On the difference between the tensile stiffness of bulk and slice samples of microstructured materials

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:

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-inclusion-structures and an interpenetrating-phase-structure. Some approaches on how the slice- vs bulk difference can be estimated are given.