Professor Christian Niordson
Professor of Materials Mechanics
Technical University of Denmark

The macroscopic yield surface of a metal depends on porosity, but also on the void size and their spatial distribution. In turn these microstructural details govern plastic deformation and ductile fracture. The influence of porosity may be analyzed based on micromechanical studies of plastic deformation around voids, and the ensuing interaction between individual voids. Such analyses are based on assumptions on void distributions. For unit cell studies an idealized regular distribution of voids are assumed. Investigations of random distrubtions of voids can be obtained based on representative volume elements (RVE) containing a large number of voids. For sufficiently large RVEs the homogenized properties exhibit little dependence on the size of the investigated domain. The extracted homogenized properties may then be used to study macroscopic behaviour, such as plastic collapse and ductile fracture, under the assumption that the length scale of the material microstructure is small compared to the scale over which there are large variations in plastic deformation.

In this presentation the statistical influence of different void distributions is investigated. Emphasis is put on how yield surfaces for porous metals may be quantified statistically from numerical analysis of different spatial distributions. 3D finite element analyses of a range of different void configurations are carried out based on representative volume elements with periodic boundary conditions. The statistical effects are quantified and compared to a regular FCC void distribution. For a given porosity, the standard deviation of the yield surfaces as well as their mean are determined based on 15 different realizations. Results are obtained for three different void volume fractions. It is quantified how the standard deviation of the different yield surfaces is small at low stress triaxialities (T) but substantial for large triaxialities with a maximum around T=5. 

It is discussed how the statistical study of intermediate size RVEs may give valuable input to macroscopic models where the spatial variation of material properties are essential. 

Finally, it is shown that the Gurson-Tvergaard model is in good agreement with the predictions for the mean of the yield surfaces, and a simple method for modelling the statistical effects in the context of the Gurson-Tvergaard model is proposed.


Brief CV:

Christian NiordsonChristian Niordson is a Professor of Materials Mechanics at the Technical University of Denmark (DTU) and Head of the Solid Mechanics Section. His research interests are centered around the influence of material microstucture and size on the macroscopic properties of metals such as plastic deformation, ductile failure and fatigue.

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