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This thesis provides a report on the numerical analysis of stress distributions within granular materials held in silos and hoppers. Stress distributions within granular materials stored in silos and hoppers have been the subject of research for over 100 years, work starting in this field in 1895 (Janssen). Knowledge of stress distributions within the granular materials contained is essential to allow structural design of the silo and hopper shell and attachments, and to allow estimation of likelihood and location of cohesive arch formation. National design codes for silos and hoppers (including BS EN 1993-4-1:2007 Eurocode 3 and DIN 1055-6:2005-03) are based on approximate techniques that assume vertical and horizontal directions of principal stresses, with constant horizontal stress across the silos. According to the knowledge of the author there are no industrial standards that allow calculation of loading on inserts within hoppers. The objective of the research project is to develop algorithms to predict stresses in hoppers and silos using principal stress arc geometry methods, and implementation of these methods in various silo and hopper configurations including those with inserts for the purposes of aiding flow. The research project algorithms are spreadsheet- and QB64 platform-based, and are able to produce stress distributions within silos and hoppers. This is achieved by extension of the principal stress arc method of analysis. The new algorithms allow prediction of common flow problems and provide new information on structural loading of silos and hoppers, including inserts used to promote flow. The research project models allow estimation of azimuthal stresses within three-dimensional case studies.

Abstract: In this work, rapid solidification microstructures and mechanical properties of Al1.5Mg0.2Sc and Al3Mg0.2Sc are investigated. Samples in the form of powders and strips / deposits of different thermal histories are obtained by means of impulse atomization technique. Cooling rates of the powders, varying from 300K/s to 900K/s within the investigated size range, are estimated using a thermal model of a solidifying droplet in a stagnant gas. Whereas cooling rates of the strips are measured by a two-color pyrometer at the strip-substrate interface and is found to average 1.7K/s. The effects of Mg content, cooling rate and melt superheat on the scale of microstructures and mechanical properties are investigated. The role of Sc is also analyzed. The increase in Mg content and cooling rate are found to yield finer microstructures. For both powders and strips, a reduction in cell spacing is found to have limited impacts on microhardness. However, increasing Mg content (from 1.5wt% to 3wt %) is found to have a strengthening effect estimated by a hardness value of about 20 HV0.1. While cell spacing of the powders is found to increase with melt superheat, no noticeable difference in cell spacing or microhardness is observed. The effects of heat treatment on mechanical properties is also investigated. Aging of the as-atomized powders and strips are carried out at 300 °C for up to 2 hours in a DSC. Microhardness is measured on both as-atomized and aged samples. Maximum hardness is reached for both powders and strips after 2 hours of aging. For both alloy compositions compositions, a hardness increase of 40 HV0.1 is obtained. From DSC results and phase diagram, Sc precipitation is found to be responsible for the aging response. Compared with published industrial data on cooling rate, cell spacing, and response to aging, the combinations of the impulse atomization and impulse atomization with spray deposition exhibit the possibility of being used as a small scale platform for novel alloys testing and development for industrialized rapid solidification processes, such as twin-belt strip casting process.