Local elastic moduli of simple random composites computed at different length scales

Published

December 3, 2020

Author(s)

Edward Garboczi, Pietro Lura

Abstract

Techniques like nanoindentation and atomic force microscopy can estimate the local elastic moduli in a region surrounding the probe tip used. For composites with phase regions much larger than the size of the probe, these procedures can identify the phases via their different elastic moduli, but identifying phase regions that are on the same size scale as the indent is more problematic. This paper looks at three random 3D 8003 voxel composite models, each consisting of a matrix and spherical inclusions. Two models have overlapping spheres, with two and three distinct phases, and one model has non-overlapping spheres. The linear elastic problem is solved for each microstructure, and histograms are made of the local Young's moduli over a number of subvolumes (SVs), averaged over very small to progressively larger SVs. There are interesting changes in the number and shape of histogram peaks as they change from N delta functions, where N is the number of elastically distinct phases, at the 1 voxel SV limit, to a single delta function located at the value of the effective global Young's modulus, when the SV equals the unit cell volume. The phase volume fractions are also tracked for each bin in the Young's modulus histograms, showing the phase make-up of each peak. There are clear differences seen between the non-overlapping and three-phase overlapping models and the two-phase overlapping sphere model, with the two-phase overlapping sphere model requiring a larger SV region to approach the global limit than either of the other two models, due to its larger average cluster size. For the two-phase models, the standard deviations for both phase volume fraction and Young's modulus computed over SVs and plotted vs. SV size are in approximate agreement with theoretical predictions for the large-size SV limit, while the three-phase model appears to give different exponents. These results give some guidance as to what probe size might be useful in distinguishing different phases

Citation

Materials and Structures

Volume

53

Pub Type

Journals

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DOI Link

Keywords

random, composite, elastic moduli, nanoindentation, local moduli distribution, local moduli, overlapping spheres, nonoverlapping spheres, atomic force microscopy

Citation

Garboczi, E. and Lura, P. (2020), Local elastic moduli of simple random composites computed at different length scales, Materials and Structures, [online], https://doi.org/10.1617/s11527-020-01592-8 (Accessed October 31, 2024)