Mechanical Behavior Laboratory University of Nevada, Reno


[J51] Zhang, J. and Jiang, Y., 2008, "Constitutive Modeling of Cyclic Plasticity Deformation of a Pure Polycrystalline Copper," International Journal of Plasticity, Vol.24, pp.1890-1915. doi: 10.1016/j.ijplas.2008.02.00

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Paper Abstract

Cyclic plasticity experiments were conducted on a pure polycrystalline copper and the material was found to display significant cyclic hardening and nonproportional hardening. An effort was made to describe the cyclic plasticity behavior of the material. The model is based on the framework using a yield surface together with the Armstrong-Frederick type kinematic hardening rule. No isotropic hardening is considered and the yield stress is assumed to be a constant. The backstress is decomposed into additive parts with each part following the Armstrong-Frederick type hardening rule. A memory surface in the plastic strain space is used to account for the strain range effect. The Tanaka fourth order tensor is used to characterize nonproportional loading. A set of material parameters in the hardening rules are related to the strain memory surface size and they are used to capture the strain range effect and the dependence of cyclic hardening and nonproportional hardening on the loading magnitude. The constitutive model can describe well the transient behavior during cyclic hardening and nonproportional hardening of the polycrystalline copper. Modeling of long-term ratcheting deformation is a difficult task and further investigations are required.


Paper Figures

Fig. 1

Fig. 1. Stress range-plastic strain range curve used to determine c(i) and r(i) (Download data).

Fig. 2

Fig. 2. Variation of the saturated values of r(i) (i = 1, 2, ... , M) with the saturated plastic strain amplitude. (Download data).

Fig. 3

Fig. 3. Relationship between c(q) and q in Eq. (27) (Download data).

Fig. 4

Fig. 4. Comparison of hysteresis loops after saturation (Download data).

Fig. 5

Fig. 5. Cyclic stress-strain curves under tension-compression and nonproportional loading (Download data).

Fig. 6

Fig. 6. Cyclic hardening curves under tension-compression (Download data).

Fig. 7

Fig. 7. Nonproportional loading: (a) experimentally applied strain-controlled loading path; (b) experimentally measured stress response; (c) predicted stress response (Download data).

Fig. 8

Fig. 8. Cyclic hardening curve under 90 degree out-of-phase nonproportional loading (Download data).

Fig. 9

Fig. 9. Experimental data and simulation results for a three-step block loading history (Download data).

Fig. 10

Fig. 10. High-low sequence uniaxial loading (Download data).

Fig. 11

Fig. 11. Variation of the equivalent stress magnitude with the number of loading cycles when the loading mode is changed from nonproportional loading to proportional loading (Download data).

Fig. 12

Fig. 12. Experimental ratcheting deformation results of polycrystalline copper under uniaxal loading with a mean stress (Δ σ/2 = 84 MPa, Δm = 15 MPa) (Download data).

Fig. 13

Fig. 13. Variation of ratcheting strain with the number of loading cycles (Download data).

Fig. 14

Fig. 14. Variation of ratcheting rate with the number of loading cycles (Download data).