A novel mathematical model for predicting a sustainable selective laser melting and controlled densification

References

• Al-Kadi, O. S. 2014. Fractal Dimension (1.0.0.0). MATLAB Central File Exchange. https://www.mathworks.com/matlabcentral/fileexchange/44951-fractal-dimension.
   Google Scholar
• Al-Kadi, O. S., and D. Watson. 2008. “Texture Analysis of Aggressive and Nonaggressive Lung Tumor CE CT Images.” IEEE Transactions on Biomedical Engineering 55 (7): 1822–1830. https://doi.org/10.1109/TBME.2008.919735.
   PubMed Web of Science ®Google Scholar
• Barenblatt, G. I. 1987. Dimensional Analysis. Amsterdam: Gordon and Breach Science Publishers.
   Google Scholar
• Barenblatt, G. I. 1996. Scaling, Self-Similarity, and intermediate asymptotics. United Kingdom: Cambridge University Press.
   Google Scholar
• Cardaropoli, F., V. Alfieri, F. Caiazzo, and V. Sergi. 2012. “Dimensional Analysis for the Definition of the Influence of Process Parameters in Selective Laser Melting of Ti-6Al-4V Alloy.” Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 226 (7): 1136–1142. https://doi.org/10.1177/0954405412441885.
   Google Scholar
• Conti, P., F. Cianetti, and P. Pilerci. 2018. “Parametric Finite Elements Model of SLM Additive Manufacturing Process.” Procedia Structural Integrity 8 (2017): 410–421. https://doi.org/10.1016/j.prostr.2017.12.041.
   Google Scholar
• Ebrahimi, A., and M. Mohammadi. 2018. “Numerical Tools to Investigate Mechanical and Fatigue Properties of Additively Manufactured MS1-H13 Hybrid Steels.” Additive Manufacturing 23 (May): 381–393. https://doi.org/10.1016/j.addma.2018.07.009.
   Google Scholar
• Enneti, R. K., R. Morgan, and S. V. Atre. 2018. “Effect of Process Parameters on the Selective Laser Melting (SLM) of Tungsten.” International Journal of Refractory Metals and Hard Materials 71 (October 2017): 315–319. https://doi.org/10.1016/j.ijrmhm.2017.11.035.
   Google Scholar
• Estrada, J. 2020. Dimensional Analysis for Tuning Selective Laser Melting Parameters for Near-Full Density of Inconel 718 [Instituto Tecnológico y de Estudios Superiores de Monterrey]. https://repositorio.tec.mx/handle/11285/638016.
   Google Scholar
• Estrada-Díaz, J. A., A. ElíElíAs-Zúñiga, O. Martínez-Romero, and D. Olvera-Trejo. 2021. “Enhanced Mathematical Model for Producing Highly Dense Metallic Components Through Selective Laser Melting.” Materials 14 (6): 1571. https://doi.org/10.3390/ma14061571.
   PubMed Web of Science ®Google Scholar
• Estrada-Díaz, J. A., A. ElíElíAs-Zúñiga, O. Martínez-Romero, J. Rodríguez-Salinas, and D. Olvera-Trejo. 2021. “A Mathematical Dimensional Model for Predicting Bulk Density of Inconel 718 Parts Produced by Selective Laser Melting.” Materials 14 (3): 512. https://doi.org/10.3390/ma14030512.
   PubMed Web of Science ®Google Scholar
• Estrada-Díaz, J. A., O. MartÍnez-Romero, D. Olvera-Trejo, and A. ElÍas-Zúñiga. 2022. “Elucidating the Fractal Nature of Powder Bed in Selective Laser Melting of Metallic Components.” Fractals 30 (3): 104256. https://doi.org/10.1142/S0218348X22500621.
   Google Scholar
• Estrada-Díaz, J. A., D. Olvera-Trejo, A. Elías-Zúñiga, and O. Martínez-Romero. 2021. “A Mathematical Dimensionless Model for Electrohydrodynamics.” Results in Physics 25:104256. https://doi.org/10.1016/j.rinp.2021.104256.
   Web of Science ®Google Scholar
• Ferro, V., and R. Pecoraro. 2000. “Incomplete Self-Similarity and Flow Velocity in Gravel Bed Channels.” Water Resources Research 36 (9): 2761–2769. https://doi.org/10.1029/2000WR900164.
   Web of Science ®Google Scholar
• Fredriksson, C. 2019. “Sustainability of Metal Powder Additive Manufacturing.” Procedia Manufacturing 33:139–144. https://doi.org/10.1016/j.promfg.2019.04.018.
   Google Scholar
• Großmann, A., J. Mölleney, T. Frölich, H. Merschroth, J. Felger, M. Weigold, A. Sielaff, and C. Mittelstedt. 2020. “Dimensionless Process Development for Lattice Structure Design in Laser Powder Bed Fusion.” Materials and Design 194:108952. https://doi.org/10.1016/j.matdes.2020.108952.
   Web of Science ®Google Scholar
• Hajnys, J., M. Pagáč, J. Měsíček, J. Petru, and M. Król. 2020. “Influence of Scanning Strategy Parameters on Residual Stress in the SLM Process According to the Bridge Curvature Method for AISI 316L Stainless Steel.” Materials 13 (7): 1659. https://doi.org/10.3390/ma13071659.
   PubMed Web of Science ®Google Scholar
• He, J. H., and Q. T. Ain. 2020. “New Promises and Future Challenges of Fractal Calculus: From Two-Scale Thermodynamics to Fractal Variational Principle.” Thermal Science 24 (January): 659–681. https://doi.org/10.2298/TSCI200127065H.
   Google Scholar
• He, J.-H., and F.-Y. Ji. 2019. “Two-Scale Mathematics and Fractional Calculus for Thermodynamics.” Thermal Science 23 (4): 2131–2133. https://doi.org/10.2298/TSCI1904131H.
   Web of Science ®Google Scholar
• Jung, S., L. B. Kara, Z. Nie, T. W. Simpson, and K. S. Whitefoot. 2023. “Is Additive Manufacturing an Environmentally and Economically Preferred Alternative for Mass Production?.” Environmental Science & Technology 57 (16): 6373–6386. https://doi.org/10.1021/acs.est.2c04927.
   PubMedGoogle Scholar
• Kellens, K., M. Baumers, T. G. Gutowski, W. Flanagan, R. Lifset, and J. R. Duflou. 2017. “Environmental Dimensions of Additive Manufacturing: Mapping Application Domains and Their Environmental Implications.” Journal of Industrial Ecology 21 (S1): S49–S68. https://doi.org/10.1111/jiec.12629.
   Google Scholar
• Khan, K., G. Mohr, K. Hilgenberg, and A. De. 2020. “Probing a Novel Heat Source Model and Adaptive Remeshing Technique to Simulate Laser Powder Bed Fusion with Experimental Validation.” Computational Materials Science 181 (October 2019): 109752. https://doi.org/10.1016/j.commatsci.2020.109752.
   Google Scholar
• Kinsner, W. 2007. “A Unified Approach to Fractal Dimensions.” International Journal of Cognitive Informatics and Natural Intelligence 1 (4): 26–46. https://doi.org/10.4018/jcini.2007100103.
   Google Scholar
• Lopes, R., and N. Betrouni. 2009. “Fractal and Multifractal Analysis: A Review.” Medical Image Analysis 13 (4): 634–649. https://doi.org/10.1016/j.media.2009.05.003.
   PubMed Web of Science ®Google Scholar
• Ma, L., and H. Bin. 2007. “Temperature and Stress Analysis and Simulation in Fractal Scanning-Based Laser Sintering.” The International Journal of Advanced Manufacturing Technology 34 (9–10): 898–903. https://doi.org/10.1007/s00170-006-0665-5.
   Web of Science ®Google Scholar
• Mandelbrot, B. B. 1982. The Fractal Geometry of Nature. United States of America: W. H. Freeman and Co.
   Google Scholar
• Noh, J., J. Lee, Y. Seo, S. Hong, Y. S. Kwon, and D. Kim. 2022. “Dimensionless Parameters to Define Process Windows of Selective Laser Melting Process to Fabricate Three-Dimensional Metal Structures.” Optics and Laser Technology 149 (December 2021): 107880. https://doi.org/10.1016/j.optlastec.2022.107880.
   Google Scholar
• Olakanmi, E. O., R. F. Cochrane, and K. W. Dalgarno. 2015. “A Review on Selective Laser Sintering/Melting (SLS/SLM) of Aluminium Alloy Powders: Processing, Microstructure, and Properties.” Progress in Materials Science 74:401–477. https://doi.org/10.1016/j.pmatsci.2015.03.002.
   Web of Science ®Google Scholar
• Petrou, M. M. P., and P. G. Sevilla. 2006. Image Processing: Dealing with Texture. Wiley. https://books.google.com.ec/books?id=F%5C_BRAAAAMAAJ.
   Google Scholar
• Read, N., W. Wang, K. Essa, and M. M. Attallah. 2015. “Selective Laser Melting of AlSi10mg Alloy: Process Optimisation and Mechanical Properties Development.” Materials & Design 65:417–424. https://doi.org/10.1016/j.matdes.2014.09.044.
   Web of Science ®Google Scholar
• Renishaw. 2017. In718-0405 Powder for Additive Manufacturing. Renishaw. https://www.renishaw.com/resourcecentre/en/details/Data-sheet-In718-0405-powder-for-additive-manufacturing–94192.
   Google Scholar
• Sarkar, N., and B. B. Chaudhuri. 1994. “An Efficient Differential Box-Counting Approach to Compute Fractal Dimension of Image.” IEEE Transactions on Systems, Man and Cybernetics 24 (1): 115–120. https://doi.org/10.1109/21.259692.
   Web of Science ®Google Scholar
• Shi, X., S. Ma, C. Liu, C. Chen, Q. Wu, X. Chen, and J. Lu. 2016. “Performance of High Layer Thickness in Selective Laser Melting of Ti6Al4V.” Materials 9 (12): 975. https://doi.org/10.3390/ma9120975.
   PubMed Web of Science ®Google Scholar
• Sonin. 2001. “The Physical Basis of Dimensional Analysis.” In Massachussets Institute of Technology, vol. 2. Massachusets Institute of Technology. https://doi.org/10.1243/095440603322310459
   Google Scholar
• Spears, T. G., and S. A. Gold. 2016. “In-Process Sensing in Selective Laser Melting (SLM) Additive Manufacturing.” Integrating Materials and Manufacturing Innovation 5 (1): 16–40. https://doi.org/10.1186/s40192-016-0045-4.
   Google Scholar
• Torres-Carrillo, S., H. R. Siller, C. Vila, C. López, and C. A. Rodríguez. 2020. “Environmental Analysis of Selective Laser Melting in the Manufacturing of Aeronautical Turbine Blades.” Journal of Cleaner Production 246:119068. https://doi.org/10.1016/j.jclepro.2019.119068.
   Web of Science ®Google Scholar
• Tunchel, S., A. Blay, R. Kolerman, E. Mijiritsky, and J. A. Shibli. 2016. “3D Printing/Additive Manufacturing Single Titanium Dental Implants: A Prospective Multicenter Study with 3 Years of Follow-Up.” International Journal of Dentistry 2016:1–9. https://doi.org/10.1155/2016/8590971.
   Google Scholar
• Van Elsen, M. 2007. Complexity of Selective Laser Melting: A New Optimisation Approach. In K.U.Leuven. https://lirias.kuleuven.be/handle/1979/497.
   Google Scholar
• van Elsen, M., F. Al‐Bender, and J. Kruth. 2008. “Application of Dimensional Analysis to Selective Laser Melting.” Rapid Prototyping Journal 14 (1): 15–22. https://doi.org/10.1108/13552540810841526.
   Web of Science ®Google Scholar
• Wang, S., Y. Liu, W. Shi, B. Qi, J. Yang, F. Zhang, D. Han, and Y. Ma. 2017. “Research on High Layer Thickness Fabricated of 316L by Selective Laser Melting.” Materials 10 (9): 1055. https://doi.org/10.3390/ma10091055.
   PubMed Web of Science ®Google Scholar
• Waqar, S., Q. Sun, J. Liu, K. Guo, and J. Sun. 2020. “Numerical Investigation of Thermal Behavior and Melt Pool Morphology in Multi-Track Multi-Layer Selective Laser Melting of the 316L Steel.” International Journal of Advanced Manufacturing Technology 112 (3–4): 879–895. https://doi.org/10.1007/s00170-020-06360-0.
   Web of Science ®Google Scholar
• Yakout, M., M. A. Elbestawi, and S. C. Veldhuis. 2018. “A Review of Metal Additive Manufacturing Technologies.” Solid State Phenomena 278:1–14. https://doi.org/10.4028/www.scientific.net/SSP.278.1.
   Google Scholar
• Yan, X., J. Pang, and Y. Jing. 2019. “Ultrasonic Measurement of Stress in SLM 316L Stainless Steel Forming Parts Manufactured Using Different Scanning Strategies.” Materials 12 (17): 2719. https://doi.org/10.3390/ma12172719.
   PubMed Web of Science ®Google Scholar
• Yap, C. Y., C. K. Chua, Z. L. Dong, Z. H. Liu, D. Q. Zhang, L. E. Loh, and S. L. Sing. 2015. “Review of Selective Laser Melting: Materials and Applications.” Applied Physics Reviews 2 (4): 041101. https://doi.org/10.1063/1.4935926.
   Web of Science ®Google Scholar
• Zakrzewski, T., J. Kozak, M. Witt, and M. Debowska-Wasak. 2020. “Dimensional Analysis of the Effect of SLM Parameters on Surface Roughness and Material Density.” Procedia CIRP 95:115–120. https://doi.org/10.1016/j.procir.2020.01.182.
   Google Scholar
• Zhang, J., D. Gu, Y. Yang, H. Zhang, H. Chen, D. Dai, and K. Lin. 2019. “Influence of Particle Size on Laser Absorption and Scanning Track Formation Mechanisms of Pure Tungsten Powder During Selective Laser Melting.” Engineering, 5 (4): 736–745. https://doi.org/10.1016/j.eng.2019.07.003.
   Web of Science ®Google Scholar
• Zhang, D., P. Zhang, Z. Liu, Z. Feng, C. Wang, and Y. Guo. 2018. “Thermofluid Field of Molten Pool and Its Effects During Selective Laser Melting (SLM) of Inconel 718 Alloy.” Additive Manufacturing 21 (100): 567–578. https://doi.org/10.1016/j.addma.2018.03.031.
   Web of Science ®Google Scholar