Substructural organization, dislocation plasticity and harmonic generation in cyclically stressed wavy slip metals

Organized substructural arrangements of dislocations formed in wavy slip, face–centred–cubic metals during cyclic stress–induced fatigue are shown analytically to engender a substantial nonlinearity in the microelastic–plastic deformation resulting from an impressed stress perturbation. The non–Hookean stress–strain relationship is quantified by a material nonlinearity parameter βthat for a given fatigue state is highly sensitive to the volume fractions of veins and persistent slip bands (PSBs), PSB internal stresses, dislocation multipole configurations, dislocation loop lengths, dipole heights and the densities of secondary dislocations in the substructures. The effects on β of vacancy, microcrack and macrocrack formation are also addressed. The connection between β and acoustic harmonic generation is obtained. The model is applied to calculations of β for fatigued polycrystalline nickel as a function of per cent life to fracture. For cyclic stress–controlled loading at 241 MPa, the model predicts a monotonic increase in β of ca. 360% over the fatigue life. For strain–controlled loading at a total strain of 1.75 × 10−3, a monotonic increase in β of ca. 375% over the fatigue life is predicted.