- Email: [email protected]
Prediction of Residual Stress and Part Distortion in Selective Laser Melting
Available online at www.sciencedirect.com
ScienceDirect Procedia CIRP 45 (2016) 171 – 174
3rd CIRP Conference on Surface Integrity (CIRP CSI)
Prediction of Residual Stress and Part Distortion in Selective Laser Melting C. Li, J.F. Liu, Y.B. Guo* Dept. of Mechanical Engineering, The University of Alabama, Tuscaloosa, AL35487, USA * Corresponding author. Tel.: +1-205-348-2615; fax: +1-205-348-6419. E-mail address: [email protected]
Abstract Selective laser melting (SLM) is widely used to make functional metal parts. The high-temperature process will produce large tensile residual stress (RS) which leads to part distortion and poor product performance. Traditional modeling approaches are not practical to predict residual stress and part distortion due to the exceedingly high computational cost. In this study, two efficient multiscale modeling methods have been developed to across microscale laser scan, mesoscale layer hatch, and macroscale part buildup for fast prediction of residual stress and part distortion. A concept of equivalent heat source has been developed from the microscale laser scan model. In the “stress-thread” method, the local residual stress field was predicted by the mesoscale layer hatch model using the equivalent heat source, then the residual stress field is imported, i.e., “stress-thread”, to the macroscale part buildup model to predict residual stress and part distortion. In the temperature-thread method, the powder–liquid–solid material transition has been incorporated. A body heat flux obtained from the microscale laser scan model is applied, i.e., “temperature-thread”, to the hatch layer. Then multiple hatches are sequentially “deposited” in the macroscale part buildup model with different scanning strategies. The predicted part distortions by both methods were compared and compared with the experimental data. © 2016 The Authors. Published by Elsevier Elsevier B.V. B.V.This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the scientific committee of the 3rd CIRP Conference on Surface Integrity (CIRP CSI) (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 3rd CIRP Conference on Surface Integrity (CIRP CSI) Keywords: residual stress; selective laser melting; distortion, multiscale modeling; selective laser melting; additive manufacturing
1. Introduction 1.1. SLM process and part distortion Selective laser melting (SLM) is capable of producing functional parts in a layer upon layer fashion directly from CAD data [1]. Parts by SLM are near full density and have mechanical properties comparable to bulk materials [2, 3]. In a typical SLM system, a fine powder layer is placed on a substrate inside an inert chamber and is fully melted by a laser. After one layer is deposited, another layer will be placed and melted until a part is produced. Several defects usually exist in a SLM part. High thermal stress would lead to part distortion and cracks. The balling effect may result in poor surface finish [4]. Also, residual gas content, unmelted powder, and oxidized particles may lead to porosity of the component [5, 6]. The uneven heat input as well as the rapid cooling of the process generates large amounts of tensile residual stresses in the component. It not only reduces the part geometrical
accuracy but also and detrimentally affects the functional performance of the end-use parts. Simulation work [7, 8] has been done to predict residual stress and distortion of SLM parts on the micro or mesoscale, in which only single tracks or multi-tracks were considered. Some studies [9, 10] predicted residual stress and part distortion in SLM on the macroscale. In these models a constant heat flux was applied to heat an entire scan line or an entire layer at the same instant to predict the temperature and residual stress distribution of macro part. 1.2. Pressing issues and research objective A coupled thermal-mechanical analysis for several single scans with a fine mesh model is very time consuming. A practical SLM part on the macroscale requires millions of microscale laser scans which dramatically increases the computational load for the calculation of a coupled analysis. Thus, it is impossible in practice to predict the distortion of a practical SLM part if every scan is simulated.
2212-8271 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 3rd CIRP Conference on Surface Integrity (CIRP CSI) doi:10.1016/j.procir.2016.02.058
172
C. Li et al. / Procedia CIRP 45 (2016) 171 – 174
The objectives of this study are to develop and compare temperature-thread based and stress-thread based multi-scale approaches for efficient prediction of part distortion and residual stress by: (a) developing a novel equivalent heat source in mesoscale layer hatch from a microscale laser scan; (b) calculating the residual stress field and distortion of a practical part at macroscale; and (c) compare the predicted distortion results with the experimental data.
based on the thermal data in the microscale scan model for both methods, the heat load is directly applied to the mesoscale hatch model. Third, the thermal history of one hatch layer is applied to the macroscale part model, and each hatch layer is activated one by one until the whole part is built.
2. SLM experiment conditions
Model dimensions In the microscale scan model, a thermal analysis was conducted using the FEA package ABAQUS/Standard to predict the temperature field in the melt pool. The powder layer with thickness of 0.15 mm was placed on the substrate. The powder layer was 5 mm in length, 0.3 mm in width and 0.15 mm in thickness. The substrate was 5 mm in length, 0.3 mm in width and 5 mm in height. The initial temperature of the whole model was set to room temperature 20 °C. Laser heat source modeling A moving Gaussian distributed heat flux is developed to model the heat input of the scanning laser in the microscale model. The temperature field of the melt pool was captured when the laser travelled to the center point of scan track, and this field was used to develop equivalent heat source for stress-thread based method. The thermal history (heating and cooling) of the center point of scanning track was recorded for equivalent heat source development for temperature-thread based method. Temperature data output Fig. 2(a) shows the temperature field of the cross-section of the melt pool when the laser is located at the center of the scan track. This temperature field will be extended on a larger scale with scan spacing considered, used for mesoscale model in stress-thread method. Fig. 2(b) shows the thermal history of the melt pool center which will be used for developing an equivalent heat source for temperature-thread method.
The laser source in this study is a continuous Nd:YAG laser with a wavelength of 1064 nm. The process parameters are listed in Table 1[3]. This study aims to predict part distortion and validate with the experimental data using the lab-made iron-based powders, but the material properties are not available, so a commercial powder with similar chemical composition is used instead as an approximation, it would be a future research subject to investigate the effect of temperature-dependent material data on model accuracy. The temperature-independent mechanical and thermal material properties are [11]: the elastic modulus is 130 GPa, the Possion’s ratio is 0.41, the tensile and yield stress is 600 and 400 MPa, the melting point is 1330 oC, the coefficient of thermal expansion is 9 × 10-6/K, the thermal conductivity is 13 W/m·K, and the specific heat is 375 J/kg·K. Table 1 SLM process parameters [3] Laser power
Beam dia.
Scan speed
Scan spacing
Layer thickness
300 W
600 μm
50 mm/s
100 μm
150 μm
3. Multiscale simulation approaches Two types of multi-scale finite element methods have been developed and compared, i.e., the stress-thread based and temperature-thread based methods. Detailed procedure for both methods is shown in Fig. 1. For both methods, the powder material is melted by a moving heat flux to capture the thermal data of a melt pool in the microscale laser scan model. In the stress-thread method, the temperature field of the melt pool is recorded. In the temperature-thread method, the entire thermal history of the melt pool is recorded. Second, two types of equivalent heat sources are developed Output x Melt pool geometry x Temp. field of the melt pool
Meso layer hatch model x Thermal-mechanical analysis x Equivalent heat input x Whole hatch heated at same time Stress-Thread
Output x RS field x Part distortion
3.2. Meso layer hatch model Scan spacing is an important SLM process parameter and defined as the length of overlap between two neighboring scan tracks. In this study, the scan spacing was incorporated in the equivalent heat source in the mesoscale hatch model for both the stress-thread and temperature-thread methods.
Micro laser scan model x Thermal analysis x Powder heated by moving heat flux Stress-Thread
Output x Temp. field of one hatch x Local RS field
3.1. Micro laser scan model
Macro part model x Mechanical analysis x Apply local RS field x Applied hatch by hatch
Output x Melt pool geometry x Temp. history of the melt pool
Temperature-Thread Meso layer hatch model x Thermal analysis x Equivalent heat input x Whole hatch heated at same time
Output x Temp. history of one hatch
Temperature-Thread Macro part model x Thermal-mechanical analysis x Apply equivalent heat source x Applied hatch by hatch
Output x RS field x Part distortion
Fig. 1 Stress-Thread based and Temperature-thread based method for the prediction of distortion of SLM parts.
173
C. Li et al. / Procedia CIRP 45 (2016) 171 – 174
Temperature field in the c cross-section of melt pool
5000 4000
Temp. (°C)
(a)Stress-thread
Cooling
Heating
3000
Temp. (°C)
2000 1000
0 0
Melt pool center
0.05
0.1
Time (s) (b) Temp.-
Fig. 2 Output of microscale laser scan model. (a) Stress-thread: temperature field in the cross-section of melt pool; (b) Temperature-thread: temperature contour in the melt pool and temperature history at the center of melt pool.
Equivalent heat source modeling For the stress-thread method, an equivalent heat source was developed based on the temperature field of the crosssection of the melt pool from the micro scan model. Multiple scan tracks were deposited simultaneously with the fixed scan spacing taken into consideration. The mesoscale hatch model for the stress-thread method was a thermal-mechanical coupled model. After the powder and substrate were cooled down to room temperature, the residual stress field of the part , and this averaged residual stress will be averaged as tensor was applied to each corresponding patch, detail method could be found in [12]. For the temperature-thread method, the melt pool shape was simplified to a cuboid with a length of laser spot diameter ds, a width of scan spacing H, and a depth of melt pool dm. The equivalent body flux was defined as the power density (W/m3) which represents the input power for unit volume of melted material. An equivalent heat source model was developed based on the thermal history of the melt pool from the microscale model [13]. The heat input was modeled by a body heat flux q which is associated with laser power P, laser absorption coefficient A, laser spot diameter ds, melt pool depth dm, and hatch spacing H. The body heat flux q was given by Eqn. (1):
from the mesoscale hatch model was assigned to each element as an initial stress tensor in the corresponding patch. Macro part model of the temperature-thread based method is a coupled thermal-mechanical analysis. Three heat loss mechanisms were considered in the macro part model, i.e., heat conduction to the substrate, the heat convection of the melt pool to the surrounding powder bed and atmosphere, and the heat radiation to the atmosphere. For both methods, the two sides of the substrate was fixed during the process and released at the last step. Part dimensions: 35 mm × 15 mm × 0.15 mm 45 mm
1 mm
A P ds dm H
(1)
Element size: 250 × 250 × 50 μm
22 mm
Fig. 3 Mesh design and dimensions in the macro part model.
Part build-up modeling The scanning strategy in the SLM experiment [3] is a sequential scan pattern (totally near 70 scans) as shown in Fig. 4(a). In this study, the sequential pattern was simplified by dividing the part into seven zones: from #1 to #7 shown in Fig. 4(b). Number in each zone represents the scanning order for each patch. In the stress-thread method, the local residual stress field was assigned as an initial stress tensor to all elements in the corresponding patch. At first, all the element of the part was deactivated. As the process was started, separated zone will be activated one by one according to the scanning order. ᬅᬆᬇᬈᬉᬊᬋ Y X
q
Substrat Part
Scanning order
(a) Sequential pattern (vertical scan) (b) Equivalent heat input model Fig. 4 Scanning pattern applied to the macro part model.
3.3. Macro part buildup model Model dimensions and mesh In the macro part model, one powder layer (highlighted by the red dashed line in Fig. 3) was deposited on a 1 mm thick steel substrate. The dimensions of the substrate were shown in Fig. 3. The part dimensions were 35 mm (length) × 15 mm (width) × 0.15 mm (height) (Fig. 3). The same mesh was used for both stress-thread and temperature-thread based methods. The initial temperature of powder and substrate was set to 20 °C. Boundary conditions Macro part model of the stress-thread based method is a mechanical analysis. The local residual stress field calculated
In the temperature-thread method, zone #1 was first heated by the equivalent body heat flux and then cooled down for ten seconds. Same heating and cooling conditions were applied to other 6 zones sequentially. 4. Model validation and discussion 4.1. Part distortion The normalized distortions in the Z direction along this nodal path as shown in Fig. 5 for both of the methods were compared. The predictions and experimental data show the same bending trend. And the distortion predicted by temperature-thread based method is much closer to
174
C. Li et al. / Procedia CIRP 45 (2016) 171 – 174
measurement than that of stress-thread based method. The possible reason could be that the part distortion was caused by tensile residual stress which is the mechanical response of SLM part to the thermal load. In temperature-thread based method, the thermal history of the whole part is closer to the real process compared to the stress-thread based method. Thus, a closer part distortion compared to the measurement was predicted using temperature-thread method. For both of the two methods, a concave up shape curve was observed. The formation of this curve is due to the thermal history of the part and the substrate. At first, the material located in the upper layer of the part expanded because of the laser heating. As the material cools down, the plastic strain in the upper layers becomes smaller than the lower layers. Finally, a concave shaped distortion was formed.
5. Conclusions Two multiscale modeling approaches, namely, the stressthread and the temperature-thread based methods, have been developed for efficient prediction of part distortion in SLM. Simulation methodology and results for the two approaches have been compared. The key findings are as follows: x Using the stress-thread method, the local residual stress predicted in the mesoscale model is incorporated in the macroscale part to predict part distortion. Using the temperature-thread method, an equivalent heat source has been applied to the mesoscale model, and incorporated in the macroscale part to predict part distortion. x Similar bending trends were found for both methods. The stress-tread method underestimated part distortion compared to the temperature-thread method. x Tensile residual stress with a magnitude near the yield point of the work material was found on the top surface of the part. A typical residual stress profile in depth direction for a SLMed part was predicted. References [1]
[2]
Fig. 5 Part distortion prediction: stress-thread vs. temp.-thread methods.
4.2. Residual stress
[3]
Fig. 6(a) shows residual stress S11 profile comparison of temperature-thread and stress-thread methods in depth direction. A similar residual stress characteristic was found for both of the two methods. In the temperature-thread based method, the maximum tensile residual stress was found on the top surface of the part, and the tensile stress decreases as the depth increases. In stress-thread method, a slight change of residual stress in depth direction was observed. For both methods, a sudden change of residual stress (S11) was found on the boundary between the part and substrate, changing from tensile on the part to compressive on the substrate. The predicted residual stress profile was very similar to the typical p simplified residual stress pprofile in depth direction [14].
[4]
[5]
[6]
[7]
[8] [9]
Z
[10]
Part
+ [11]
_
[12] Substrate
[13] +
0
σyeild
(b) Fig. 6 Residual stress profile characteristics in depth direction: (a) residual stress profile prediction by stress-thread method vs. temperature-thread method; (b) characteristics of residual stress profiles (redraw from [14]).
σ
[14]
Levy, G.N., Schindel, R., Kruth, J., 2003. Rapid manufacturing and rapid tooling with layer manufacturing (LM) technologies, state of the art and future perspectives, CIRP Annals-Manufacturing Technology 52, p. 589609. Kruth, J., Levy, G., Klocke, F., Childs, T., 2007. Consolidation phenomena in laser and powder-bed based layered manufacturing, CIRP Annals-Manufacturing Technology 56, p. 730-759. Kruth, J., Froyen, L., Van Vaerenbergh, J., Mercelis, P., Rombouts, M., Lauwers, B., 2004. Selective laser melting of iron-based powder, Journal of Materials Processing Technology 149, p. 616-622. Tolochko, N.K., Mozzharov, S.E., Yadroitsev, I.A., Laoui, T., Froyen, L., Titov, V.I., Ignatiev, M.B., 2004. Balling processes during selective laser treatment of powders, Rapid Prototyping Journal 10, p. 78-87. Lewis, G.K., Schlienger, E., 2000. Practical considerations and capabilities for laser assisted direct metal deposition, Materials & Design 21, p. 417-423. Dadbakhsh, S., Hao, L., Sewell, N., 2012. Effect of selective laser melting layout on the quality of stainless steel parts, Rapid Prototyping Journal 18, p. 241-249. Dai, K., Shaw, L., 2004. Thermal and mechanical finite element modeling of laser forming from metal and ceramic powders, Acta Materialia 52, p. 69-80. Aggarangsi, P., Beuth, J.L., 2006. Localized preheating approaches for reducing residual stress in additive manufacturing, p. 709-720. Nickel, A., Barnett, D., Prinz, F., 2001. Thermal stresses and deposition patterns in layered manufacturing, Materials Science and Engineering: A 317, p. 59-64. Zaeh, M.F., Ott, M., 2011. Investigations on heat regulation of additive manufacturing processes for metal structures, CIRP Annals Manufacturing Technology 60, p. 259-262. EOS GmbH, 2004. Direct Metal and DirectSteel materials for EOSINT M 250 Xtended. Li, C., Fu, C.H., Guo, Y.B., Fang, F.Z., 2016. A multiscale modeling approach for fast prediction of part distortion in selective laser melting, Journal of Materials Processing Technology 229, p. 703-712. Li, C., Liu, J., Guo, Y., Li, Z., 2015. A Temperature-Thread Multiscale Modeling Approach for Efficient Prediction of Part Distortion by Selective Laser Melting, Proc. of the 26th SFF Symposium p. 1166-1181. Kruth, J., Deckers, J., Yasa, E., Wauthlé, 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 226, p. 980-991.
ScienceDirect Procedia CIRP 45 (2016) 171 – 174
3rd CIRP Conference on Surface Integrity (CIRP CSI)
Prediction of Residual Stress and Part Distortion in Selective Laser Melting C. Li, J.F. Liu, Y.B. Guo* Dept. of Mechanical Engineering, The University of Alabama, Tuscaloosa, AL35487, USA * Corresponding author. Tel.: +1-205-348-2615; fax: +1-205-348-6419. E-mail address: [email protected]
Abstract Selective laser melting (SLM) is widely used to make functional metal parts. The high-temperature process will produce large tensile residual stress (RS) which leads to part distortion and poor product performance. Traditional modeling approaches are not practical to predict residual stress and part distortion due to the exceedingly high computational cost. In this study, two efficient multiscale modeling methods have been developed to across microscale laser scan, mesoscale layer hatch, and macroscale part buildup for fast prediction of residual stress and part distortion. A concept of equivalent heat source has been developed from the microscale laser scan model. In the “stress-thread” method, the local residual stress field was predicted by the mesoscale layer hatch model using the equivalent heat source, then the residual stress field is imported, i.e., “stress-thread”, to the macroscale part buildup model to predict residual stress and part distortion. In the temperature-thread method, the powder–liquid–solid material transition has been incorporated. A body heat flux obtained from the microscale laser scan model is applied, i.e., “temperature-thread”, to the hatch layer. Then multiple hatches are sequentially “deposited” in the macroscale part buildup model with different scanning strategies. The predicted part distortions by both methods were compared and compared with the experimental data. © 2016 The Authors. Published by Elsevier Elsevier B.V. B.V.This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the scientific committee of the 3rd CIRP Conference on Surface Integrity (CIRP CSI) (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 3rd CIRP Conference on Surface Integrity (CIRP CSI) Keywords: residual stress; selective laser melting; distortion, multiscale modeling; selective laser melting; additive manufacturing
1. Introduction 1.1. SLM process and part distortion Selective laser melting (SLM) is capable of producing functional parts in a layer upon layer fashion directly from CAD data [1]. Parts by SLM are near full density and have mechanical properties comparable to bulk materials [2, 3]. In a typical SLM system, a fine powder layer is placed on a substrate inside an inert chamber and is fully melted by a laser. After one layer is deposited, another layer will be placed and melted until a part is produced. Several defects usually exist in a SLM part. High thermal stress would lead to part distortion and cracks. The balling effect may result in poor surface finish [4]. Also, residual gas content, unmelted powder, and oxidized particles may lead to porosity of the component [5, 6]. The uneven heat input as well as the rapid cooling of the process generates large amounts of tensile residual stresses in the component. It not only reduces the part geometrical
accuracy but also and detrimentally affects the functional performance of the end-use parts. Simulation work [7, 8] has been done to predict residual stress and distortion of SLM parts on the micro or mesoscale, in which only single tracks or multi-tracks were considered. Some studies [9, 10] predicted residual stress and part distortion in SLM on the macroscale. In these models a constant heat flux was applied to heat an entire scan line or an entire layer at the same instant to predict the temperature and residual stress distribution of macro part. 1.2. Pressing issues and research objective A coupled thermal-mechanical analysis for several single scans with a fine mesh model is very time consuming. A practical SLM part on the macroscale requires millions of microscale laser scans which dramatically increases the computational load for the calculation of a coupled analysis. Thus, it is impossible in practice to predict the distortion of a practical SLM part if every scan is simulated.
2212-8271 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 3rd CIRP Conference on Surface Integrity (CIRP CSI) doi:10.1016/j.procir.2016.02.058
172
C. Li et al. / Procedia CIRP 45 (2016) 171 – 174
The objectives of this study are to develop and compare temperature-thread based and stress-thread based multi-scale approaches for efficient prediction of part distortion and residual stress by: (a) developing a novel equivalent heat source in mesoscale layer hatch from a microscale laser scan; (b) calculating the residual stress field and distortion of a practical part at macroscale; and (c) compare the predicted distortion results with the experimental data.
based on the thermal data in the microscale scan model for both methods, the heat load is directly applied to the mesoscale hatch model. Third, the thermal history of one hatch layer is applied to the macroscale part model, and each hatch layer is activated one by one until the whole part is built.
2. SLM experiment conditions
Model dimensions In the microscale scan model, a thermal analysis was conducted using the FEA package ABAQUS/Standard to predict the temperature field in the melt pool. The powder layer with thickness of 0.15 mm was placed on the substrate. The powder layer was 5 mm in length, 0.3 mm in width and 0.15 mm in thickness. The substrate was 5 mm in length, 0.3 mm in width and 5 mm in height. The initial temperature of the whole model was set to room temperature 20 °C. Laser heat source modeling A moving Gaussian distributed heat flux is developed to model the heat input of the scanning laser in the microscale model. The temperature field of the melt pool was captured when the laser travelled to the center point of scan track, and this field was used to develop equivalent heat source for stress-thread based method. The thermal history (heating and cooling) of the center point of scanning track was recorded for equivalent heat source development for temperature-thread based method. Temperature data output Fig. 2(a) shows the temperature field of the cross-section of the melt pool when the laser is located at the center of the scan track. This temperature field will be extended on a larger scale with scan spacing considered, used for mesoscale model in stress-thread method. Fig. 2(b) shows the thermal history of the melt pool center which will be used for developing an equivalent heat source for temperature-thread method.
The laser source in this study is a continuous Nd:YAG laser with a wavelength of 1064 nm. The process parameters are listed in Table 1[3]. This study aims to predict part distortion and validate with the experimental data using the lab-made iron-based powders, but the material properties are not available, so a commercial powder with similar chemical composition is used instead as an approximation, it would be a future research subject to investigate the effect of temperature-dependent material data on model accuracy. The temperature-independent mechanical and thermal material properties are [11]: the elastic modulus is 130 GPa, the Possion’s ratio is 0.41, the tensile and yield stress is 600 and 400 MPa, the melting point is 1330 oC, the coefficient of thermal expansion is 9 × 10-6/K, the thermal conductivity is 13 W/m·K, and the specific heat is 375 J/kg·K. Table 1 SLM process parameters [3] Laser power
Beam dia.
Scan speed
Scan spacing
Layer thickness
300 W
600 μm
50 mm/s
100 μm
150 μm
3. Multiscale simulation approaches Two types of multi-scale finite element methods have been developed and compared, i.e., the stress-thread based and temperature-thread based methods. Detailed procedure for both methods is shown in Fig. 1. For both methods, the powder material is melted by a moving heat flux to capture the thermal data of a melt pool in the microscale laser scan model. In the stress-thread method, the temperature field of the melt pool is recorded. In the temperature-thread method, the entire thermal history of the melt pool is recorded. Second, two types of equivalent heat sources are developed Output x Melt pool geometry x Temp. field of the melt pool
Meso layer hatch model x Thermal-mechanical analysis x Equivalent heat input x Whole hatch heated at same time Stress-Thread
Output x RS field x Part distortion
3.2. Meso layer hatch model Scan spacing is an important SLM process parameter and defined as the length of overlap between two neighboring scan tracks. In this study, the scan spacing was incorporated in the equivalent heat source in the mesoscale hatch model for both the stress-thread and temperature-thread methods.
Micro laser scan model x Thermal analysis x Powder heated by moving heat flux Stress-Thread
Output x Temp. field of one hatch x Local RS field
3.1. Micro laser scan model
Macro part model x Mechanical analysis x Apply local RS field x Applied hatch by hatch
Output x Melt pool geometry x Temp. history of the melt pool
Temperature-Thread Meso layer hatch model x Thermal analysis x Equivalent heat input x Whole hatch heated at same time
Output x Temp. history of one hatch
Temperature-Thread Macro part model x Thermal-mechanical analysis x Apply equivalent heat source x Applied hatch by hatch
Output x RS field x Part distortion
Fig. 1 Stress-Thread based and Temperature-thread based method for the prediction of distortion of SLM parts.
173
C. Li et al. / Procedia CIRP 45 (2016) 171 – 174
Temperature field in the c cross-section of melt pool
5000 4000
Temp. (°C)
(a)Stress-thread
Cooling
Heating
3000
Temp. (°C)
2000 1000
0 0
Melt pool center
0.05
0.1
Time (s) (b) Temp.-
Fig. 2 Output of microscale laser scan model. (a) Stress-thread: temperature field in the cross-section of melt pool; (b) Temperature-thread: temperature contour in the melt pool and temperature history at the center of melt pool.
Equivalent heat source modeling For the stress-thread method, an equivalent heat source was developed based on the temperature field of the crosssection of the melt pool from the micro scan model. Multiple scan tracks were deposited simultaneously with the fixed scan spacing taken into consideration. The mesoscale hatch model for the stress-thread method was a thermal-mechanical coupled model. After the powder and substrate were cooled down to room temperature, the residual stress field of the part , and this averaged residual stress will be averaged as tensor was applied to each corresponding patch, detail method could be found in [12]. For the temperature-thread method, the melt pool shape was simplified to a cuboid with a length of laser spot diameter ds, a width of scan spacing H, and a depth of melt pool dm. The equivalent body flux was defined as the power density (W/m3) which represents the input power for unit volume of melted material. An equivalent heat source model was developed based on the thermal history of the melt pool from the microscale model [13]. The heat input was modeled by a body heat flux q which is associated with laser power P, laser absorption coefficient A, laser spot diameter ds, melt pool depth dm, and hatch spacing H. The body heat flux q was given by Eqn. (1):
from the mesoscale hatch model was assigned to each element as an initial stress tensor in the corresponding patch. Macro part model of the temperature-thread based method is a coupled thermal-mechanical analysis. Three heat loss mechanisms were considered in the macro part model, i.e., heat conduction to the substrate, the heat convection of the melt pool to the surrounding powder bed and atmosphere, and the heat radiation to the atmosphere. For both methods, the two sides of the substrate was fixed during the process and released at the last step. Part dimensions: 35 mm × 15 mm × 0.15 mm 45 mm
1 mm
A P ds dm H
(1)
Element size: 250 × 250 × 50 μm
22 mm
Fig. 3 Mesh design and dimensions in the macro part model.
Part build-up modeling The scanning strategy in the SLM experiment [3] is a sequential scan pattern (totally near 70 scans) as shown in Fig. 4(a). In this study, the sequential pattern was simplified by dividing the part into seven zones: from #1 to #7 shown in Fig. 4(b). Number in each zone represents the scanning order for each patch. In the stress-thread method, the local residual stress field was assigned as an initial stress tensor to all elements in the corresponding patch. At first, all the element of the part was deactivated. As the process was started, separated zone will be activated one by one according to the scanning order. ᬅᬆᬇᬈᬉᬊᬋ Y X
q
Substrat Part
Scanning order
(a) Sequential pattern (vertical scan) (b) Equivalent heat input model Fig. 4 Scanning pattern applied to the macro part model.
3.3. Macro part buildup model Model dimensions and mesh In the macro part model, one powder layer (highlighted by the red dashed line in Fig. 3) was deposited on a 1 mm thick steel substrate. The dimensions of the substrate were shown in Fig. 3. The part dimensions were 35 mm (length) × 15 mm (width) × 0.15 mm (height) (Fig. 3). The same mesh was used for both stress-thread and temperature-thread based methods. The initial temperature of powder and substrate was set to 20 °C. Boundary conditions Macro part model of the stress-thread based method is a mechanical analysis. The local residual stress field calculated
In the temperature-thread method, zone #1 was first heated by the equivalent body heat flux and then cooled down for ten seconds. Same heating and cooling conditions were applied to other 6 zones sequentially. 4. Model validation and discussion 4.1. Part distortion The normalized distortions in the Z direction along this nodal path as shown in Fig. 5 for both of the methods were compared. The predictions and experimental data show the same bending trend. And the distortion predicted by temperature-thread based method is much closer to
174
C. Li et al. / Procedia CIRP 45 (2016) 171 – 174
measurement than that of stress-thread based method. The possible reason could be that the part distortion was caused by tensile residual stress which is the mechanical response of SLM part to the thermal load. In temperature-thread based method, the thermal history of the whole part is closer to the real process compared to the stress-thread based method. Thus, a closer part distortion compared to the measurement was predicted using temperature-thread method. For both of the two methods, a concave up shape curve was observed. The formation of this curve is due to the thermal history of the part and the substrate. At first, the material located in the upper layer of the part expanded because of the laser heating. As the material cools down, the plastic strain in the upper layers becomes smaller than the lower layers. Finally, a concave shaped distortion was formed.
5. Conclusions Two multiscale modeling approaches, namely, the stressthread and the temperature-thread based methods, have been developed for efficient prediction of part distortion in SLM. Simulation methodology and results for the two approaches have been compared. The key findings are as follows: x Using the stress-thread method, the local residual stress predicted in the mesoscale model is incorporated in the macroscale part to predict part distortion. Using the temperature-thread method, an equivalent heat source has been applied to the mesoscale model, and incorporated in the macroscale part to predict part distortion. x Similar bending trends were found for both methods. The stress-tread method underestimated part distortion compared to the temperature-thread method. x Tensile residual stress with a magnitude near the yield point of the work material was found on the top surface of the part. A typical residual stress profile in depth direction for a SLMed part was predicted. References [1]
[2]
Fig. 5 Part distortion prediction: stress-thread vs. temp.-thread methods.
4.2. Residual stress
[3]
Fig. 6(a) shows residual stress S11 profile comparison of temperature-thread and stress-thread methods in depth direction. A similar residual stress characteristic was found for both of the two methods. In the temperature-thread based method, the maximum tensile residual stress was found on the top surface of the part, and the tensile stress decreases as the depth increases. In stress-thread method, a slight change of residual stress in depth direction was observed. For both methods, a sudden change of residual stress (S11) was found on the boundary between the part and substrate, changing from tensile on the part to compressive on the substrate. The predicted residual stress profile was very similar to the typical p simplified residual stress pprofile in depth direction [14].
[4]
[5]
[6]
[7]
[8] [9]
Z
[10]
Part
+ [11]
_
[12] Substrate
[13] +
0
σyeild
(b) Fig. 6 Residual stress profile characteristics in depth direction: (a) residual stress profile prediction by stress-thread method vs. temperature-thread method; (b) characteristics of residual stress profiles (redraw from [14]).
σ
[14]
Levy, G.N., Schindel, R., Kruth, J., 2003. Rapid manufacturing and rapid tooling with layer manufacturing (LM) technologies, state of the art and future perspectives, CIRP Annals-Manufacturing Technology 52, p. 589609. Kruth, J., Levy, G., Klocke, F., Childs, T., 2007. Consolidation phenomena in laser and powder-bed based layered manufacturing, CIRP Annals-Manufacturing Technology 56, p. 730-759. Kruth, J., Froyen, L., Van Vaerenbergh, J., Mercelis, P., Rombouts, M., Lauwers, B., 2004. Selective laser melting of iron-based powder, Journal of Materials Processing Technology 149, p. 616-622. Tolochko, N.K., Mozzharov, S.E., Yadroitsev, I.A., Laoui, T., Froyen, L., Titov, V.I., Ignatiev, M.B., 2004. Balling processes during selective laser treatment of powders, Rapid Prototyping Journal 10, p. 78-87. Lewis, G.K., Schlienger, E., 2000. Practical considerations and capabilities for laser assisted direct metal deposition, Materials & Design 21, p. 417-423. Dadbakhsh, S., Hao, L., Sewell, N., 2012. Effect of selective laser melting layout on the quality of stainless steel parts, Rapid Prototyping Journal 18, p. 241-249. Dai, K., Shaw, L., 2004. Thermal and mechanical finite element modeling of laser forming from metal and ceramic powders, Acta Materialia 52, p. 69-80. Aggarangsi, P., Beuth, J.L., 2006. Localized preheating approaches for reducing residual stress in additive manufacturing, p. 709-720. Nickel, A., Barnett, D., Prinz, F., 2001. Thermal stresses and deposition patterns in layered manufacturing, Materials Science and Engineering: A 317, p. 59-64. Zaeh, M.F., Ott, M., 2011. Investigations on heat regulation of additive manufacturing processes for metal structures, CIRP Annals Manufacturing Technology 60, p. 259-262. EOS GmbH, 2004. Direct Metal and DirectSteel materials for EOSINT M 250 Xtended. Li, C., Fu, C.H., Guo, Y.B., Fang, F.Z., 2016. A multiscale modeling approach for fast prediction of part distortion in selective laser melting, Journal of Materials Processing Technology 229, p. 703-712. Li, C., Liu, J., Guo, Y., Li, Z., 2015. A Temperature-Thread Multiscale Modeling Approach for Efficient Prediction of Part Distortion by Selective Laser Melting, Proc. of the 26th SFF Symposium p. 1166-1181. Kruth, J., Deckers, J., Yasa, E., Wauthlé, 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 226, p. 980-991.