Abstract
In this article, we present our take on modeling the Bauschinger effect. The main goal is to correlate the microstructure-based modeling developed for uniaxial tension/compression deformation and the tensorial modeling approach of the continuum mechanics. After a brief historial review, we present a microstructure-related model that was proven to provide an adequate description of the Bauschinger effect in terms of kinematic and isotropic strain hardening. Its generalization to the case of multiaxial loading is then formulated in terms of a continuum mechanics model. The full tensorial model developed is now being offered to the solid mechanics and physical metallurgy communities as an advanced modeling tool.
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J. Bauschinger, Met. Civ. NF 27, 289 (1881)
J. Bauschinger, Mittheilungen aus dem Mechanisch-Technischen Laboratorium der Königlichen, vol. 13 (Technical University, Munich, 1886), p. 31
G. Masing, in Wissenschaftliche Veröffentlichungen aus dem Siemens-Konzern, ed. by C.D. Harries (Springer, Berlin, Heidelberg, 1923), pp. 231–239
E. Heyn, A few questions from the field of metal testing. Metall. u. Erz. 15(411–422), 436–441 (1918)
E. Orowan, Discussion on Internal Stresses, in Symp. Internal Stresses in Metals and Alloys (The Institute of Metals, London, 1948), pp. 451–453.
M.E. Kassner, P. Geantil, L.E. Levine, B.C. Larson, Mater. Sci. Forum 604–605, 39 (2009). https://doi.org/10.4028/www.scientific.net/MSF.604-605.39
Z. Li, P. La, J. Sheng, Y. Shi, X. Zhou, Q. Meng, Met. Mater. Int. 27, 2562 (2021). https://doi.org/10.1007/s12540-020-00662-4
J.G. Kim, M.J. Jang, H.K. Park, K.-G. Chin, S. Lee, H.S. Kim, Met. Mater. Int. 25, 912 (2019). https://doi.org/10.1007/s12540-019-00258-7
F. He, Z. Yang, S. Liu, D. Chen, W. Lin, T. Yang, D. Wei, Z. Wang, J. Wang, J. Kai, Int. J. Plasticity 144, 103022 (2021). https://doi.org/10.1016/j.ijplas.2021.103022
Y. Zhu, K. Ameyama, P.M. Anderson, I.J. Beyerlein, H. Gao, H.S. Kim, E. Lavernia, S. Mathaudhu, H. Mughrabi, R.O. Ritchie, N. Tsuji, X. Zhang, X. Wu, Mater. Res. Lett. 9, 1 (2021). https://doi.org/10.1080/21663831.2020.1796836
J.G. Kim, J.W. Bae, J.M. Park, W. Woo, S. Harjo, S. Lee, H.S. Kim, Met. Mater. Int. 27, 376 (2021). https://doi.org/10.1007/s12540-020-00657-1
W. Lu, P. Cao, C. Zhao, Y. Song, C. Tang, Met. Mater. Int. 27, 4397 (2021). https://doi.org/10.1007/s12540-020-00853-z
H.-W. Son, J.-C. Lee, H.S. Park, S.-K. Hyun, Met. Mater. Int. 27, 4894 (2021). https://doi.org/10.1007/s12540-020-00677-x
J. Moon, J.M. Park, J.W. Bae, N. Kang, J. Oh, H. Shin, H.S. Kim, Scripta Mater. 186, 24 (2020). https://doi.org/10.1016/j.scriptamat.2020.04.044
S.C. Song, J. Moon, H.S. Kim, Mater. Sci. Eng. A 799, 140275 (2021). https://doi.org/10.1016/j.msea.2020.140275
J. Li, W. Lu, S. Chen, C. Liu, Int. J. Plasticity 126, 102626 (2020). https://doi.org/10.1016/j.ijplas.2019.11.005
T.J. Barrett, M. Knezevic, Comput. Methods Appl. Mech. Eng. 354, 245 (2019). https://doi.org/10.1016/j.cma.2019.05.035
T.J. Barrett, R.J. McCabe, D.W. Brown, B. Clausen, S.C. Vogel, M. Knezevic, J. Mech. Phys. Solids 138, 103924 (2020). https://doi.org/10.1016/j.jmps.2020.103924
S. Berbenni, V. Taupin, R.A. Lebensohn, J. Mech. Phys. Solids 135, 103808 (2020). https://doi.org/10.1016/j.jmps.2019.103808
A. Eghtesad, M. Knezevic, Mater. Sci. Eng. A 803, 140478 (2021). https://doi.org/10.1016/j.msea.2020.140478
A. Abel, Mater. Forum 10, 11 (1987). http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=0023314138&origin=inward.
G.M. Castelluccio, D.L. McDowell, Int. J. Plasticity 98, 1 (2017). https://doi.org/10.1016/j.ijplas.2017.06.002
Z. Feng, S.-Y. Yoon, J.-H. Choi, T.J. Barrett, M. Zecevic, F. Barlat, M. Knezevic, Mech. Mater. 148, 103422 (2020). https://doi.org/10.1016/j.mechmat.2020.103422
S. Ghorbanpour, M. Zecevic, A. Kumar, M. Jahedi, J. Bicknell, L. Jorgensen, I.J. Beyerlein, M. Knezevic, Int. J. Plasticity 99, 162 (2017). https://doi.org/10.1016/j.ijplas.2017.09.006
M. Zecevic, M. Knezevic, Int. J. Plasticity 72, 200 (2015). https://doi.org/10.1016/j.ijplas.2015.05.018
M. Zecevic, Y.P. Korkolis, T. Kuwabara, M. Knezevic, J. Mech. Phys. Solids 96, 65 (2016). https://doi.org/10.1016/j.jmps.2016.07.003
S. Jeunehomme, Ph.D. thesis, Ecole des Mines de Paris (1991)
S. Allain, O. Bouaziz, Mater. Sci. Eng. A 496, 329 (2008). https://doi.org/10.1016/j.msea.2008.06.009
M.W. Kapp, C. Kirchlechner, R. Pippan, G. Dehm, J. Mater. Res. 30, 791 (2015). https://doi.org/10.1557/jmr.2015.49
S. Gao, K. Yoshino, D. Terada, Y. Kaneko, N. Tsuji, Scripta Mater. 211, 114503 (2022). https://doi.org/10.1016/j.scriptamat.2022.114503
J. Gil Sevillano, F. de Las Cuevas, Mater. Sci. Technol. 35, 409 (2019). https://doi.org/10.1080/02670836.2019.1567044
O. Bouaziz, D. Barbier, J.D. Embury, G. Badinier, Phil. Mag. 93, 247 (2013). https://doi.org/10.1080/14786435.2012.704419
O. Bouaziz, J. Moon, H.S. Kim, Y. Estrin, Scripta Mater. 191, 107 (2021). https://doi.org/10.1016/j.scriptamat.2020.09.022
F.A. McClintock, A.S. Argon (eds.), Mechanical Behavior of Materials (Addison-Wesley, Reading, 1966), p. 277
E. Orowan, Causes and effects of internal stresses, in Proceedings of the Symposium on Internal Stresses and Fatigue in Metals, Detroit and Warren, ed. by G.M. Rassweiler, W.L. Grube, (Elsevier, Amsterdam, 1958) pp. 59–80.
M.F. Ashby, Phil. Mag. A 21, 399 (1970). https://doi.org/10.1080/14786437008238426
L.M. Brown, W.M. Stobbs, Phil. Mag. A 23, 1201 (1971). https://doi.org/10.1080/14786437108217406
O. Bouaziz, Y. Bréchet, Scripta Mater. 60, 366 (2009). https://doi.org/10.1016/j.scriptamat.2008.11.002
H. Mughrabi, Acta Metall. 31, 1367 (1983). https://doi.org/10.1016/0001-6160(83)90007-X
Y. Estrin, L.S. Tóth, A. Molinari, Y. Bréchet, Acta Mater. 46, 5509 (1998). https://doi.org/10.1016/S1359-6454(98)00196-7
A. Vinogradov, Y. Estrin, A. Molotnikov, Unpublished results.
L. Li, L. Shen, G. Proust, Appl. Mech. Mater. 553, 22 (2014). https://doi.org/10.4028/www.scientific.net/AMM.553.22
B.J. Schäfer, X. Song, P. Sonnweber-Ribic, H. Hassan, A. Hartmaier, Metals 9, 368 (2019). https://doi.org/10.3390/met9030368
G.Z. Voyiadjis, S.H. Hoseini, G.H. Farrahi, J. Eng. Mater. Technol. 135, 011002 (2013). https://doi.org/10.1115/1.4007386
B. Holmedal, Int. J. Plasticity 123, 86 (2019). https://doi.org/10.1016/j.ijplas.2019.07.009
P.J. Armstrong, C.O. Frederick, A mathematical representation of multiaxial Bauschinger effect, in CEGB Internal research report in Materials at High Temperatures, Vol. 24, pp. 1–26 (1966)
J. Lemaitre, J.-L. Chaboche, Mechanics of Solid Materials (Cambridge University Press, Cambridge,1990)
W. Prager, J. Appl. Mech. 23, 493 (1956). https://doi.org/10.1115/1.4011389
E. Melan, Ingenieur-Archiv 9, 116 (1938). https://doi.org/10.1007/BF02084409
B. Berisha, P. Hora, A. Wahlen, L. Tong, Int. J. Plasticity 26, 126 (2009). https://doi.org/10.1016/j.ijplas.2009.06.001
T. J. R. Hughes, in Theoretical Foundations for Large Scale Computations of Nonlinear Material Behaviour, ed. by S. Nemat-Nasser, R. Asaro, G. Hegemier, Martinus Nijhoff. Mechanics of elastic and inelastic solids 6, vol 6 (Springer, Dordrecht, 1984). https://doi.org/10.1007/978-94-009-6213-2_3.
E. Voce, J. Inst. Met. 74, 537 (1948)
M.F. Horstemeyer, D.J. Bammann, Int. J. Plasticity 26, 1310 (2010). https://doi.org/10.1016/j.ijplas.2010.06.005
Y. Estrin, Dislocation-density-related constitutive modelling, in Unified Constitutive Laws of Plastic Deformation, ed. by A.S. Krausz, K. Krausz (Academic Press, New York, 1996), pp. 69–106
B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Mater. Sci. Eng. A 375–377, 213 (2004). https://doi.org/10.1016/j.msea.2003.10.257
Z. Li, C.C. Tasan, K.G. Pradeep, D. Raabe, Acta Mater. 131, 323 (2017). https://doi.org/10.1016/j.actamat.2017.03.069
G. Laplanche, J. Bonneville, C. Varvenne, W.A. Curtin, E.P. George, Acta Mater. 143, 257 (2018). https://doi.org/10.1016/j.actamat.2017.10.014
O. Bouaziz, S. Allain, C. Scott, Scripta Mater. 58, 484 (2008). https://doi.org/10.1016/j.scriptamat.2007.10.050
M. Yang, Y. Pan, F. Yuan, Y. Zhu, X. Wu, Mater. Res. Lett. 4, 145 (2016). https://doi.org/10.1080/21663831.2016.1153004
Johann Bauschinger 1834–1893, Holz als Roh- und Werkstoff - European Journal of Wood and Wood Industries 30, 239 (1972) https://doi.org/10.1007/BF02617596
Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2021R1A2C3006662). Useful comments of Prof. Ron Armstrong on the manuscript are gratefully appreciated.
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Bouaziz, O., Kim, H.S., Lee, J. et al. Bauschinger Effect or Kinematic Hardening: Bridging Microstructure and Continuum Mechanics. Met. Mater. Int. 29, 280–292 (2023). https://doi.org/10.1007/s12540-022-01227-3
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DOI: https://doi.org/10.1007/s12540-022-01227-3