Investigation of the relationship between the effective stiffness of three-dimensional material samples and thin layers

• Applicant: Professor Dr.-Ing. Holm Altenbach, since 5/2021
• Subject Area: Mechanics ; Materials in Sintering Processes and Generative Manufacturing Processes ; Mechanical Properties of Metallic Materials and their Microstructural Origins
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 446204641

The aim of the project is to predict the effective 3D stiffness of a material with microstructure when the material is layered. A typical example is a cast skin. The 3D stiffness of a casting depends on the surface distance. This can be measured layer by layer in tensile tests. However, thin layers behave softer than 3D samples with identical microstructure. Experiments have shown that for polypropylene (PP) the ratio of the 2D to 3D Young moduli averaged over the sample is approximately 0.7. This was verified in simulations. The value is typical, for other microstructures and phase properties it lies between 0.2 and 1.0. In preliminary investigations it was found that the difference in the phase's Poisson coefficients is decisive for this ratio. This can be understood by means of the load flow and from the point of view of the technique of representative volume elements (RVE). At micro level, the load flow tends to run through the stiffer phases. If one locally forces a plane stress state by reducing the sample thickness, one dimension for load distribution is missing, so that the load flow is diverted into the softer phase. In homogenization, this effective stiffness reduction at homogeneous stress boundary conditions is known. There are numerous convergence studies where the RVE size is varied but the aspect ratios are maintained. However, to clarify the 2D to 3D Young's modulus ratio, the zero and infinity limits of a single specimen dimension must be investigated in a tensile test. This question has hardly been addressed so far. Therefore the following investigations are proposed:1) Experimental tensile tests with in-situ measurement of the local lateral strain are planned. On the one hand, these should reveal similarities within and differences between material classes. 2) Furthermore, RVE simulations for grain structures will be carried out to extend the database of the preliminary investigations, in which matrix-inclusion structures and interpenetrating phases were investigated. 3) Unfortunately, the 2D-3D transition has hardly been investigated theoretically so far. For the development of suitable extrapolation rules from 2D to 3D different strategies are proposed, the detailed investigation of which is part of the project. 4) Based on the experimental and numerical database, automatic regressions with as many parameters and high accuracy as possible and simple manual regressions with few parameters are to be constructed. The former can be used for applications and should be published together with the experimental and numerical data. The latter shall support the theory development by identifying relevant parameters and the associated influencing variables.

• DFG Programme: Research Grants
• Ehemaliger Antragsteller: Privatdozent Dr.-Ing. Rainer Glüge, until 4/2021