The mechanical performance of a heterogeneous material depends on a hierarchy of details in the specific microstructure of a given sample. The goal of the present work is to identify microstructural features that control elastic, plastic, and fracture/failure behavior in heterogeneous materials as a function of the class of microstructures studied. Specifically, various statistical correlation functions are extracted from a 2d micrograph of an experimental “parent” microstructure and these correlation functions are then used in a digital “microstructure reconstruction” method developed by Torquato et al. to generate “child” microstructures that are statistically similar to the parent structure. Each of the child microstructures is then tested numerical using the finite element method to predict stress-strain behavior and localization/fracture and then to assess similarities and differences among the nominally-identical microstructures. Advantages of such a method are that it applies to arbitrary microstructures, the correlation functions can guide the choice of representative unit volumes, anisotropy is easily identified and included, and that 3d microstructures can be built from the statistical information extracted from 2d micrographs of the parent structure. The method is applied to a model system of ductile iron. Results show the insensitivity of elastic modulus and work hardening to higher-order correlation functions and the onset of localization around particular microstructural features in each child. The “hot spots” at which high stresses or strains occur in a particular child microstructure are identified and methods to numerically assess the locality of the “hot spots” are discussed.
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