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Inclusion modelling on the basis of metallographic observations as input for FEM simulation of mechanical properties
By Wolfgang Gaudig
Idealization of inclusions as rotational ellipsoids; conversion of metallographic 2D shape parameters to 3D aspect ratio; extension of current 2D shape parameters virtually covering oblate ellipsoids only, to prolate ellipsoids by properly modified 2D shape parameters; suggested simulation of mechanical properties by dual ellipsoid unit cell model
The simulation of mechanical properties of materials containing inclusions by the finite element method is very complicated and too time consuming if all the structural details are taken into consideration. It is, therefore, common use to considerably simplify this problem by representing the various shapes of the inclusions by a single geometric form. It is straightforward to choose this form to be a rotational ellipsoid, thus capturing the most noticeable and contrary features of real inclusions, i. e. spherical, oblate and prolate. Hence, inclusions in materials are modelled by randomly oriented rotational ellipsoids of equal dimensions. These ellipsoids are characterized by their aspect ratio, i. e. the ratio of the length c of the ellipsoid's rotational symmetry semi-axis to the length a of the semi-axes across. The aspect ratio is a 3-dimensional shape parameter and, therefore, not directly observable. The goal is therefore to determine the 3D aspect ratio from adequately defined metallographic 2D shape parameters. The value of the aspect ratio c/a determines the various shapes of inclusions, i. e. spherical (c/a = 1), oblate rotational ellipsoidal (disc-shaped, c/a < 1), and prolate rotational ellipsoidal (cigar-shaped, c/a > 1). The finite element method is then usually carried out by setting up a unit cell containing the representative inclusion, e. g. as proposed by the author in 2003. The purpose of such calculations is (i) to determine mechanical material constants just by metallography, and (ii) to straightforwardly develop desired material properties by finding the optimum conditions for content and shape of the inclusions, thus saving empirical work.
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