On the Difference Between the Tensile Stiffness of Bulk and Slice Samples of Microstructured Materials
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On the Difference Between the Tensile Stiffness of Bulk and Slice Samples of Microstructured Materials ¨ 1 Rainer Gluge
· Holm Altenbach2 · Nasir Mahmood3 · Mario Beiner3
Received: 21 July 2020 / Accepted: 28 September 2020 / © Springer Nature B.V. 2020
Abstract Many materials with a microstructure are statistically inhomogeneous, like casting skins in polymers or grain size gradients in polycrystals. It is desirable be able to account for the structural gradient. The first step is to measure the location dependent properties, for example by tensile testing of thin slices. Unfortunately, the slices properties can differ significantly from the bulk properties, since the slices lack a scale separation in one direction. For Polypropylen, we measured that Young’s modulus of the slices is approximately 70% of the respective bulk value. We have identified three significant effects, all making the slices appear softer than the bulk material:
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Load path confinement: The approximate plane stress forces the load path through a softer phase where in 3D-of-plane load distribution is possible. Free lateral straining: In thin slices, small regions can contract freely, while phases have to contract concurrently in the bulk. Therefore, when two phases have very different Poisson ratios, the bulk appears stiffer than a slice. Topological changes upon slicing: Interpenetrating phases in the bulk can show features of a matrix-inclusion-structure in the slices.
We examine and quantify these effects in the linear elastic range for matrix-inclusionstructures and an interpenetrating-phase-structure. Some approaches on how the slice- vs bulk difference can be estimated are given. Rainer Gl¨uge
[email protected] Holm Altenbach [email protected] Nasir Mahmood [email protected] Mario Beiner [email protected] 1
University of Bremen, Bremen, Germany
2
Otto-von-Guericke–University, Magdeburg, Germany
3
Fraunhofer Institute for Microstructure of Materials and Systems IMWS, Halle, Germany
Applied Composite Materials
Keywords Stiffness · Homogenization · Plane stress · Elasticity · Micro structure · Layers
1 Introduction With the advancement of analytic and simulation tools, it becomes feasible to account for structural gradients and statistical inhomogeneous microstructures in engineering parts. Today, methods for optimizing a microstructure w.r.t. desired effective material properties are established, and textbook knowledge is available [1, 10]. The next step is to do such adjustments locally, as for example in [2] who optimized the local material distribution of a structure. A more recent example is the work of [6] who optimized the density of a polymer lattice in a cantilever beam. By this method, gradient structures are the result of a design process to enhance a part’s functionality, but they also occur unintentional, for example as casting skins in polymers [15] or grain size gradients in metals [14]. To set up simulation models of such parts, the local material parameters are needed
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