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Modeling and characterization of cyclic relaxation and ratcheting using the distributed-element model. (English) Zbl 1388.74119

Summary: Constitutive modeling of cyclic relaxation and ratcheting (cumulative inelastic deformation) is developed on the basis of the distributed-element model (DEM). Although the original DEM is capable of describing general, elastic-plastic behavior for cyclically stabilized materials, it has the inadequacy of not being able to account for the effect of cyclic relaxation and ratcheting. By introducing the nonlinear kinematic hardening rule proposed by Armstrong and Frederick into element behavior of the DEM, the model becomes effective in characterizing the behavior of cyclic relaxation and ratcheting. Validation of the modified DEM is conducted by simulating cyclic behavior of various metal materials, including CS 1018, heat-treated rail steel, and Grade 60 steel. The results show that the modified DEM demonstrates realistic behavior of materials in both uniaxial and biaxial cyclic relaxation and ratcheting. Furthermore, detailed investigation of element behavior in the model provides us with additional insight into complex behavior and characteristics of materials in cyclic relaxation and ratcheting.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
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[1] Kyriakides, S.; Shaw, P. K., Inelastic buckling of tubes under cyclic bending, ASME J. Pressure Vessel Technol., 109, 169-178 (1987)
[2] Pan, W. F.; Her, Y. S., Viscoplastic collapse of thin-walled tubes under cyclic bending, ASME J. Eng. Mater. Technol., 120, 287-290 (1998)
[3] L Chaboche, J., Constitutive equations for cyclic plasticity and cyclic viscoplasticity, Int. J. Plasticity, 5, 246-302 (1989) · Zbl 0695.73001
[4] Estrin, Y.; Braasch, H.; Brechet, Y., A dislocation density based constitutive model for cyclic deformation, ASME J. Eng. Mater. Technol., 118, 4, 441-447 (1996)
[5] Portier, L.; Calloch, S.; Marquis, D.; Geyer, P., Ratchetting under tension-torsion loadings: experiments and modeling, Int. J. Plasticity, 16, 303-335 (2000) · Zbl 0948.74502
[6] Bari, S.; Hassan, T., An advancement in cyclic plasticity modeling for multiaxial ratcheting simulation, Int. J. Plasticity, 18, 873-894 (2002) · Zbl 1050.74010
[7] Bari, S.; Hassan, T., Kinematic hardening rules in uncoupled modeling for multiaxial ratcheting simulation, Int. J. Plasticity, 17, 885-905 (2001) · Zbl 1059.74013
[8] Bari, S.; Hassan, T., Anatomy of coupled constitutive models for ratcheting simulation, Int. J. Plasticity, 16, 381-409 (2000) · Zbl 1004.74020
[9] Moosbrugger, J. C., Some developments in the characterization of material hardening and rate sensitivity for cyclic viscoplasticity models, Int. J. Plasticity, 7, 405-419 (1991)
[10] McDowell, D. L., Stress state dependence of cyclic ratcheting behavior of two rails steels, Int. J. Plasticity, 11, 4, 397-421 (1995)
[11] P.J. Armstrong, C.O. Frederick, A mathematical representation of multiaxial Bauschinger effect, G.E.G.B. Report RD/B/N 731, 1966.; P.J. Armstrong, C.O. Frederick, A mathematical representation of multiaxial Bauschinger effect, G.E.G.B. Report RD/B/N 731, 1966.
[12] Bower, A. F., Cyclic hardening properties of hard-drawn copper and rail steel, J. Mech. Phys. Solids, 37, 4, 455-470 (1989)
[13] Prager, W., The theory of plasticity – a survey of recent achievements, Proc. Inst. Mech. Eng., London, 169, 41-57 (1955)
[14] Ziegler, H., A modification of Prager’s hardening rule, Quart. Appl. Math., 17, 55-65 (1958) · Zbl 0086.18704
[15] Mroz, Z., On the description of anisotropic workhardening, J. Mech. Phys. Solids, 15, 163-175 (1967)
[16] Chaboche, J. L.; Rousselier, G., On the plastic and viscoplastic constitutive equations – part I: rules developed with internal variable concept, ASME J. Pressure Vessel Technol., 105, 153-158 (1983)
[17] Chaboche, J. L.; Nouailhas, D., Constitutive modeling of ratcheting effects, ASME J. Eng. Mater. Technol., 111, 3, 384-389 (1989)
[18] Chaboche, J. L., On some modification of kinematic hardening to improve the description of ratchetting effects, Int. J. Plasticity, 7, 661-678 (1991)
[19] Ohno, N.; Wang, J. D., Transformation of a nonlinear kinematic hardening rule to a multi-surface form under isothermal and nonisothermal conditions, Int. J. Plasticity, 7, 879-892 (1991) · Zbl 0755.73043
[20] Chiang, D. Y.; Beck, J. L., A new class of distributed-element models for cyclic plasticity - I. theory and applications, Int. J. Solids Struct., 31, 4, 469-484 (1994) · Zbl 0790.73026
[21] Chiang, D. Y.; Beck, J. L., A new class of distributed-element models for cyclic plasticity - II. on important properties of material behavior, Int. J. Solids Struct., 31, 4, 485-496 (1994) · Zbl 0790.73026
[22] Chiang, D. Y., A phenomenological model for cyclic plasticity, ASME J. Eng. Mater. Technol., 119, 1, 7-11 (1997)
[23] Iwan, W. D., On a class of models for the yielding of continuous and composite system, ASME J. Appl. Mech., 34, 3, 612-617 (1967)
[24] Besseling, J. F., A theory of elastic, plastic and creep deformation of an initially isotropic material showing strain hardening, creep recovery, and secondary creep, ASME J. Appl. Mech., 25, 529-536 (1958) · Zbl 0084.20501
[25] Meijers, P.; Roode, F., Experimental verification of constitutive equations for creep and plasticity based on overlay models, ASME J. Pressure Vessel Technol., 105, 277-284 (1983)
[26] Chiang, D. Y., Modeling and identification of elastic-plastic systems using the distributed-element model, ASME J. Eng. Mater. Technol., 119, 4, 332-336 (1997)
[27] H.R. Jhansale, T.H. Topper, Engineering analysis of the inelastic stress response of structure metal under variable cyclic strains, in: ASTM STP 519, Cyclic Stress-Strain Behavior-Analysis, Experimentation, and Failure Prediction, 1973, pp. 246-270.; H.R. Jhansale, T.H. Topper, Engineering analysis of the inelastic stress response of structure metal under variable cyclic strains, in: ASTM STP 519, Cyclic Stress-Strain Behavior-Analysis, Experimentation, and Failure Prediction, 1973, pp. 246-270.
[28] Jackson, P. J., The mechanisms of plastic relaxation in single-crystal deformation, Mater. Sci. Eng., 81, 169-178 (1986)
[29] Doong, S.-H.; Socie, D. F.; Robertson, I. M., Dislocation substructures and nonproportional hardening, ASME J. Eng. Mater. Technol., 112, 4, 456-463 (1990)
[30] Kuhlmann-Wilsdorf, D., Theory of plastic deformation properties of low energy dislocation structures, Mater. Sci. Eng. A, 113, 1-41 (1989)
[31] Khan, A. S.; Huang, S., Continuum Theory of Plasticity (1995), John Wiley and Sons, (Chapter 6) · Zbl 0856.73002
[32] Dafalias, Y. F.; Popov, E. P., Plastic internal variables formalism of cyclic plasticity, ASME J. Appl. Mech., 43, 645-651 (1976) · Zbl 0351.73048
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