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Porous metals can be created through a wide variety of processing techniques, and the pore morphology resulting from these processes is equally diverse. The structural and functional properties of metal foams are directly dependent on the size, shape, interconnectedness and volume fraction of pores, so accurately quantifying the pore characteristics is of great importance. Methods for analyzing porous materials are presented here and applied to a copper-based metallic foam generated through solid state foaming via oxide reduction and expansion. This process results in large voids (10s of microns) between sintered particles and small pores (10 microns to less than 50 nm) within particles. Optical and electron microscopy were used to image the porosity over this wide range, and the pore characteristics were quantified using image segmentation and statistical analysis. Two-dimensional pore analysis was performed using the Chan-Vese method, and two-point correlation and lineal path functions were used to assess three-dimensional reconstructions from FIB tomography. Two-dimensional analysis reveals distinct size and morphological differences in porosity between particles and within them. Three-dimensional analysis adds further information on the high level interconnectedness of the porosity and irregular shape it takes, forming tortuous pathways rather than spherical cells. Mechanical polishing and optical microscopy allow large areas to be created and analyzed quickly, but methods such as focused ion beam (FIB) sectioning can provide additional insight about microstructural features. In particular, after FIB milling is used to create a flat surface, that surface can be analyzed for structural and compositional information.

Microstructure reconstruction and compression techniques are designed to identify microstructures with desired properties. While a microstructure reconstruction involves searching for a microstructure with prescribed statistical properties, a microstructure compression focuses on efficient representation of material morphology for the purpose of multiscale modelling. Successful application of these techniques, nevertheless, requires proper understanding of the underlying statistical descriptors quantifying morphology of a material. In this paper, we focus on a lineal path function designed to capture short-range effects and phase connectedness, which can hardly be handled by the commonly used two-point probability function. Usage of the lineal path function is, however, significantly limited because of huge computational requirements. So as to examine the properties of the lineal path function during computationally exhaustive compression and reconstruction processes, we start with an acceleration of the lineal path evaluation, namely by porting part of its code to a graphics processing unit using the CUDA (Compute Unified Device Architecture) programming environment. This allows us to present a unique comparison of the entire lineal path function with the commonly used rough approximation based on the Monte Carlo and/or sampling template. Moreover, this accelerated version of the lineal path function is then compared to the two-point probability function during the compression and reconstruction of two-phase morphologies. Their significant features are discussed and illustrated using a set of artificial periodic as well as real-world random microstructures. [ABSTRACT FROM AUTHOR]

Abstract: The objective of this research is to examine the use of statistical descriptors in the microstructure reconstruction process and the associated effect on microstructure properties. In this work, two-point correlation functions and lineal path functions were used to study the efficiency and accuracy of microstructure reconstruction. A polar plot of the two-point correlation functions is used to quantitatively evaluate the agreement with the target microstructure. In general, as more microstructure descriptors are added for the microstructure reconstruction process, the computational time increases and the reconstructed microstructures quantitatively agree better with the target microstructure. However, in some cases, adding lineal path functions did not always result in a better microstructural representation. Last, finite element analysis of thermal loading in the reconstructed microstructures of loaded nuclear waste glass is used to evaluate the property predictions with those of the target microstructure. Identifying which statistical descriptors are best for different microstructures may provide insight into optimizing the microstructure reconstruction process from limited statistical descriptors. [Copyright &y& Elsevier]

A stochastic reconstruction scheme via the simulated Annealing method (SA) is developed here in order de represent the 3D microstructure of a porous material so, its properties can be estimated. The 2D image, obtained by Scanning Electron Microscope (SEM), is treated and then the different statistical information contained, as the 2-points correlation function and the lineal path function are extracted from this image. [ABSTRACT FROM AUTHOR]

We report the stochastic reconstruction of chalk pore networks from limited morphological information that may be readily extracted from 2D backscatter electron (BSE) images of the pore space. The reconstruction technique employs a simulated annealing (SA) algorithm, which can be constrained by an arbitrary number of morphological descriptors. Backscatter electron images of a high-porosity North Sea chalk sample are analyzed and the morphological descriptors of the pore space are determined. The morphological descriptors considered are the void-phase two-point probability function and lineal path function computed with or without the application of periodic boundary conditions (PBC). 2D and 3D samples have been reconstructed with different combinations of the descriptors and the reconstructed pore networks have been analyzed quantitatively to evaluate the quality of reconstructions. The results demonstrate that simulated annealing technique may be used to reconstruct chalk pore networks with reasonable accuracy using the void-phase two-point probability function and/or void-phase lineal path function. Void-phase two-point probability function produces slightly better reconstruction than the void-phase lineal path function. Imposing void-phase lineal path function results in slight improvement over what is achieved by using the void-phase two-point probability function as the only constraint. Application of periodic boundary conditions appears to be not critically important when reasonably large samples are reconstructed. [Copyright &y& Elsevier]