Evaluating the effectiveness of combined hardening models to determine the behavior of a plate with a hole under combined loadings

Year 2022, Volume: 6 Issue: 2, 97 - 104, 26.06.2022

Melih Çaylak Toros Arda Akşen Mehmet Fırat

https://doi.org/10.26701/ems.1051057

Abstract

Geometrical discontinuities in a material such as holes and notches on machine elements are called as critical regions due to the stress concentrations. They are the potential failure initiation locations Therefore, researchers put significant effort on the prediction of the material response in these discontinuities under repetitive loadings.
Cyclic plasticity is concerned with the nonlinear material response under cyclic loadings. In this study, numerical cyclic stress – strain response of a plate with a hole was evaluated under the combined loadings which are cyclic bending and tensile loadings. Oxygen Free High Thermal Conductivity (OFHC) Copper alloy was considered as material, and finite element simulations were performed in Marc software. A user defined material subroutine known as Hypela2 was utilized in order to define the material response. The plasticity model used in the present study comprises J2 plasticity along with combined isotropic – kinematic hardening model. Evolution of the backstress was introduced by Armstrong – Frederic type kinematic hardening model. The results were compared with the literature study, and it was seen that presented hardening model provides accurate results in small cyclic strain range.

Keywords

Cyclic Plasticity, Armstrong-Frederic Model, Kinematic Hardening, Small Strain, Finite Element Method

References

• [1] Prager, W. (1956). A new method of analyzing stresses and strains in work hardening plastic solids. ASME Journal of Applied Mechanics, 23: 493-496. DOI:10.1115/1.4011389.
• [2] Besseling, J.F. (1958). A theory of plastic and creep deformations of an initially isotropic material. ASME Journal of Applied Mechanics, 25: 529-536, DOI:10.1115/1.4011867.
• [3] Mroz, Z. (1967). On the description of anisotropic work hardening. Journal of Mechanics and Physics of Solids, 15: 163-175, DOI:10.1016/0022-5096(67)90030-0.
• [4] Dafalias, Y.F., Popov, E.F. (1976). Plastic internal variables formalism of cyclic plasticity. ASME Journal of Applied Mechanics, 98: 645-651. DOI:10.1115/1.3423948.
• [5] Ohno, N., Wang, J.D., (1993). Kinematic hardening rules with critical state of dynamic recovery. Part 1: Formulations and basic features for ratcheting behavior. International Journal of Plasticity, 9: 375-390. DOI:10.1016/0749-6419(93)90042-O.
• [6] Armstrong, P.J., Frederic, C.O. (1966). A mathematical representation of the multiaxial Bauschinger effect. G.E.G.B. Report RD/B/N 731.
• [7] Ziegler, H.A. (1959). A modification of Prager’s hardening rule. Quarterly of Applied Mechanics, 17: 55-65. DOI:10.1090/qam/104405.
• [8] Firat, M. (2011). Notch strain calculation of a notched specimen under axial-torsion loadings. Materials and Design, 32: 3876–3882. DOI:10.1016/j.matdes.2011.03.005.
• [9] Firat, M. (2012). Cyclic plasticity modeling and finite element analyzes of a circumferentially notched round bar under combined axial and torsion loadings. Materials and Design, 34: 842-852. DOI:10.1016/j.matdes.2011.07.022.
• [10] Aksen, T.A., Esener, E., Firat, M. (2019). Investigation of Notch Root Strain Behaviors Under Combined Loadings, European Journal of Engineering and Natural Sciences, 3: 42-51.
• [11] Joo, G., Huh, H. (2018). Rate-dependent isotropic‒kinematic hardening model in tension ‒compression of TRIP and TWIP steel sheets. International Journal of Mechanical Sciences, 146–147: 432–444. DOI:10.1016/j.ijmecsci.2017.08.055.
• [12] Joo, G., Huh, H., Choi, M.K. (2016). Tension/compression hardening behaviors of auto-body steel sheets at intermediate strain rates. International Journal of Mechanical Sciences, 108-109: 174–187. DOI:10.1016/j.ijmecsci.2016.01.035.
• [13] Ohno, N., Tsuda, M., Kamei, T. (2013). Elastoplastic implicit integration algorithm applicable to both plane stress and three-dimensional stress states. Finite Elements in Analysis and Design, 66:1–11. DOI: 10.1016/j.finel.2012.11.001.
• [14] Zhang, M., Benitez, J.M., Montáns, F.J. (2018). Cyclic plasticity using Prager’s translation rule and both nonlinear kinematic and isotropic hardening: Theory, validation, and algorithmic implementation. Computer Methods in Applied Mechanics and Engineering, 328:565–593. DOI:10.1016/j.cma.2017.09.028.
• [15] Zhang, M., Montáns, F.J., (2019). A simple formulation for large-strain cyclic hyperelasto-plasticity using elastic correctors. Theory and algorithmic implementation. International Journal of Plasticity, 113: 185–217. DOI:10.1016/j.ijplas.2018.09.013.
• [16] Fu, S., Yu, D., Chen, G., Chen, X. (2016). Ratcheting of 316L stainless steel thin wire under tension-torsion loading. Fracture and Structural Integrity, 38: 141-147. DOI:10.3221/IGF-ESIS.38.19.
• [17] Shojaei, A., Eslami, M.R., Mahbadi, H. (2010). Cyclic loading of beams based on the Chaboche model. International Journal of Mechanics and Materials in Design, 6:217–228. DOI:10.1007/s10999-010-9131-5.
• [18] Badnava, H., Pezeshki, S.M., Nejad, F., Farhoudi, H.R. (2012). Determination of combined hardening material parameters under strain controlled cyclic loading by using the genetic algorithm method. Journal of Mechanical Science and Technology, 26(10):3067~3072. DOI:10.1007/s12206-012-0837-1.
• [19] Tasavori, M., Zehsaz, M., Tahami, F.V. (2020). Ratcheting assessment in the tube sheets of heat exchangers using the nonlinear isotropic/kinematic hardening model. International Journal of Pressure Vessels and Piping, 183:104-103. DOI:10.1016/j.ijpvp.2020.104103.
• [20] Nath, A., Ray, K.K., Barai, V. (2019). Evaluation of ratcheting behaviour in cyclically stable steels through use of a combined kinematic-isotropic hardening rule and a genetic algorithm optimization technique. International Journal of Mechanical Sciences, 152:138–150. DOI:10.1016/j.ijmecsci.2018.12.047.
• [21] Lee, E., Stoughton, T.B., Yoon, J.W. (2019). Kinematic hardening model considering directional hardening response. International Journal of Plasticity, 110:145–165. DOI:10.1016/j.ijplas.2018.06.013.
• [22] Qin, J., Holmedal, B., Hopperstad, O.S. (2018). A combined isotropic, kinematic, and distortional hardening model for aluminum and steels under complex strain-path changes. International Journal of Plasticity, 101: 156–169. DOI:10.1016/j.ijplas.2017.10.013.
• [23] Shahabi, M., Nayebi, A. (2015). Springback modeling in L-Bending process using continuum damage mechanic’s concept. Journal of Applied and Computational Mechanics, 1: 161-167. doi: 10.22055/jacm.2015.11020.
• [24] Meggiolaro, M.A., Castro, J.T.P., Wu, H. (2015). On the applicability of multi-surface, two-surface and non-linear kinematic hardening models in multiaxial fatigue. Fracture and Structural Integrity, 33: 357-367. DOI: 10.3221/IGF-ESIS.33.39.
• [25] Chen, J., Xiao, Y., Ding, W., Zhu, X. (2015). Describing the non-saturating cyclic hardening behavior with a newly developed kinematic hardening model and its application in springback prediction of DP sheet metals. Journal of Materials Processing Technology, 215: 151–158. DOI:10.1016/j.jmatprotec.2014.08.014.
• [26] Adin, H., Sağlam, Z,. & Adin, M.Ş. (2021). Numerical Investigation of Fatigue Behavior of Non-patched and Patched Aluminum/Composite Plates. European Mechanical Science, 5 (4): 168-176 . DOI: 10.26701/ems.923798.
• [27] Paul, S.K., Sivaprasad, S., Dhar, S., Tarafder, M., Tarafder, S. (2010). Simulation of cyclic plastic deformation response in SA333 C-Mn steel by a kinematic hardening model. Computational Materials Science, 48: 662-671. DOI:10.1016/j.commatsci.2010.02.037.
• [28] Marc 2018.1 Volume A: Theory and User Manual.
• [29] Marc 2018.1 Volume B: Element Library.