A comparative study of crack detection in nanobeams using molecular dynamics simulation, analytical formulations, and finite element method

Document Type : Research Paper

Authors

1 Faculty of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran

2 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

Abstract

The study of material behavior in the presence of defects is one of the studies that can help us recognize and predict material behavior. Studying the behavior of materials in nanoscale illuminates a broad view of the behavior of materials. A variety of studies are available for such a study: numerical, experimental, and quasi-experimental methods. Molecular dynamics is one of the methods that can be used to study the behavior of materials. The vibrational behavior of structures has been the focus of many researchers to analyze and investigate mortar materials' properties. The study of vibrational behavior at the nanoscale can give us a broad view of materials' properties. Therefore, in this study, we study nanowires' vibrational behavior in the presence of edge cracks using molecular dynamics. The influence of crack position and depth on the natural frequencies and shape of iron nanobeam modes with BCC crystal structure have been investigated. Clamped-Clamped boundary conditions with different cracks position and depth have been applied by simulating molecular dynamics. Also, the data obtained from molecular dynamics simulations have been compared with the finite element method and different crack models in one dimensional beams . In order to extract the shape of natural modes and frequencies by molecular dynamics method, FFT applied on the  displacement history of nanobeam atoms after excitation of an amplitude in the center of nanobeam in x and y directions have been used. The crack models studied in this study were linear and rotational crack models on beams with Timoshenko theory. Molecular dynamics simulation data compared to other methods have shown a decrease in the value of natural frequencies in the presence of cracks. Also, finite element data and molecular dynamics are well matched. However, the molecular dynamics method has shown a more significant reduction in natural frequency values   than finite element methods and various crack models with Timoshenko theory. We have also found that in molecular dynamics bribery, the initial excitation type of nanobeams is very useful in extracting nanobeam modes' shape.

Keywords

[1] Husain, A., Hone, J., Postma, H. W. C., Huang, X. M. H., Drake, T., Barbic, M., ... & Roukes, M. L. (2003). Nanowire-based very-high-frequency electromechanical resonator. Applied Physics Letters, 83(6), 1240-1242.
[2] Li, M., Mayer, T. S., Sioss, J. A., Keating, C. D., & Bhiladvala, R. B. (2007). Template-grown metal nanowires as resonators: performance and characterization of dissipative and elastic properties. Nano letters, 7(11), 3281-3284.
[3] Liao, M., Hishita, S., Watanabe, E., Koizumi, S., & Koide, Y. (2010). Suspended Single‐Crystal Diamond Nanowires for High‐Performance Nanoelectromechanical Switches. Advanced Materials, 22(47), 5393-5397.
[4] Wang, Z. L., & Song, J. (2006). Piezoelectric nanogenerators based on zinc oxide nanowire arrays. Science, 312(5771), 242-246.
[5] P. Xie, Q. Xiong, Y. Fang, Q. Qing and C. M. Lieber, Nat. Nanotechnol., 2011, 7, 119-125.
[6] Eom, K., Park, H. S., Yoon, D. S., & Kwon, T. (2011). Nanomechanical resonators and their applications in biological/chemical detection: Nanomechanics principles. Physics Reports, 503(4-5), 115-163.
[7] Kim, S. Y., & Park, H. S. (2008). Utilizing mechanical strain to mitigate the intrinsic loss mechanisms in oscillating metal nanowires. Physical review letters, 101(21), 215502.
[8] Pourkermani, A. G., Azizi, B., & Pishkenari, H. N. (2020). Vibrational analysis of Ag, Cu and Ni nanobeams using a hybrid continuum-atomistic model. International Journal of Mechanical Sciences, 165, 105208.
[9] Kowalczyk-Gajewska, K., & Maździarz, M. (2018). Atomistic and mean-field estimates of effective stiffness tensor of nanocrystalline copper. International Journal of Engineering Science, 129, 47-62.
[10] Yang, X., Sun, Y., Wang, F., & Zhao, J. (2015). Surface effects on the initial dislocation of Ag nanowires. Computational Materials Science, 106, 23-28.
[11] Ahadi, A., & Melin, S. (2016). Size dependence of the Poisson’s ratio in single-crystal fcc copper nanobeams. Computational Materials Science, 111, 322-327.
[12] Pishkenari, H. N., Afsharmanesh, B., & Akbari, E. (2015). Surface elasticity and size effect on the vibrational behavior of silicon nanoresonators. Current Applied Physics, 15(11), 1389-1396.
[13] Reddy, J., Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science, 2007. 45(2-8): p. 288-307.
[14] Wang, C. M., Zhang, Y. Y., & He, X. Q. (2007). Vibration of nonlocal Timoshenko beams. Nanotechnology, 18(10), 105401.
[15] Behera, L. and S. Chakraverty, Free vibration of Euler and Timoshenko nanobeams using boundary characteristic orthogonal polynomials. Applied Nanoscience, 2014. 4(3): p.347-358.
[16] Wu, L.-Y., et al., Vibrations of nonlocal Timoshenko beams using orthogonal collocation method. Procedia Engineering, 2011. 14: p. 2394-2402.
[17] Eltaher, M., A. E. Alshorbagy, and F. Mahmoud, Vibration analysis of Euler–Bernoulli nanobeams by using finite element method. Applied Mathematical Modelling, 2013. 37(7): p.4787-4797.
[18] Beni, Y. T., A. Jafaria, and H. Razavi, Size effect on free transverse vibration of cracked nano-beams using couple stress theory. International Journal of EngineeringTransactions B: Applications, 2014. 28(2): p. 296-304.
[19] Hasheminejad, S. M., et al., Free transverse vibrations of cracked nanobeams with surface effects. Thin Solid Films, 2011. 519(8): p. 2477-2482.
[20] Loghmani, M. and M. R. Hairi Yazdi, An analytical method for free vibration of multi cracked and stepped nonlocal nanobeams based on wave approach. Results in Physics, 2018. 11: p. 166-181.
 [21] Roostai, H. and M. Haghpanahi, Vibration of nanobeams of different boundary conditions with multiple cracks based on nonlocal elasticity theory. Applied Mathematical Modelling, 2014. 38(3): p. 1159-1169.
[22] Chondros, T. G., Dimarogonas, A. D., & Yao, J. (1998). A continuous cracked beam vibration theory. Journal of sound and vibration, 215(1), 17-34.
[23] Barad, K. H., Sharma, D. S., & Vyas, V. (2013). Crack detection in cantilever beam by frequency based method. procedia engineering, 51, 770-775.
[24] Mousavi Nejad Souq, S. S., & Baradaran, G. H. (2015). Crack detection in frame Structures with regard to changes in natural frequencies by using finite element method and ACOR. Modares Mechanical Engineering, 15(8), 51-58.(in Persian)
[25] Khalkar, V., & Ramachandran, S. (2017). Vibration analysis of a cantilever beam for oblique cracks. ARPN J. Eng. Appl. Sci., 12(4), 1144-1151.
[26] Swamidas, A. S. J., Yang, X., & Seshadri, R. (2004). Identification of cracking in beam structures using Timoshenko and Euler formulations. Journal of Engineering Mechanics, 130(11), 1297-1308.
[27] Khaji, N., Shafiei, M., & Jalalpour, M. (2009). Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions. International Journal of Mechanical Sciences, 51(9-10), 667-681.
[28] Batihan, A. Ç., & Kadioğlu, F. S. (2016). Vibration analysis of a cracked beam on an elastic foundation. International Journal of Structural Stability and Dynamics, 16(05), 1550006.
[29] Viola, E., Nobile, L., & Federici, L. (2002). Formulation of cracked beam element for structural analysis. Journal of engineering mechanics, 128(2), 220-230.
[30] Yokoyama, T., & Chen, M. C. (1998). Vibration analysis of edge-cracked beams using a line-spring model. Engineering Fracture Mechanics, 59(3), 403-409.
[31] Mendelev, M. I., Han, S., Srolovitz, D. J., Ackland, G. J., Sun, D. Y., & Asta, M. (2003). Development of new interatomic potentials appropriate for crystalline and liquid iron. Philosophical magazine, 83(35), 3977-3994.
[32] Plimpton, S. (1995). Fast parallel algorithms for short-range molecular dynamics. Journal of computational physics, 117(1), 1-19.
[33] Loya, J. A., Rubio, L., & Fernández-Sáez, J. (2006). Natural frequencies for bending vibrations of Timoshenko cracked beams. Journal of Sound and Vibration, 290(3-5), 640-653.
[34] Biswal, A. R., Roy, T., Behera, R. K., Pradhan, S. K., & Parida, P. K. (2016). Finite element based vibration analysis of a nonprismatic Timoshenko beam with transverse open crack. Procedia Engineering, 144, 226-233.
[35] Nguyen, K. V. (2014). Mode shapes analysis of a cracked beam and its application for crack detection. Journal of Sound and Vibration, 333(3), 848-872.
[36] Orhan, S. (2007). Analysis of free and forced vibration of a cracked cantilever beam. Ndt & E International, 40(6), 443-450.
[37] Zeng, J., Ma, H., Zhang, W., & Wen, B. (2017). Dynamic characteristic analysis of cracked cantilever beams under different crack types. Engineering Failure Analysis, 74, 80-94.
[38] Zheng, D. Y., & Kessissoglou, N. J. (2004). Free vibration analysis of a cracked beam by finite element method. Journal of Sound and vibration, 273(3), 457-475.
[39] Ebrahimi, A., Meghdari, A., Behzad, M. (2005). A New Approach for Vibration Analysis of a Cracked Beam. International Journal of Engineering, 18(4), 319-330.
[40] Stukowski, A. (2009). Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool. Modelling and Simulation in Materials Science and Engineering, 18(1), 015012.
[41] Shi, D., Wang, Q., Shi, X., & Pang, F. (2015). An accurate solution method for the vibration analysis of Timoshenko beams with general elastic supports. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 229(13), 2327-2340.
[42] Tada, H., Paris, P. C., & Irwin, G. R. (1973). The stress analysis of cracks. Handbook, Del Research Corporation, 34.
 [43] Lellep, J. A. A. N., & Lenbaum, A. R. T. U. R. (2016). Natural vibrations of a nano-beam with cracks. International Journal of Theoretical and Applied Mechanics, 1(1), 247-252.
[44] COMSOL, A. (2018). Comsol multiphysics® v. 5.4 www. comsol. com. Stockholm, Sweden. COMSOL AB.
Volume 52, Issue 3
September 2021
Pages 408-422
  • Receive Date: 25 April 2021
  • Revise Date: 28 June 2021
  • Accept Date: 29 June 2021
  • First Publish Date: 23 August 2021