journal article·2025-02-27Open access

Cyclic Elasto-Plastic Behaviour of 51CrV4 Steel for Railway Parabolic Leaf Spring Design

Vítor M. G. Gomes, Rita Dantas, José A. F. O. Correia, Abílio M. P. de Jesus

Applied Sciences· Volume 15· Issue 5

Abstract

Parabolic leaf springs are components typically found in suspensions of freight railway rolling stock. These components are produced in high-strength alloyed steel, DIN 51CrV4, to resist severe loading and environmental conditions. Despite the material’s good mechanical characteristics, the geometric notches and high surface roughness that features its leaves might raise local stress levels to values above the elastic limit, with cyclic elasto-plastic behaviour models being more appropriate. In this investigation, the parameters of the Chaboche model combining the kinematic and isotropic hardening models are determined using experimental data previously obtained in strain-controlled cyclic tests. Once the parameters of the cyclic hardening model are determined, they are validated using a finite element approach considering the Chaboche cyclic plasticity model. As a result, the material properties specified in this investigation can be used in the fatigue mechanical design of parabolic leaf springs made with 51CrV4 (local approaches to notches and at surface roughness level) or even in other components produced with the same steel.
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Research context

OpenAlex topics: Mechanical Engineering and Vibrations Research · Mechanical Failure Analysis and Simulation · Metal Alloys Wear and Properties

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Affiliations

FEUP—Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal

INEGI—Institute of Science and Innovation in Mechanical and Industrial Engineering, 4200-465 Porto, Portugal

ICS—Institute for Sustainable Construction, 4300-506 Porto, Portugal

Funding

Portuguese Foundation for Science and Technology, IP (FCT) · European Regional Development Fund (ERDF) · Recovery and Resilience Plan

References (100+)

Show source-provided references
1. Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study
2. Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads10.1155/2013/261926 ↗
3. Numerical studies on influence of friction coefficient in multi-leaf spring on suspension basic characteristics10.1063/1.5092052 ↗
4. Dynamics stand tests and numerical research of multi-leaf springs with regard to clearances and friction10.1177/1687814019853353 ↗
5. Study on the modeling method of leaf spring based on assembly pre-stress10.4028/www.scientific.net/AMR.663.545 ↗
6. Study of leaf spring fracture behavior used in the suspension systems in the diesel truck vehicles10.1088/1757-899X/541/1/012046 ↗
7. The analysis of the failure of leaf spring used as the rear suspension system in 110 PS diesel trucks10.1063/5.0119820 ↗
8. Premature fracture in automobile leaf springs10.1016/j.engfailanal.2008.02.008 ↗
9. Analysis of the Leaf Spring Failure in Light Duty Dump Truck10.4028/p-4ft3s2 ↗
10. Failure Analysis of Leaf Spring Used in Transport Utility Vehicles10.1007/s11668-022-01470-1 ↗
11. Chen, Y.H., Chen, G.C., Wu, C.T., Lee, C.L., Chen, Y.R., Huang, J.F., Hsiao, K.H., and Lin, J.I. (2020). Object investigation of industrial heritage: The forging and metallurgy shop in Taipei railway workshop. Appl. Sci., 10.10.3390/app10072408 ↗
12. Matej, J., Seńko, J., and Awrejcewicz, J. (2013, January 2–5). Dynamic Properties of Two-Axle Freight Wagon with UIC Double-Link Suspension as a Non-smooth System with Dry Friction. Proceedings of the Applied Non-Linear Dynamical Systems, Łódź, Poland.10.1007/978-3-319-08266-0_18 ↗
13. Model of the UIC link suspension for freight wagons10.1007/s00419-003-0305-6 ↗
14. Dynamics of two-axle railway freight wagons with UIC standard suspension10.1080/00423110600869594 ↗
15. Dynamics of railway freight vehicles10.1080/00423114.2015.1037773 ↗
16. (2007). Wagons—Suspension Gear—Standardisation (Standard No. UIC517).
17. (1996). Spring Design Manual, Society of Automotive Engineers Spring Committee. Technical Report.
18. Increasing the Efficiency of Railway Transport by Improvement of Suspension of Freight Wagons10.7307/ptt.v24i6.1202 ↗
19. Yamada, Y. (2007). Materials for Springs, Springer.
20. Smith, W.F. (1999). Principles of Materials Science and Engineering, McGraw Hill.
21. Effect of tempering temperature on microstructure and mechanical properties of AISI 6150 steel
22. (2004). Heat-Treatable Steels, Alloy Steels and, Free-Cutting Steels Part 14: Hot-Rolled Steels for Quenched and Tempered Springs (Standard No. ISO683-14).
23. On the effects of heat and surface treatment on the fatigue performance of high-strength leaf springs10.1051/matecconf/202134904007 ↗
24. Gomes, V.M., Souto, C.D., Correia, J.A., and de Jesus, A.M. (2024). Monotonic and Fatigue Behaviour of the 51CrV4 Steel with Application in Leaf Springs of Railway Rolling Stock. Metals, 14.10.3390/met14030266 ↗
25. Tribological behavior of heat treated AISI 6150 steel10.1016/j.jmrt.2020.08.089 ↗
26. Fatigue strength of spring steel under axial and torsional loading in the very high cycle regime10.1016/j.ijfatigue.2008.07.004 ↗
27. Effect of the shot peening process on the fatigue strength of SAE 5160 steel10.1177/0954406218816349 ↗
28. Gomes, V.M.G., De Jesus, A.M.P., Figueiredo, M., Correia, J.A.F.O., and Calcada, R. (2021, January 15–17). Fatigue Failure of 51CrV4 Steel Under Rotating Bending and Tensile. Proceedings of the XX International Colloquium on Mechanical Fatigue of Metals (ICMFM XX), Wrocław, Poland.10.1007/978-3-030-97822-8_36 ↗
29. Ceyhanli, U.T., and Bozca, M. (2020). Experimental and numerical analysis of the static strength and fatigue life reliability of parabolic leaf springs in heavy commercial trucks. Adv. Mech. Eng., 12.10.1177/1687814020941956 ↗
30. Failure analysis of a parabolic spring belonging to a railway wagon10.1016/j.engfailanal.2022.106526 ↗
31. Gomes, V., Correia, J., Calçada, R., Barbosa, R., and de Jesus, A. (2020, January 9–11). Fatigue in Trapezoidal Leaf Springs of Suspensions in Two-Axle Wagons—An Overview and Simulation. Proceedings of the Virtual Conference on Mechanical Fatigue, Online.
32. Evaluation of a leaf spring failure10.1361/154770205X76303 ↗
33. Life assessment methodologies incoroporating shot peening process effects: Mechanistic consideration of residual stresses and strain hardening: Part 1—Effect of shot peening on fatigue resistance10.1179/1743284713Y.0000000222 ↗
34. Study of the effects produced by shot peening on the surface of quenched and tempered steels: Roughness, residual stresses and work hardening10.1016/j.apsusc.2015.08.110 ↗
35. Recent developments in the mathematical theory of plasticity
36. On the description of anisotropic workhardening10.1016/0022-5096(67)90030-0 ↗
37. A model of nonlinearly hardening materials for complex loading10.1007/BF01181053 ↗
38. A practical two surface plasticity theory10.1115/1.3423656 ↗
39. Theory of creep with anisotropic hardening10.1016/0020-7403(72)90065-3 ↗
40. A mathematical representation of the multiaxial Bauschinger effect
41. A review of some plasticity and viscoplasticity constitutive theories10.1016/j.ijplas.2008.03.009 ↗
42. Jiang, Y. (1993). Cyclic Plasticity with an Emphasis on Ratchetting. [Ph.D. Thesis, University of Illinois at Urbana-Champaign]. Available online: https://www.proquest.com/openview/a233be354ea54bea768e6987de8e4f77/1?pq-origsite=gscholar&cbl=18750&diss=y.
43. Hu, W., Wang, C.H., and Barter, S. (1999). Analysis of Cyclic Mean Stress Relaxation and Strain Ratchetting Behaviour of Aluminium 7050, Technical Report.
44. Calibration of a combined isotropic-kinematic hardening material model for the simulation of thin electrical steel sheets subjected to cyclic loading10.1002/mawe.202100341 ↗
45. Analysis of uniaxial ratcheting behavior and cyclic mean stress relaxation of a duplex stainless steel10.1016/j.ijplas.2014.06.008 ↗
46. Ratcheting in cyclic plasticity, Part I: Uniaxial behavior10.1016/0749-6419(92)90040-J ↗
47. Cyclic elastoplastic performance of aluminum 7075-T6 under strain-and stress-controlled loading10.1007/s11665-017-3047-2 ↗
48. Determination of combined hardening material parameters under strain controlled cyclic loading by using the genetic algorithm method10.1007/s12206-012-0837-1 ↗
49. Constitutive modeling of cyclic deformation of metals under strain controlled axial extension and cyclic torsion10.1007/s00707-017-1982-5 ↗
50. Elasto-visco-plasticity for the metallic materials: A review of the models10.1007/BF03404661 ↗
51. Sensitivity and optimisation of the Chaboche plasticity model parameters in strain-life fatigue predictions10.1016/j.matdes.2017.01.027 ↗
52. Cyclic uniaxial and multiaxial loading with yield surface distortion consideration on prediction of ratcheting10.1016/j.mechmat.2012.01.005 ↗
53. Optimization of Chaboche kinematic hardening parameters for 20MnMoNi55 reactor pressure vessel steel by sequenced genetic algorithms maintaining the hierarchy of dependence10.1080/0305215X.2020.1726340 ↗
54. On the calibration of the Chaboche hardening model and a modified hardening rule for uniaxial ratcheting prediction10.1016/j.ijsolstr.2009.04.002 ↗
55. Sajjad, H.M., Hanke, S., Güler, S., ul Hassan, H., Fischer, A., and Hartmaier, A. (2019). Modelling Cyclic Behaviour of Martensitic Steel with J2 Plasticity and Crystal Plasticity. Materials, 12.10.3390/ma12111767 ↗
56. Using the nonlinear kinematic hardening material model of Chaboche for elastic–plastic ratcheting analysis10.1115/1.4028659 ↗
57. Effect of cyclic softening and mean stress relaxation on fatigue crack initiation in a hemispherical notch10.1111/ffe.13834 ↗
58. A strategy to fast determine Chaboche elasto-plastic model parameters by considering ratcheting10.1016/j.ijpvp.2019.01.017 ↗
59. Low cycle fatigue life prediction of 316 L(N) stainless steel based on cyclic elasto-plastic response10.1016/j.nucengdes.2012.08.024 ↗
60. Shao, X., Du, J., Fu, X., Xiong, F., Li, H., Tian, J., Lu, X., and Xie, H. (2022). Simplified Elastoplastic Fatigue Correction Factor Analysis Approach Based on Minimum Conservative Margin. Metals, 12.10.3390/met12060943 ↗
61. Low cycle fatigue properties and cyclic elasto-plastic response of modified 9Cr-1Mo steel10.1007/s12666-015-0800-9 ↗
62. Multiaxial low cycle fatigue of notched 10CrNi3MoV steel and its undermatched welds10.1016/j.ijfatigue.2021.106309 ↗
63. Surface roughness influence in micromechanical fatigue lifetime prediction with crystal plasticity models for steel10.1016/j.ijfatigue.2022.106792 ↗
64. Ratchetting-multiaxial fatigue damage analysis in gear rolling contact considering tooth surface roughness
65. Crystal plasticity FEM analysis for variation of surface morphology under low cycle fatigue condition of austenitic stainless steel10.1016/j.ijfatigue.2019.06.032 ↗
66. Radaj, D., Vormwald, M., and Vormwald, M. (2013). Elastic-plastic fatigue crack growth. Advanced Methods of Fatigue Assessment, Springer.10.1007/978-3-642-30740-9 ↗
67. Fatigue crack growth determination based on cyclic plastic zone and cyclic J-integral in kinematic–isotropic hardening materials with considering Chaboche model10.1111/ffe.13330 ↗
68. Fatigue crack growth modelling based on CTOD for the 7050-T6 alloy10.1111/ffe.12582 ↗
69. Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q34510.1016/j.ijfatigue.2016.03.026 ↗
70. The Chaboche nonlinear kinematic hardening model: Calibration methodology and validation10.1007/s11012-008-9115-9 ↗
71. Determination of Chaboche combined hardening parameters with dual backstress for ratcheting evaluation of AISI 52100 bearing steel10.1016/j.ijfatigue.2019.01.009 ↗
72. Numerical and experimental study of an interference fitted joint using a large deformation Chaboche type combined isotropic–kinematic hardening law and mortar contact method10.1016/j.ijmecsci.2015.10.012 ↗
73. Gomes, V.M., Eck, S., and De Jesus, A.M. (2023). Cyclic hardening and fatigue damage features of 51CrV4 steel for the crossing nose design. Appl. Sci., 13.10.3390/app13148308 ↗
74. Probabilistic modeling of uncertainties in fatigue reliability analysis of turbine bladed disks10.1016/j.ijfatigue.2020.105912 ↗
75. Constitutive model for full-range cyclic behavior of high strength steels without yield plateau10.1016/j.conbuildmat.2017.11.128 ↗
76. Experimental investigation and modeling of cyclic behavior of high strength steel10.1016/j.jcsr.2014.09.009 ↗
77. Cyclic behavior and constitutive model of high strength low alloy steel plate10.1016/j.engstruct.2020.110798 ↗
78. Application of Ramberg-Osgood plasticity to determine cyclic hardening parameters
79. Unified Elastic–Plastic Analytical Method for Estimating Notch Local Strains in Real Time under Multiaxial Irregular Loading10.1007/s11665-021-06085-5 ↗
80. Ramberg, W., and Osgood, W.R. (2022, March 30). Description of Stress-Strain Curves by Three Parameters, Available online: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930081614.pdf.
81. Fatigue fracture and fatigue life assessment of railway wheel using non-linear model for fatigue crack growth10.1016/j.ijfatigue.2021.106516 ↗
82. Fatigue performance prediction of S235 base steel plates in the riveted connections10.1016/j.istruc.2020.11.082 ↗
83. Experimental study and parameter determination of cyclic constitutive model for bridge steels10.1016/j.jcsr.2021.106738 ↗
84. Fatigue crack growth of a railway wheel steel and fatigue life prediction under spectrum loading conditions10.1016/j.ijfatigue.2022.106722 ↗
85. Hu, Y., Shi, J., Cao, X., and Zhi, J. (2021). Low cycle fatigue life assessment based on the accumulated plastic strain energy density. Materials, 14.10.3390/ma14092372 ↗
86. Global-local fatigue approaches for snug-tight and preloaded hot-dip galvanized steel bolted joints10.1016/j.ijfatigue.2021.106486 ↗
87. Kreithner, M., Niederwanger, A., and Lang, R. (2023). Influence of the Ductility Exponent on the Fatigue of Structural Steels. Metals, 13.10.3390/met13040759 ↗
88. Cyclic Material Behavior of High-Strength Steels Used in the Fatigue Assessment of Welded Crane Structures with a Special Focus on Transient Material Effects10.4271/2017-01-0342 ↗
89. Study on Ramberg-Osgood and Chaboche models for 42CrMo4 steel and some approximations10.1016/j.jcsr.2017.05.010 ↗
90. (2009). Metallic Materials-Tensile Testing-Part 1: Method of Test at Ambient Temperature (Standard No. ISO6892-1).
91. (1998). Standard Test Method for Strain-Controlled Fatigue Testing (Standard No. ASTME606).
92. Montgomery, D.C., and Runger, G.C. (2001). Applied Statistics and Probability for Engineers, John Wiley and Sons, Inc.. [6th ed.].
93. Martins, J.R., and Ning, A. (2021). Engineering Design Optimization, Cambridge University Press.10.1017/9781108980647 ↗
94. Algorithm 851: CG_DESCENT, a conjugate gradient method with guaranteed descent10.1145/1132973.1132979 ↗
95. Revels, J., Lubin, M., and Papamarkou, T. (2016). Forward-mode automatic differentiation in Julia. arXiv.
96. The equivalence of the radial return and Mendelson methods for integrating the classical plasticity equations10.1007/s00466-007-0228-0 ↗
97. Accuracies of numerical solution methods for the elastic-perfectly plastic model10.1115/1.3454568 ↗
98. Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator10.1145/272991.272995 ↗
99. Twisted GFSR generators10.1145/146382.146383 ↗
100. A Modified Universal Slopes Equation for Estimation of Fatigue Characteristics of Metals10.1115/1.3226010 ↗