Issue 33

M.A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 33 (2015) 357-367; DOI: 10.3221/IGF-ESIS.33.39 366 C ONCLUSIONS n this work, it is concluded that the Mróz-Garud multi-surface formulation can lead to very poor multiaxial stress- strain predictions in the presence of significant mean stresses, severely limiting their application in multiaxial fatigue analysis. The two-surface model better accounts for unbalanced loadings, however its application is mostly recommended for monotonic plastic processes, since it does not appropriately deal with complex variable amplitude loading histories, with decreasing amplitudes and several layers of hysteresis loops within loops, which are very common under spectrum loading. On the other hand, NLK models can accurately deal with non-proportional loadings, either balanced or unbalanced. Moreover, contrary to two-surface models, they deal with complex variable amplitude spectrum loading, as long as a sufficiently high number of backstress components (i.e. number of hardening surfaces) is adopted in a refined NLK formulation, to efficiently store plastic memory effects. Therefore, this analysis shows that NLK models should be preferred over multi-surface and two-surface models in multiaxial fatigue calculations under variable amplitude loading. R EFERENCES [1] Mróz, Z. On the description of anisotropic workhardening, J Mech Phys Solids, 15(3) (1967) 163-175. [2] Garud, Y.S., A new approach to the evaluation of fatigue under multiaxial loading, J Eng Mater Tech, 103 (1981) 118-125, [3] Jiang, Y.; Sehitoglu, H., Comments on the Mróz multiple surface type plasticity models, Int J Solids Struct, 33 (1996) 1053- 1068. [4] Armstrong, P.J., Frederick, C.O., A mathematical representation of the multiaxial Bauschinger effect. CEGB Report RD/B/N731, Berkeley Nuclear Laboratory, (1966). [5] Chaboche, J.L., Dang Van, K., Cordier,G. Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. Transactions 5 th Int Conf Struct Mech Reactor Technology, Div. L, Berlin, (1979). [6] Prager, W., Recent developments in the mathematical theory of plasticity, J Appl Phys, 20 (1949) 235-241. [7] Ziegler, H., A modification of Prager’s hardening rule, Appl Math, 17 (1959) 55-65. [8] Bari, S., Hassan, T., Kinematic hardening rules in uncoupled modeling for multiaxial ratcheting simulation, Int J Plasticity 17 (2001) 885-905. [9] Jiang, Y., Kurath, P. Characteristics of the Armstrong-Frederick type plasticity models, Int J Plasticity, 12 (1996) 387-415. [10] Ohno, N., Wang, J.D., Transformation of a nonlinear kinematic hardening rule to a multisurface form under isothermal and non-isothermal conditions, Int J Plasticity, 7 (1991) 879-891. [11] Meggiolaro, M.A., Castro, J.T.P., Wu, H., A general class of non-linear kinematic models to predict mean stress relaxation and multiaxial ratcheting in fatigue problems, In: Int Conf Fatigue Damage Struct Mater X, Hyannis, MA, (2014). [12] Chaboche, J.L., Rousselier, G., On the plastic and viscoplastic constitutive equations - part I: rules developed with internal variable concept. J Press Vess-T ASME, 105 (1983) 153-158. [13] Burlet, H., Cailletaud, G., Numerical techniques for cyclic plasticity at variable temperature. Eng Computation, 3 (1986) 143-153. [14] Ohno, N., Wang, J.D., Kinematic hardening rules with critical state of dynamic recovery, part I: formulations and basic features for ratchetting behavior, Int J Plasticity, 9 (1993) 375-390. [15] Ohno, N., Wang, J.D., Kinematic hardening rules with critical state of dynamic recovery, Part II: application to experiments of ratchetting behavior, Int J Plasticity, 9 (1993) 391-403. [16] Delobelle, P., Robinet, P., Bocher, L., Experimental study and phenomenological modelization of ratchet under uniaxial and biaxial loading on an austenitic stainless steel, Int J Plasticity, 11 (1995) 295-330. [17] Jiang, Y., Sehitoglu, H., Modeling of cyclic ratchetting plasticity, part I: development of constitutive relations. J Appl Mech- T ASME, 63 (1996) 720-725. [18] Jiang, Y., Sehitoglu, H., Modeling of cyclic ratchetting plasticity, part II: comparison of model simulations with experiments. J Appl Mech-T ASME, 63 (1996) 726-733. [19] Chen, X., Jiao, R., Modified kinematic hardening rule for multiaxial ratcheting prediction, Int J Plasticity, 20 (2004) 871-898. [20] Chen, X., Jiao, R., Kim, K.S., On the Ohno-Wang kinematic hardening rules for multiaxial ratcheting modeling of medium carbon steel, Int J Plasticity, 21 (2005) 161-184. [21] Dafalias,Y.F., Popov, E.P., Plastic internal variables formalism of cyclic plasticity, J Appl Mech-T ASME, 43 (1976) 645- 651. [22] Krieg, R.D., A practical two-surface plasticity theory, J Appl Mech-T ASME, 42 (1975) 641-646. I