Acoustic harmonic generation from fatigue-generated dislocation substructures in copper single crystals. Apple, T. M., Cantrell, J. H., Amaro, C. M., Mayer, C. R., Yost, W. T., Agnew, S. R., & Howe, J. M. Philosophical Magazine, 93(21):2802–2825, July, 2013.
Acoustic harmonic generation from fatigue-generated dislocation substructures in copper single crystals [link]Paper  doi  abstract   bibtex   
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 .
@article{apple_acoustic_2013,
	title = {Acoustic harmonic generation from fatigue-generated dislocation substructures in copper single crystals},
	volume = {93},
	issn = {1478-6435},
	url = {http://dx.doi.org/10.1080/14786435.2013.789144},
	doi = {10.1080/14786435.2013.789144},
	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 .},
	number = {21},
	urldate = {2016-02-26},
	journal = {Philosophical Magazine},
	author = {Apple, T. M. and Cantrell, J. H. and Amaro, C. M. and Mayer, C. R. and Yost, W. T. and Agnew, S. R. and Howe, J. M.},
	month = jul,
	year = {2013},
	pages = {2802--2825},
	file = {Snapshot:C\:\\Users\\rwk6aw\\AppData\\Roaming\\Zotero\\Zotero\\Profiles\\bavaocl1.default\\zotero\\storage\\464CWJEM\\14786435.2013.html:text/html}
}

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