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AIAS 2017 International Conference on Stress Analysis, AIAS 2017, 6-9 September 2017, Pisa, AIAS 2017 International Conference on Stress Analysis, AIAS 2017, 6-9 September 2017, Pisa, Italy Italy
Parametric Finite Elements Model of SLM Additive Manufacturing process Additive Manufacturing process Thermo-mechanicalP.Conti modeling of a high pressure turbine blade of an a, * a a a, *, F. Cianettia, P. Pilercia P.Conti Cianetti , P. Pilerci airplane, F.gas turbine engine University of Perugia - Department of Engineering, via G. Duranti 67, Perugia, Italy
XV Portuguese Conference on Fracture, 2016, 10-12 February Paço de Arcos, Portugal Parametric FinitePCF Elements Model of2016, SLM
00
00
a a
University of Perugia - Department of Engineering, via G. Duranti 67, Perugia, Italy
P. Brandãoa, V. Infanteb, A.M. Deusc*
a
AbstractDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Abstract b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, An obstacle to the diffusion of additive technology is the difficulty Portugal of predicting the residual stresses introduced during the cobstacle An to the This diffusion of additive technology is the difficulty predicting stresses introduced during the fabrication process. problem has Engineering, a considerable practical interest asofevidenced bythe the abundant literature on 1,residual stresses CeFEMA, Department of Mechanical Instituto Superior Técnico, Universidade de residual Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, fabrication process. This a considerable practicaland interest as evidenced by theAdditive abundantManufacturing). literature on residual stresses and distortion induced byproblem the SLMhas (Selective Laser Melting) EBAM (Electron Beam Portugal and distortion by the (Selective LaserofMelting) EBAM (Electronon Beam Additive Manufacturing). The purpose ofinduced this paper is toSLM evaluate the effect differentand process parameters the heat distribution and residual stresses in The purpose of this with paperSLM is to evaluate theThree effectaspects of different process parameters on the heat distribution and residual stresses in components made technique. are developed and illustrated: a) thermomechanical modeling of the Abstract components made with Threewhich aspects are developed a) the thermomechanical modeling of the growth process, based onSLM Finitetechnique. Elements (FE), considers changes and in theillustrated: behavior of material (powderliquidsolid) growth on Finite (FE),technique which considers changes in the behavior of the of material (powderliquidsolid) throughprocess, the finitebased element “birth”Elements and “death” that enables the progressive activation the elements as the component During their modern engine components are the subjected increasingly operating conditions, through thesensitivity finiteoperation, element “birth” andaircraft “death” technique thatcharacteristics enables progressive activation ofdemanding the elements as the component grows; b) analysis of the model to the physical of thetomaterial (conductivity, specific heat capacity, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent grows; b) sensitivity analysis of the model to the physical characteristics of the material (conductivity, specific heat capacity, Young’s modulus). This is an important aspect allowing to focus on the most significant parameters to be determined degradation, one which model using the effects finitetoelement method was developed, in order be able to predict Young’s modulus). This is isancreep. important aspect on process the (FEM) mostparameters significant parameters toto be determined experimentally withofhigh reliability; c)Aevaluation ofallowing the offocus different (laser power, scan speed, overlap the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation experimentally with highonreliability; c) evaluation of the effects of different process parameters (laser power, scan speed, overlap between adjacent paths) the process. company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model between adjacent paths) the process. The article illustrates theontheoretical thermal model and the detail of the strategy used in the FE analysis. The most influential needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were The article illustrates the theoretical thermal model and the detail of the strategy used in the FE analysis. The most influential characteristics the that material are highlighted finally, criteria for choosing the were optimal of process3D obtained. Theofdata was gathered was fed and, into the FEMgeneral model and different simulations run,combination first with a simplified characteristics of the material are highlighted and, finally, general criteria for choosing the optimal combination of process parameters to limit residual stresses are provided. rectangular blockthe shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The parameters to limit behaviour the residualinstresses provided. was observed, in particular at the trailing edge of the blade. Therefore such a overall expected terms ofare displacement © model 2017 The Authors. Published by Elsevier B.V. can be useful in the goal of predicting turbine blade life, given a set of FDR data. Copyright © 2018 The Authors. Published by Elsevier © 2017 The Authors. Published by B.V. B.V. Peer-review under responsibility of Elsevier the Scientific Committee of AIAS 2017 International Conference on Stress Analysis. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis Peer-review under responsibility theElsevier Scientific Committee of AIAS 2017 International Conference on Stress Analysis. © 2016 The Authors. Publishedofby B.V. Keywords: FE model, Additive Manufacturing, Residual Selective Laser2016. Melting Peer-review under responsibility of the Scientificstresses, Committee of PCF Keywords: FE model, Additive Manufacturing, Residual stresses, Selective Laser Melting
Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.
* *
Corresponding author. Tel.: +39 075 585 3710; fax: +39 075 585 3703 E-mail address:author.
[email protected] Corresponding Tel.: +39 075 585 3710; fax: +39 075 585 3703 E-mail address:
[email protected]
2452-3216 © 2017 The Authors. Published by Elsevier B.V.
2452-3216 © 2017 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby Scientific Committee of AIAS 2017 International Conference on Stress Analysis. Peer-review underauthor. responsibility the Scientific Committee of AIAS 2017 International Conference on Stress Analysis. * Corresponding Tel.: +351of218419991.
E-mail address:
[email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 Copyright 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis 10.1016/j.prostr.2017.12.041
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Nomenclature
Φ �� � ℎ � R0 � � �� � �
absorbance of the layer surface emissivity void content (porosity) Stefan-Boltzman constant density time specific heat capacity Young modulus convection coefficient thermal conductivity laser spot radius power of the laser beam heat flux overlap ratio between two laser scans temperature beam scan speed
(W/m2 °K4) (Kg/m3) (sec) (J/Kg °K) (Pa) (W/m² °K) (W/m °K) (μm) (W) (W/m2) (%) (°K) (mm/sec)
1. Introduction Selective laser melting (SLM) is an additive manufacturing (AM) technique through witch a complex metal part can be fabricated by piling up layers of melted material, I. Gibson et al. (2010), A.E. Patterson et al. (2017). During the process, a thin metal powder layer is selectively melted by a controlled laser beam; the material undergoes many physical transformations (from powder to liquid and then to solid) and severe temperature fluctuations resulting in relevant residual stresses, significant distortions and, in some cases, cracks and delaminations, P. Mercelis et al. (2006). The evaluation and elimination of the residual stresses in parts fabricated with A.M. is a paramount aspect and many efforts are addressed to this goal, R. Paul et al. (2014); a review of the literature on FE analysis in SLM can be found in K. Zeng et al. (2012) , A.E. Patterson et al. (2017) and Markl et al. (2016). In SLM, the laser spot scans the powder layer according to a particular pattern and builds up the component layer by layer; some areas will overlay previous solidified layers, other areas could overhang unprocessed powder areas, therefore some support structure must be foreseen to link the part to the base plate and limit the distortions that could be induced. The process parameters like laser power, scanning parameters, scanning speed must be optimized to ensure that the powder is fully melted and bonded to the underlying layer. The scanning strategy heavily influences the final result in terms of defects, porosity, resistance but also in terms of microstructure of the material and thermal behavior, L.N. Carter et al.(2014). The SLM process develops large cyclic thermal gradients generating high stresses and deformations depending on the scanning strategy, P. Mercelis and J.P. Kruth (2006), J.P. Kruth et al. (2012), J.P. Kruth et al. (2004). A numerical model of the process can be a useful and cheap tool to compare different parameter settings and suggest the most suitable choice. A numerical model must rely on an accurate formulation of the thermal history the material undergoes during its transformation from a powder to a solid. Many studies are available on this subject; modeling of the laser spot was developed by many authors, J. Goldak et al. (1984), S. Kolossov et al. (2004); complete heating models are proposed, A.V.G. Gusarov et al. (2009), K. Dai and L. Shaw (2005); some models were experimentally tested with sophisticated techniques, A.S. Wo et al. (2014) and some specific experimental procedures are proposed, D. Cerniglia et al. (2015). All the numerical models, based on Finite Elements (FE), try to forecast residual stresses and deformations and many results are available, N. Contuzzi et al.(2011), A. Hussein et al. (2013), J.C. Heigel et al. (2015), A. Ahmadi et al.(2016), F. Mukerjee et al. (2017). An overview of the thermal analyses proposed can be found in K. Zeng (2012). The present paper is intended to evaluate the sensibility of the model with respect to uncertainties on the real value of the main physical proprieties of the material in order to understand where to concentrate the experimental
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characterization activity. The model also allows to choose the most promising combination of technological parameters (scan speed, laser power, path overlapping). The work is based on FE modeling of a thin stack of layers realized with SLM technique, the material considered is stainless steel AISI316L, a material often used in industrial applications; the bulk characteristics of AISI316L can be found in K.C. Mills (2002). The more relevant simplified hypotheses adopted in the work are:
The thermal characteristics are assumed to be piecewise linearly dependent from temperature as shown below, The powder characteristics are assumed to be linearly dependent from porosity, Absorbance is assumed constant for powder and bulk material, Latent melting energy is not explicitly considered but its effect is simulated by a steep rise of the specific heat capacity.
2. Model description 2.1. Thermal balance In order to model the selective laser process, many physical aspects must be taken into account. During the creation of a component a laser beam scans a thin layer of metal powder and heats up a small cell until the melting temperature is reached; afterwards the cell cools down again as the laser spot moves away. In this process, the material undergoes many state transformations (powder liquid solid) accompanied by shrinkage, density change, material structure changes. Moreover, the same cell will be cyclically heated up and cooled down as the laser beam impinges neighboring regions of the same layer or the corresponding region of the next layer. A model of the process must consider all these aspects (Y. Li et al. 2014) which depend on temperature history; the main problem to be addressed is therefore the mathematical formulation of the thermal process. A balance of heat input and heat output in a single cell must be established. During the SLM process, the heat input is represented by the laser beam energy absorbed by the layer surface and the heat outputs are represented by heat losses from the cell due to conduction, radiation and convention, I.A. Roberts et al. (2009). The balance between input and output heats up the cell and supplies the latent heat to melt the powder. The governing equation of the thermal balance is, J.C. Heigel et al. (2015), K. Dai (2005):
�� �(�) �(�)� = ��� � · ∇�� + �� �(�) · �� (�) �(�) · �� (�)
(1)
Eq. (1) must be completed with boundary conditions on the free edges represented by the radiation losses and convection losses, respectively ���� = ��(��� − ��� ) and ����� = ℎ(�� − �� ) where �� represents the surface temperature and �� the fabrication room temperature. All the parameters are temperature dependent, L. Papadakis et al. (2014). Moreover, during the phase change, a further term should be added to the right side of Eq. (1) to take into account the latent heat. In this paper - as illustrated below - the influence of the latent heat was simulated by a sudden rise of the specific heat at the melting temperature, A. Hussein et al. (2013). 2.2 Model of the laser beam spot The incident energy flux from the laser beam is assumed to have an axisymmetric Gaussian distribution. With this hypothesis, �(�, �, �) - the energy flux - is related to the laser power through the following relation, K. Dai (2005): �
2�� ��� ��� � � �(�, �, �) = �� ���
�
(2)
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Where �� is the radius of the laser beam at which the heat flux is reduced by a factor 0.13 with respect to the flux at the center of the beam; �, � are the coordinates on the building plate (� will be the growth direction) in a reference system centered in the laser beam center and � is the laser power.
2.3 Material characteristics
As shown in Eq. (1), many thermal characteristics must be evaluated, moreover, the characteristics will differ between powder and bulk material, they will be temperature dependent and will switch from one to another during the melting process. Let’s first consider the powder characteristics dependence from porosity. Following the approach suggested by A. Hussein et al. (2013), porosity can be defined through the void fraction Φ corresponding to:
Φ=
����� − ������� �����
(3)
We assume thermal conductivity to be linearly dependent from porosity, and, of course, also the density will obey to the same scheme.
������� = ����� (1 − Φ)
(4a) (4b)
������� = ����� (1 − Φ)
The dependence of the characteristics with the temperature must also be considered. The approach suggested by A. Hussein et al. (2013), was adopted. In K.C. Mills (2002) many data on variation of the thermal characteristics of AISI 316L steel with temperature are reported and the assumption in the present work are based on these data. The temperature range was divided in three intervals bounded by the ambient temperature (293 °K) and the transition melting range bounds (1670 °K and 1723 °K respectively). A linear variation was assumed inside every temperature span in accordance with the model of A. Hussein et al. (2013). The specific heat of the powder is not directly dependent from the temperature as in Eq. (1) the dependence is introduced by the variation of the density according to Eq. 4b. Thermal expansion was assumed to be zero in the powder at room temperature and steeply increasing up to bulk material at melting temperature. 9000
900 Bulk Powder
850
8000
specific heat [J/(kg°K)]
800
density [kg/m3]
7000
6000
5000
750 700 650 600 550 500
4000
450 3000
400
3
10
temperature [°K]
Fig. 1. Density vs. temperature
3
10
temperature [°K]
Fig. 2. Specific heat vs. temperature
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3
x 10
-5
35 Bulk Powder
thermal conductivity [W/(m°K)]
thermal expansion coefficient [1/°K]
2.5
2
1.5
1
0.5
0
Bulk Powder
30
25
20
15
10
5
0
3
10
3
10
temperature [°K]
temperature [°K]
Fig. 3. Thermal expansion coefficient vs. temperature
Fig. 4. Thermal conductivity vs. temperature
Young's modulus [Pa]
The resulting dependence of the thermal characteristics with temperature is summarized in fig. 1 to 4. The Young modulus was assumed very small (the value should be virtually zero but a small value was adopted to obtain a positive definite stiffness matrix) for the powder and for the melted material; the other values were interpolated from data reported in K.C. Mills (2002). Fig. 5 summarizes the dependence of the Young’s modulus from temperature. 10
12
10
10
10
8
10
6
10
4
10
2
10
0
Bulk Powder
3
10
temperature [°K]
Fig. 5. Young’s modulus vs. temperature
2.4 Finite element model The Finite Elements (FE) model is intended to reproduce the SLM strategy called “Island Scan Strategy” developed by Concept Laser ™ to reduce residual stresses and deformation. The idea is to randomly scan very small areas across the layer to limit local strains. The layer area is first broken into a square grid and then single squares (“islands”) - randomly chosen - are scanned with a regular pattern, L.N. Carter et al. (2014). Two adjacent islands have always orthogonal scanning directions. The strategy is explained in Fig. 6 (from I. Gibson et al. (2010)). The scope of this work is limited to the simulation of a single island. The iterative FE analysis reproduces the scanning pattern, the square area will be scanned with path snaking from left to right, and right to left at fixed speed until the entire area has been scanned.
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Two adjacent scanning paths can overlap and will have opposite scanning vectors. During this process, every cell will be heated up and cooled down many times as the laser beam impinges its neighborhood. While the layers pile up a new scanning pattern (orthogonal to the former) will be added and again every pixel will be heated up to melting temperature and cooled down.
Fig. 6. “Island Scan Strategy” - Gibson et al. (2010)
Fig. 7. Physical description of the model
To consider this scenario, the “birth and death” technique implemented in the commercial code ANSYS was adopted. With this technique, a complete FE model can be built with some elements “active” and some “idle”. At each recursive analysis, the idle elements can be switched on (birth) and active elements can be switched off (death). A control loop determines when an element is activated according to whether its temperature after a load step has surpassed or not the melting point. This a very powerful approach that allows to model the entire structures but each step takes into account only a part of the model. In the present work, the entire stack of layers was modeled at the beginning but only the elements belonging to the scanned layer and the underlying layers where active; this reduces significantly the calculus burden.
Fig. 8. FE model
During the production of a component with SLM, the first layer is attached to e support plate and the layers pile up during the growth. The FE model considers the plate, three layers of powder (at the beginning only the first one will be active and, progressively the other will be switched on thanks to the “birth and death” technology. Fig.7 shows the model, the gray region corresponds to the plate and the brownish region represents the powder. As one can see, a large region around the scanned island is modeled to better simulate the thermal behavior. The FE model was realized with 8-nodes hexahedral elements (SOLID5), every powder layer was split into three elements trough the thickness while the plate is modeled with one element only through the thickness. Fig. 8 displays the meshed model (only one layer is displayed) and the physical dimensions are listed in tab I.
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The boundary conditions simulate the laser heating without any mechanical load. The room temperature is set at 353 °K and the bottom face of the baseplate has all the nodes with the same constant temperature (353 °K). At each step, a subroutine defines the position of the laser beam (depending on the scan speed) and calculates the heat flux to be assigned to the element nodes belonging to the beam area in accordance with Eq. (2). Each step consists in an incremental analysis divided in sub steps of nearly 0.001 sec. At each sub step the thermomechanical characteristics are updated according to the new temperature. When the melting temperature is reached the thermal characteristics switch from “powder” to “bulk”. When the temperature lowers again below the melting point, the Young’s modulus switches from “liquid” to “solid”. Tab. I Physical characteristics of the FE model Geometrical characteristic Scanned island size Layer thickness Entire model size Baseplate thickness Laser beam diameter (Ro) Element side Porosity of the powder Absorbance of the layer N° of elements per scanned island side
Value
Units
1×1 20 5×5 10 50 25 × 25 0.2 0.3 40
[mm] [μm] [mm] [mm] [µm] [μm]
3. Numerical testing program Two sets of FE analysis were performed. The first one to investigate the robustness of the SLM model with respect to small changes in the material characteristics because many of them are evaluated with simplified extrapolation from literature data. The second one to compare different sets of three technological parameters (laser power, overlap and beam speed) in order to evaluate if a FE approach can help in optimizing the SLM process. Both the investigation rely on a DOE approach. 3.1. Robustness evaluation The parameter to investigate are thermal conductivity, specific heat capacity and Young’s modulus. The diagram of fig.2, 4 and 5 were modified and the values were first magnified by a factor 1.1 and then reduced by a factor 0.9 corresponding to a high level and a low level of the characteristics. A set of 8 FE analyses was carried on according to the plan reported in the left side of Tab. II The results of a specific test (test no. 1) with ܵ = ݒ0.25, ܸ= 25 mm/sec and ܳ = 100 W is displayed in fig.9 and 10. The figures represent the temperature pattern (fig. 9-a) and the residual stresses at the end of the last iteration (fig.9-b). As one can see in fig.9-a, the red spot at the top right of the scanning island is at very high temperature and the material is melted. Moving away from the beam center the material is cooling down. The temperature pattern is not symmetrical because the laser beam was moving from left to right. Fig.9-b display the stress field. Again, the top right corner is free of stress because the material is still liquid. Away from the melted pool, the residual stresses are high because the baseplate prevents the solidified layer from shrinking. We must point out that the stress values are not really significant as the model did not consider the plasticization of the material; the residual deformation should be more significant; the stress values can be used only for comparison purpose between different analyses. Fig.10 displays a detail of fig.9. In this figure, it appears that some cell at the border of the island are not melted and some other, outside, are melted. One must however keep in mind that the islands grow one next to another and these defects will disappear when the surrounding cells will melt at their turn.
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Tab.II – Results of the finite elements analyses Test number 1 2 3 4 5 6 7 8
Analyses plan Conductivity Specific heat level (݇) level ()ܥ × 0.9 × 0.9 × 0.9 × 0.9 × 0.9 × 1.1 × 0.9 × 1.1 × 1.1 × 0.9 × 1.1 × 0.9 × 1.1 × 1.1 × 1.1 × 1.1
Young’s modulus ܧ × 0.9 × 1.1 × 0.9 × 1.1 × 0.9 × 1.1 × 0.9 × 1.1
Results Max. Temp Max. Stress [°K] (diag.) [MPa] 2890 880 2890 1075 2813 864 2813 1056 2527 824 2527 1008 2459 828 2459 1012
Fig. 9a – Test no.1 – Temperature pattern (all the model)
Fig. 9b – Stress pattern (all the model)
Fig.10a – Test no.1. Temperature pattern (only scan island)
Fig.10b – Test no.1. Stress pattern (only scan island)
The data were analyzed with DOE techniques to verify the influence of the physical parameters on the process performances. Two performance features were considered; the first one is the maximum temperature in the scanned island: it is a clue of the complete melting of the layer. The second one is the maximum stress along the diagonal (down-left/top right). It was chosen, instead of the absolute maximum stress, because of some non-meaningful stress concentrations around the non-melted pixels that could bias the result. The complete results are displayed in Tab. II, right side. As one can see, the maximum temperature are identical for every couple of tests; it is an expected result as the only difference between the parameters set is the Young’s modulus which does not affect the thermal behaviour.
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Fig. 11 synthetizes the results of the DOE analysis with regards to maximum temperature in the entire process. The bar diagram shows the relative influence of the physical parameters and their cross effects. It is evident that the influence of the Young modulus is null, as expected; the heat capacity has not a very significant influence but the parameter k, thermal conductivity, has a relevant importance as it represent the main cooling mechanism. We can argue that a reliable FE model requires a precise knowledge of the thermal conductivity, more experimental studies must investigate the evolution of the thermal conductivity in the powders at different void content and temperature. Fig. 12 synthetizes the results of the DOE analysis with regards to maximum stress along the diagonal in the entire process. Here all the parameters have some significant influence but, of course, the most important factor is Young modulus. Again, the thermal conductivity is important but a combined effect of specific heat capacity and conductivity is relevant too; this last result can suggest that the important parameter could be a combination of the two formers and therefore thermal diffusivity, �/���, could be a more meaningful parameter for the optimization of the SLM process.
A = Thermal conductivity B = Specific heat capacity C = Young modulus
A = Thermal conductivity B = Specific heat capacity C = Young modulus Fig. 11 – Effects on maximum temperature
Fig. 12 – Effect on maximum stress
3.2. Optimization of the technological parameters The scope of this analysis is the comparison of different sets of three technological parameters (laser power, overlap and beam speed). For every parameter three levels were considered (Tab III). Tab. III – Parameters levels Laser power [W] Scan speed [m/sec] Overlap [%]
Low level 100 25 0
Mean level 120 50 25
High level 150 100 50
A set of ten FE analyses were carried on. Two different aspects can be considered in order to compare the performance of the parameter set: the maximum temperature and percentage of melted elements. Tab. IV summarizes the results. On the basis of the first 8 test of Tab. IV it appears that the most significant parameter is the speed of the laser beam. This result is highlighted in fig.13 - based on DOE analysis of the first 8 tests - where the influence of the different parameters is displayed. The parameter sets of the first 8 tests are in accordance with an L8 orthogonal test array (R.K. Roy, 2001). Tests no. 9 to no. 10, which do not belong to an orthogonal array, confirmed the results. The last column of Tab. IV shows that in many tests the quantity of elements melted was too low, only the tests with low speed yield acceptable performances Two results are displayed in fig.14 and 15. Fig 14 refers to test no. 6: only 70% of the elements are melted because the heat does not penetrate inside the layer. Fig. 15, corresponding to test no. 9, shows a comparison between the melted elements and the initial meshed model; here 97% of the elements are melted.
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The results allow to conclude that the FE model could suggest the most appropriate combination of the process parameters. Tab. IV – Results of the second set of tests Test N°
Power [W]
Speed [mm/s)]
Overlap [%]
Temperature [K]
Melted elements [%]
1
100
50
0
2301
33
2
100
50
25
2286
51
3
100
100
0
1962
13
4
100
100
25
1961
21
5
120
50
0
2679
54
6
120
50
25
2661
77
7
120
100
0
2255
24
8
120
100
25
2240
39
9
120
25
25
2846
97
10
150
50
25
3202
95
A = Laser power B = Beam speed C = Overlapping Fig. 13 – Effect on fraction of melted elements
Fig. 14 – Test no. 6 – Temperature pattern. Only melted elements are displayed (70%)
Fig. 15 – Test no.9 – Elements Only melted elements are displayed (97%)
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4. Conclusions This work presented represents an attempt to model additive manufacturing and to forecast the performances. The specific heat dependence and thermal conductivity from the temperature have been greatly simplified; these simplifications make the model a useful tool for assessing the influence of individual parameters and comparison of different settings of project parameters although not very accurate. All the results are purely numeric and therefore an experimental is test program required to correctly tune the FE model. An observation concerns the model of the heat source; the effect of the Gaussian distribution in our model is not significant because the laser area affects at most sixteen elements and only four elements at a time are completely illuminated by laser spot and twelve are partially illuminated; a uniform laser beam could be modeled without significant effect on the results. A more refined discretization should be used to make the Gaussian distribution meaningful but this would increase dramatically the analysis time. On the basis of the results some future improvement can be foreseen:
the latent melting heat must be considered in a more sophisticated to better adhere to the physic of the process; the dependence of the thermal conductivity from the temperature and its variation between powder and bulk material must be studied more deeply. The use of a different program, more suitable for thermomechanical combined analysis, could give more accurate results, the method could be a tool to create a useful base of knowledge in terms of deformations and residual stresses of different materials (aluminum, titanium alloy, steel, etc.).
References Ahmadi A., Moghaddam N.S., Haluk M.E., Karaca E., Mirzaeifar R., 2016. Finite Element Modeling of Selective Laser Melting 316L Stainless Steel Parts for Evaluating the Mechanical Properties. ASME 2016 11th International Manufacturing Science and Engineering Conference, Volume 2. Carter L.N., Martin C., Withers P.J., Attallah M.M., 2014. The Influence of the Laser Scan Strategy on Grain Structure and Cracking Behavior in SLM Powder-Bed Fabricated Nickel Superalloy. Journal of Alloys and Compounds, 615, 338-347. Cerniglia D., Scafidi M., Pantano A., Rudlin J., 2015. Inspection of additive manufactured layered components. Ultrasonics 62. 292-298. Contuzzi N., Campanelli S.L., Ludovico A.D., 2011. 3d Finite element analysis in the selective laser melting process. International Journal simulation model, 10(3), 113-121. Dai K., Shaw L., 2005. Finite Element Analysis of the Effect of Volume Shrinkage During Laser Densification, Acta Material, 53, 4743-4754 Gibson I., Rosen D.W., Stucker B., 2010. Additive Manufacturing Technologies. Springer. Goldak J., Chakravarti A., Bibby M., 1984. A new finite element model for welding heat sources. Metallurgical Transactions B, 15, 299-305. Gusarov A.V., Yadroitsev I., Bertrand Ph., Sumurov I., 2009. Model of Radiation and Heat Transfer in Laser-Powder Interaction Zone at Selective Laser Melting. Journal of heat Transfer, 131. Heigel J.C., Micharelis ThP., Reutzel. E.W., 2015. Thermomechanical model development and validation of direct energy deposition additive manufacturing of Ti-6Al-4V. Additive manufacturing, 5, 9-19. Hussein A., Hao L., Yan C., Everson R., 2013. Finite Element Simulation of the Temperature and Stress Fields in Single Layers Built WithoutSupport in Selective Laser Melting. Materials and Design, 52, 638-647 Kolossov S., Boillat E., Glardon R., Fischer P., Locher M, 2004. 3D FE Simulation for temperature evolution in the selective laser sintering process. Int. J. Machine Tools and Manufacture, 44, 117-123. Kruth, J. Deckers J.P., Yasa E., Wauthé R., 2012. Assessing and comparing influencing factors of residual stresses in selective laser melting using a novel analysis method. Proceedings of the institution of mechanical engineers, Part B: Journal of Engineering Manufacture. Kruth J.P., Froyen L., Van Vaerenbergh J., Mercelis P., Rombouts P., Lowers B., 2004. Selective laser melting of iron-based powder. Journal of Materials Processing Technology 149, 616-622. Li Y., Gu D., 2014. Parametric analysis of thermal behavior during selective laser melting additive manufacturing of aluminum alloy powder. Materials and Design, 63, 856–867 Markl M. and Korner, C., 2016. Multiscale Modeling of Powder Bed-Based Additive Manufacturing. Annual Review of Materials Research, 46, 93-123 Mercelis P., Kruth J.P., 2006. Residual stresses in selective laser sintering and selective laser melting Rapid Prototyping Journal, 12(5), 254-265 Mills K.C., 2002. Recommended Values of Thermophysical Properties for Selected Commercial Alloys. Woodhead Publishing. Mukherjee T., Zhang W., DebRoy T., 2017. An improved prediction of residual stresses and distortion in additive manufacturing. Computational Materials Science, 126, 360-372. Papadakis L., Loizou, A, Bremen, S, Risse J.and Schrage J., 2014. A computational reduction model for appraising effects in selective laser melting. Virtual and Physical Prototyping, 9(1), 17-25.
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Patterson A.E., Messimer S.L., Farrington P.A., 2017. Overhanging Features and the SLM/DMLS Residual Stresses Problem: Review and Future Research Need (Special Issue in Additive Manufacturing Technologies and Applications). Technologies, 5, 1–21 Paul R., Anand S., Gerner F., 2014. Effect of thermal deformation on part errors in metal powder based additive manufacturing processes Journal of manufacturing Science and Engineering, 136. Roberts I.A., Wang C.J., Esterlein R., Stanford M., Mynors D.J., 2009. A three-dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing Int J Mach Tools Manuf, 49(12), 916-923 Roy R.K., 2001. Design of experiments usimg the Taguchi approach. John Wiley & sons. Wo A.S., Brown D.W., Kumar M., Gallegos G.F., King W.E., 2014. An Experimental Investigation into Additive Manufacturing-Induced Residual Stresses in 316L Stainless Steel. Metallurgical and Materials Transactions A, 45(13), 6260–6270. Zeng K., Pal D., Stucker B., 2012. A review of thermal analysis methods in laser sintering and selective laser melting, Proceedings of Solid Freeform Fabrication. Symposium, 23, 796–814.
