Stress concentration factor of a variable circular cross section beam under flexion
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Published:
Feb 27, 2023
Keywords:
rotating beam fatigue testing machine, dog-bone shaped specimen, finite element method, stress concentration factor, variable cross section beam
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Abstract
Fatigue testing in rotating beam fatigue systems requires the usage of specimens with standardized geometry, which exhibits a changing cross section to guarantee that the failure occurs within the gauge length. The proper calculation of the stress within the gauge length requires that a stress concentration factor is calculated, which has not been previously reported by the specialized literature. Therefore, in this work both the Finite Element Method and the Beam Theory was used aimed at calculating the calculation of stress concentration factor of a specimen with complex cross section change. For that, half specimen was modeled in a finite elements software as a cantilever beam and the stress in the supported end was determined. Analytically, stress of the testing machine under the consideration of a four-point bending beam was calculated. Results of both calculations were compared in order to establish the stress concentration factor. It was determined that, without considering the stress concentration factor, stress of the specimen calculated with analytical beam theory is 24% smaller than that obtained with the finite element software.
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Rodríguez-Reyes, V. I., & Abúndez Pliego, A. (2023). Stress concentration factor of a variable circular cross section beam under flexion. Ingenio Magno, 13(2), 81-88. Retrieved from http://revistas.ustatunja.edu.co/index.php/ingeniomagno/article/view/2613
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Articulos
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References
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[14] Mayén, J., Abúndez, A., Pereyra, I., Colín, J., Blanco, A., & Serna, S. (2017). Comparative analysis of the fatigue short crack growth on Al 6061-T6 alloy by the exponential crack growth equation and a proposed empirical model. Engineering Fracture Mechanics, 177, 203–217. https://doi.org/10.1016/j.engfracmech.2017.03.036
[15] Meggiolaro, M. A., Castro, J. T. P., & de Moura Nogueira, R. (2017). A fast rotating bending fatigue test machine. Procceedings of the 24th ABCM International Congress of Mechanical Engineering. https://doi.org/10.26678/ABCM.COBEM2017.COB17-1824
[16] Moore, R. R. (1939). Material testing machine (Patent Núm. US2154277A). U.S. Patent and Trademark Office. https://patents.google.com/patent/US2154277A/en
[17] Mott, R. L., Vavrek, E. M., & Wang, J. (2017). Machine Elements in Mechanical Design (6a ed.). Pearson Education, Inc.
[18] Ozkan, M. T., & Erdemir, F. (2021). Determination of theoretical stress concentration factor for circular/elliptical holes with reinforcement using analytical, finite element method and artificial neural network techniques. Neural Computing and Applications, 33(19), 12641–12659. https://doi.org/10.1007/s00521-021-05914-x
[19] Özkan, M. T., Kaygisiz, M., & Toktas, I. (2016). Definition of stress concentration factor of column with angled holed under bending stress using finite element analysis. 21st International Scientific Conference MECHANIKA 2016, 199–205.
[20] Pérez Olivas, P. A., Limón Leyva, P. A., Aguilera Gómez, E., Plascencia Mora, H., & Jiménez López, E. (2014). Daño acumulado teórico-experimental del aluminio 6061-T6: método de Palmgren-Miner. 2014 – Memorias de Divulgación Científica, Tecnológica e Innovación de la SOMIM – XX Congreso, 375–380. http://somim.org.mx/siam/librosomim2014/pdfs/A1/A1_278.pdf
[21] Petatan Bahena, K. E., Gutierrez Rojas, I., Abúndez Pliego, A., Mayen Chaires, J., & Blanco Ortega, A. (2021). Efecto de la velocidad de avance en torneado CNC en seco y el acabado superficial en la vida a fatiga de una aleación de aluminio 6061-T6. Jornada de Ciencia y Tecnología Aplicada, 4(1), 235–240. https://jcyta.cenidet.tecnm.mx/revistas/jcyta/06-Revista_JCyTA_Vol-4-Num-1_Ene-Jun_2021.pdf
[22] Pilkey, W. D., Pilkey, D. F., & Zhuming, B. (2020). Peterson’s Stress Concentrations Factors (4th ed.). John Wiley & Sons, Inc.
[23] Sallberg, D. W., Lawson, T. J., & Cardon, M. H. (1989). Multi-axial fatigue testing machine (Patent Núm. US4802365A). U.S. Patent and Trademark Office. https://patents.google.com/patent/US4802365
[24] Schütz, W. (1996). A history of fatigue. Engineering Fracture Mechanics, 54(2), 263–300. https://doi.org/10.1016/0013-7944(95)00178-6
[25] Slotwinski, J., & Moylan, S. (2014). Applicability of Existing Materials Testing Standards for Additive Manufacturing Materials. https://doi.org/10.6028/NIST.IR.8005
[26] Tlapanco Rios, E. I., Castaño Urrego, C. A., Lopez Perez, J. R., & Forero Rubiano, F. R. A. (2020). Método de comparación de resultados de modelado CAD-CAE contra probetas de ensayo destructivo. Acta Universitaria, 30, 1–16. https://doi.org/10.15174/au.2020.2668
[27] Toktaş, İ., Özkan, M. T., Erdemir, F., & Yuksel, N. (2020). Determination of Stress Concentration Factor (Kt) for a Crankshaft Under Bending Loading: An Artificial Neural Networks Approach. Politeknik Dergisi, 23(3), 813–819. https://doi.org/10.2339/politeknik.683270
[28] Yang, H., Zhang, Z., Tan, C., Ito, M., Pan, P., & Wang, X. (2018). Rotating Bending Fatigue Microscopic Fracture Characteristics and Life Prediction of 7075-T7351 Al Alloy. Metals, 8(4), 210. https://doi.org/10.3390/met8040210
[29] Zakaria, K. A., Abdullah, S., & Ghazali, M. J. (2016). A Review of the Loading Sequence Effects on the Fatigue Life Behaviour of Metallic Materials. Journal of Engineering Science and Technology Review, 9(5), 189–200. https://doi.org/10.25103/jestr.095.30
[30] Zuno Silva, J. (2016). Fatigue resistance improvement of a forging medium carbon steel using Mischmetal (rare earths) as inclusions (MnS) modifier element. Nova Scientia, 8(17), 97. https://doi.org/10.21640/ns.v8i17.483
[2] Araque de los Ríos, Ó. J., & Quintana Ávila, S. (2018). Design of a fatigue test bench in rotary flexion to evaluate the behavior to cyclical loads. Scientia Et Technica, 23(3), 324–333. https://doi.org/10.22517/23447214.16891
[3] ASTM International. (2002). ASTM E466-96, Standard Practice for Conducting Force Controlled Constant Amplitude Axial Fatigue Tests of Metallic Materials. Astm International, 03(Reapproved). https://doi.org/10.1520/E0466-21
[4] Beer, F. P., Johnston, E. R., Dewolf, J. T., & Mazurek, D. (2020). Mechanics of materials (8th ed.). McGraw-Hill Education Ltd.
[5] Ceballos, W. F., León Gómez, A., & Coronado Marín, J. J. (2010). Comportamiento a fatiga del acero SAE 4140 usando alta rugosidad superficial y ambiente corrosivo. DYNA. Revista de la Facultad de Minas, 77(162), 125–135. https://revistas.unal.edu.co/index.php/dyna/article/view/15842
[6] Cruz Castro, E., González Vizcarra, B., Ávila Puc, M., Gonzalez Lopez, Y., Colín Ocampo, J., Mayen Chaires, J., & Abúndez-Pliego, A. (2019). Diseño, construcción y puesta en marcha de una máquina para pruebas de fatiga de flechas en condiciones de resonancia. XXV Congreso Internacional Anual de la SOMIM, 26–30. http://somim.org.mx/memorias/memorias2019/articulos/A1_124.pdf
[7] Domínguez Almaraz, G. M., Ávila Ambriz, J. L., & Cadenas Calderón, E. (2012). Fatigue endurance and crack propagation under rotating bending fatigue tests on aluminum alloy AISI 6063-T5 with controlled corrosion attack. Engineering Fracture Mechanics, 93, 119–131. https://doi.org/10.1016/j.engfracmech.2012.06.012
[8] Dominguez Almaraz, G. M., Mercado Lemus, V. H., & Jesús Villalon Lopez, J. (2010). Rotating bending fatigue tests for aluminum alloy 6061-T6, close to elastic limit and with artificial pitting holes. Procedia Engineering, 2(1), 805–813. https://doi.org/10.1016/j.proeng.2010.03.087
[9] Dowling, N. E. (2013). Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue (4a ed.). Pearson Education Limited.
[10] Gallegos-Melgar, A., González-López, Y., Abúndez, A., Flores-Ruiz, F. J., Díaz-Guillén, J. C., Betancourt-Cantera, J. A., Hernández-Hernández, M., Trápaga-Martínez, G., Poblano-Salas, C. A., Acevedo-Dávila, J. L., & Mayen, J. (2020). Characterization of a C-Based Coating Applied on an AA6063 Alloy and Developed by a Novel Electrochemical Synthesis Route. Coatings, 10(2), 145. https://doi.org/10.3390/coatings10020145
[11] González López, Y. (2019). Evaluación de la influencia de tratamientos superficiales en la vida a la fatiga de materiales [TecNM/Cenidet]. http://187.188.90.136:8880/file.php?code=lRor9A-QBQ3V
[12] Gutierrez Rojas, I., Abúndez Pliego, A., González López, Y., Mayén Chaires, J., Alfonso Rosas, G., Siqueiros Hernández, M., & González Vizcarra, B. (2020). Efecto del voltaje de electrodeposición sobre la vida a fatiga de aluminio recubierto con carbono. Jornada de Ciencia y Tecnología Aplicada, 3(2), 139–146. https://jcyta.cenidet.tecnm.mx/revistas/jcyta/05-Revista_JCyTA_Vol-3-Num-2_Jul-Dic_2020.pdf
[13] Landín, R. A., Ramírez Villareal, D., & Garza Espinoza, B. S. (2014). Cálculo del factor de concentración de esfuerzos utilizando Solidworks. Proyectos institucionales y de vinculación, 2(3), 29–38. http://eprints.uanl.mx/id/eprint/9826
[14] Mayén, J., Abúndez, A., Pereyra, I., Colín, J., Blanco, A., & Serna, S. (2017). Comparative analysis of the fatigue short crack growth on Al 6061-T6 alloy by the exponential crack growth equation and a proposed empirical model. Engineering Fracture Mechanics, 177, 203–217. https://doi.org/10.1016/j.engfracmech.2017.03.036
[15] Meggiolaro, M. A., Castro, J. T. P., & de Moura Nogueira, R. (2017). A fast rotating bending fatigue test machine. Procceedings of the 24th ABCM International Congress of Mechanical Engineering. https://doi.org/10.26678/ABCM.COBEM2017.COB17-1824
[16] Moore, R. R. (1939). Material testing machine (Patent Núm. US2154277A). U.S. Patent and Trademark Office. https://patents.google.com/patent/US2154277A/en
[17] Mott, R. L., Vavrek, E. M., & Wang, J. (2017). Machine Elements in Mechanical Design (6a ed.). Pearson Education, Inc.
[18] Ozkan, M. T., & Erdemir, F. (2021). Determination of theoretical stress concentration factor for circular/elliptical holes with reinforcement using analytical, finite element method and artificial neural network techniques. Neural Computing and Applications, 33(19), 12641–12659. https://doi.org/10.1007/s00521-021-05914-x
[19] Özkan, M. T., Kaygisiz, M., & Toktas, I. (2016). Definition of stress concentration factor of column with angled holed under bending stress using finite element analysis. 21st International Scientific Conference MECHANIKA 2016, 199–205.
[20] Pérez Olivas, P. A., Limón Leyva, P. A., Aguilera Gómez, E., Plascencia Mora, H., & Jiménez López, E. (2014). Daño acumulado teórico-experimental del aluminio 6061-T6: método de Palmgren-Miner. 2014 – Memorias de Divulgación Científica, Tecnológica e Innovación de la SOMIM – XX Congreso, 375–380. http://somim.org.mx/siam/librosomim2014/pdfs/A1/A1_278.pdf
[21] Petatan Bahena, K. E., Gutierrez Rojas, I., Abúndez Pliego, A., Mayen Chaires, J., & Blanco Ortega, A. (2021). Efecto de la velocidad de avance en torneado CNC en seco y el acabado superficial en la vida a fatiga de una aleación de aluminio 6061-T6. Jornada de Ciencia y Tecnología Aplicada, 4(1), 235–240. https://jcyta.cenidet.tecnm.mx/revistas/jcyta/06-Revista_JCyTA_Vol-4-Num-1_Ene-Jun_2021.pdf
[22] Pilkey, W. D., Pilkey, D. F., & Zhuming, B. (2020). Peterson’s Stress Concentrations Factors (4th ed.). John Wiley & Sons, Inc.
[23] Sallberg, D. W., Lawson, T. J., & Cardon, M. H. (1989). Multi-axial fatigue testing machine (Patent Núm. US4802365A). U.S. Patent and Trademark Office. https://patents.google.com/patent/US4802365
[24] Schütz, W. (1996). A history of fatigue. Engineering Fracture Mechanics, 54(2), 263–300. https://doi.org/10.1016/0013-7944(95)00178-6
[25] Slotwinski, J., & Moylan, S. (2014). Applicability of Existing Materials Testing Standards for Additive Manufacturing Materials. https://doi.org/10.6028/NIST.IR.8005
[26] Tlapanco Rios, E. I., Castaño Urrego, C. A., Lopez Perez, J. R., & Forero Rubiano, F. R. A. (2020). Método de comparación de resultados de modelado CAD-CAE contra probetas de ensayo destructivo. Acta Universitaria, 30, 1–16. https://doi.org/10.15174/au.2020.2668
[27] Toktaş, İ., Özkan, M. T., Erdemir, F., & Yuksel, N. (2020). Determination of Stress Concentration Factor (Kt) for a Crankshaft Under Bending Loading: An Artificial Neural Networks Approach. Politeknik Dergisi, 23(3), 813–819. https://doi.org/10.2339/politeknik.683270
[28] Yang, H., Zhang, Z., Tan, C., Ito, M., Pan, P., & Wang, X. (2018). Rotating Bending Fatigue Microscopic Fracture Characteristics and Life Prediction of 7075-T7351 Al Alloy. Metals, 8(4), 210. https://doi.org/10.3390/met8040210
[29] Zakaria, K. A., Abdullah, S., & Ghazali, M. J. (2016). A Review of the Loading Sequence Effects on the Fatigue Life Behaviour of Metallic Materials. Journal of Engineering Science and Technology Review, 9(5), 189–200. https://doi.org/10.25103/jestr.095.30
[30] Zuno Silva, J. (2016). Fatigue resistance improvement of a forging medium carbon steel using Mischmetal (rare earths) as inclusions (MnS) modifier element. Nova Scientia, 8(17), 97. https://doi.org/10.21640/ns.v8i17.483