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Kinking nonlinear elastic solids: theory and experiments
Dissertation   Open access

Kinking nonlinear elastic solids: theory and experiments

Aiguo Zhou
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2008
DOI:
https://doi.org/10.17918/etd-2804
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Abstract

Elastic solids Metals Materials Science
Recently it was postulated that most, if not all, plastically anisotropic solids can be classified as kinking nonlinear elastic (KNE) solids because their response to stress is nonlinear and fully reversible. Furthermore it was proposed that the large mechanical hysteresis observed was due to the fully reversible growth and shrinkage of incipient kink bands (IKBs). IKBs, the precursors of regular kink bands, are comprised of parallel dislocation loops, confined to two dimensions that remain extended if a load is applied and disappear if the load is removed. The stress-strain curves of KNE solids can be described by 4 parameters: stress, nonlinear strain, stored nonlinear energy and dissipated energy per unit volume per cycle. In this dissertation an IKB-based microscale model is proposed to relate the four parameters. Remarkable agreement between model and experiment is achieved. The model is so powerful that a decent picture of the size, densities and distribution of the dislocations that nucleate during the reversible loops emerges. Most important, the critical resolved shear stress of the IKB dislocations is obtainable from a simple compression experiment on a polycrystalline solid. The model was tested on select MAX phases (Ti₃SiC₂, Ti₂AlC and some of their solids solutions) and the hexagonal metals (Ti, Mg, Co). All the experimental results, and some literature results, were shown to agree quite well with theoretical prediction. The model not only quantifies mechanical damping but also elucidates the nature of microyielding in a variety of solids, including the hexagonal metals. The nature of damping and microyielding in hexagonal metals were to date not fully understood or misunderstood for a long time. The phenomenological Preisach-Mayergoyz model was also applied to KNE solids. From the model, the stress distributions needed to nucleate and grow the hysteretic elements - viz. the IKBs - was determined. Once determined, this distribution can then be used to predict the response of these materials to any stress history. Based on this work there is little doubt that incipient kink bands constitute one of the last pieces in the deformation-of-solids puzzle, without which much of their early deformation cannot be understood.

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