13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Strain Concentrations in Tensile, Fatigue and Fracture Behaviour Stephen D. Antolovich1*, Ronald W. Armstrong2 1 Schools of Materials Science and Mechanical Engineering, Georgia Tech, Atlanta, GA,30332-0245 USA & School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920 USA 2 Center for Energetic Concepts Development, University of Maryland, College Park, MD 20742 USA * Corresponding author: stevea@gatech.edu. Abstract A critical survey has been made of tensile, fracture, shear banding and fatigue measurements and interpretations reported for different types of materials and test conditions. The mechanical properties of the materials are shown to be largely determined by microscopic plastic strain concentrations which depend on the inhomogeneity of the material microstructure, especially including importantly inhomogeneity of the dislocation substructure. Understanding this inhomogeneity is shown to provide a number of connections between seemingly disparate phenomena. The evolution of the dislocation substructure and its relationship to crystallography and various levels of microstructure are critically important. Professor Cottrell made seminal contributions to understanding the fundamental mechanisms involved in determining such strain concentrations. His work continues to provide clarity and guidance to current research accomplishments. Keywords Pile-ups, Cleavage, PLC, ASB, PSB 1. Introduction An article entitled "Plastic Strain Localizations in Metals: Origins and Consequences" has just been completed for the 2013 publication of the periodical: Progress in Materials Science [1]. The article has provided the basis for us to report in the ICF13 Cottrell Memorial Symposium on a number of important sub-topics on which Alan Cottrell has paved the way forward to modern developments. Four such sub-topics are: (1) The Cottrell virtual work equation for a single-ended dislocation pile-up was first reported in Progress in Metal Physics [2] preceding Cottrell’s seminal book on dislocations [3]; the equation is (1) Where * = stress at blocking obstacle, n = total number of dislocations in pile-up, o = effective applied stress. (2) The Cottrell-Bilby carbon locking of dislocations theory which provided a basis for understanding the Portevin-Le Chatelier (PLC) effect of serrated plastic flow; (3) The Cottrell dislocation crack reaction for understanding cleavage in bcc metals and related materials; and (4) The Cottrell-Hull analysis of slip band intrusions/extrusions for fatigue crack development associated with persistent slip band structures. 2. Deformation Behaviour – Dislocation Pile-ups One of the most important parameters in a vast array of materials is grain size and the effects of grains on deformation, a topic to which Prof. Cottrell has made numerous contributions. His work was followed by the well-known Eshelby, Frank and Nabarro (EFN) analysis for the n – τ0 relationship in the equilibrium equation for the pile-up dislocations spread over a length, L [4]: (2)
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