Stress concentration factors for bending with symmetric opposite notches in thin beam evaluated by FEM and ANN
-
Muhammed Ikbal Sahin
Muhammed Ikbal Sahin, born in 1997, studied Mechanical Engineering at the Faculty of Engineering, Department of Mechanical Engineering, University of Gazi, Ankara, Turkey. He has been studying MSc degree at the same university. His main fields of interests are machine design, manufacturing, finite element method, and product design.
and
Murat Tolga Ozkan
Prof. Dr. Murat Tolga Ozkan, born in 1971, studied Manufacturing at the Faculty of Technology, Department of Machine, University of Gazi, Ankara, Turkey and completed his MSc and PhD at the same university. He promoted as Associate Professor in the Department of Industrial Design Engineering, Faculty of Technology, University of Gazi, Ankara at 2018. Currently, He is working as Professor, Department of Industrial Design Engineering, Faculty of Technology, University of Gazi, Ankara at 2020. His main fields of interest are manufacturing, machine design, finite element method, artificial neural network, mechanisms, and biomechanics.
Abstract
In machine design, numerous tables are utilized, but only a few are used intensively. The development of scientific techniques and software has allowed frequently used tables to become more user-friendly. This study focuses on converting previously nondigitized experimental data into a more practical format using advanced computer technology and software. Fatigue is the primary cause of failure in machine parts. During the design phase, features like holes, channels, grooves, and protrusions disrupt the continuity of the part, and dimensionless part size parameters play a crucial role in the design process. This research investigates bending with symmetric opposite notches in a thin beam, based on data compiled by Peterson that had not been digitized before. Initially, the curves from the tables were digitized and organized while adhering to the original parameters. A parametric Finite Element solid model was created, and analyses were conducted using the obtained parametric values. Each curve from the original table was validated through regression methods using Finite Element results. Furthermore, an Artificial Neural Network (ANN) model was developed based on the original curve data. The original curves, finite element results, and ANN model were compared, and a new model proposal was made.
About the authors
Muhammed Ikbal Sahin, born in 1997, studied Mechanical Engineering at the Faculty of Engineering, Department of Mechanical Engineering, University of Gazi, Ankara, Turkey. He has been studying MSc degree at the same university. His main fields of interests are machine design, manufacturing, finite element method, and product design.
Prof. Dr. Murat Tolga Ozkan, born in 1971, studied Manufacturing at the Faculty of Technology, Department of Machine, University of Gazi, Ankara, Turkey and completed his MSc and PhD at the same university. He promoted as Associate Professor in the Department of Industrial Design Engineering, Faculty of Technology, University of Gazi, Ankara at 2018. Currently, He is working as Professor, Department of Industrial Design Engineering, Faculty of Technology, University of Gazi, Ankara at 2020. His main fields of interest are manufacturing, machine design, finite element method, artificial neural network, mechanisms, and biomechanics.
-
Research ethics: Not applicable.
-
Informed consent: Not applicable.
-
Author contributions: Muhammed Ikbal SAHIN, Murat Tolga OZKAN. Muhammed İkbal Şahin converted graphical data into numerical data, created and solved the FEA simulation model, and completed the writing process of the article. Murat Tolga Özkan determined the study's steps, converted and verified the data, validated the FEA model, and developed and designed the ANN model. He organized and proofread all figures, tables, and text of the study.
-
Use of Large Language Models, AI and Machine Learning Tools: None declared.
-
Conflict of interest: Not applicable.
-
Research funding: Not applicable.
-
Data availability: If you need we can send our analysis and chart data.
References
[1] W. D. Pilkey and D. F. Pilkey, Peterson’s Stress Concentration Factors, Stress Concentration Factors, 3th ed. New York, USA, John Wiley & Sons, Inc, 2008, pp. 103–147.10.1002/9780470211106Search in Google Scholar
[2] M. A. S. Akanda, S. M. Mamun, S. Majumder, and M. Kharshiduzzaman, “Theoretical stress concentration factors for short flat tension bars with opposite u-shaped notches,” in Proceedings of the International Conference on Mechanical Engineering ICME07-AM-65, Banglladesh, 2007, pp. 1–6.Search in Google Scholar
[3] N. Troyani, S.I. Hernandez, G. Villarroel, Y. Pollonais, and C. Gomes, “Theoretical stress concentration factors for short flat bars with opposite U-shaped notches subjected to in-plane bending,” Int. J. Fatig., vol. 26, no. 10, pp. 1303–1310, 2004, https://doi.org/10.1016/j.ijfatigue.2004.04.007.Search in Google Scholar
[4] H. M. Tlilan, N. Sakai, and T. Majma, “Effect of notch depth on strain-concentration factor of rectangular bars with a single-edge notch under pure bending,” Int. J. Solids Struct., vol. 43, no. 2, pp. 459–474, 2006, https://doi.org/10.1016/j.ijsolstr.2005.03.069.Search in Google Scholar
[5] A. Ching, S. Okuba, and C. Taso, “Stress-concentration factors for multiple semielliptical notches in beams under pure bending,” Exp. Mech., vol. 8, no. 4, p. 19N–24N, 1968. https://doi.org/10.1007/BF02326348.Search in Google Scholar
[6] C. H. Tsao, A. Ching, and S. Okuba, “Stress-concentration factors for semielliptical notches in beams under pure bending,” Exp. Mech., vol. 5, no. 3, p. 19A–23A, 1965. https://doi.org/10.1007/BF02323214.Search in Google Scholar
[7] T. G. F. Gray, F. Tournery, J. Spence, and D. Brennan, “Closed-form functions for elastic stress concentration factors in notched bars,” J. Strain Anal., vol. 30, no. 2, pp. 143–154, 1995, https://doi.org/10.1243/03093247V302143.Search in Google Scholar
[8] J. B. Hartman and M. M. Leven, “Factors of stress concentration for the bending case of fillets in flat bars and shafts with a central enlarged section,” Proc. Soc. Exp. Stress Anal., vol. 8, no. 2, pp. 53–62, 1951.Search in Google Scholar
[9] J. Kisija, J. Kaemarcik, and A. Karac, “Determination of stress concentration factors via numerical methods for bars of circular cross section with U-shaped groove subjected to tension and bending,” in 13th International Research/Expert Conference Trends in the Development of Machinery and Associated Technology, TMT 2009 Hammamet, Tunisia, 2009, pp. 493–496.Search in Google Scholar
[10] N. A. Noda, M. A. Tsubaki, and H. Nisitani, “Stress concentration of a strip with V or U-shaped notches under transverse bending,” Eng. Fract. Mech., vol. 30, no. 1, pp. 119–133, 1988, https://doi.org/10.1016/0013-7944(88)90126-9.Search in Google Scholar
[11] B. Atzori, P. Lazzarin, and R. Tovo, “Stress distributions for V-shaped notches under tensile and bending loads,” Fatigue Fract. Eng. Mater. Struct., vol. 20, no. 9, pp. 1083–1092, 1997, https://doi.org/10.1111/j.1460-2695.1997.tb00314.x.Search in Google Scholar
[12] I. H. Wilson and D. J. White, “Stress-concentration factors for shoulder fillets and grooves in plates,” J. Strain Anal., vol. 8, no. 1, pp. 43–51, 1973, https://doi.org/10.1243/03093247V081043.Search in Google Scholar
[13] M. T. Ozkan and F. Erdemir, “Determination of stress concentration factors for shafts under tension,” Mater. Test., vol. 62, no. 4, pp. 413–421, 2020, https://doi.org/10.3139/120.111500.Search in Google Scholar
[14] M. T. Ozkan and F. Erdemir, “Determination of theoretical stress concentration factor for circular/elliptical holes with reinforcement using analytical, finite element method and artificial neural network techniques,” Neural Comput. Appl., vol. 33, no. 19, pp. 12641–12659, 2021. https://doi.org/10.1007/s00521-021-05914-x.Search in Google Scholar
[15] M. T. Ozkan and I. Toktas, “Determination of the stress concentration factor (kt) in a rectangular plate with a hole under tensile stress using different methods,” Mater. Test., vol. 58, no. 10, pp. 839–847, 2016, https://doi.org/10.3139/120.110933.Search in Google Scholar
[16] H. Ulas, M. Bilgin, H. Sezer, and M. T. Ozkan, “Performance of coated and uncoated carbide/cermet cutting tools during turning,” Mater. Test., vol. 60, no. 9, pp. 893–901, 2018, https://doi.org/10.3139/120.111228.Search in Google Scholar
[17] J. B. Kosmatka, R. H. Fries, and C. F. Reinholtz, “Tension and bending stress concentration factors in ‘U’, ‘V’, and opposed ‘U’-’V’ notches,” J. Strain Anal. Eng. Des., vol. 25, no. 4, pp. 233–240, 1990, https://doi.org/10.1243/03093247V254233.Search in Google Scholar
[18] H. Nisitani and N.-A. Noda, “Stress concentration of a strip with double edge notches under tension or in-plane bending,” Eng. Fract. Mech., vol. 23, no. 6, pp. 1051–1065, 1986. https://doi.org/10.1016/0013-7944(86)90147-5.Search in Google Scholar
[19] B. Padhiyar, P. Sharma, and Y. Mishra, “Determine stress concentration for simply supported beam with opposite elliptical notch subjected to pure bending,” Int. J. Adv. Technol. Eng. Sci., vol. 2, no. 5, pp. 332–337, 2014.Search in Google Scholar
[20] H. Nisitani and N.-A. Noda, “Stress concentration of a cylindrical bar with a V-shaped circumferential groove under torsion, tension or bending,” Eng. Fract. Mech., vol. 20, no. 5–6, pp. 743–766, 1984. https://doi.org/10.1016/0013-7944(84)90084-5.Search in Google Scholar
[21] V. Chmelko, M. Harakal, P. Žlábek, M. Margetin, and R. Ďurka, “Simulation of stress concentrations in notches,” Metals, vol. 12, no. 1, pp. 1–9, 2022, https://doi.org/10.3390/met12010043.Search in Google Scholar
[22] N. A. Noda and Y. Takase, “Stress concentration factor formulas useful for all notch shapes in a flat test specimen under tension and bending,” J. Test. Eval., vol. 30, no. 5, pp. 369–381, 2002, https://doi.org/10.1520/JTE12327J.Search in Google Scholar
[23] N.-A. Noda, M. Sera, and Y. Takase, “Stress concentration factors for round and flat test specimens with notches,” Int. J. Fatig., vol. 17, no. 3, pp. 163–178, 1995. https://doi.org/10.1016/0142-1123(95)98937-X.Search in Google Scholar
[24] F. I. Baratta and D. M. Neal, “Stress-concentration factors in U-shaped and semi-elliptical edge notches,” J. Strain Anal., vol. 5, no. 2, pp. 121–127, 1970. https://doi.org/10.1243/03093247V052121.Search in Google Scholar
[25] B. Atzori, S. Filippi, P. Lazzarin, and F. Berto, “Stress distributions in notched structural components under pure bending and combined traction and bending,” Fatig. Fract. Eng. Mater. Struct., vol. 28, no. 1–2, pp. 13–23, 2005. https://doi.org/10.1111/j.1460-2695.2004.00831.x.Search in Google Scholar
[26] ANSYS 2019R1 (2019). Ansys Inc.Search in Google Scholar
[27] Matlab 2018b (2018). Matwork.Search in Google Scholar
[28] M. T. Ozkan, “Surface roughness during the turning process of a 50CrV4 (SAE 6150) steel and ANN based modeling,” Mater. Test., vol. 57, no. 10, pp. 889–896, 2015, https://doi.org/10.3139/120.110793.Search in Google Scholar
[29] STATISTICA (2007). TIBCO Software Inc.Search in Google Scholar
[30] H. B. Ulas, M. T. Ozkan, and Y. Malkoc, “Vibration prediction in drilling processes with HSS and carbide drill bit by means of artificial neural networks,” Neural Comput. Appl., vol. 31, no. 8, pp. 5547–5562, 2019, https://doi.org/10.1007/s00521-018-3379-3.Search in Google Scholar
[31] H. B. Ulas and M. T. Ozkan, “Turning processes investigation of materials austenitic, martensitic and duplex stainless steels and prediction of cutting forces using artificial neural network (ANN) techniques,” Indian J. Eng. Mater. Sci.(IJEMS), vol. 26, no. 2, pp. 93–104, 2019.Search in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
