Smoothed Particle Hydrodynamics Approach for Simulation of Non-Newtonian Flow of Feedstocks Used in Powder Injection Molding
Abstract
:1. Introduction
2. Materials and Methods
2.1. Governing Equations of Feedstock Flow
2.2. Numerical Simulation
2.3. Rheological Models
2.4. Model Input Data and Experimental Validations
2.4.1. Feedstock Preparation
2.4.2. Feedstock Characterization
2.4.3. Mold Geometries and Real-Scale Injection Validation Setup
3. Results and Discussion
3.1. Selection of the Viscosity Model
3.2. Selection of the Interparticle Distance
3.3. Selection of the Boundary Friction Factor
3.3.1. Friction Factor for a Low Injection Flow Rate
3.3.2. Validation of the Friction Factor for a High Injection Flow Rate
3.4. Validation of the SPH Model to Simulate PIM Injections
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Heaney, D.F. Handbook of Metal Injection Molding; Woodhead Publishing: Sawston, UK, 2012; ISBN 9780857096234. [Google Scholar]
- González-gutiérrez, J.; Beulke Stringari, G.; Emri, I.; Stringari, G.B.; Emri, I. Powder Injection Molding of Metal and Ceramic Parts; IntechOpen: London, UK, 2012; ISBN 978-953-51-0297-7. [Google Scholar]
- Yarlagadda, P.K.D.V. Development of an Integrated Neural Network System for Prediction of Process Parameters in Metal Injection Moulding. J. Mater. Process. Technol. 2002, 130–131, 315–320. [Google Scholar] [CrossRef]
- Bilovol, V.V.; Kowalski, L.; Duszczyk, J.; Katgerman, L.; Bilovol, V.V.; Kowalski, L.; Duszczyk, J.; Katgerman, L. Comparison of Numerical Codes for Simulation of Powder Injection Moulding. Powder Metall. 2003, 46, 55–60. [Google Scholar] [CrossRef]
- Zheng, Z.S.; Qu, X.H. Numerical Simulation of Powder Injection Moulding Filling Process for Intricate Parts Numerical Simulation of Powder Injection Moulding Filling Process for Intricate Parts. Powder Metall. 2006, 49, 167–172. [Google Scholar] [CrossRef]
- Aggarwal, G.; Park, S.J.; Smid, I. Development of Niobium Powder Injection Molding: Part I. Feedstock and Injection Molding. Int. J. Refract. Met. Hard Mater. 2006, 24, 253–262. [Google Scholar] [CrossRef]
- Ahn, S.; Chung, S.T.; Atre, S.V.; Park, S.J.; German, R.M.; Chung, S.T.; Atre, S.V.; Park, S.J.; Integrated, R.M.G.; Ahn, S.; et al. Integrated Filling, Packing and Cooling CAE Analysis of Powder Injection Moulding Parts Integrated Filling, Packing and Cooling CAE Analysis of Powder Injection Moulding Parts. Powder Metall. 2008, 51, 318–326. [Google Scholar] [CrossRef]
- Urval, R.; Lee, S.; Atre, S.V.; Park, S.; German, R.M.; Lee, S.; Atre, S.V.; Park, S.; Optimisation, R.M.G.; Urval, R.; et al. Optimisation of Process Conditions in Powder Injection Moulding of Microsystem Components Using a Robust Design Method: Part I. Primary Design Parameters. Powder Metall. 2008, 51, 133–142. [Google Scholar] [CrossRef]
- Ahn, S.; Park, S.J.; Lee, S.; Atre, S.V.; German, R.M. Effect of Powders and Binders on Material Properties and Molding Parameters in Iron and Stainless Steel Powder Injection Molding Process. Powder Technol. 2009, 193, 162–169. [Google Scholar] [CrossRef]
- Kate, K.H.; Enneti, R.K.; Onbattuvelli, V.P.; Atre, S.V. Feedstock Properties and Injection Molding Simulations of Bimodal Mixtures of Nanoscale and Microscale Aluminum Nitride. Ceram. Int. 2013, 39, 6887–6897. [Google Scholar] [CrossRef]
- Lenz, J.; Enneti, R.K.; Park, S.J.; Atre, S.V. Powder Injection Molding Process Design for UAV Engine Components Using Nanoscale Silicon Nitride Powders. Ceram. Int. 2014, 40, 893–900. [Google Scholar] [CrossRef]
- Kim, J.; Ahn, S.; Atre, S.V.; Park, S.J.; Kang, T.G.; German, R.M. Imbalance Filling Ofmulti-Cavity Tooling during Powder Injection Molding. Powder Technol. 2014, 257, 124–131. [Google Scholar] [CrossRef]
- Sardarian, M.; Mirzaee, O.; Habibolahzadeh, A. Numerical Simulation and Experimental Investigation on Jetting Phenomenon in Low Pressure Injection Molding (LPIM) of Alumina. J. Mater. Process. Tech. 2017, 243, 374–380. [Google Scholar] [CrossRef]
- Sardarian, M.; Mirzaee, O.; Habibolahzadeh, A. Influence of Injection Temperature and Pressure on the Properties of Alumina Parts Fabricated by Low Pressure Injection Molding (LPIM). Ceram. Int. 2017, 43, 4785–4793. [Google Scholar] [CrossRef]
- Sardarian, M.; Mirzaee, O.; Habibolahzadeh, A. Mold Filling Simulation of Low Pressure Injection Molding (LPIM) of Alumina: Effect of Temperature and Pressure. Ceram. Int. 2017, 43, 28–34. [Google Scholar] [CrossRef]
- Azzouni, M.; Demers, V.; Dufresne, L. Mold Filling Simulation and Experimental Investigation of Metallic Feedstock Used in Low-Pressure Powder Injection Molding. Int. J. Mater. Form. 2021, 14, 961–972. [Google Scholar] [CrossRef]
- Ye, T.; Pan, D.; Huang, C.; Liu, M. Smoothed Particle Hydrodynamics (SPH) for Complex Fluid Flows: Recent Developments in Methodology and Applications. Phys. Fluids 2019, 31, 011301. [Google Scholar] [CrossRef]
- Liu, M.B.; Liu, G. Smoothed Particle Hydrodynamics (SPH): An Overview and Recent Developments. Arch. Comput. Methods Eng. 2010, 17, 25–76. [Google Scholar] [CrossRef]
- Hosain, M.L.; Fdhila, R.B. Literature Review of Accelerated CFD Simulation Methods towards Online Application. Energy Procedia 2015, 75, 3307–3314. [Google Scholar] [CrossRef]
- Xu, X.; Ouyang, J.; Yang, B.; Liu, Z. SPH Simulations of Three-Dimensional Non-Newtonian Free Surface Flows. Comput. Methods Appl. Mech. Eng. 2013, 256, 101–116. [Google Scholar] [CrossRef]
- Shadloo, M.S.; Oger, G.; Le Touzé, D. Smoothed Particle Hydrodynamics Method for Fluid Flows, towards Industrial Applications: Motivations, Current State, And Challenges. Comput. Fluids 2016, 136, 11–34. [Google Scholar] [CrossRef]
- Monaghan, J.J. Smoothed Particle Hydrodynamics and Its Diverse Applications. Annu. Rev. Fluid Mech. 2012, 44, 323–346. [Google Scholar] [CrossRef]
- Cleary, P.; Prakash, M.; Ha, J.; Sinnott, M.; Nguyen, T.; Grandfield, J.; Hydrodynamics, S.; Cleary, P.; Prakash, M.; Ha, J.; et al. Modeling of Cast Systems Using Smoothed-Particle Hydrodynamics. JOM 2004, 56, 67–70. [Google Scholar] [CrossRef]
- Hu, M.Y.; Cai, J.J.; Li, N.; Yu, H.L.; Zhang, Y.; Sun, B.; Sun, W.L. Flow Modeling in High-Pressure Die-Casting Processes Using SPH Model. Int. J. Met. 2018, 12, 97–105. [Google Scholar] [CrossRef]
- Cleary, P.W.; Ha, J.; Prakash, M.; Nguyen, T. 3D SPH Flow Predictions and Validation for High Pressure Die Casting of Automotive Components. Appl. Math. Model. 2006, 30, 1406–1427. [Google Scholar] [CrossRef]
- Cleary, P.W. Extension of SPH to Predict Feeding, Freezing and Defect Creation in Low Pressure Die Casting. Appl. Math. Model. 2010, 34, 3189–3201. [Google Scholar] [CrossRef]
- Cleary, P.; Ha, J.; Alguine, V.; Nguyen, T. Flow Modelling in Casting Processes. Appl. Math. Model. 2002, 26, 171–190. [Google Scholar] [CrossRef]
- Ellingsen, K.; Coudert, T.; M’Hamdi, M. SPH Based Modelling of Oxide and Oxide Film Formation in Gravity Die Castings. IOP Conf. Ser. Mater. Sci. Eng. 2015, 84, 012064. [Google Scholar] [CrossRef]
- Cleary, P.W.; Prakash, M.; Ha, J. Novel Applications of Smoothed Particle Hydrodynamics (SPH) in Metal Forming. J. Mater. Process. Technol. 2006, 177, 41–48. [Google Scholar] [CrossRef]
- Afrasiabi, M.; Luthi, C.; Bambach, M.; Wegener, K. Smoothed Particle Hydrodynamics Modeling of the Multi-layer Laser Powder Bed Fusion Process. Procedia CIRP 2022, 107, 276–282. [Google Scholar] [CrossRef]
- Dao, M.H.; Lou, J. Simulations of Laser Assisted Additive Manufacturing by Smoothed Particle Hydrodynamics. Comput. Methods Appl. Mech. Eng. 2021, 373, 113491. [Google Scholar] [CrossRef]
- Long, T.; Huang, H. An improved high order smoothed particle hydrodynamics method for numerical simulations of selective laser melting process. Eng. Anal. Bound. Elem. 2023, 147, 320–335. [Google Scholar] [CrossRef]
- Ichimiya, M.; Yamagata, N. High Viscous Flow Analysis in the 3D Printer by SPH. Mech. Mach. Sci. 2020, 75, 309–317. [Google Scholar] [CrossRef]
- Zhang, Z.; Shu, C.; Khalid, M.S.U.; Liu, Y.; Yuan, Z.; Jiang, Q.; Liu, W. SPH modeling and investigation of cold spray additive manufacturing with multi-layer multi-track powders. J. Manuf. Process. 2022, 84, 565–586. [Google Scholar] [CrossRef]
- Kiselev, S.P.; Kiselev, V.P.; Vorozhtsov, E.V. Smoothed Particle Hydrodynamics Method Used for Numerical Simulation of Impact Between an Aluminum Particle and a Titanium Target. J. Appl. Mech. Tech. Phys. 2022, 63, 1035–1049. [Google Scholar] [CrossRef]
- Lee, J.; Subedi, K.K.; Huang, G.W.; Lee, J.; Kong, S.-C. Numerical Investigation of YSZ Droplet Impact on a Heated Wall for Thermal Spray Application. J. Therm. Spray Technol. 2022, 31, 2039–2049. [Google Scholar] [CrossRef]
- Chaussonnet, G.; Dauch, T.; Keller, M.; Okraschevski, M.; Ates, C.; Schwitzke, C.; Koch, R.; Bauer, H.J. Progress in the Smoothed Particle Hydrodynamics Method to Simulate and Post-process Numerical Simulations of Annular Airblast Atomizers. Flow Turbul. Combust. 2020, 105, 1119–1147. [Google Scholar] [CrossRef]
- Guo, X.-G.; Li, M.; Dong, Z.-G.; Zhai, R.-F.; Jin, Z.-J.; Kang, R.-K. Smooth particle hydrodynamics modeling of cutting force in milling process of TC4. Adv. Manuf. 2019, 7, 364–373. [Google Scholar] [CrossRef]
- Falcone, M.; Buss, L.; Fritsching, U. Model assessment of an open-source smoothed particle hydrodynamics (SPH) simulation of a vibration-assisted drilling process. Fluids 2022, 7, 189. [Google Scholar] [CrossRef]
- Fan, X.-J.; Tanner, R.I.; Zheng, R. Smoothed Particle Hydrodynamics Simulation of Non-Newtonian Moulding Flow. J. Nonnewton. Fluid Mech. 2010, 165, 219–226. [Google Scholar] [CrossRef]
- Xu, X.; Yu, P. Modeling and Simulation of Injection Molding Process of Polymer Melt by a Robust SPH Method. Appl. Math. Model. 2017, 48, 384–409. [Google Scholar] [CrossRef]
- Xu, X.; Yu, P. Extension of SPH to Simulate Non-Isothermal Free Surface Flows during the Injection Molding Process. Appl. Math. Model. 2019, 73, 715–731. [Google Scholar] [CrossRef]
- He, L.; Lu, G.; Chen, D.; Li, W.; Chen, L.; Yuan, J.; Lu, C. Smoothed Particle Hydrodynamics Simulation for Injection Molding Flow of Short Fiber-Reinforced Polymer Composites. J. Compos. Mater. 2018, 52, 1531–1539. [Google Scholar] [CrossRef]
- Greiner, A.; Kauzlari, D.; Korvink, J.G.; Heldele, R.; Schulz, M.; Piotter, V.; Hanemann, T.; Weber, O.; Haußelt, J. Simulation of Micro Powder Injection Moulding: Powder Segregation and Yield Stress Effects during Form Filling. J. Eur. Ceram. Soc. 2011, 31, 2525–2534. [Google Scholar] [CrossRef]
- Lind, S.J.; Rogers, B.D.; Stansby, P.K. Review of Smoothed Particle Hydrodynamics: Towards Converged Lagrangian Flow Modelling. Proc. R. Soc. A Math. Phys. Eng. Sci. 2020, 476, 20190801. [Google Scholar] [CrossRef]
- Kauzlarić, D.; Pastewka, L.; Bretthauer, C.; Greiner, A.; Jan, G.K. SPH Simulation of the Embossing and Injection Moulding of Micro-Parts: Softening and Aggregation Aspects. In Proceedings of the 3rd International Conference on Multi-Material Micro Manufacture, 4M 2007; Whittles: Dunbeath, UK, 2007; pp. 23–29. [Google Scholar]
- Fourtakas, G.; Rogers, B.D. Modelling Multi-Phase Liquid-Sediment Scour and Resuspension Induced by Rapid Flows Using Smoothed Particle Hydrodynamics (SPH) Accelerated with a Graphics Processing Unit (GPU). Adv. Water Resour. 2016, 92, 186–199. [Google Scholar] [CrossRef]
- Mokos, A.D. Multi-Phase Modelling of Violent Hydrodynamics Using Smoothed Particle Hydrodynamics (SPH) on Graphics Processing Units (GPUs). Ph.D. Thesis, University of Manchester, Manchester, UK, 2014. [Google Scholar]
- Kauzlarić, D.; Pastewka, L.; Meyer, H.; Heldele, R.; Schulz, M.; Weber, O.; Piotter, V.; Hausselt, J.; Greiner, A.; Korvink, J.G.; et al. Smoothed Particle Hydrodynamics Simulation of Shear-Induced Powder Migration in Injection Moulding. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 2011, 369, 2320–2328. [Google Scholar] [CrossRef] [PubMed]
- Demers, V.; Fareh, F.; Turenne, S.; Demarquette, N.R.; Scalzo, O. Experimental study on moldability and segregation of Inconel 718 feedstocks used in low-pressure powder injection molding. Adv. Powder Technol. 2018, 29, 180–190. [Google Scholar] [CrossRef]
- Poh, L.; Della, C.; Ying, S.; Goh, C.; Li, Y. Powder distribution on powder injection moulding of ceramic green compacts using thermogravimetric analysis and differential scanning calorimetry. Powder Technol. 2018, 328, 256–263. [Google Scholar] [CrossRef]
- Lamarre, S.G.; Demers, V.; Chatelain, J.F. Low-Pressure Powder Injection Molding Using an Innovative Injection Press Concept. Int. J. Adv. Manuf. Technol. 2017, 91, 2595–2605. [Google Scholar] [CrossRef]
- ASTM-E8/E8M; Standard Test Methods for Tension Testing of Metallic Materials. ASTM International: West Conshohocken, PA, USA, 2022. [CrossRef]
- ASTM-E466; Standard Practice for Conducting Force Controlled Constant Amplitude Axial Fatigue Tests of Metallic Materials. ASTM International: West Conshohocken, PA, USA, 2021. [CrossRef]
- Arès, F. Influence des Paramètres D’injection sur la Pression dans un Moule et sur la Qualité des Pieces à Vert 662 en LPIM. Master’s Thesis, École de Technologie Supérieure, Montreal, QC, Canada, 27 October 2022. [Google Scholar]
- Lind, S.J.; Stansby, P.K.; Rogers, B.D.; Lloyd, P.M. Numerical Predictions of Water-Air Wave Slam Using Incompressible-Compressible Smoothed Particle Hydrodynamics. Appl. Ocean Res. 2015, 49, 57–71. [Google Scholar] [CrossRef]
Carreau–Yasuda | Herschel–Bulkley–Papanastasiou | ||
---|---|---|---|
n | 0.65 | n | 0.70 |
1.0 | 9.75 | ||
λ | 1.5 | 0 | |
14 | 0 | ||
0 |
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Meiabadi, S.; Demers, V.; Dufresne, L. Smoothed Particle Hydrodynamics Approach for Simulation of Non-Newtonian Flow of Feedstocks Used in Powder Injection Molding. Metals 2023, 13, 1580. https://doi.org/10.3390/met13091580
Meiabadi S, Demers V, Dufresne L. Smoothed Particle Hydrodynamics Approach for Simulation of Non-Newtonian Flow of Feedstocks Used in Powder Injection Molding. Metals. 2023; 13(9):1580. https://doi.org/10.3390/met13091580
Chicago/Turabian StyleMeiabadi, Saleh, Vincent Demers, and Louis Dufresne. 2023. "Smoothed Particle Hydrodynamics Approach for Simulation of Non-Newtonian Flow of Feedstocks Used in Powder Injection Molding" Metals 13, no. 9: 1580. https://doi.org/10.3390/met13091580
APA StyleMeiabadi, S., Demers, V., & Dufresne, L. (2023). Smoothed Particle Hydrodynamics Approach for Simulation of Non-Newtonian Flow of Feedstocks Used in Powder Injection Molding. Metals, 13(9), 1580. https://doi.org/10.3390/met13091580