Interferometric Pointilism

This paper develops a new experimental technique that measures mechanical stress at multiple spatial length scales. The method uses Vertical Scanning Interferometry (VSI) as well as a mechanical device that provides for the transverse loading of a cantilever beam. Because of the extreme sensitivity of VSI to height differences (on the order of 1 nanometer) and its good lateral resolution (approximately 1 micron with 10x objective), stress estimates at a sub-continuum length scale for many materials can be obtained. The experimental procedure has the advantage of being uniformly applicable at spatial scales that vary across several orders of magnitude, thereby allowing the gradual ‘homogenization' of the stress field to be experimentally observed as the resolution of the optical measurements are gradually reduced. For demonstration purposes, this paper considers a 304 Stainless Steel prismatic cantilever beam subjected to a point load, and undertakes to experimentally determine the elastic stress field near its clamped end. The power of the observational technique is demonstrated by its ability to simultaneously capture the quantitative stress states at more than one spatial scale. In so doing, we show how the stress field changes character as the spatial scale is varied. From length scales smaller than the individual grains of steel, where we see that microstructure controls the spatial arrangement of stress, to larger spatial scales where the stress state varies continuously. As an aid to understanding our observational results we draw an analogy from Seurat's Sunday Afternoon on the Island of La Grande Jatte.