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M. Vogric, E. Povoden-Karadeniz:
"An Eshelby inclusion based model for cementite variants in hypereutectoid steel";
Poster: Materials Science and Engineering - MSE 2018, Darmstadt; 2018-09-26 - 2018-09-28.

A multiscale homogenization model has been developed for the description of the elastic properties of hypereutectoid pearlitic steels with proeutectoid grain boundary cementite precipitates through the calculation of their stiffness matrix. This model is based on the Eshelby inclusion problem [Ref 1]. The different cases that have been tested for the microstructure are a lamellar or spheroidized structure of the pearlite, and the presence of a continuous or discontinuous layer of proeutectoid cementite around the pearlite grains. Depending on the case, Benveniste´s approach of the Mori-Tanaka method [Ref 2] or classical or generalized self-consistent calculation schemes [Ref 3, 4] have been used. Employing elastic moduli of respectively the pearlitic ferrite, the pearlitic cementite and of the proeutectoid cementite, and the volume fraction of each of these phases, a two steps homogenization calculation is conducted, with first the determination of the stiffness matrix of the pearlite grains followed by the determination of the homogenized stiffness matrix of the metal sample. In the case of presence of lamellar pearlite grains, an additional parameter has been introduced to pilot the diversity of the pearlite grain orientations. Our first results regarding the coefficients of the homogenized stiffness matrix are quite encouraging when compared to the literature. Such a model applies for polycrystalline hypereutectoid steels tools which have already been widely used since years for composite materials. It would allow a fast prediction of the elastic properties of a steel sample following thermokinetic phase transformation simulations.

Ref 1: J.D. Eshelby, "The determination of the elastic field of an ellipsoidal inclusion, and related problems", Proc. Roy. Soc. London A241, pp. 376-396, 1957
Ref 2: Y. Benveniste, "A new approach to the application of Mori-Tanaka´s theory in composite materials", Mechanics of Materials 6, pp. 147-157, 1987
Ref 3: R. Hill, "A self-consistent mechanics of composite materials", J. Mech. Phys. Solids, Vol. 13, pp. 213-222, 1965
Ref 4: Y. Benveniste, "Revisiting the generalized self-consistent scheme in composites: Clarification of some aspects and a new formulation", J. Mech. Phys. Solids, Vol 56, pp. 2984-3002, 2008

elasticity, pearlite, cementite, hypereutectoid steel, Eshelby, homogenization

https://publik.tuwien.ac.at/files/publik_285698.pdf

Project Head Erwin Povoden-Karadeniz:
CDL-IPE