Functionally Graded Materials are the material systems whose properties vary spatially through the solid. These material systems are fairly new and though expensive to fabricate; they serve as excellent engineering materials for various applications. The material system we consider in this work is a metal- ceramic system, which can easily substitute for heat shielding tiles on the reentry space vehicles replacing the conventional ceramic tiles. This system while providing a structurally and thermally excellent heat shielding also reduces the weight penalty by introducing metal in the system without compromising on the strength. In this thesis we study the behavior and characteristics of the FGM in terms of fractals. There has been no prior literature on linking FGM and fractals. We characterize the interfaces between the two- phase FGM using fractals and estimate an interfacial fractal dimension for varying degrees of coarseness. Also, the variation in local fractal dimension as we move lengthwise (left to right) in the domain is characterized by a Fourier fit, and a simpler relation using a Beta function. Assuming an isotropic nature of both Titanium and Titanium Monoboride (TiB), pure shear tests are simulated using ABAQUS for coarseness level of 50, 100 and 200 under the Uniform Kinematic Boundary Condition (UKBC) and the Uniform Static Boundary Condition (USBC). The material response observed under both these BC???s shows a high sensitivity of these systems to loading conditions. Furthermore, plastic evolution of Titanium grains assuming isotropic plastic hardening shows fractal plane filling behavior. Fractal dimensions of sets of plastic grains are calculated using the box counting method, and it validates our mechanical results, thus again showing high sensitivity of this material system to loading conditions.
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