Estimate Elastic Moduli of Nanostructured NiAl Alloy using 2D Image Analysis 2010-01-1151
Mechanical properties of porous materials such as bones for example are controlled by the geometry and structure of the pore space. Traditionally, most attempts to understand the effect of pore structure on mechanical properties have assumed that the pores can be modeled as ellipsoids Eshelby  etc. Nevertheless pictures taken by SEM show that pore shapes are never as simple as circles or ellipses. But the use of real pore shapes in the modeling process has been hindered by the lack of analytical solutions for these shapes. Zimmermann  suggested that the pore compressibility Cpc scales approximately with where A is the area of the pore space and P is the perimeter surrounding the pore space. Forcing this scaling law to be exact for a circular hole leads to the approximation . Zimmerman  showed that this approximation has an error of less than 8% for all hypotrochoids and an error of about 23% for thin, crack-like pores, which he suggested might be the "worst-case" shape. The bulk and shear compliances are then estimated using the two scaling laws discussed below based on the perimeter and area of each pore. Areally-weighted mean values of these compliances are calculated for each material, and the differential effective medium scheme is used to obtain expressions for the moduli as functions of porosity. Ekneligoda successfully used these methods to predict the effective moduli of sandstones and ceramic based on information obtained from two-dimensional pore space images which compared well with the values determined using boundary element method and experiments. Authors in this paper would like to predict the bulk modulus and shear modulus of Ni-Al nanostructured intermetallic alloys using the above scaling laws and based on two-dimensional images of the pore space. These alloys are most commonly used in automotive industry for their properties at high temperatures. It is pertinent to note that the earlier work done was for macro-sized materials whereas authors in the present paper are trying to study the viability of applying the same procedure for nano-sized Ni-Al intermetallic alloys. Four samples with porosity of 18%, 60%, 70%, and 75% are used. Starting with scanning electron micrographs, image analysis software (Matlab) is used to isolate and extract each pore from the host material. The bulk and shear compliances are estimated using the procedure described above. The computed results are tabulated below. There are no experimental or theoretical values available for the bulk and shear modulus of Ni-Al alloys. The porosities of the samples (>50%) used are very much on the high side. Therefore the results of sample with 18% porosity compared well with the results obtained by Ekneligoda  in dissertation for some other materials.