روش جدید تخمین کرنش تراکمی سازه‌های سلولی با استفاده از مدل‌سازی میکروساختار فوم‌ها بر اساس چینش لاگوئر

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک، دانشگاه صنعتی خواجه نصیر الدین طوسی، تهران، ایران

2 صنعتی خواجه نصیرالدین طوسی

چکیده

در این تحقیق به بررسی رفتار جذب انرژی سازه‌های سلولی نظیر فوم‌ها از جنس آلومینوم پرداخته شده‌است. یکی از اهداف، توسعه‌ی مدل‌سازی میکروساختارسازه‌های سلولی و تحلیل رفتار پلاستیک آن‌ها از طریق روش المان محدود می‌باشد. در این تحقیق، ابتدا یک سلول واحد برای کاهش محاسبات عددی و همچنین مدل‌سازی تهیه می‌شود که دارای خواص آماری فوم موردنظر می‌باشد و سپس رفتار دینامیکی این سلول واحد تحت ضربه شبیه‌سازی شده‌است. همچنین، روش تحلیلی برای بدست‌آوردن مقدار کرنش تراکمی فوم‌ها با استفاده از نتایج المان محدود ارائه شده‌ به طوری‌که حل المان محدود ارائه‌شده در این تحقیق دارای تطابق مناسبی با روش‌های تئوری دیگر پژوهش‌های انجام‌شده می‌باشد. به عبارت دیگر، با استفاده از روش تحلیلی، روش المان محدود و شبیه‌سازی مورد ارزیابی قرار گرفته‌است. با استفاده از آزمایش‌های شبیه‌سازی‌شده، یک مدل با استفاده از روش سطح پاسخ برای بدست‌آوردن کرنش تراکمی ارائه شده‌است که نتایج حاصل از این مدل نیز مورد ارزیابی قرار گرفته‌است. نتایج حاصل ازاین پژوهش، نشان داد که امکان مدل‌سازی و تحلیل جذب انرژی (ضربه) فوم‌ها با استفاده از روش ارائه‌شده در این پژوهش امکان‌پذیر خواهد بود و می‌تواند در پژوهش‌های آینده به معادله ساختاری مناسب برای تحلیل میکروساختار انواع فوم‌ها دست یافت.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

A new method for estimating the compressive strain of cellular structures using microstructure of foams based on Laguerre tessellations

نویسندگان [English]

  • Ali Shiravand 1
  • Masood Asgari 2
1 Faculty of Mechanical Engineering, K. N. Toosi University of Technology,Tehran, Iran
چکیده [English]

In this study, energy absorption behavior of cellular structures such as foams will be investigated. In this paper, developing microstructural modeling of cellular structures and analyzing their plastic behavior through the finite element method is the main goal. In this research, a unit cell is first developed for numerical computation reduction as well as modeling that has the desired foam statistical properties, and then the dynamic behavior of this unit cell under simulated impact will be analyzed. An analytical method to obtain the compressive strain value of the foams with the help of numerical solution results will be presented. In other words, using the analytical method, the finite element method and the simulation will be evaluated. Then, using simulated experiments, a model using the response surface methodology  to obtain the compressive strain will be presented and the results of this model will be evaluated by numerical method. The results of this study showed that it is possible to model and analyze the energy absorption of the foams using the method presented in this study and as a result, suitable structural equation for microstructural analysis of foams can be obtained in future researches.
 

کلیدواژه‌ها [English]

  • Energy absorption
  • Closed-cell foams
  • Response surface method
  • Compression strain
  • Laguerre method
[1] G. Lu, T. Yu, Energy absorption of structures and materials, Elsevier, 2003.
[2] A. Shiravand, M. Asgari, Hybrid metal-composite conical tubes for energy absorption; theoretical development and numerical simulation, Thin-Walled Structures, 145 (2019) 106442.
[3] M.B. Azimi, M. Asgari, A new bi-tubular conical–circular structure for improving crushing behavior under axial and oblique impacts, International Journal of Mechanical Sciences, 105 (2016) 253-265.
[4] Z. Liu, Z. Huang, Q. Qin, Experimental and theoretical investigations on lateral crushing of aluminum foam-filled circular tubes, Composite Structures, 175 (2017) 19-27.
[5] Q. Feng, C. Liao, Y. Ma, G. Yang, Optimization of Pore Walls Microstructure in Open Cell Aluminum Foams Utilizing Self-Propagating Reaction, MATERIALS TRANSACTIONS,  (2019) MT-M2019124.
[6] H. Zhu, A. Windle, Effects of cell irregularity on the high strain compression of open-cell foams, Acta Materialia, 50(5) (2002) 1041-1052.
[7] H. Zhu, J. Hobdell, A. Windle, Effects of cell irregularity on the elastic properties of open-cell foams, Acta materialia, 48(20) (2000) 4893-4900.
[8] Y.-L. Yuan, Z.-X. Lu, Calculation of the elastic modulus of low density open-cell foams with random model, Acta Aeronautica Et Astronautica Sinica, 25(2) (2004) 130-132.
[9] Y. Gan, C. Chen, Y. Shen, Three-dimensional modeling of the mechanical property of linearly elastic open cell foams, International Journal of Solids and Structures, 42(26) (2005) 6628-6642.
[10] K. Li, X.-L. Gao, G. Subhash, Effects of cell shape and strut cross-sectional area variations on the elastic properties of three-dimensional open-cell foams, Journal of the Mechanics and Physics of Solids, 54(4) (2006) 783-806.
[11] Z. Fan, Y. Wu, X. Zhao, Y. Lu, Simulation of polycrystalline structure with Voronoi diagram in Laguerre geometry based on random closed packing of spheres, Computational Materials Science, 29(3) (2004) 301-308.
[12] Y. Song, Z. Wang, L. Zhao, J. Luo, Dynamic crushing behavior of 3D closed-cell foams based on Voronoi random model, Materials & Design, 31(9) (2010) 4281-4289.
[13] C. Redenbach, I. Shklyar, H. Andrä, Laguerre tessellations for elastic stiffness simulations of closed foams with strongly varying cell sizes, International Journal of Engineering Science, 50(1) (2012) 70-78.
[14] Q.H. Jebur, Characterisation and modelling of transversely isotropic flexible viscoelastic foam, University of Glasgow, 2013.
[15] Z. Li, C. Xi, L. Jing, Z. Wang, L. Zhao, Effect of loading rate on the compressive properties of open-cell metal foams, Materials Science and Engineering: A, 592 (2014) 221-229.
[16] Y. Chen, R. Das, M. Battley, Effects of cell size and cell wall thickness variations on the stiffness of closed-cell foams, International Journal of Solids and Structures, 52 (2015) 150-164.
[17] S. Wang, Y. Ding, C. Wang, Z. Zheng, J. Yu, Effect of relative density of the dynamic impact behaviors of closed cell foam, in:  Proceedings of the ASME 35th International Conference on Ocean, Offshore and Arctic Engineering (OMAE’16), 2016.
[18] P. Zhang, Z. Wang, L. Zhao, Dynamic crushing behavior of open-cell aluminum foam with negative Poisson’s ratio, Applied Physics A, 5(123) (2017) 1-11.
[19] C. Chen, T. Lu, N. Fleck, Effect of imperfections on the yielding of two-dimensional foams, Journal of the Mechanics and Physics of Solids, 47(11) (1999) 2235-2272.
[20] D. Bourne, P. Kok, S. Roper, W. Spanjer, Laguerre tessellations and polycrystalline microstructures: A fast algorithm for generating grains of given volumes, arXiv preprint arXiv:1912.07188,  (2019).
[21] Y. Sun, Q. Li, Dynamic compressive behaviour of cellular materials: A review of phenomenon, mechanism and modelling, International Journal of Impact Engineering, 112 (2018) 74-115.
[22] L.J. Gibson, M.F. Ashby, Cellular solids: structure and properties, Cambridge university press, 1999.
[23] M.F. Ashby, A. Evans, N.A. Fleck, L.J. Gibson, J.W. Hutchinson, H.N. Wadley, Metal foams: a design guide: Butterworth-Heinemann, Oxford, UK, ISBN 0-7506-7219-6, Published 2000, Hardback, 251 pp., $75.00, in, Elsevier, 2002.
[24] M. Avalle, G. Belingardi, R. Montanini, Characterization of polymeric structural foams under compressive impact loading by means of energy-absorption diagram, International Journal of Impact Engineering, 25(5) (2001) 455-472.
[25] E.B. Matzke, The three-dimensional shape of bubbles in foam-an analysis of the role of surface forces in three-dimensional cell shape determination, American Journal of Botany,  (1946) 58-80.
[26] S. Kanaun, O. Tkachenko, Mechanical properties of open cell foams: Simulations by laguerre tesselation procedure, International Journal of Fracture, 140(1-4) (2006) 305-312.
[27] K. Li, X.-L. Gao, G. Subhash, Effects of cell shape and cell wall thickness variations on the elastic properties of two-dimensional cellular solids, International Journal of Solids and Structures, 42(5) (2005) 1777-1795.
[28] F. Rhines, B. Patterson, Effect of the degree of prior cold work on the grain volume distribution and the rate of grain growth of recrystallized aluminum, Metallurgical Transactions A, 13(6) (1982) 985-993.
[29] G. Ma, Z. Ye, Z. Shao, Modeling loading rate effect on crushing stress of metallic cellular materials, International Journal of Impact Engineering, 36(6) (2009) 775-782.
[30] S. Zhu, G.B. Chai, Low-velocity impact response of fibre–metal laminates–Experimental and finite element analysis, Composites Science and Technology, 72(15) (2012) 1793-1802.
[31] R.H. Myers, D.C. Montgomery, C.M. Anderson-Cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley, 2016.
[32] H. Salaripoor, M.B. Azimi, M. Asgari, Optimized foam filling configuration in bi-tubular crush boxes; a comprehensive experimental and numerical analysis, Engineering Research Express,  (2020).