Micro-Structural Evolution and Size-Effects in Plastically Deformed Single Crystals: Strain Gradient Continuum Modeling

Salim Abdallah El-Naaman

Research output: Book/ReportPh.D. thesis

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An extensive amount of research has been devoted to the development of micro-mechanics based gradient plasticity continuum theories, which are necessary for modeling micron-scale plasticity when large spatial gradients of plastic strain appear. While many models have proven successful in capturing the macroscopic effects related to strain gradients, most predict smooth micro-structures. The evolution of dislocation micro-structures, during plastic straining of ductile crystalline materials, is highly complex and nonuniform. Published experimental measurements on deformed metal crystals show distinct pattern formation, in which dislocations, of the geometrically necessary kind, are arranged in wall and cell structures. This particular subset of signed dislocations, which have a net Burg-ers vector, are the main source for the observed size-effects and are directly linked to the gradients in plastic strain. It is clear that many challenges are associated with modeling dislocation structures, within a framework based on continuum fields, however, since the strain gradient effects are attributed to the dislocation micro-structure, it is a natural step, in the further development of gradient theories, to focus on their ability to capture realistic micro-structural evolution. This challenge is the main focus of the present thesis, which takes as starting point a non-work conjugate type back stress based higher order crystal plasticity theory. Within this framework, several possibilities for the back stress relation are formulated, based on a postulate of a gradient energy as well as by engaging in a phenomenological approach. Through an extensive numerical investigation, the proposed back stress formulations are shown to offer novel modeling capabilities both in terms of micro-structural predictions but also in terms of capturing complex macroscopic behavior tied to the presence of long range internal stresses. A formulation based on a near linear gradient energy reveals striking similarities to formulations based on discrete dislocation theory, and shows promising capabilities within the adopted higher order theory. Moreover, the present work offers new insight into plane strain modeling of face centered cubic crystals.
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages151
ISBN (Electronic)978-87-7475-465-7
Publication statusPublished - 2016
SeriesDCAMM Special Report


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