Comparative analysis of stress distributions and safety factor in tensile test specimens with different notch and hole geometries by finite element method

Sümeyye Erdem Korkmaz; Esma Gavgalı

doi:10.17714/gumusfenbil.1799320

EN

Comparative analysis of stress distributions and safety factor in tensile test specimens with different notch and hole geometries by finite element method

Abstract

This study analyzes the effects of different notch and hole geometries (V-Notched, U-Notched, circular hole) on stress concentration in Ti-6Al-4V (Grade 5) Titanium alloy tensile specimens to provide optimized design recommendations for aerospace and biomedical applications. Finite element method (ANSYS Workbench) was employed to analyze three geometries under 15000 N static tensile loading. SOLID186 20-node quadratic solid elements were used with optimal mesh (31100 elements) determined through convergence study. Von Mises stress distributions and stress concentration factors (Kt) were calculated and validated against Peterson and Neuber theoretical formulas with average error ±1.5%. Results revealed that V-Notched exhibited highest stress concentration (Kt = 5.78, σmax = 1156 MPa), while circular hole showed lowest (Kt = 2.25, σmax = 454.12 MPa). U-Notched demonstrated intermediate performance (Kt = 2.84, σmax = 995.45 MPa). Increasing notch root radius from 0.5 mm to 2.0 mm achieved 51% reduction in stress concentration factor. Maximum shear stress values were 232.74 MPa, 506.38 MPa, and 640 MPa for circular, U-Notched, and V-Notched respectively, while maximum normal stress values reached 467.06 MPa, 1015.1 MPa, and 1809 MPa. Safety factor analysis showed that circular hole configuration meets aerospace standards (FS = 2.05 > 1.5), while U-Notched (FS = 0.93) and V-Notched (FS = 0.80) fall below minimum safety criteria. U-Notched exhibited highest total displacement (1.210 mm), indicating compliance effects. For aerospace and biomedical applications, circular holes should be preferred over sharp notches (154% stress reduction), and minimum corner radius ≥2.0 mm is recommended. The critical finding that geometric optimization provides 2.6× safety improvement without material changes demonstrates the powerful role of design in structural reliability for weight-critical applications.

Keywords

Finite element method , Notched geometry , Safety factor , Stress analysis , Titanium alloy

Kaynakça

ASTM B265-20. (2020). Standard specification for titanium and titanium alloy strip, sheet, and plate. ASTM International. https://doi.org/10.1520/B0265-20
Azevedo, L., Kashaev, N., Horstmann, C., Ventzke, V., Furtado, C., Moreira, P. M. G. P., & Tavares, J. (2022). Fatigue behaviour of laser shock peened AISI D2 tool steel. International Journal of Fatigue, 165(107226). https://doi.org/10.1016/j.ijfatigue.2022.107226
Boyer, R., Welsch, G., & Collings, E.W. (1994). Materials Properties Handbook: Titanium Alloys. ASM International
Chmelko, V., Harakal’, M., Žlábek, P., Margetin, M., & Ďurka, R. (2022). Simulation of stress concentrations in notches. Metals, 12(1), 1–9. https://doi.org/10.3390/met12010043
du Plessis, A., & Beretta, S. (2020). Killer notches: The effect of as-built surface roughness on fatigue failure in AlSi10Mg produced by laser powder bed fusion. Additive Manufacturing, 35 (101424). https://doi.org/10.1016/j.addma.2020.101424
Dutt, A. K., Gwalani, B., Tungala, V., Carl, M., Mishra, R. S., Tamirisakandala, S. A., Young, M. L., Cho, K. C., & Brennan, E. B. (2019). A novel nano-particle strengthened titanium alloy with exceptional specific strength. Sci Reports, 9(11726). https://doi.org/10.1038/s41598-019-48139-8
Fazlali, B., Upadhyay, S., Ashodia, S. A., Mesquita, F., Lomov, S. V., Carvelli, V., & Swolfs, Y. (2023). Specimen designs for accurate tensile testing of unidirectional composite laminates. Composites Part A, 175(107799). https://doi.org/10.1016/j.compositesa.2023.107799
Haritos, G.K., Nicholas, T., Lanning, D.B. (1999). Notch size effects in HCF behavior of Ti-6Al-4V. International Journal of Fatigue, 21(7), 643-652. DOI: 10.1016/S0142-1123(99)00023-7
Haseeb, S. A., Kumar, A. S., Chaitra, M. P., Vinaya, K. C., Gudal, S. S., Rahman, F. P., & Babaji, P. (2023). Finite element analysis to assess stress and deformation in bone with glass fiber reinforced poly ether ether ketone, zirconia, and titanium implants. Tzu Chi Medical Jornal, 35(3), 231-236. https://doi.org/10.4103/tcmj.tcmj_184_22
Holmes, J., Sommacal, S., Das, R., Stachurski, Z., & Compston, P. (2023). Digital image and volume correlation for deformation and damage characterisation of fibre-reinforced composites: A review. Composites Structures, 315(116994). https://doi.org/10.1016/j.compstruct.2023.116994

Jabri, A. A., & Gharaibeh, M. A. (2025). Investigation of stress concentration factors in countersunk holes of biaxially loaded isotropic plates. International Journal of Applied Mechanics and Engineering, 30(1), 79-88. https://doi.org/10.59441/ijame/197486
Lanning, D. B., Nicholas, T., & Palazotto, A. (2005). The effect of notch geometry on critical distance high cycle fatigue predictions. International Journal of Fatigue, 27(10–12), 1623–1627. https://doi.org/10.1016/j.ijfatigue.2005.06.017
Lerda, S., Marchese, G., Bassini, E., Lombardi, M., Ugues, D., Fino, P., & Biamino, S. (2024). Microstructural stability of IN625 reinforced by the addition of TiC produced by laser powder bed fusion after prolonged thermal exposure. Materials, 17(4532). https://doi.org/10.3390/ma17184532
Li, S., Li, Y., Wang, P., Han, F., & Ma, Z. (2025). On experimental and numerical damage evolution of multi open-holes composite laminates with local to global method. Composite Structures, 371(119397). https://doi.org/10.1016/j.compstruct.2025.119397
Liu, G., & Tang, K. (2016). Study on stress concentration in notched cross-ply laminates under tensile loading. Journal Composite Materials, 50(3), 283–296. https://doi.org/10.1177/0021998315573802
Liu, J., & Phoenix, S. L. (2023). Analytical prediction and numerical verification of stress concentration profile around an in-situ tow break in resin-impregnated filament-wound composites. Composite Structures, 341(118185). https://doi.org/10.1016/j.compstruct.2024.118185
Ma, H., Qu, R., Song, K., & Liu, F. (2024). Notch strength of ductile materials with different work-hardening behaviors. Journal of Materials Research and Technology, 33, 8974-8982. https://doi.org/10.1016/j.jmrt.2024.11.219
Mane, S. (2023). Review study on finite element analysis method used for aerospace structure applications. International Journal of New Media Studies (IJNMS), 10(1), 8-13.
Myers, T., Sutton, M. A., Schreier, H., Tofts, A., & Kattil, S. R. (2024). Direct pointwise comparison of fe predictions to stereodic measurements: developments and validation using double edge-notched tensile specimen. Computer Modeling in Engineering and Sciences, 140(2), 1263–1298. http://dx.doi.org/10.32604/cmes.2024.048743
Neuber, H. (1961). Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law. Journal of Applied Mechanics, 28(4), 544-550. https://doi.org/10.1115/1.3641780
Ogunnowo, E. O., Adewoyin, M. A., Fiemotongha, J. E., Igunma, T. O., & Adeleke, A. K. (2023). A conceptual framework for reliability-centered design of mechanical components using FEA and DFMEA integration. Journal of Frontiers in Multidisciplinary Research, 4(1), 342–361. https://doi.org/10.54660/.JFMR.2023.4.1.342-361
Pereira, I. C. S., de Sousa, J. R. M., & Costa, C. A. (2024). Evaluation of U-Notch and V-Notch geometries on the mechanical behavior of PVDF: The DIC Technique and FEA Approach. Polymers (Basel), 16(20). https://doi.org/10.3390/polym16202906
Peterson, R. E. (1974). Stress concentration factors. John Wiley & Sons.
Pilkey, W. D., & Pilkey, D. F. (2008). Peterson's stress concentration factors (3rd ed.). John Wiley & Sons. https://doi.org/10.1002/9780470211106
Pilkey, W. D., Pilkey, D. F., & Bi, Z. (2020). Peterson's stress concentration factors (4th ed.). John Wiley & Sons. https://doi.org/10.1002/9781119532552
Pinto, C. C., de A. Silva, F., & Guidi, E. S. (2025). Analytical, experimental, and finite element study of stress concentration for samples printed on masked stereolithography devices. Applied Mechanics, 6(21). https://doi.org/10.3390/applmech6010021
Polatov, A., Ikramov, A., Adambaev, U., & Pulatov, S. (2024). Simulation of the stress concentration process in a fiber plate with strengthening holes. 2024 AIP Conf Proc, 3119(1), 040005, Tashkent, Uzbekistan. https://doi.org/10.1063/5.0214776
Rabbitt, D., Villapún, V. M., Carter, L. N., Man, K., Lowther, M., O’Kelly, P., Knowles, A. J., Mottura, A., Tang, Y. T., Luerti, L., Reed, R. C., and Cox, S. C. (2025). Rethinking biomedical Titanium alloy design: A review of challenges from biological and manufacturing perspectives. Advanced Healthcare Materials, 14. https://doi.org/10.1002/adhm.202403129
Ramachandran, K., Soni, A., & Jayaseelan, D. D. (2024). Investigating the impact of notch shapes on oxide–oxide ceramic matrix composites strength: A computational approach. International Journal of Ceramic Engineering and Science, 6. https://doi.org/10.1002/ces2.10238
Rettl, M., Waly, C., Pletz, M., & Schuecker, C. (2025). Validation of a FEM-based method to predict crack initiation from arbitrary-shaped notches. Journal of Composites Science, 9(102). https://doi.org/10.3390/jcs9030102
Ribas, M., Akhavan-Safar, A., Adam-Cottard, P., Carbas, RJC., Marques, E. A. S., Wenig, S., & da Silva, L. F. M. (2024). Exploring strain rate variation in the adhesive layer during constant speed mode I fracture tests: Loading speed and test temperature effects. Theoretical and Applied Fracture Mechanics, 130(104274). https://doi.org/10.1016/j.tafmec.2024.104274
Sánchez, M., Cicero, S., Arroyo, B., & Alberto Álvarez, J. (2020). Coupling finite element analysis and the theory of critical distances to estimate critical loads in Al6060-T66 tubular beams containing notches. Metals, 10(10), 1–11. https://doi.org/10.3390/met10101395
Sivák, P., Delyová, I., & Bocko, J. (2023). Comparison of stress concentration factors obtained by different methods. Applied Sciences, 13(24). https://doi.org/10.3390/app132413328
Tian, F., Tang, X., Xu, T., Yang, J., & Li, L. (2019). A hybrid adaptive finite element phase-field method for quasi-static and dynamic brittle fracture. International Journal for Numerical Methods in Engineering, 120(9), 1108–1125. https://doi.org/10.1002/nme.6172
Wang, J.K., Yang, X.G. (2012). HCF strength estimation of notched Ti-6Al-4V specimens considering the critical distance size effect. International Journal of Fatigue, 40, 97-104. DOI: 10.1016/j.ijfatigue.2011.12.019
Wang, L., Zhao, X., Wang, X., Shang, S., Xiu, Z., Xi, Y., Jia, H., Xu, S., Liu, H., Wen, L., Liu, R., & Ji, J. (2024). Current status review of corrosion resistance applications of titanium alloys in the petroleum industry. Coatings, 14(941). https://doi.org/10.3390/coatings14080941 Yang, X., Song, X., Zhang, G., Xu, S., Wang, W., Sun, K., Ma, X., Sun, S., Pan, Y., Li, J., Ren, G., & Zhang, W. (2024). Design, analysis and optimization of porous Titanium alloys scaffolds by using additive manufacture. Modelling and Optimization of Complex Systems with Advanced Computational Techniques, 15(16). https://doi.org/10.1051/smdo/2024013
Yang, Y., Yan, M., Zhang, Z., Hao, D., Chen, X., & Chen, W. (2025). Steady-state and transient thermal stress analysis using a polygonal finite element method. Finite Elements in Analysis and Design, 215(104413). https://doi.org/10.1016/j.finel.2025.104413
Zhao, Z., Ji, H., Zhong, Y., Han, C., & Tang, X. (2022). Mechanical properties and fracture behavior of a TC4 Titanium alloy sheet. Materials, 15(8589). https://doi.org/10.3390/ma15238589
Zheng, B. (2024). Analysis of static and dynamic characteristics and lightweight design of Titanium alloy frame. Manufacturing Technology, 24(3), 507–519. https://doi.org/10.21062/mft.2024.053
Zhu, S., Zhu, C., Luo, D., Zhang, X., & Zhou, K. (2023). Development of a low-density and high-strength Titanium alloy. Metals, 13(251). https://doi.org/10.3390/met13020251

Ayrıntılar

Birincil Dil

İngilizce

Konular

Katı Mekanik

Bölüm

Araştırma Makalesi

Yazarlar

Sümeyye Erdem Korkmaz
0000-0002-5518-2716
Türkiye

Esma Gavgalı ^*
0000-0003-0954-1957
Türkiye

Yayımlanma Tarihi

20 Şubat 2026

Gönderilme Tarihi

8 Ekim 2025

Kabul Tarihi

5 Şubat 2026

Yayımlandığı Sayı

Yıl 2026 Cilt: 16 Sayı: 1

DOI

https://doi.org/10.17714/gumusfenbil.1799320

IZ

https://izlik.org/JA67AX32EY

APA

Erdem Korkmaz, S., & Gavgalı, E. (2026). Comparative analysis of stress distributions and safety factor in tensile test specimens with different notch and hole geometries by finite element method. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 16(1), 160-178. https://doi.org/10.17714/gumusfenbil.1799320

e-ISSN: 2146-538X Yayın Modeli: Sürekli Yayın Atıf Dizinleri: TR Dizin , SCOPUS

Comparative analysis of stress distributions and safety factor in tensile test specimens with different notch and hole geometries by finite element method

Comparative analysis of stress distributions and safety factor in tensile test specimens with different notch and hole geometries by finite element method

Abstract

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