Chaboche Model for Fatigue by Ratcheting Phenomena of Austenitic Stainless Steel under Biaxial Sinusoidal Loading

Fatiha Boussalih, Kamel Fedaoui, Tahar Zarza


This study deals with the investigation of the cyclic behaviour of 316L and 304L austenitic stainless steels in oligocyclic fatigue under biaxial loading. As a first step, we investigated the prediction of the character of 316L steel under imposed stress, by the fixation of a stress and the evolution of another, forming a cross-proportional loading path in a range of stresses. In addition, the analysis of the behavior of steel 304L with respect to the bi-axial union (primary and secondary loadings) was studied in order to produce the ratcheting phenomenon induced by the non-zero mean stress, governing the structure to damage in two opposite directions, diagonally symmetrical. An appreciable confrontation of the intrinsic characters of the two steels under the same loading conditions was discussed in the last intervention, controlled in strain, generating the phenomenon of cross-hardening and imposed stress. Producing the progressive strain that manifests itself at each loading cycle will make it possible to quantify the degree of plasticity of each material and optimize the most relevant steel. In this numerical study, the Chaboche model is selected, which is based mainly on perfect predictions and robust constitutive laws capable of reproducing observed macroscopic phenomena. All the simulations were carried out using the ZéBulon computation code. A lot of work on the behavior of 304L and 316L stainless steel has been carried out by several researchers in recent years. The results of previous experiments and numerical simulations have been compared to the results of this study, and a good match has been found.


Doi: 10.28991/CEJ-2022-08-03-07

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316L SS; 304L SS; Sinusoidal Fatigue; Ratcheting; Plastic; Chaboche Model.


Tong, J., Zhan, Z. L., & Vermeulen, B. (2004). Modelling of cyclic plasticity and viscoplasticity of a nickel-based alloy using Chaboche constitutive equations. International Journal of Fatigue, 26(8), 829–837. doi:10.1016/j.ijfatigue.2004.01.002.

Steglich, D., Pirondi, A., Bonora, N., & Brocks, W. (2005). Micromechanical modelling of cyclic plasticity incorporating damage. International Journal of Solids and Structures, 42(2), 337–351. doi:10.1016/j.ijsolstr.2004.06.041.

Wolff, M., & Taleb, L. (2008). Consistency for two multi-mechanism models in isothermal plasticity. International Journal of Plasticity, 24(11), 2059–2083. doi:10.1016/j.ijplas.2008.03.001.

Böhm, E., Kurek, M., Junak, G., Cieśla, M., & Łagoda, T. (2014). Accumulation of Fatigue Damage Using Memory of the Material. Procedia Materials Science, 3, 2–7. doi:10.1016/j.mspro.2014.06.002.

Lin, Y. C., Chen, X. M., & Chen, G. (2011). Uniaxial ratcheting and low-cycle fatigue failure behaviors of AZ91D magnesium alloy under cyclic tension deformation. Journal of Alloys and Compounds, 509(24), 6838–6843. doi:10.1016/j.jallcom.2011.03.129.

Lu, J., Becker, A., Sun, W., & Tanner, D. (2014). Simulation of Cyclic Plastic Behavior of 304L Steel Using the Crystal Plasticity Finite Element Method. Procedia Materials Science, 3, 135–140. doi:10.1016/j.mspro.2014.06.025.

Mao, J., Engler-Pinto, C. C., Li, T., Hsieh, J., & Su, X. (2015). Effect of Constitutive Model on Thermo-mechanical Fatigue Life Prediction. Procedia Engineering, 133, 655–668. doi:10.1016/j.proeng.2015.12.647.

Kang, G., Gao, Q., Cai, L., & Sun, Y. (2002). Experimental study on uniaxial and non-proportionally multiaxial ratcheting of SS304 stainless steel at room and high temperatures. Nuclear Engineering and Design, 216(1–3), 13–26. doi:10.1016/S0029-5493(02)00062-6.

Kang, G. (2004). A visco-plastic constitutive model for ratcheting of cyclically stable materials and its finite element implementation. Mechanics of Materials, 36(4), 299–312. doi:10.1016/S0167-6636(03)00024-3.

Johansson, G., Ekh, M., & Runesson, K. (2005). Computational modeling of inelastic large ratcheting strains. International Journal of Plasticity, 21(5), 955–980. doi:10.1016/j.ijplas.2004.05.013.

Taleb, L., Cailletaud, G., & Blaj, L. (2006). Numerical simulation of complex ratcheting tests with a multi-mechanism model type. International Journal of Plasticity, 22(4), 724–753. doi:10.1016/j.ijplas.2005.05.003.

Hassan, T., Taleb, L., & Krishna, S. (2008). Influence of non-proportional loading on ratcheting responses and simulations by two recent cyclic plasticity models. International Journal of Plasticity, 24(10), 1863–1889. doi:10.1016/j.ijplas.2008.04.008.

Taleb, L., & Hauet, A. (2009). Multiscale experimental investigations about the cyclic behavior of the 304L SS. International Journal of Plasticity, 25(7), 1359–1385. doi:10.1016/j.ijplas.2008.09.004.

Taleb, L., & Cailletaud, G. (2011). Cyclic accumulation of the inelastic strain in the 304L SS under stress control at room temperature: Ratcheting or creep? International Journal of Plasticity, 27(12), 1936–1958. doi:10.1016/j.ijplas.2011.02.001.

Halama, R., Sedlák, J., & Šofer, M. (2012). Phenomenological Modelling of Cyclic Plasticity. Numerical Modelling. IntechOpen, 329-354. doi:10.5772/35902.

Meggiolaro, M. A., Pinho De Castro, J. T., & Wu, H. (2015). Computationally-efficient non-linear kinematic models to predict multiaxial stress-strain behavior under variable amplitude loading. Procedia Engineering, 101(C), 285–292. doi:10.1016/j.proeng.2015.02.032.

Meggiolaro, M. A., De Castro, J. T. P., Wu, H., & Sanchez, E. C. M. (2016). A general class of non-linear kinematic models to predict mean stress relaxation and multiaxial ratcheting in fatigue problems - Part II: Generalized surface translation rule. International Journal of Fatigue, 82, 167–178. doi:10.1016/j.ijfatigue.2015.08.031.

Boussalih, F., Meziani, S., Fouathia, A., & Fedaoui, K. (2019). Behavior of 304L stainless steel under uniaxial loading and effect of the mean stress on the ratcheting by simulation using chaboche model. UPB Scientific Bulletin, Series D: Mechanical Engineering, 81(2), 179–190.

Belattar, A., & Taleb, L. (2021). Experimental and numerical analyses of the cyclic behavior of austenitic stainless steels after prior inelastic histories. International Journal of Pressure Vessels and Piping, 189, 104256. doi:10.1016/j.ijpvp.2020.104256.

Bocher, L., Delobelle, P., Robinet, P., & Feaugas, X. (2001). Mechanical and microstructural investigations of an austenitic stainless steel under non-proportional loadings in tension-torsion-internal and external pressure. International Journal of Plasticity, 17(11), 1491–1530. doi:10.1016/S0749-6419(01)00013-4.

Chen, X., Jiao, R., & Kim, K. S. (2003). Simulation of ratcheting strain to a high number of cycles under biaxial loading. International Journal of Solids and Structures, 40(26), 7449–7461. doi:10.1016/j.ijsolstr.2003.08.009.

Kulkarni, S. C., Desai, Y. M., Kant, T., Reddy, G. R., Prasad, P., Vaze, K. K., & Gupta, C. (2004). Uniaxial and biaxial ratchetting in piping materials-experiments and analysis. International Journal of Pressure Vessels and Piping, 81(7), 609–617. doi:10.1016/j.ijpvp.2004.04.001.

Kang, G., Li, Y., & Gao, Q. (2005). Non-proportionally multiaxial ratcheting of cyclic hardening materials at elevated temperatures: Experiments and simulations. Mechanics of Materials, 37(11), 1101–1118. doi:10.1016/j.mechmat.2005.01.006.

Poncelet, M., Barbier, G., Raka, B., Courtin, S., Desmorat, R., Le-Roux, J. C., & Vincent, L. (2010). Biaxial high cycle fatigue of a type 304L stainless steel: Cyclic strains and crack initiation detection by digital image correlation. European Journal of Mechanics, A/Solids, 29(5), 810–825. doi:10.1016/j.euromechsol.2010.05.002.

Fremy, F., Pommier, S., Galenne, E., & Courtin, S. (2012). A scaling approach to model history effects in fatigue crack growth under mixed mode I + II + III loading conditions for a 316L stainless steel. International Journal of Fatigue, 42, 207–216. doi:10.1016/j.ijfatigue.2011.10.013.

Rezaiee-Pajand, M., & Sinaie, S. (2013). Calibration of hardening rules for cyclic plasticity. International Journal of Engineering, Transactions A: Basics, 26(4), 351–364. doi:10.5829/idosi.ije.2013.26.04a.04.

Creuziger, A., Hu, L., Gnäupel-Herold, T., & Rollett, A. D. (2014). Crystallographic texture evolution in 1008 steel sheet during multi-axial tensile strain paths. Integrating Materials and Manufacturing Innovation, 3(1), 1–19. doi:10.1186/2193-9772-3-1.

Mazánová, V., Polák, J., Škorík, V., & Kruml, T. (2017). Multiaxial elastoplastic cyclic loading of austenitic 316L steel. Frattura Ed Integrita Strutturale, 11(40), 162–169. doi:10.3221/IGF-ESIS.40.14.

Yaguchi, M., & Takahashi, Y. (2005). Ratchetting of viscoplastic material with cyclic softening, part 2: Application of constitutive models. International Journal of Plasticity, 21(4), 835–860. doi:10.1016/j.ijplas.2004.05.012.

Sai, K., & Cailletaud, G. (2007). Multi-mechanism models for the description of ratcheting: Effect of the scale transition rule and of the coupling between hardening variables. International Journal of Plasticity, 23(9), 1589–1617. doi:10.1016/j.ijplas.2007.01.011.

Chaboche, J. L. (2008). A review of some plasticity and viscoplasticity constitutive theories. International Journal of Plasticity, 24(10), 1642–1693. doi:10.1016/j.ijplas.2008.03.009.

Taheri, S., Hauet, A., Taleb, L., & Kpodekon, C. (2011). Micro-macro investigations about the fatigue behavior of pre-hardened 304L steel. International Journal of Plasticity, 27(12), 1981–2004. doi:10.1016/j.ijplas.2011.06.004.

Budaházy, V., & Dunai, L. (2013). Parameter-refreshed Chaboche model for mild steel cyclic plasticity behaviour. Periodica Polytechnica Civil Engineering (Vol. 57, Issue 2, pp. 139–155). doi:10.3311/PPci.7170.

Saleh, M., Kariem, M. M., Luzin, V., Toppler, K., Li, H., & Ruan, D. (2018). High strain rate deformation of ARMOX 500T and effects on texture development using neutron diffraction techniques and SHPB testing. Materials Science and Engineering A, 709, 30–39. doi:10.1016/j.msea.2017.09.022.

Novak, J. S., Bona, F. De, & Benasciutti, D. (2019). Numerical simulation of cyclic plasticity in mechanical components under low cycle fatigue loading: Accelerated material models. Procedia Structural Integrity, 19, 548–555. doi:10.1016/j.prostr.2019.12.059.

Xie, X. F., Jiang, W., Chen, J., Zhang, X., & Tu, S. T. (2019). Cyclic hardening/softening behavior of 316L stainless steel at elevated temperature including strain-rate and strain-range dependence: Experimental and damage-coupled constitutive modeling. In International Journal of Plasticity (Vol. 114, pp. 196–214). doi:10.1016/j.ijplas.2018.11.001.

Chaboche, J. L. (1989). Constitutive equations for cyclic plasticity and cyclic viscoplasticity. International Journal of Plasticity, 5(3), 247–302. doi:10.1016/0749-6419(89)90015-6.

Djimli, L., Taleb, L., & Meziani, S. (2010). The role of the experimental data base used to identify material parameters in predicting the cyclic plastic response of an austenitic steel. International Journal of Pressure Vessels and Piping, 87(4), 177–186. doi:10.1016/j.ijpvp.2010.02.002.

Besson, J., Leriche, R., Foerch, R., & Cailletaud, G. (1998). Object-oriented programming applied to the finite element method part II. Application to material behaviors. Revue Européenne des Éléments Finis, 7(5), 567-588. doi:10.1080/12506559.1998.10511322.

Roy, S. C., Goyal, S., Sandhya, R., & Ray, S. K. (2013). Analysis of hysteresis loops of 316L (N) stainless steel under low cycle fatigue loading conditions. Procedia engineering, 55, 165-170. doi: 10.1016/j.proeng.2013.03.237.

Moslemi, N., Zardian, M. G., Ayob, A., Redzuan, N., & Rhee, S. (2019). Evaluation of sensitivity and calibration of the chaboche kinematic hardening model parameters for numerical ratcheting simulation. Applied Sciences (Switzerland), 9(12), 2578. doi:10.3390/app9122578.

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DOI: 10.28991/CEJ-2022-08-03-07


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