Fatigue Life Prediction of Notched Components after Plastic Overload Using Theory of Critical Distance

Document Type : Original Research Paper


Mechanical Engineering Department, Engineering Faculty, Bu-Ali Sina University, Hamedan, Iran.


The aim of this work is providing a suitable method based on the theory of critical distance (TCD) to estimate the fatigue life of notched components in the presence of residual stress induced by the overload cycle. Presented method is relied on a virtual stress field to equalize the effects of real stress distribution in the hot spot around the notch root. This method is noted as equivalent virtual stress (EVS) method. The EVS method combined with some versions of the TCD method, such as the point method (PM) and line method (LM), were applied for two types of notched samples. Samples were made with U- and V-notches with axial stress concentration factors as 2.45 and 5.55, respectively. The test material was AA 2024-T3 due to its considerable resistance to fatigue failures. The PM was found more conservative, while LM showed more accuracy, especially when the critical distance parameter locates far from critical regions. A good agreement was observed between experimental and predicted results.


[1] R.G. Budynas, J.K. Nisbett, Shigley’s Mechanical Engineering Design, 11th Edition, McGraw-Hill, USA, (2020).
[2] E. Haibach, Analytical Strength Assessment of Components in Mechanical Engineering. FKMGuideline, VDMA, (2003).
[3] D. Taylor, The Theory of Critical Distances: A New Perspective in Fracture Mechanics, Elsevier, (2010).
[4] Y. Chang, C. Sun, Y. Qiu, Effective notch stress method for fatigue assessment of sheet alloy material and bi-material welded joints, Thin-Walled Struct., 151 (2020) 106745.
[5] N. Habibi, M. Amoorezayi, A 3D simulation of bolted joint and fatigue life estimation using critical distance technique, J. Stress Anal., 4(1) (2019) 53-63.
[6] M. Kamal, M. Rahman, Advances in fatigue life modeling: A review, Renew. Sustain. Energy Rev., 82 (2018) 940-949.
[7] I. Al Zamzamia, S.M.J. Razavi, F. Berto, L. Susmel, The critical distance method to estimate the fatigue strength of notched additively manufactured titanium alloys, Procedia Struct. Integrity, 28 (2020) 994-1001.
[8] M.D. Chapetti, A.O. Guerrero, Estimation of notch sensitivity and size effect on fatigue resistance, Procedia Eng., 66 (2013) 323-333.
[9] L. Susmel, D. Taylor, A simplified approach to apply the theory of critical distances to notched components under torsional fatigue loading, Int. J. Fatigue, 28(4) (2006) 417-430.
[10] D. Taylor, Geometrical effects in fatigue: a unifying theoretical model, Int. J. Fatigue, 21(5) (1999) 413-420.
[11] L. Susmel, D. Taylor, An elasto-plastic reformulation of the theory of critical distances to estimate lifetime of notched components failing in the low/medium-cycle fatigue regime, J. Eng. Mater. Technol., 132(2) (2010) 021002.
[12] S. Bentachfine, G. Pluvinage, J. Gilgert, Z. Azari, D. Bouami, Notch effect in low cycle fatigue, Int. J. Fatigue, 21(5)(1999) 421-430.
[13] G. Qilafku, N. Kadi, J. Dobranski, Z. Azari, M. Gjonaj, G. Pluvinage, Fatigue of specimens subjected to combined loading, Role of hydrostatic pressure, Int. J. Fatigue, 23(8) (2001) 689-701.
[14] G. Qylafku, Z. Azari, N. Kadi, M. Gjonaj, G. Pluvinage, Application of a new model proposal for fatigue life prediction on notches and key-seats, Int. J. Fatigue, 21(8) (1999) 753-760.
[15] R. Seifi, M.R. Mohammadi, Fatigue life estimation of the overloaded notched components, J. Brazilian Society Mech. Sciences Eng., 42 (2020) 51.
[16] A. Spaggiari, D. Castagnetti, E. Dragoni, S. Bulleri, Fatigue life prediction of notched components: a comparison between the theory of critical distance and the classical stress-gradient approach, Procedia Eng., 10 (2011) 2755-2767.
[17] D. Taylor, G. Wang, The validation of some methods of notch fatigue analysis, Fatigue Fract. Eng. Mater. Struct., 23(5) (2000) 387-394.
[18] L. Susmel, Multiaxial Notch Fatigue, Woodhead Publishing, Elsevier, (2009).
[19] M. Leitner, M. Vormwald, H. Remes, Statistical size effect on multiaxial fatigue strength of notched steel components, Int. J. Fatigue, 104 (2017) 322-333.
[20] M. Braun, A.M. Müller, A.S. Milaković, W. Fricke, S. Ehlers, Requirements for stress gradientbased fatigue assessment of notched structures according to theory of critical distance, Fatigue Fract. Eng. Mater. Struct., 43(7) ( 2020) 1541-1554.
[21] ASTM Standard E8/E8M-16a. Standard Test Methods for Tension Testing of Metallic Materials, vol 03.01., Annual Book of ASTM Standards, (2016).
[22] Alumium Association. International Alloy Designations and Chemical Composition Limits for Wrought Aluminum and Wrought Aluminum Alloys, Arlington, (2009).
[23] ASTM Standard E466-15: Standard Practice for Conduction Force Controlled Constant Amplitude Axial Fatigue Test of Metallic Materials, vol. 03.01. Annual Book of ASTM Standards, (2015).
[24] Dassult Simulia. Analysis User Manual. Abaqus/Standard, (2021).
[25] Battelle Memorial Institute. Metallic Materials Properties Development and Standardization (MMPDS-11), 11 (2016).
[26] Y. Fujimoto, K. Hamada, E. Shintaku, G. Pirker. Inherent damage zone model for strength evaluation of small fatigue cracks, Eng. Fract. Mech., 68(4) (2001) 455-473.
[27] W. Illg, Fatigue tests on notched and unnotched sheet specimens of 2024-T3 and 7075-T6 aluminum alloys and of SAE 4130 steel with special consideration of the life range from 2 to 10,000 cycles, NACA Technical Notes, (1956).
[28] D. Taylor, S. Kasiri, A comparison of critical distance methods for fracture prediction, Int. J. Mech. Sci., 50(6) (2008) 1075-1081.