In engineering, materials are often assumed to be homogeneous and isotropic; in actuality, material properties do change with sample direction and location. This variation is due to the anisotropy of the individual grains and their spatial distribution in the material. Currently there is a lack of communication between the design engineer, material scientist, and processor for solving multi-objective/constrained designs. If communication existed between these groups then materials could be designed for applications, instead of the reverse. Microstructure sensitive design introduces a common language, a spectral representation, where both design properties and microstructures are expressed. Using Hill bounds, effective elastic properties are expressed within the spectral representation. For the elastic properties, two FCC materials, copper and nickel, were chosen for computation and to demonstrate how symmetry enters into the methodology. This spectral representation renders properties as hyper-surfaces that translate through a multi-dimensional Fourier space depending on the property value of the hyper-surface. Property closures are generated by condensing the information contained within the multi-dimensional Fourier space into a 2-D representation. This compaction of information is beneficial for a quick determination of property limits for a particular alloy system. The design engineer can now dictate the critical design properties and receive sets of microstructures that satisfy the design objectives.

Texture evolution is a vital component of many computational tools that link structure, properties and processes of polycrystalline materials. By definition, this evolution process involves the manipulation, via rotation, of points in orientation space. The computational requirements of the current methods being used to rotate crystalline orientations are a significant limiting factor in the drive to merge the texture information of materials into the engineering design process. The goal of this research is to find and implement a practical rotation algorithm that can significantly decrease the computation time required to rotate macroscopic and microscopic crystallographic textures. Three possible algorithms are considered in an effort to improve the computational efficiency and speed of the rotation process. The first method, which will be referred to as the Gel'fand method, is based on a paper, [1], that suggests a practical application of some of Gel'fand's theories for rotations [2]. The second method, which will be known as the streamline method, is a variation on the Gel'fand method. The third method will be known as the principal orientation method. In this method, orientations in Fourier space are written as linear combinations of points on the convex surface of the microstructure hull to reduce the number of points that must be rotated during each step in the texture evolution process. This thesis will discuss each of these methods, their strengths and weaknesses, and the accuracy of the computational results obtained from their implementation.

Reverse engineering - defined as extracting information about a product from the product itself - is a design tactic commonly used in industry from competitive benchmarking to product imitation. While reverse engineering is a legitimate practice - as long as the product was legally obtained - innovative products are often reverse engineered at the expense of the pioneering company. However, by designing products with built-in barriers to reverse engineering, competitors are no longer able to effectively extract critical information from the product of interest. Enabling the quantification of barriers to reverse engineering, this dissertation presents a set of metrics and parameters that can be used to calculate the barrier to reverse engineer any product as well as the time required to do so. To the original designer, these numerical representations of the barrier and time can be used to strategically identify and improve product characteristics so as to increase the difficulty and time to reverse engineer them. On the other hand, these quantitative measures enable competitors who reverse engineer original designs to focus their efforts on products that will result in the greatest return on investment. In addition to metrics that estimate the reverse engineering barrier and time, this dissertation also presents a methodology to strategically plan for, select, design, and implement reverse engineering barriers. The methodology presented herein considers barrier development cost, barrier effectiveness in various product components, impact on performance, and return on investment. This process includes sensitivity analysis, modeling of the return on investment, and exploration of multiobjective design spaces. The effectiveness of the presented methodology is demonstrated by making a solar-powered unmanned aerial vehicle difficult to reverse engineer. In the example, the propeller is selected to be the critical component where a series of voids are introduced to decrease the propeller weight and increase the flutter speed (a desirable attribute in propellers). Our tenet is that the use of such a framework contributes greatly to the sustainability of technological, economical, and security advantages enjoyed by those who developed the technology. Designers benefit because (i) products do not readily disclose trade secrets, (ii) competitive advantages can be maintained by impeding competitors from reverse engineering and imitating innovative products, and (iii) the return on investment can be increased.

Establishing process-structure-property relationships is an important objective in the paradigm of materials design in order to reduce the time and cost needed to develop new materials. A method to link phase field (process-structure relations) and microstructure-sensitive finite element (structure-property relations) modeling is demonstrated for subsolvus polycrystalline IN100. A three-dimensional (3D) experimental dataset obtained by orientation imaging microscopy performed on serial sections is utilized to calibrate a phase field model and to calculate inputs for a finite element analysis. Simulated annealing of the dataset realized through phase field modeling results in a range of coarsened microstructures with varying grain size distributions that are each input into the finite element model. A rate dependent crystal plasticity constitutive model that captures the first order effects of grain size, precipitate size, and precipitate volume fraction on the mechanical response of IN100 at 650°C is used to simulate stress-strain behavior of the coarsened polycrystals. Model limitations and ideas for future work are discussed.

In this research, the homogenization relations for elastic properties in isotropic and anisotropic materials are studied by applying two-point statistical functions to composite and polycrystalline materials. The validity of the results is investigated by direct comparison with experimental results. In todays technology, where advanced processing methods can provide materials with a variety of morphologies and features in different scales, a methodology to link property to microstructure is necessary to develop a framework for material design. Statistical distribution functions are commonly used for the representation of microstructures and also for homogenization of materials properties. The use of two-point statistics allows the materials designer to consider morphology and distribution in addition to properties of individual phases and components in the design space. This work is focused on studying the effect of anisotropy on the homogenization technique based on two-point statistics. The contribution of one-point and two-point statistics in the calculation of elastic properties of isotropic and anisotropic composites and textured polycrystalline materials will be investigated. For this purpose, an isotropic and anisotropic composite is simulated and an empirical form of the two-point probability functions are used which allows the construction of a composite Hull. The homogenization technique is also applied to two samples of Al-SiC composite that were fabricated through extrusion with two different particle size ratios (PSR). To validate the applied methodology, the elastic properties of the composites are measured by Ultrasonic methods. This methodology is then extended to completely random and textured polycrystalline materials with hexagonal crystal symmetry and the effect of cold rolling on the annealing texture of near- Titanium alloy are presented.

The methods of MSD are applied to the design of functionally graded materials. Analysis models are presented to allow the design of compliant derailleur for a case study and constraints are placed on the design. Several methods are presented for relating elements of the microstructure to the properties of the material, including Taylor yield theory, Hill elastic bounds, and precipitation hardening. Applying n-point statistics to the MSD framework is also discussed. Some results are presented for the information content of the 2-point correlation statistics that follow from the methods used to integrate functionally graded materials into MSD. For the compliant beam case study, the best design (98%Al-2%Li) was a 97% improvement over the worst (100%Al). The improvements were primarily due to the precipitation hardening, although anisotropy also significantly impacted the design. Under the constraints for the design, allowing the beam to be functionally graded had little effect on the overall design, unless there was significant stiffening occurring along with particulate formation.