Construction of statistically similar rves for the quantification of uncertainty associated with the material's microstructure morphology
D. Balzani, N. Miska, S. Pruger.
UNCECOMP 2017 - Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, 419-425, (2017)
Various engineering applications require the use of modern materials. In particular with view to automotive applications, where increased safety standards at reduced weight are important, multiphase steels are advantageous. These steels make use of a pronounced mi- crostructure in order to achieve a high ductility with high strength. The morphology of these microstructures varies over the location in the macroscopic part and over different specimen. As the macroscopic response of the steel is governed by the microstructure morphology, the randomness of the microscopic morphology implies uncertainties regarding the macroscopic material response. We propose to create statistically similar representative volume elements (SSRVE) to enable access to the incorporation of these uncertainties in numerical computations. The SSRVEs are obtained by minimizing a least-square functional consisting of higher order statistical measures, which describe the morphology of the microstructure. The resulting geometries are significantly less complex than the real microstructure and exhibit an advantage regarding meshing and computing the problem. Aside from these advantages, the method also provides a basis to construct various SSRVEs which are within predefined bounds regarding the microstructure statistics. These bounds may be obtained from measurements performed by analyzing the microstructures at different locations in one material. Rased on this variety of applicable SSRVEs multiple Finite Element (FE) simulations can be performed to obtain the homogenized response and thus, to quantify statistics regarding macroscopic material parameters. In order to automatize these numerical simulations the Finite Cell Method (FCM) can be applied such that a conforming FE mesh for each of the SSRVEs is not needed to be constructed. © 2017 The Authors. Published by Eccomas Proceedia.
Keyword(s): uncertainty quantifications, statistically similar representative volume elements, morphology, microstructure, dual phase steel
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