In this thesis, investigations into the suitability of three 'weak-link' models, designed for the simulation of superconducting cluster systems, are reported. The focus of the investigation is on both the accuracy of the transport properties produced by these models, and the time taken to produce their results. The thesis develops the theory behind a previous approach which was exclusively used to model percolation systems for coverages below the critical coverage. The modifications made allow the simulations to extend to system coverages above the critical coverage. An additional 'current-ramping' algorithm, to simulate the systematic increase or decrease of current forced through the system, is described and explored. The results for the three models are compared, and their suitability for future investigations is discussed.

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The effects of pore density and distribution were investigated on the fatigue crack initiation behavior in an A713 sand cast aluminum alloy plate of 12 mm thickness. The applied stress- the number of cycles to failure (S-N) curves of the samples taken from 2 mm and 5 mm from the free surface were obtained using four-point bend fatigue testing at room temperature, frequency of 20 Hz, stress ratio of 0.1, sinusoidal waveform, and in ambient air. The fatigue strengths of both, the 2 mm and 5 mm samples were 60% of the yield strength (σy=171.9 MPa) of the alloy. Optical microscopy, SEM, and EDS mapping were used to characterize pores and particles in 2 mm and 5 mm samples. The average pore sizes of the 2 mm and 5 mm samples were measured to be 10 to 14 μm, and 14 to 32 μm, respectively. The pore number densities in 5 mm and 2 mm samples were comparable, but higher number densities of non-clustered coarse pores (gas pores) were observed in 5 mm samples. The crack population found after fatigue testing showed a Weibull function of stress level. The peaks of strength distributions of fatigue weak link density of 5 mm and 2 mm samples were measured to be 0.017 mm-2 at 67.6 % σy, and 0.01027 mm-2 at 69.5% σy. Crack populations, when normalized by number densities of gas pores (non-clustered) and number densities of shrinkage pores (clustered), giving crack nucleation rate (crack/pore, mm-2), showed a good fit with the Weibull function in 2 mm and 5 mm samples. Shrinkage and gas pores could both become the main crack initiation sites (i.e. fatigue weak links) in this alloy. Higher nucleation rates of gas pores and shrinkage pores were observed in 5 mm samples compared to those rates in 2 mm samples. At high applied stresses, the 2 mm samples showed better fatigue lives than those of 5 mm samples. Fractured surfaces were analyzed using SEM and found that the main crack initiation were predominately from pores. The pores on the fractured surfaces were counted and their depth and width were measured. It was found that the cracks may not necessarily initiate from coarse pores, but sometimes from shrinkage pores (i.e. group of pores). The depth from the free surface, the width, the size, and the orientation of pores are key factors in increasing the driving force for crack initiation and subsequently those pores turn into long cracks. Moreover, the aspect ratios of pores on the main cracks were measured and found that in 5 mm samples, some pores have an aspect ratios of less than 0.7, which means that these pores are elongated in depth and have a narrow width which increase the stress concentration on the surface, thus, increasing the driving force for crack nucleation.