A substructure mixtures model for the cyclic plasticity of single slip oriented nickel single crystal at low plastic strain amplitudes

The cyclic plasticity behavior of nickel single crystals oriented for single slip is characterized by uniaxial, symmetric, tension–compression, strain controlled tests carried out at constant plastic strain amplitudes ranging from 5(10−5) to 1(10−3). Annealed single crystals are cycled in this manner to post-cyclic saturation and microstructural characterizations, including transmission electron microscopy and optical micrographs of specimen surface replicas are used to verify and evaluate dislocation substructures. Stress–strain and microstructure data are used to construct a mixtures model that couples cyclic plasticity models for three substructures as well as a model for reverse magnetostriction (Villari effect) that is a significant component of inelastic strain at the lower plastic strain amplitudes. The model is used to correlate the stress–plastic strain hysteresis loop responses over the range of plastic strain amplitudes and from cumulative plastic strains from 0.3 to post-cyclic saturation. Complex evolution of substructure plastic strain amplitudes toward their so-called intrinsic values upon the formation of persistent slip bands is modeled. Additionally, bulk Young’s modulus is found to vary significantly with plastic strain amplitude and cumulative plastic strain. A correlation of this behavior is included.