Two point microstructure sensitive design and experimental verification

Rectangular models of material microstructure are described by their 1- and 2-point (spatial) correlation statistics of placement of local state. It is illustrated that generalized 2-point Hashin-Shtrikman bounds for elastic stiffness can be obtained that are linear in components of the correlation statistics. The concept of an eigen-microstructure within the microstructure hull is introduced. A method is developed for generating a sequence of archetypes of eigen-microstructure, from the 2-point correlation statistics of local state, assuming that the 1-point statistics are stationary. The method is illustrated by a case study.; Extension of the first-order theory of microstructure design to considerations of morphological texture is addressed. It is shown that the correlation functions can be expressed in terms of an intermediate construct, called the texture function; the correlation functions have quadratic dependence in the texture functions. A complete (finite) texture hull is readily constructed for the texture functions in Fourier space, and is found to be a convex polytope. Eigen-texture functions occupy its corner (extreme) points. This gives rise to (combined) properties closures, from which second-order microstructure design can proceed. This is demonstrated in a brief case study.; Experimental methods are introduced for obtaining two-point microstructure pair correlation functions in polycrystalline material. A particular tessellation of the fundamental zone of Euler angle space is described; individual orientations of the data set are binned into discrete tesserae. Elementary relationships between the two-point pair correlation functions and the grain size distribution and coherence length are explored.; The one- and two-point distributions of orientation were recovered for three textures (as-received stainless steel, as-received copper and copper with cube texture). Elastic bounds for these textures are calculated including one-point bounds and generalized Hashin-Shtrikman bounds. Finite Element Analysis (FEA), incorporating the estimated elastic properties, is used to predict the strain field around a hole in the plate subjected to uniaxial loading. High Sensitivity Moire Interferometry (HSMI) is used to measure the strain experimentally. The results show that the two-point bounds on effective properties lead to predictions in better agreement with the HSMI results as compared to the one-point bounds.