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.
Highlights
With the advancement of analytic and simulation tools, it becomes feasible to account for structural gradients and statistical inhomogeneous microstructures in engineering parts
The traction-free surfaces in tensile tests correspond to the homogeneous stress case, the slices appear softer in tensile tests
1[20] proposed a homogeneous stress field in a different context, but in homogenization the term has been established for the harmonic mean of the stiffness, as it relies on the same assumption
Summary
With the advancement of analytic and simulation tools, it becomes feasible to account for structural gradients and statistical inhomogeneous microstructures in engineering parts. These behave different from the bulk material, since the sliced samples lack a scale separation in one direction Homogeneous stress boundary conditions, like a traction-free surface in a tensile test, correspond to a minimum of kinematic constraints and a minimum of reaction stresses, so they underestimate the effect of embedding the RVE in a similar material. 1[20] proposed a homogeneous stress field in a different context, but in homogenization the term has been established for the harmonic mean of the stiffness, as it relies on the same assumption Note that this effect can well be described in a purely classical, size-insensitive modelling framework, and does not require strain gradient modelling or micropolar approaches.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
