Continuum Mechanics-Discrete Defect Modeling and Bubble Raft Simulation of Cracked Specimen Response in Nanoscale Geomet
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Continuum Mechanics-Discrete Defect Modeling and Bubble Raft Simulation of Cracked Specimen Response in Nanoscale Geometries Michael J. Starr1, Walter J. Drugan2†, Maria d. C. Lopez-Garcia3, and Donald S. Stone2‡ 1 Structural Dynamics Research Department, Sandia National Laboratories, Albuquerque, NM 87185-0847, U.S.A. 2 Mechanics and Materials Program, University of Wisconsin-Madison, Madison, WI 53706, U.S.A. † Department of Engineering Physics ‡Materials Science and Engineering 3 Department of Chemical Engineering, University of Puerto Rico-Mayaguez, Mayaguez, P.R. ABSTRACT In a continuation of prior work, a new group of Bragg bubble model experiments have been performed to explore the effects of nanoscale crack size and nanoscale structural geometry on atomically-sharp crack tip dislocation emission behavior. The experiments have been designed to correspond to the theoretical limits that bound the expected crack tip response. Continuum elasticity analyses of these situations have also been carried out, in which the leading-order terms in the Williams expansion (the K and T terms) are determined, and the predictions of these continuum analyses coupled with discrete dislocation theory are compared with the experimental results. The experiments exhibit fascinating changes in crack tip dislocation emission direction with changing crack and structural size, crack location and loading conditions, as well as substantial changes in the magnitude of the resolved shear stress that drives dislocation emission. These changes are predicted well by the continuum elasticity-discrete dislocation model down to extremely small dimensions, on the order of a few atomic spacings. Preliminary experiments were performed with layered and two-atom basis rafts to establish crucial comparisons between theory and experiment that validate the applicability of continuum elasticity theory to make predictions directly related to nanoscale fracture behavior. INTRODUCTION The nominal fracture response of a cracked material can be considered to be a competition between cleavage crack growth and the spontaneous emission of blunting dislocations [1]. With nanoscale multilayered geometries this framework indicates potential length-scale-induced material transitions due to high densities of physical boundaries. Novel multilayered structures therefore may exhibit transitional behaviors, through the modification of strength and fracture toughness, that are not experienced on larger scales. An alternative to discrete lattice calculations, proceeding ab initio from quantum mechanics, is the bubble model introduced by Bragg and Nye [2]. The nominal material behavior of the bubble model has been established through the calculation of inter-bubble potential and force law, and is shown to appropriately capture the short-range response of atomic interaction in close-packed materials, most notably copper [3, 4]. The bubble interaction characteristics have made it an attractive means of simulating microscopic phenomena [5-7]. Recently, a study was perfo
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