The goal of this thesis is to present a comprehensive study of the parabolic and hyperbolic Anderson models with constant initial condition, driven by a Gaussian noise which is fractional in space with index H > 1/2 or H < 1/2, and is either white in time, or fractional in time with index H_0 > 1/2. As a preliminary step, we study the linear stochastic heat and wave equations with the same type of noise. In the case H_0 > 1/2 and H < 1/2, we present a new result, regarding the solution of the parabolic Anderson model with general initial condition given by a measure.

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The automotive industry has become a major user of magnesium components. However, use of magnesium sheet products is quite limited, due to difficulties in producing cost effective components. Any sheet currently produced is formed at elevated temperatures, making magnesium parts relatively expensive. Knowledge of the microstructural effects on magnesium formability will help reduce the cost of these products. In this thesis, the microstructural factors that affect the formability of rolled and extruded magnesium sheet were compared. It was found that the degree of dynamic recrystallization was the factor that controlled elongation. Dynamic recrystallization produced a finer grain size, which resulted in a transition in deformation mechanism from dislocation slip to grain boundary sliding. Digital image correlation was used to study local stresses during tensile deformation, and to determine if magnesium satisfies Considere's criterion before failure. The results indicated that local stresses developed during deformation satisfied Considere's criterion, although the global strains were lower than the theoretical predictions. / Thesis / Master of Applied Science (MASc)

The concept of the Forming Limit Diagram (FLD) has proved to be useful for representing conditions for the onset of sheet necking, and is now a standard tool for characterizing materials in terms of their overall forming behavior. In this study, the M-K approach, in conjunction with Gurson model, is used to calculate FLDs. The influences of mechanical properties, including strain hardening, strain rate sensitivity, as well as the void nucleation, growth and coalescence, on the FLDs are examined. Most sheet metals undergo multiple deformation modes (strain paths) when being formed into complex manufacturing parts. When the strain path is changed in the deformation processing of metal, it's work-hardening and flow strength differs from the monotonic deformation characteristics. As a consequence, sheet metal formability is very sensitive to strain path changes. In this study, the hardening behavior and damage evolution under non-proportional loading paths are investigated. The effect of strain path change on FLDs is studied in detail. FLDs are conventionally constructed in strain space and are very sensitive to strain path changes. Alternatively, many researchers represented formability based on the state of stress rather than the state of strain. They constructed a Forming Limit Stress Diagram (FLSD) by plotting the calculated principal stresses at necking. It was concluded that FLSDs were almost path-independent. In this work, the FLSD has been constructed under non-proportional loading conditions to assess its path dependency when damage effect is included. / Thesis / Master of Applied Science (MASc)

A series of lateral load tests were conducted on assemblies of four, 4 foot long U.S. Steel PS32 (regular strength) and PSX32 (high strength) straight web sheet pile sections. The instrumentation adopted in the testing program was geared toward monitoring the assembly displacements, load transfer characteristics, and interlock response. Average effective E-ratios over three different pressure ranges were computed, interlock force versus pressure relationships were derived, the stress states in the pile webs were examined, and interlock force versus interlock displacement trends were obtained from the resulting data. A total of 12 assemblies were tested, 6 each of the PS32 and PSX32 types. Three tests from each lot of 6 incorporated pretensioning of the assembly prior to application of the lateral pressure; whereas, the remaining tests initiated lateral loading of the assemblies while they were in a slacked state. The results from the tests were generally grouped according to assembly designation (PS32 or PSX32) and type of test (pretensioning or no pretensioning). The tabulation of E-ratios and pile web stresses, and interlock force versus pressure plots revealed consistent relationships among tests in a particular grouping over the 0-30 psi loading range. Interlock force versus interlock displacement trends were physically correct, but provided no conclusive information regarding the response at an interlock connection. / M.S.

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