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Abstract
Dislocations generated during cyclic loading of metals self-organize into substructures that produce substantial changes in the nonlinear response. The nonlinearity is quantified by the material nonlinearity parameter extracted from acoustic harmonic generation measurements. Measurements of
on copper single crystals oriented for single-slip ([1 2 3] loading axis) and fatigued in plastic strain control are compared to calculations of
obtained from the Cantrell model for which measured values of model parameters associated with the substructures are required. Transmission electron microscopy measurements of the volume fractions of veins and persistent slip bands, dislocation loop lengths, dipole heights and the densities of primary and secondary dislocations in the fatigue-generated substructures are obtained for input into the model calculations. The model predictions agree with the values observed experimentally. In particular, the experimental data show an increase in
proportional to
where
is the cumulative plastic strain and m is 0.7 and 0.4, respectively, for acoustic wave propagation along the
and
crystal axes. Such dependence is consistent with the Cantrell model and at variance with models, based on assumed variations in the third-order elastic constants, which predict an exponential dependence on
.
Acknowledgement
This work was supported by NASA Grant No. NNX07AU57A, NASA Langley Research Centre, Hampton, VA.
Notes
1. In this context, microplastic does not denote small permanent deformation. Rather it denotes reversible deformation accommodated by dislocation motion.