The dislocation substructures created in 1100 aluminum, OFHC copper, and type 304 and 310 stainless steels by in-phase (proportional) and 90 deg out-of-phase (nonproportional) tension-torsion cyclic loading were examined with a transmission electron microscope. Multislip structures (cells and subgrains) are observed in aluminum under both in-phase and 90 deg out-of-phase tension-torsion loading. For copper and stainless steel, single-slip structures (planar dislocations, matrix veins, and ladders) are observed after proportional loading, whereas multislip structures (cells and labyrinths) are observed after nonproportional loading. The increased cyclic hardening of copper and stainless steels under nonproportional loading is attributed to the change of dislocation substructures. Based on these observations, formulation of a nonproportionality parameter for constitutive modeling is discussed.
A two-surface kinematic hardening model for the stress-strain response of metals under nonproportional tension-torsion cyclic loading is developed and verified with critical experiments. In this model, both the yield and limit surfaces are assumed to be ellipses in the two-dimensional stress plane to account for anisotropic cyclic hardening. Areas of the yield and limit surfaces are changed in order to model the overall isotropic cyclic hardening (or softening) behavior. The strength anisotropy is modeled by changing the ellipticity and orientation of the elliptical surfaces with respect to the stress axes. A nonproportionality parameter based on the plastic strain history is developed to estimate the cyclic hardening level under nonproportional loading. It is shown that this model is able to model a number of important deformation features of metals under complex nonproportional cyclic loading.
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