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In any microstructure analysis and design framework, the choice of material structure representation is fundamental. In the Microstructure Sensitive Design (MSD) approach, the material description is considered to be statistical in nature, and different levels of information are available in a hierarchy of correlation functions. The simplest measure of material structure is in the form of 1-pt statistics, which simply capture the volume fractions of distinct (measurable) local states present in the internal structure of the material. A salient aspect of MSD is that microstructure-property linkages are transformed into an efficient Fourier space, resulting in two main constructs: microstructure hulls and property closures. The primary advantages of the MSD approach lie in its consideration of anisotropy of the properties at the local length scales, exploration of the complete set of relevant microstructures leading to global optima, and invertibility of the microstructure-property relationships. The complete set of theoretically feasible microstructures is captured in the fundamental MSD construct – the microstructure hull. For example, if orientation is considered as the material state at each point in the microstructure then in the 1-pt world, the microstructure hull is simply the space of all possible textures, sometimes known as the texture hull. The texture hull for hexagonal-orthorhombic textures is shown in the figure in the first three dimensions of the Fourier space. It should be understood that any physically realizable texture has to have a representation inside the depicted hull.

In the MSD framework, the microstructure description is then linked to its effective elastic and plastic properties using generalized composite theories resulting in property closures. Property closures delineate the complete set of theoretically feasible macroscale (homogenized) anisotropic property combinations in a given material system, and are of tremendous interest in optimizing the performance of engineering components. The next figure shows a series of closures for a range of cubic orthorhombic and hexagonal orthorhombic materials for a selected pair of effective elastic properties corresponding to the effective modulus in unaxial strain and the effective shear modulus in the sample. The property combinations correpsonding to all possible textures are represented by shaded areas inside the closures, and each property combination can be mapped back to a set of textures in the texture hull that exhibit that set of properties. The unique ability of the MSD methodology to rapidly search such complete property closures gives it a major advantage over other competing material design approaches.

MSD considers a broader class of plastic properties of metals that pertain to strain hardening and concurrent evolution of microstructure due to plastic strain. Prime examples of such properties include the uniform ductility and the ultimate tensile strength. Because of their influence on the toughness exhibited by the material, these properties play an important role in materials selection for critical structural components. Since these properties directly influence the formability (and thereby the success of certain deformation processing operations), they are also of tremendous interest for deformation processing of metals. An example of the property closures for uniform ductility and ultimate tensile strength is depicted in the figure. The textures predicted to exhibit superior combinations of ultimate tensile strength and uniform ductility lie on the A-C and B-D boundaries of the closures. Different points on these boundaries provide different trade-offs in the achievable combinations of ultimate tensile strength and uniform ductility in the two alloys studies.