Abstract
Microstructures of materials differ fundmentally from the structures of isolated objects, in that objects normally possess specific form and size, whereas microstructure goes on and on as a continnum, never appearing quite the same in any two places and having no beginning or ending. Such “unbounded irregular structures” are amenable to precise characterization by the use of parameters that can be expressed in terms of totals in unit volume of material, sometimes called the “global parameters”. The methods of quantitative microscopy have, thus far, provided eight parameters of this kind, namely: length of line, area of surface, volume fraction, curvature of line, torsion of line, curvature of surface, number, and connectivity. Whenever a physical property can be related simply and directly to one of these parameters, the relation is insensitive to the value of any other geometric property of the structure, that is, it is shape-insensitive. Average geometric properties of microstructure can be had by taking ratios of the fundamental parameters. These can be used to formulate structure-property relationships when the average is made up of uniquely defined components. This condition has been found to prevail when the structure is in a configuration of minimum energy.
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Rhines, F.N. Microstructure-property relationships in materials. Metall Trans A 8, 127–133 (1977). https://doi.org/10.1007/BF02677274
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DOI: https://doi.org/10.1007/BF02677274