Fatigue Strength Reduction Factors Based on Strain Energy Density Applied to Sharp and Blunt Notches under Multiaxial Loading
Source abstract
Abstract
Real mechanical assemblies favor the initiation and propagation of fatigue cracks due to stress concentration phenomena arising from the geometrical features such as notches, corners, holes, welding toes, etc. Classical fatigue analysis of notched specimens is done using an empirical formula and a fitted fatigue strength reduction factor, which is experimentally expensive and lacks physical scene. In the present paper, a simple and meaningful methodology is proposed to assess notched components against multiaxial fatigue. In this method, by precisely defining a finite-size volume surrounding the fatigue crack initiation site (notch tip), over which the strain energy is averaged, the morphological effect on the process zone is fully addressed. Such a method takes into account the effect of combination of different modes (I, II, III) and the load ratio. In order to implement it for components with a sharp or blunt notch, it is enough to analyze a linear elastic finite element model and to know only the properties of materials obtained from simple uniaxial tests. New relationships for determining an effective (tensile-type) stress and fatigue strength reduction factors are derived for notched specimens. The accuracy of the proposed model is validated by experimental data available in the literature, related to tubular specimens weakened with sharp/blunt notches under combined bending-torsion loading. Such a situation widely appears in equipment used for various branches of industry such as piping, automotive, power plant, drilling, etc.
Source: openalex_inverted_index · Quality: baseline
Research context
OpenAlex topics: Fatigue and fracture mechanics · Engineering Structural Analysis Methods · Structural Load-Bearing Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (49)
Show source-provided references
1. Rice, J.R., Some Remarks on Elastic Crack-Tip Stress Fields, Int. J. Solids Struct., 1972, vol. 8, pp. 751–758. doi https://doi.org/10.1016/0020-7683(72)90040-610.1016/0020-7683(72)90040-6 ↗
2. Filippi, S., Lazzarin, P., and Tovo, R., Developments of Some Explicit Formulas Useful to Describe Elastic Stress Fields Ahead of Notches in Plates, Int. J. Solids Struct., 2002, vol. 39, pp. 4543–4565. doi https://doi.org/10.1016/S00207683(02)00342-610.1016/S0020-7683(02)00342-6 ↗
3. Pook, L.P., Berto, F., and Campagnolo, A., State of the Art of Corner Point Singularities under in-Plane and out-of-Plane Loading, Eng. Fract. Mech., 2017, vol. 174, pp. 2–9. doi https://doi.org/10.1016/j.engfracmech.2016.10.00110.1016/j.engfracmech.2016.10.001 ↗
4. Pook, L.P., Berto, F., Campagnolo, A., and Lazzarin, P., Coupled Fracture Mode of a Cracked Disc under AntiPlane Loading, Eng. Fract. Mech., 2014, vol. 128, pp. 22–36. doi https://doi.org/10.1016/j.engfracmech.2014.07.00110.1016/j.engfracmech.2014.07.001 ↗
5. Kotousov, A., Lazzarin, P., Berto, F., and Pook, L.P., Three-Dimensional Stress States at Crack Tip Induced by Shear and Anti-Plane Loading, Eng. Fract. Mech., 2013, vol. 108, pp. 65–74. doi https://doi.org/10.1016/j.engfracmech.2013.04.01010.1016/j.engfracmech.2013.04.010 ↗
6. Liu, Y. and Mahadevan, S., Fatigue Limit Prediction of Notched Components Using Short Crack Growth Theory and an Asymptotic Interpolation Method, Eng. Fract. Mech., 2009, vol. 76, pp. 2317–2331. doi https://doi.org/10.1016/j.engfracmech.2008.06.00610.1016/j.engfracmech.2008.06.006 ↗
7. Dowling, N.E., Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, New York: Pearson, 2012.
8. Susmel, L., Multiaxial Notch Fatigue, Berlin: Elsevier, 2009.10.1533/9781845695835 ↗
9. Livieri, P. and Lazzarin, P., Fatigue Strength of Steel and Aluminium Welded Joints Based on Generalised Stress Intensity Factors and Local Strain Energy Values, Int. J. Fract., 2005, vol. 133, pp. 247–276.10.1007/s10704-005-4043-3 ↗
10. Lazzarin, P., Sonsino, C.M., and Zambardi, R., A Notch Stress Intensity Approach to Assess the Multiaxial Fatigue Strength of Welded Tube-to-Flange Joints Subjected to Combined Loadings, Fatigue Fract. Eng. Mater. Struct., vol. 27, pp. 127–140. doi https://doi.org/10.1111/j.1460-2695.2004.00733.x10.1111/j.1460-2695.2004.00733.x ↗
11. Atzori, B., Lazzarin, P., and Meneghetti, G., Fatigue Strength Assessment of Welded Joints: From the Integration of Paris’ Law to a Synthesis Based on the Notch Stress Intensity Factors of the Uncracked Geometries, Eng. Fract. Mech., 2008, vol. 75, pp. 364–378. doi https://doi.org/10.1016/j.engfracmech.2007.03.02910.1016/j.engfracmech.2007.03.029 ↗
12. Lazzarin, P. and Zambardi, R., A Finite-Volume-Energy Based Approach to Predict the Static and Fatigue Behavior of Components with Sharp V-Shaped Notches, Int. J. Fract., 2001, vol. 112, pp. 275–298. doi https://doi.org/10.1023/a:101359593061710.1023/A:1013595930617 ↗
13. Berto, F. and Lazzarin, P., A Review of the Volume-Based Strain Energy Density Approach Applied to V-Notches and Welded Structures, Theor. Appl. Fract. Mech., 2009, vol. 52, pp. 183–194. doi https://doi.org/10.1016/j.tafmec.2009.10.00110.1016/j.tafmec.2009.10.001 ↗
14. Berto, F., Lazzarin, P., and Marangon, C., Fatigue Strength of Notched Specimens Made of 40CrMoV13.9 under Pultiaxial Loading, Mater. Des., 2014, vol. 54, pp. 57–66. doi https://doi.org/10.1016/j.matdes.2013.08.01310.1016/j.matdes.2013.08.013 ↗
15. Berto, F., Lazzarin, P., and Marangon, C., Brittle Fracture of U-Notched Graphite Plates under Mixed Mode Loading, Mater. Des., 2012, vol. 41, pp. 421–432. doi https://doi.org/10.1016/j.matdes.2012.05.02210.1016/j.matdes.2012.05.022 ↗
16. Torabi, A.R., Campagnolo, A., and Berto, F., Local Strain Energy Density to Predict Mode II Brittle Fracture in Brazilian Disk Specimens Weakened by V-Notches with End Holes, Mater. Des., 2015, vol. 69, pp. 22–29.10.1016/j.matdes.2014.12.037 ↗
17. Lazzarin, P., Berto, F., and Ayatollahi, M.R., Brittle Failure of Inclined Key-Hole Notches in Isostatic Graphite under in-Plane Mixed Mode Loading, Fatigue Fract. Eng. Mater. Struct., 2013, vol. 36, pp. 942–955. doi https://doi.org/10.1111/ffe.1205710.1111/ffe.12057 ↗
18. Berto, F., Lazzarin, P., and Ayatollahi, M.R., Brittle Fracture of Sharp and Blunt V-Notches in Isostatic Graphite under Pure Compression Loading, Carbon, 2013, vol. 63, pp. 101–116. doi https://doi.org/10.1016/j.carbon.2013.06.04510.1016/j.carbon.2013.06.045 ↗
19. Torabi, A.R. and Berto, F., Strain Energy Density to Assess Mode II Fracture in U-Notched Disk-Type Graphite Plates, Int. J. Damage Mech., 2014, vol. 23, pp. 917–930.10.1177/1056789513519349 ↗
20. Gomez, F.J., Elices, M., Berto, F., and Lazzarin, P., Local Strain Energy to Assess the Static Failure of U-Notches in Plates under Mixed Mode Loading, Int. J. Fract., 2007, vol. 145, pp. 29–45. doi https://doi.org/10.1007/s10704-007-9104-310.1007/s10704-007-9104-3 ↗
21. Berto, F., Lazzarin, P., Gomez, F.J., and Elices, M., Fracture Assessment of U-Notches under Mixed Mode Loading: Two Procedures Based on the “Equivalent Local Mode I” Concept, Int. J. Fract., 2008, vol. 148, pp. 415–433. doi https://doi.org/10.1007/s10704-008-9213-710.1007/s10704-008-9213-7 ↗
22. Taghizadeh, K., Berto, F., and Barati, E., Local Strain Energy Density Applied to Martensitic Steel Plates Weakened by U-Notches under Mixed Mode Loading, Theor. Appl. Fract. Mech., 2012, vol. 59, pp. 21–28. doi https://doi.org/10.1016/j.tafmec.2012.05.00310.1016/j.tafmec.2012.05.003 ↗
23. Salavati, H., Alizadeh, Y., and Berto, F., Effect of Notch Depth and Radius on the Critical Fracture Load of Bainitic Functionally Graded Steels under Mixed Mode I + II Loading, Phys. Mesomech., 2014, vol. 17, no. 3, pp. 178–189. doi https://doi.org/10.1134/s102995991403002310.1134/S1029959914030023 ↗
24. Negru, R., Marsavina, L., Filipescu, H., Cäplescu, C., and Voiconi, T., Assessment of Brittle Fracture for {PUR} Materials Using Local Strain Energy Density and Theory of Critical Distances, Theor. Appl. Fract. Mech., 2015, vol. 79, pp. 62–69. doi https://doi.org/10.1016/j.tafmec.2015.07.01110.1016/j.tafmec.2015.07.011 ↗
25. Marsavina, L., Berto, F., Negru, R., Serban, D.A., and Linul, E., An Engineering Approach to Predict Mixed Mode Fracture of PUR Foams Based on ASED and Micromechanical Modelling, Theor. Appl. Fract. Mech., 2017, vol. 91, pp. 148–154. doi https://doi.org/10.1016/j.tafmec.2017.06.00810.1016/j.tafmec.2017.06.008 ↗
26. Berto, F., Campagnolo, A., and Welo, T., Local Strain Energy Density to Assess the Multiaxial Fatigue Strength of Titanium Alloys, Fract. Struct. Integr., 2016, pp. 69–79.10.3221/IGF-ESIS.41.12 ↗
27. Meneghetti, G., Campagnolo, A., Berto, F., and Tanaka, K., Crack Initiation Life in Notched Ti-6Al-4V Titanium Bars under Uniaxial and Multiaxial Fatigue: Synthesis Based on the Averaged Strain Energy Density Approach, Frat. Ed. Integr. Strutt., 2017, vol. 8.10.3221/IGF-ESIS.41.02 ↗
28. Razavi, S.M.J., Ferro, P., Berto, F., and Torgersen, J., Fatigue Strength of Blunt V-Notched Specimens Produced by Selective Laser Melting of Ti-6Al-4V, Theor. Appl. Fract. Mech., 2017. doi https://doi.org/10.1016/j.tafmec.2017.06.02110.1016/j.tafmec.2017.06.021 ↗
29. Mohammadi, H., Salavati, H., Mosaddeghi, M.R., Yusefi, A., and Berto, F., Local Strain Energy Density to Predict Mixed Mode I + {II} Fracture in Specimens Made of Functionally Graded Materials Weakened by V-Notches with End Holes, Theor. Appl. Fract. Mech., 2017, vol. 92, pp. 47–58. doi https://doi.org/10.1016/j.tafmec.2017.05.00910.1016/j.tafmec.2017.05.009 ↗
30. Mohammadi, H., Salavati, H., Alizadeh, Y., Abdullah, A., and Berto, F., Fracture Investigation of U-Notch Made of Tungsten-Copper Functionally Graded Materials by Means of Strain Energy Density, Fatig. Fract. Eng. Mater. Struct., 2017, vol. 40, pp. 1984–1993. doi https://doi.org/10.1111/ffe.1261610.1111/ffe.12616 ↗
31. Mohammadi, H., Salavati, H., Alizadeh, Y., Berto, F., and Panin, S.V., Fracture Investigation of V-Notch Made of Tungsten-Copper Functionally Graded Materials, Phys. Mesomech., 2017, vol. 20, pp. 457–464. doi https://doi.org/10.1134/S102995991704011710.1134/S1029959917040117 ↗
32. Salavati, H., Mohammadi, H., Yusefi, A., and Berto, F., Fracture Assessment of V-Notched Specimens with End Holes Made of Tungsten-Copper Functionally Graded Material under Mode I Loading, Theor. Appl. Fract. Mech., 2017. doi https://doi.org/10.1016/j.tafmec.2017.06.01310.1016/j.tafmec.2017.06.013 ↗
33. Mohammadi, H., Salavati, H., Alizadeh, Y., and Berto, F., Prevalent mode {{}II{}} Fracture Assessment of Inclined U-Notched Specimens Made of Tungsten-Copper Functionally Graded Material, Theor. Appl. Fract. Mech., 2017, vol. 89, pp. 90–99. doi https://doi.org/10.1016/j.tafmec.2017.01.01010.1016/j.tafmec.2017.01.010 ↗
34. Gallo, P., Sumigawa, T., Kitamura, T., and Berto, F., Static Assessment of Nanoscale Notched Silicon Beams Using the Averaged Strain Energy Density Method, Theor. Appl. Fract. Mech., 2018, vol. 95, pp. 261–269. doi https://doi.org/10.1016/j.tafmec.2018.03.00710.1016/j.tafmec.2018.03.007 ↗
35. Gallo, P. and Berto, F., Advanced Materials for Applications at High Temperature: Fatigue Assessment by Means of Local Strain Energy Density, Adv. Eng. Mater., vol. 18 (n.d.), pp. 2010–2017. doi https://doi.org/10.1002/adem.20150054710.1002/adem.201500547 ↗
36. Berto, F., Gallo, P., and Lazzarin, P., High Temperature Fatigue Tests of a Cu-Be Alloy and Synthesis in Terms of Linear Elastic Strain Energy Density, Adv. Fract. Damage Mech. XIII, Trans. Tech. Publications, 2015, pp. 77–80. doi https://doi.org/10.4028/www.scientific.net/KEM.627.7710.4028/www.scientific.net/KEM.627.77 ↗
37. Kallmeyer, A.R., Krgo, A., and Kurath, P., Evaluation of Multiaxial Fatigue Life Prediction Methodologies for Ti-6Al-4V, J. Eng. Mater. Technol., 2002, vol. 124, pp. 229–237.10.1115/1.1446075 ↗
38. Karolczuk, A. and Macha, E., A Review of Critical Plane Orientations in Multiaxial Fatigue Failure Criteria of Metallic Materials, Int. J. Fract., 2005, vol. 134, p. 267.10.1007/s10704-005-1088-2 ↗
39. Fatemi, A. and Shamsaei, N., Multiaxial Fatigue: An Overview and Some Approximation Models for Life Estimation, Int. J. Fatigue, 2011, vol. 33, pp. 948–958. doi https://doi.org/10.1016/j.ijfatigue.2011.01.00310.1016/j.ijfatigue.2011.01.003 ↗
40. Susmel, L., A Unifying Approach to Estimate the High-Cycle Fatigue Strength of Notched Components Subjected to Both Uniaxial and Multiaxial Cyclic Loadings, Fatig. Fract. Eng. Mater. Struct., vol. 27, pp. 391–411. doi https://doi.org/10.1111/j.1460-2695.2004.00759.x10.1111/j.1460-2695.2004.00759.x ↗
41. Lazzarin, P. and Zambardi, R., The Equivalent Strain Energy Density Approach Re-Formulated and Applied to Sharp V-Shaped Notches under Localized and Generalized Plasticity, Fatig. Fract. Eng. Mater. Struct., vol. 25, pp. 917–928. doi https://doi.org/10.1046/j.14602695.2002.00543.x10.1046/j.14602695.2002.00543.x ↗
42. Zappalorto, M., Lazzarin, P., and Filippi, S., Stress Field Equations for U and Blunt V-Shaped Notches in Axisymmetric Shafts under Torsion, Int. J. Fract., 2010, vol. 164, pp. 253–269.10.1007/s10704-010-9493-6 ↗
43. Lazzarin, P., Zappalorto, M., and Berto, F., Averaged Strain Energy Density and J-Integral for U- and Blunt V-Shaped Notches under Torsion, Int. J. Fract., 2014, vol. 188, pp. 173–186. doi https://doi.org/10.1007/s10704-014-9953-510.1007/s10704-014-9953-5 ↗
44. Yates, J.R. and Brown, M.W., Prediction of the Length of Non-Propagating Fatigue Cracks, Fatigue Fract. Eng. Mater. Struct., vol. 10, pp. 187–201. doi https://doi.org/10.1111/j.1460-2695.1987.tb00477.x10.1111/j.1460-2695.1987.tb00477.x ↗
45. Sonsino, C.M., Multiaxial Fatigue of Welded Joints under In-Phase and Out-of-Phase Local Strains and Stresses, Int. J. Fatigue, 1995, vol. 17, pp. 55–70. doi https://doi.org/10.1016/0142-1123(95)93051-310.1016/0142-1123(95)93051-3 ↗
46. Lazzarin, P., Berto, F., Gomez, F.J., and Zappalorto, M., Some Advantages Derived from the Use of the Strain Energy Density over a Control Volume in Fatigue Strength Assessments of Welded Joints, Int. J. Fatigue, 2008, vol. 30, pp. 1345–1357. doi https://doi.org/10.1016/j.ijfatigue.-2007.10.01210.1016/j.ijfatigue.2007.10.012 ↗
47. Lazzarin, P., Berto, F., and Zappalorto, M., Rapid Calculations of Notch Stress Intensity Factors Based on Averaged Strain Energy Density from Coarse Meshes: Theoretical Bases and Applications, Int. J. Fatigue, 2010, vol. 32, pp. 1559–1567. doi https://doi.org/10.1016/j.ijfatigue.2010.02.01710.1016/j.ijfatigue.2010.02.017 ↗
48. Salavati, H., Alizadeh, Y., and Berto, F., Fracture Assessment of Notched Bainitic Functionally Graded Steels under Mixed Mode (I + II) Loading, Phys. Mesomech., 2015, vol. 18, pp. 307–325.10.1134/S1029959915040049 ↗
49. Radaj, D., Lazzarin, P., and Berto, F., Fatigue Assessment of Welded Joints under Slit-Parallel Loading Based on Strain Energy Density or Notch Rounding, Int. J. Fatigue, 2009, vol. 31, pp. 1490–1504. doi https://doi.org/10.1016/j.ijfatigue.2009.05.00510.1016/j.ijfatigue.2009.05.005 ↗