chamber. Another case is the temperature distribution during heating, where the increase in the powder bed boundary layers temperature was observed during sintering Figure 8. The difference was in the range of 100 200 . This phenomenon is probably caused by the contact between the boundary layer and the surrounding environment and by the fact that the heat conduction, and thus the heat removal, is carried out only partially and not from all sides, as is the case of elements inside the layer. The laser beam trajectory changes as well, while the shift to the following trace is of a small extent, and, as a result, the last element of the boundary layer impacts the adjacent element. Boundary element that was monitored during the entire simulation was gradually heated and when the steady condition was achieved, the temperature values were approximately in the range of 40 45 . The temperature of the monitored element within the laser beam impact area was changing in a wider range, approximately 580 1150 , which is shown in Figure 5. During heating, the boundary element’s temperature was monitored, as well as its response to gradual heat accumulation in individual layers. The main reason why building platform thermal processes simulation was chosen is because of its significant thermal capacity. It points out when preheating is applied, it can reduce, to certain extent, the temperature changes during the application of individual layers.
Fiiguree 8 Reepressentaationn of the Reac R chedd Maaxim mum Tem mperaturees duuringg thee Sinnteriing of o a Singgle L Layeer Aftter thhe po owerr vallue is i sett to P = 170,,000 mW W/mm m3, therm t mal trace t es caaused by y the laseer beeam passsagee throough h thee surrfacee werre leess siignifficannt annd wiith looweer values of recoorded d tem mpeeratuures. Onlly with w incrreasiing num n mber of layer l rs thhey becaame mo ore visibl v le, w whicch was also a cconffirmeed bby th he in ncreaased tem mperaaturee wiithin n the pow wderr bed d. Thhe laaser mov vemeent speed s d waas seet to the valuue off 125 50 m mm/ssec, 1,25 1 m/ssec, which rrepreesentts th he standaard settin s ng for f th he ex xternnal surfa s ace ddurinng laserr sintterinng ussing the DM MLS techn t nolo ogy. A smal s ll vaariannce aand trans t smisssion n of tempperaaturee valu ues arouund the t pplace off the laseer beeam imppact on the t surfa s ace of o thhe sinntereed metal m l pow wderr lay yer iis caaused d by low w theermaal coonduuctiviity of o thhe Tii64 mate m erial with h thee vaalue of and d goood heat h rem movaal th hrouggh th he build b ding plattform m. Itt is assu umedd thaat when w mo ore laayerrs arre appplieed, whic w ch in ncreaases the partt’s thick t knesss, th his pphenomeenon willl be redu ucedd andd thee tem mperaturee varriancce will w be b more m signnificaant.
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
Obtained results are in line with the performed works and the results reported by authors [4] [17] [18] [19] [20] [21] [22] [26] . The results are in compliance with the following conclusions: 1. Presented thermal model is able to forecast the temperature distribution and temperature fields in a metal layer of the sintered powder. 2. The highest temperature was not observed precisely in the centre of the laser beam but slightly toward the descending x – axis and the ascending y – axis, but still within the laser beam area. 3. Temperature rises with the gradual increase in the number of sintered layers 4. Temperature falls with the increasing hatching allocation. 5. Indication of a high temperature gradient between the sintered surface of the powder bed and the building platform. 6. With lower scan speed of the laser beam, the melting depth increase. 7. With reduced scan speed, the peak temperature increases; this is caused by the increase in energetic density, which corresponds to higher delivered output and lower scan speed. 8. Preheating of the building platform can increase the peak temperature on the surface of the sintered layer, but it can also decrease and reduce large temperature gradients between individual applied layers and the building platform. The FEA analysis has brought also other information, in terms of possible options of an analysis in the Abaqus software. This software proved to represent an appropriate tool for the FEA analysis, which is beneficial when performing such complex tasks. As for limitations of this FEA solver, no significant limitation was observed. The only concern is still represented by high hardware requirements for the analysis execution, but this problem must also be faced in case of other FEA software products, which was confirmed also in [7] . Possible ways how to speed up the analysis are as follows: reduce the number of records and use other methods to control the time step, heat several layers concurrently/thicker layers, and increase the laser dimensions lx, ly, and Ka – use the same values in standard circumstances.
Conclusions For the purpose of the analysis of thermal processes occurring during the DMLS process, the measurement methodology was proposed, counting with the use of the finite element analysis as a suitable tool for such complex task as the laser sintering of metal powder is. The performed analysis and simulation of thermal processes occurring during the laser sintering enabled better understanding of the behaviour of manufactured parts and the impact of heat on their properties. Recommendation for further research and the follow up in this area is to carry out thermal and mechanical simulation that would bring more outputs, especially regarding the analysis of stresses and tension inside the parts manufactured by the laser sintering method. Mechanical analysis and simulation would be focused primarily on thermal stresses in structures that might be caused by nonhomogenous heat distribution and thus formation of stresses, external limitations, i.e. bonds that prevent from free deformation of the structure (support), and differing thermal expansibility coefficients that occur in heterogeneous structures, while considering the equivalent of the viscoelastic impact when the heat flux is applied to the structure. Within further research in the given area, the intension is to create a CAD model of an implant with various numbers of layers and the FEA analysis directly inside the implant, which would provide further concrete results for the implant research and development. As for the next research, it is still necessary to examine this area and obtain the highest possible amount of information; it regards mainly various experimental applications within the laser sintering, such as the use of thermal camera and software prediction attempts with various settings of the sintering equipment which can serve as the basis for the production of relevant outputs usable in practice.
Acknowledgement The presented article was supported from the project KEGA 036TUKE-4/2013 Implementation of New Technologies in Implant Designing and Manufacture into the Education Process in Biomedical Engineering and Related Disciplines and project VEGA 1/0515/13 Draft design layout and architecture of intelligent implants.
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
References [1] Wang, X. C. et al.: Direct Selective Laser Sintering of Hard Metal Powders: Experimental Study and Simulation. In: International Journal of Additive Manufacturing Technology. 2002, No. 19, p. 351 – 357. [2] Kruth, J. P. et al.: Lasers and materials in selective laser sintering. In: Assembly Automation. Vol. 23, 2003, No. 4, p. 357 – 371. [3] Simchi, A.: Direct laser sintering of metal powders: Mechanism, kinetics and microstructural features In: Materials Science and Engineering: A 428. Vol. 1, 2006, No. 2, p. 148 – 158. [4] Kolossov, S. et al.: 3D FE simulation for temperature evolution in the selective laser sintering process. In: International Journal of Machine Tools and Manufacture. Vol. 44, 2004, No. 2-3, p. 117 – 123. [5] Zhang, D. et al.: Select laser melting of W–Ni–Fe powders: simulation and experimental study. In: The International Journal of Advanced Manufacturing Technology. Vol. 51, 2010, No. 5-8, p. 649 – 658. [6] Contuzzi, N. et al.: 3D Finite element analysis in the selective laser melting process. In: International Journal of simulation model. Vol. 10, 2011, No. 3, p. 113 – 121. [7] Zeng, K. – Pal, D. – Stucker, B: A review of thermal analysis methods in Laser Sintering and Selective Laser Melting, [online]. (2012). Available at: [8] Anand, S. – Verma, N: Efects of Sintering Temperature, Heat Treatment and Tempering on Hardness of Sintered Hardened Grade Steels (SH737-2Cu0,9C). [online]. Research Articles, 2006. Available at: [9] Chiu, L. H. – Nagle, D. C. – Bonney, L. A: Thermal Analysis of SelfPropagating Reactions in Titanium, Boron, and Aluminum Powder Compacts. [online]. Metallurgical and Material Transactions A, 1999. Available at: [10] Booysen, G. J et al.: Development of patient – specific implants using Direct Metal Laser Sintering in Titanium. 2012, Innovative Developments in Virtual and Physical Prototyping, Taylor and Francis Group, London, ISBN 978-0415-68418-7. Available at: [11] Štefková, P: Studium tepelných vlastností materiálů: Dissertation thesis. Brno: VUT Chemical faculty, 2011. [12] Price, S. – Cooper, K. – Chou, K.: Evaluations of temperature measurements in powder-based electron beam additive manufacturing by near-infrared thermography. In: International Journal of Rapid Manufacturing. Vol. 4, 2014, No. 1, p. 1 – 13. [13] Taylor, C. Martin – Childs, Thomas H. C.: Thermal Experiments in Direct Metal Laser Sintering. 2002. Available at:
[14] Lienhard, IV, H. J. – Lienhard, V, H. J.: A Heat Transfer Textbook, Fourth Edition. Phlogiston Press Cambridge, Massachusetts, U.S.A., 2012 [15] Lewis, R. W. et al.: Fundamentals of the Finite Element Method for Heat and Fluid Flow. Wiley, 2004. 356 pp. ISBN 0470847891. [16] Zhang, J. et al.: Simulation of temperature field in selective laser sintering of copper powder. In Mechanic Automation and Control Engineering (MACE), International conference, 2010, p. 3282 – 3285, ISBN 978-1-4244-7737-1. [17] Ning, Y. et al.: An approach to minimize build errors in direct metal laser sintering. In IEEE Transactions on automation science and engineering. Vol. 3, 2006, No. 1, p. 73 – 80. [18] Ganeriwala, R. – Zohdi, I. T.: Multiphysics modeling and simulation of selective laser sintering manufacturing processes. In: 6th CIRP International Conference on High Performance Cutting, HCP 2014: Procedia CIRP, 2014, p. 299 – 304. [19] Williams, J.D. – Deckard, C.R: Advances in modeling the effects of selected parameters on the SLS process. In: Rapid Prototyping Journal. 1998, No. 4, p. 90 – 100. [20] Matsumoto, M. et al.: Finite element analysis of single layer forming on metallic powder bed in rapid prototyping by selective laser processing. In: International Journal of Machine Tools & Manufacture. 2002, No. 42, p. 61 – 67. [21] Shiomi, M. et al.: Finite element analysis of melting and solidifying processes in laser prototyping of metallic powders. In: International Journal of Machine Tools and Manufacture. 1999, No. 39, p. 237 – 252. [22] Dong, L. et al.: Three-dimensional transient finite element analysis of the selective laser sintering process. In: Journal of materials processing technology. 2009, No. 209, p. 700 – 706. [23] Fischer, P. et al.: Temperature measurements during selective laser sintering of titanium powder. In: International Journal of Machine Tools & Manufacture. 2004, No. 44, p. 1293 – 1296. [24] Kraft, T. – Riedel, T: Numerical simulation of solid state sintering: model and application. In: Journal of European Ceramic Society. 2004, No. 24, p. 345 – 361. [25] Klocke, F. et al.: Development of an Integrated Model for Selective Metal Laser Sintering. In:International Seminar on Manufacturing Systems, Saarbrücken: Fraunhofer, 2003, p. 387 – 392. ISBN 3-930429-58-6. [26] Song, B. et al.: Process parameter selection for selective laser melting of Ti6Al4V based on temperature distribution simulation and experimental sintering. In: The International Journal of Advanced Manufacturing Technology. Vol. 61, 2011, No. 9 – 12, p. 967 – 974. [27] Hudák, R. et al.: Material and thermal analysis of laser sinterted products. In: Acta Mechanica et Automatica. Vol. 7, no. 1, 2013, p. 15-19. - ISSN 18984088. [28] Šarik, M. et al.: Analysis of thermal processes during the direct laser sintering of titanium powder. In: Novus Scientia: Košice : TU, 2013 s. 1-6. - ISBN 978-80-553-1380-1.
S0263-2241(16)30439-0 http://dx.doi.org/10.1016/j.measurement.2016.07.072 MEASUR 4259
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
29 May 2016 21 July 2016 25 July 2016
Please cite this article as: J. Živč ák, M. Šarik, R. Hudák, FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder, Measurement (2016), doi: http://dx.doi.org/10.1016/ j.measurement.2016.07.072
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FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder J. Živčák1, M. Šarik, R. Hudák Faculty of machanical engineering, TU Košice, Department of Biomedical engineering and measurement, Letná 9, 042 00 Košice, Slovakia
Abstract: With regard to the fact that laser sintering belongs to the high-temperature processes in which metal particles are sintered by a high-power laser, forming a homogenous structure, it is necessary and important to know the characteristics and the mechanism of these thermal processes. A high-power laser system produces three forms of heat that include convection, conduction, and radiation. These thermal processes affect the formation of internal stresses and tension that lead to deformations and rapidly influence the resulting quality, dimensions, density, micro-structure, and mechanical properties of fabricated parts. In response to this fact, it was important to analyse these heat transfer methods instantly during the direct metal laser sintering (DMLS) process simulation and subsequently monitor the parameters and settings of the sintering equipment in order to obtain acceptable manufacture outputs intended for further use. This work is focused on the creation of a FEA simulation model and the simulation of thermal processes across an object during and after the sintering process in the cooling stage, when it is important to consider a laser beam trajectory, temperatures of individual elements affected by the laser beam, and current laser energy in time. A 3D FEA simulation model was created in order to represent actual behaviour of a part during the sintering process. The simulation model consisted of two sub-models, particularly the building platform model with the dimensions of 250 mm x 250 mm x 22 mm, with stainless steel as the selected material, and the model of individual layers of sintered titanium powder with the dimensions of 10 mm x 10 mm x 0.03 mm. The total number of used layers was 12, which represents the total thickness of 0.36 mm. Applied power was P = 170 W. The simulation as such was carried out using the FEA software, Simulia Abaqus supported on the Windows x86-64 platform, which uses an integrated solver to make thermal and mechanic calculations. The calculations included also the impact of the protective argon atmosphere located in the process chamber. Mutual impact between individual layers was also considered. The simulation results were confronted with the results of already performed experimental studies of other scientific works, with the compliance and confirmation of assumptions being on a very good level.
1
Corresponding author. Tel.: +421 55 6022381, E-mail address: [email protected]
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
Keywords: additive manufacturing;laser sintering; FEM; thermal simulation.
1
Introduction
In the field of fast manufacture of prototypes, laser sintering has become a productive part of 3D object fabrication from metal materials. The laser sintering process is complicated especially due to the laser’s scan rate and material changes occurring in a very short period of time. Thermal fields were assessed as nonhomogenous in many previous researches [1] [2] [3] [4] [5] [6] . High temperature gradients increase the residual stresses and deformations and can lead to the formation of cracks in manufactured parts. Thermal deformations of a manufactured part represent one of the fundamental issues in the field of laser sintering [7] . In the meantime, the development in this area showed that this process has a significant impact on the quality of final parts and large thermal changes can cause gathering of disturbances in the manufactured product. A case study of main characteristics of the temperature distribution during the laser sintering and the effects of the process parameters on the temperature were summarised in [7] . As laser sintering represents a high-temperature process in which individual layers of melted material are gradually solidified, it must be taken into account that internal stresses and tension occur during this process. After products are removed from the building platform, these stresses are demonstrated in form of deformations and shape changes; these shape changes, however, are unacceptable in this type of manufacture, due to high accuracy requirements. Thermal analysis of laser processes can be used to predict thermal loads and micro-structures during the manufacture and in a finished part. Thermal analysis is also the basis for the feedback inspection of laser parameters in the manufacture. For the purpose of the analysis of thermal processes occurring during the DMLS process, the measuring methodology was proposed, using the Abaqus simulation software that operates on the principle of finite element analysis (FEA). The most important step is the determination of boundary conditions, i.e. the input data that are required for the performance of measurements. The quality of parts manufactured using the laser sintering technology largely depends on an appropriate, and thus correct, selection of manufacture parameters, such as laser power, scan rate, laser point size, and material. These parameters significantly affect the temperature distribution in the powder bed. Homogenous thermal field can lead to better product micro-structure and mechanical properties. In number of studies, combinations of experimental methods were used for the detection and verification of thermal conduct during the treatment. The combination of the thermal analysis (thermal experiments) and the FEA analysis was used in many subsequent studies [8] [9] [12] [13] . Analytical solutions were often derived from
the Rosenthal’s solution and other implemented theories. In recent years, some thermal measuring systems were implemented to verify the simulation results.
2
Materials and methods
Thermal field is a scalar function of temperature as the function of spatial coordinates (x, y, z) and time t.
T = T(t, x, y, z)
(1)
Thermal field can be steady or unsteady, depending on whether the temperature is, or is not, the function of time. If the temperature changes in the direction of only one spatial coordinate, the thermal field is unidirectional; if it changes in the direction of several spatial coordinates, it is a multidirectional field, particularly two- or three-directional. We characterise several thermophysical parameters, including thermal conductivity, specific heat capacity, and thermal diffusivity. Thermal conductivity expresses the ability of the given material to conduct heat. In figures, it expresses the amount of heat that is transferred in a steady condition through the unit cross-section of the material in the unit gradient per unit time. A parameter characterizing the ability of the given material to conduct heat is the heat transfer coefficient (thermal conductivity, thermal conductance, specific thermal conductivity) and is defined by the Fourier’s Law[11] : Δ
(2)
where, – is the heating capacity generated in the unit volume of the material, or the unit output of a heat source . . , – is the heat flux density . . , – is the gradient of thermodynamic temperature at the same spot of the material, – is the constant thermal conductivity . . . Heat conduction is the most frequent method of heat distribution in solid objects. Comparison of different materials by their thermal conductivity is possible due to the parameter – heat transfer coefficient. Materials of higher densities are usually better heat conductors; metals are excellent heat conductors. These materials are called heat conductors[11] . Specific heat capacity is the heat necessary for a slight increase in the temperature of the material in , divided by the mass of the material and the temperature increase [11] :
.
(3)
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
In figures, the specific heat capacity equals the heat necessary for heating one kilogram of material in 1 . We distinguish between the specific heat capacity at constant pressure and the specific heat capacity at constant volume . For solid materials and fluids we usually mean the specific heat capacity at constant pressure; for gases there is an evident difference between both specific heat capacities and their ratio represents the so-called Poisson constant. In majority of materials, specific heat capacity increases with increasing temperature. The SI unit is . . [11] . Thermal diffusivity expresses the material’s ability to balance differing temperatures at constant heat conduction in homogenous environment. Thermal conductivity is also referred to as the thermal diffusivity. This parameter indicates how the material conducts heat, i.e. how easily the temperature differences are balanced inside the material. For the simplification purposes, the following parameter is implemented[11] :
.
(4)
It equals the quotient of thermal conductivity . ିଵ . ିଵ . ିଵ and the product of its density . ିଷ and the specific heat capacity at constant pressure [11] . Heat conduction can be divided into: 1. Steady state heat conduction: o the difference in temperatures of individual object parts does not change in time. 2. Transient heat conduction: o temperature differences between individual object parts, between which the heat is transferred, are gradually balanced. 1.
Steady state heat conduction:
Heat transferred through the surface is determined by the so-called heat flux. The quantity of heat transfered through the surface in time is denoted as the heat flux density. If an object (e.g. a board), through which the heat is transferred, consists of layers with various thermal conductivities and thickness of for the layer , then in the steady state the heat flux density in all layers is identical, it means that:
(5)
For the overall difference in temperatures we will then get: . . . ∑
(6)
The heat flux density for such a board can be expressed as:
(7)
∑
The / quotient is called the specific thermal resistance of a layer. 2.
Unsteady state heat conduction:
We are examining the case of heat conduction through a board, occurring at sudden temperature increase on one of the board surfaces. If we divide the board into layers with the thickness of ∆ , the heat flux density in all the layers will not be identical to the one formed in the steady state heat conduction. The reason is that certain proportion of heat entering the layer is consumed to heat up the layer. The flux in the subsequent layer is then lacking this heat proportion. In our case, heat ! "∆# enters the layer with the thickness of ∆ and the surface of " in time ∆# and from the same layer, in the same period of time, the heat ! "∆# exits, while and are heat flux densities on the entering and exiting surfaces. The temperature of the layer is thus increased in the heat representing the difference between these temperatures, i.e.: ! ! "∆# Δ"∆#
(8)
If the specific heat capacity of the layer is $ and its mass is ∆ %"∆ , where % is the layer’s thickness, then: ! ! $Δ∆&
(9)
For the time change of the mean temperature of the layer, we will get the following expression from the calculations of relations above (in the limit for Δ ' 0 and ∆# ' 0) we will get the expression:
(10)
This relation represents a one-dimensional differential equation of heat conduction. This equation can be simply generalised for a three-dimensional case:
)
*
(11)
Conductivity or the heat transfer coefficient: +
∆
(12)
+ – conductivity W. m . K Then the Fourier’s Law can be described as: ∆ ∆
+. / ∆
(13)
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
Reciprocity within the heat conduction means that the conduction is reciprocally connected with the thermal resistance 0, which is determined by: 0
∆
∆ ∆
(14)
∆
It is the resistance which is additive, if several conductive layers are located between hot and cold regions, as / and ! are the same for all layers. In a multilayer section, the overall conductivity relates to the conductivities of individual layers:
(15)
in the solution of a multi-layer section, the following relation is applied:
o ∆
∆
∆
(16)
∆ ∆
Heat transfer from one object to another object by means of moving fluids (gases). A dominant form for fluids and gas. It comprises combined conduction processes, including especially thermal diffusion and heat transfer through a part of the fluid flow. Convective heat transfer coefficientin thermodynamics and in mechanical and chemical engineering, it is used when calculating the heat transfer, typically by convection or phase transfer (the transfer between the fluid and a solid object): 1
(17)
.∆
where, ! – heat flux / , 1 - heat transfer coefficient / , / – heat transfer area , ∆ – difference in temperatures of the solid surface and the surrounding environment. Table 1 Convective Heat Transfer Coefficient Values h 2/3! 4 Gases(no convection) Gases (convection) Fluids (no convection) Fluids (convection) Boiling fluids Condensing steam
15 15 – 250 100 100 – 2000 2000 – 35000 2000 – 25000
1 - is proportional to the coefficient between the heat transfer, i.e. heat flux, through the a unit area !// and the thermodynamic controlling force for the heat flux, i.e. the temperature difference ∆.
Heat transfer coefficient represents the inversion to the thermal insulation resistance (thermal insulation). It is often calculated from the Nusselt number which is dimensionless. Understanding of boundary layers of the flow requires understanding of convective heat transfer between the surface and the fluid flowing through it. Thermal boundary layer is described when the free thermal flux of the fluid and the surface temperature are different. The thermal profile exists with regard to the energy exchange resulting from this thermal difference. Heat transfer can be expressed as: ! 1. /" #
(18)
and as the heat transfer on the surface is carried out by conduction, ! . /.
$ $
" /5 0
(19)
The Newton’s Law that requires the constant heat transfer coefficient states that the heat loss value is proportional to the difference of temperatures between the object and the surroundings. Heat transfer value under these circumstances is derived as follows:
1. /& %& 1. /. Δ&
(20)
where, ! – is the thermal energy . , 1 - is the conductive heat transfer coefficient, / – is the area , – is the temperature of the object’s surface and its interior 6, %& – is the temperature of the environment, for example the temperature corresponding to the distance from the surface. ∆& & %& – is the time – dependent temperature gradient between the environment and the object.1 - dependson physical properties of the fluid and the physical situation in which the convection occurs. Radiation output: o thermal radiation capacity of the black body per a unit spatial angle and per unit frequency ν is determined by the Planck’s Law as: 78,
'(
.
%
(21)
or, 7 ,
)
.
%
(22)
where, : – is a constant The relation is derived as an indefinite sum of all possible frequencies. Energy ; 18 of each photon is multiplied by the number of possible conditions for the given frequency and the probability that each one of these possible conditions will be occupied.
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
By integrating the previous relation through 8, we will get the power determined by the Stefan Boltzmann’s Law as : < =. /. *
(23)
where the proportionality constant = is the Stefan – Boltzmann constant and / – is the radiation surface area. The following wavelength , for which the radiation intensity is the highest, is determined by the Wien’s Law as: + >/
(24)
For surfaces that are not black bodies it is necessary to consider a frequencydependent emission factor ?8. This factor must be multiplied, prior to integration, by the radiation spectrum formula. If the constant is understood as the resulting formula for the output power, it can be written so that it contains ? as a factor. < ?. =. /. *
(25)
This type of theoretical model with frequency-independent emissivity lower than for a perfect black body is often referred to as the grey body.
Methodology of the DMLS Process Simulation Using the Abaqus FEA software. All temperature and heat data are entered as constants or as functions of time. Simulation and analysis of thermal processes in DMLS include three main steps: 1. definition of boundary conditions 2. preparation of the script for the thermal software-assisted analysis 3. modelling of simulation steps. Determination of constants: o temperature of the building platform o temperature of the metal powder in the feeder o temperature in the process chamber Consideration of variables: o various sizes (dimensions) o various thicknesses o various types of supports o various laser settings (power) o various positions (placement) on the platform o laser trajectory (motion trajectory) o laser movement speed During the sintering process, each sintered layer with the thickness of 30 µm is subsequently covered with a following metal powder layer of the same thickness,
which is then sintered on the previous layer, where certain cooling effect occurs, which is followed by the heating process.
The process of analysis and simulation represents: 1. 2. 3. 4.
Preparation of the required input parameters for the simulation. Designing of testing FEA 3D models of parts, selection of dimensions, material composition. Proposal of the script of the laser sintering simulation. Testing of the proposed script, collection of recorded data.
Preparation of input parameters o Analysis of suitable biomaterials, collection of technical parameters of given biomaterials, analysis of their properties and verification of appropriateness of their utilisation. o Analysis of the sintering process using the EOSINT M 280 equipment, study of manuals, practical exams. o Video - analysis of the sintering process during the manufacture of a trial 3D model of a part. o Analysis of the performed studies focused on thermal analysis, heat conduct and flux using the finite element analysis (FEA). o Collection and analysis of input parameters necessary for the designing and execution of the model simulation of thermal processes during the manufacture of parts by laser sintering. Building platform: o dimensions 250 x 250 x 22 mm o preheating temperature: 40 – 100 ˚C o o o o
Direct Base S22 1.1730 tool steel mechanical working 8 mm fixation holes
Figure 1 Building Platform in the DMLS Process Configuration of the EOSINT M 280 sintering equipment: Process chamber of the EOSINT M 280 equipment includes individual operating systems with the following volumes:
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
1. 2. 3. o o o o o
building system: 21B dispenser system: 26B collector system: 13B
volume of the chamber (excluding individual systems) represents: 101B operating volume of the chamber has dimensions: 250 x 250 x 325 mm overall dimensions of the processing chamber are: 350 x 430 x 675 mm minimum thickness of a sintered layer: 0.03 mm laser beam diameter: d = 0.1 – 0.5 mm
Table 2 Material Properties and Parameters as the Input Data for the Simulation
Designing the FEA simulation models Creation of a testing 3D FEA model in the Abaqus environment. The emphasis was put especially on adherence to the required dimensions, simplification of the simulation process, and reduction in the requirements regarding the calculation performance of the system and the time required to perform the analysis.
Jozeef Živččáket al.FEA A Sim mulatioon of Therm T mal Prrocessses duuring the t Direct Metal M Laserr Sinteering oof Ti664 Titaanium Pow wder
Figurre2 FEA F Sim mulattion Moddel of o the Bu uilding P Platfo orm and d Inddividuual Meta M al Poowdeer L rs annd a detaail co Layer ontaiining g thee Reepressentaation n of Indiv I vidu ual L Layerrs. Thee buuildin ng pplatfform m posssessses the t presscrib bed stand s darddizedd dim menssionss 25 50 x 250 0 x 22 2 mm, m ddimeensioons of o thhe faabricatedd mettal powd p der laayerrs aree 10 x 100 x 0.03 0 mm m. Foor th he puurpoose of o more m accu uratee callculaation n, deenserr nettting g waas created in the areea off inddividdual layeers aand also on the layeers them t mselvves. Thee num mbeer off layers is 12. 1 T The messh of o laayerss is form med by orth hogoonal elemennts with w the dim menssionss 0.225 x 0.255 mm m; iit meeans thaat in the x an nd y axees th here are 40 x 40 elem mennts, reprresenntingg 160 00 eelemeents withhin one o layeer. Nettin N ng was w cchossen after a r iniccial pre--sim mulationss wh hich hav ve shhow wn optim o mal net n denssity in the areaa off ind dividdual layer l rs foor geetting g siggnificcantt calcculattion resu ults. Scrript prop posaal foor th he DM MLS S prrocesss simullatio on o
o
Preeparationn off input param meters foor thhe simulaation n. Thhe propo p osal of scrip s pt orr subbrou utinees foor the t simuulatiion of the laseer sinte s ring pro ocesss as a su uch. Coonsid derattion of innputt variiablees annd thheir impa i act on o thhe sim mulaationn couurse. Scrript prooposaal in th he sscrip pt edditorr. The T prop posaal coountss w with grad dual appplicaationn of indiividu ual llayerrs off titaanium m po owd der, i.e. i with w the adddition n off maateriaal annd afffectting prevvious layyers.. Th he propo osal takees intto coonsidderaation varriablle seettinggs off thee equuipm ment paraametters, as well w as other o settting optio ons. It also a couunts w withh a patter p rn, or o a traje t ectorry, of thee lasser beam b m moovem ment andd thee mo ovem ment speeed.
Figgure3 3 Suubrou utinee Preeparaation n andd thee Graaphiic Model M l for the Laseer Siinterring Proccess S ulatio Simu on.
Figuure 4 T Testiing of o prroposedM Methhodo ology y and d scrript in i 2D D.
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
3
Results and disscusion
Upon successful verification of the proposed methodology of the analysis focused on the thermal processes in the DMLS, it was possible to perform the simulation using and applying real values obtained from the expert literature and from experimental measurements. The subroutine of the simulation was supplemented with the values of temperatures of the building platform, protective atmosphere inside the process chamber, with radiation between individual models, i.e. with the values of constants and variables.
Figure5 Simulation of the Heating Process with the Representation of Heat Distribution in the Powder Bed. Based on the performed simulation of heating and cooling of the direct metal laser sintering technological process we can state that the heat distribution in the powder bed during heating, and thus the heat application, is unsteady and nonhomogenous, due to its nature. The sintered layer cooling as such occurred from the edges towards the centre, i.e. the centre of the metal layer. This phenomenon is caused by the higher heat accumulation in the centre of the sintered part where the flow impact in the surrounding environment is not so significant.
Figure 6 Cooling Process Simulation Including the Representation of Heat Distribution in the Metal Layer By analysing the cooling process Figure 6, it was observed that at the completion of the powder layer sintering the temperature in the last heated element is gradually rising. It is a result of the die-away and the heat trace impact. This increase in temperature is of the short-term nature and subsequently the temperature begins to fall due to convection.
Temperature (˚C)
1200
Tmax = 1039,8
1000 800 600
Tmin = 576
400 200 0 0
1
2
3
4
5
6
7
8
Time (s) Figure7 Temperature Development in the Course of Sintering a Single Powder Layer with the Thickness of 0.03 mm
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
Figure 7shows that during the sintering of a single powder layer the maximum achieved temperature was ௫ 1039.8 and the minimum temperature was 576 . The average temperature was ௩ 748.948 . A decisive factor in the heat distribution is the size of sintered parts, their thickness and the resulting number of powder layers. With increasing number of layers, the demonstrations of heat accumulation and more even heat distribution in individual layers begin to occur. At the same time, with a growing number of layers, the heat trace is more significantly demonstrated after the laser beam is applied, but in a relatively short period of time, the cooling and the heat trace reduction occur when the thermal conductivity and heat flux begin in the chamber. Another case is the temperature distribution during heating, where the increase in the powder bed boundary layers temperature was observed during sintering Figure 8. The difference was in the range of 100 200 . This phenomenon is probably caused by the contact between the boundary layer and the surrounding environment and by the fact that the heat conduction, and thus the heat removal, is carried out only partially and not from all sides, as is the case of elements inside the layer. The laser beam trajectory changes as well, while the shift to the following trace is of a small extent, and, as a result, the last element of the boundary layer impacts the adjacent element. Boundary element that was monitored during the entire simulation was gradually heated and when the steady condition was achieved, the temperature values were approximately in the range of 40 45 . The temperature of the monitored element within the laser beam impact area was changing in a wider range, approximately 580 1150 , which is shown in Figure 5. During heating, the boundary element’s temperature was monitored, as well as its response to gradual heat accumulation in individual layers. The main reason why building platform thermal processes simulation was chosen is because of its significant thermal capacity. It points out when preheating is applied, it can reduce, to certain extent, the temperature changes during the application of individual layers.
Fiiguree 8 Reepressentaationn of the Reac R chedd Maaxim mum Tem mperaturees duuringg thee Sinnteriing of o a Singgle L Layeer Aftter thhe po owerr vallue is i sett to P = 170,,000 mW W/mm m3, therm t mal trace t es caaused by y the laseer beeam passsagee throough h thee surrfacee werre leess siignifficannt annd wiith looweer values of recoorded d tem mpeeratuures. Onlly with w incrreasiing num n mber of layer l rs thhey becaame mo ore visibl v le, w whicch was also a cconffirmeed bby th he in ncreaased tem mperaaturee wiithin n the pow wderr bed d. Thhe laaser mov vemeent speed s d waas seet to the valuue off 125 50 m mm/ssec, 1,25 1 m/ssec, which rrepreesentts th he standaard settin s ng for f th he ex xternnal surfa s ace ddurinng laserr sintterinng ussing the DM MLS techn t nolo ogy. A smal s ll vaariannce aand trans t smisssion n of tempperaaturee valu ues arouund the t pplace off the laseer beeam imppact on the t surfa s ace of o thhe sinntereed metal m l pow wderr lay yer iis caaused d by low w theermaal coonduuctiviity of o thhe Tii64 mate m erial with h thee vaalue of and d goood heat h rem movaal th hrouggh th he build b ding plattform m. Itt is assu umedd thaat when w mo ore laayerrs arre appplieed, whic w ch in ncreaases the partt’s thick t knesss, th his pphenomeenon willl be redu ucedd andd thee tem mperaturee varriancce will w be b more m signnificaant.
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
Obtained results are in line with the performed works and the results reported by authors [4] [17] [18] [19] [20] [21] [22] [26] . The results are in compliance with the following conclusions: 1. Presented thermal model is able to forecast the temperature distribution and temperature fields in a metal layer of the sintered powder. 2. The highest temperature was not observed precisely in the centre of the laser beam but slightly toward the descending x – axis and the ascending y – axis, but still within the laser beam area. 3. Temperature rises with the gradual increase in the number of sintered layers 4. Temperature falls with the increasing hatching allocation. 5. Indication of a high temperature gradient between the sintered surface of the powder bed and the building platform. 6. With lower scan speed of the laser beam, the melting depth increase. 7. With reduced scan speed, the peak temperature increases; this is caused by the increase in energetic density, which corresponds to higher delivered output and lower scan speed. 8. Preheating of the building platform can increase the peak temperature on the surface of the sintered layer, but it can also decrease and reduce large temperature gradients between individual applied layers and the building platform. The FEA analysis has brought also other information, in terms of possible options of an analysis in the Abaqus software. This software proved to represent an appropriate tool for the FEA analysis, which is beneficial when performing such complex tasks. As for limitations of this FEA solver, no significant limitation was observed. The only concern is still represented by high hardware requirements for the analysis execution, but this problem must also be faced in case of other FEA software products, which was confirmed also in [7] . Possible ways how to speed up the analysis are as follows: reduce the number of records and use other methods to control the time step, heat several layers concurrently/thicker layers, and increase the laser dimensions lx, ly, and Ka – use the same values in standard circumstances.
Conclusions For the purpose of the analysis of thermal processes occurring during the DMLS process, the measurement methodology was proposed, counting with the use of the finite element analysis as a suitable tool for such complex task as the laser sintering of metal powder is. The performed analysis and simulation of thermal processes occurring during the laser sintering enabled better understanding of the behaviour of manufactured parts and the impact of heat on their properties. Recommendation for further research and the follow up in this area is to carry out thermal and mechanical simulation that would bring more outputs, especially regarding the analysis of stresses and tension inside the parts manufactured by the laser sintering method. Mechanical analysis and simulation would be focused primarily on thermal stresses in structures that might be caused by nonhomogenous heat distribution and thus formation of stresses, external limitations, i.e. bonds that prevent from free deformation of the structure (support), and differing thermal expansibility coefficients that occur in heterogeneous structures, while considering the equivalent of the viscoelastic impact when the heat flux is applied to the structure. Within further research in the given area, the intension is to create a CAD model of an implant with various numbers of layers and the FEA analysis directly inside the implant, which would provide further concrete results for the implant research and development. As for the next research, it is still necessary to examine this area and obtain the highest possible amount of information; it regards mainly various experimental applications within the laser sintering, such as the use of thermal camera and software prediction attempts with various settings of the sintering equipment which can serve as the basis for the production of relevant outputs usable in practice.
Acknowledgement The presented article was supported from the project KEGA 036TUKE-4/2013 Implementation of New Technologies in Implant Designing and Manufacture into the Education Process in Biomedical Engineering and Related Disciplines and project VEGA 1/0515/13 Draft design layout and architecture of intelligent implants.
Jozef Živčáket al.FEA Simulation of Thermal Processes during the Direct Metal Laser Sintering of Ti64 Titanium Powder
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