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.

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