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|Title: ||Measurement of granular contact forces using frequency scanning interferometry|
|Authors: ||Osman, Mohammad S.|
|Issue Date: ||2002|
|Publisher: ||© Mohammad Shahril Osman|
|Abstract: ||The propagation of stress within a granular material has been studied for many
years, but only recently have models and theories focused on the micromechanical
(single grain) level. Experiments at this level are still rather limited in number. For this
reason, a system using optical techniques has been developed.
The substrate on which the granular bed is assembled is a double layer elastic
substrate with high modulus epoxy constituting the top layer and silicone rubber as the
bottom layer. In between the two layers, gold is coated which acts as a reflective film. To
design the substrate, a Finite Element Analysis package called LUSAS was used. By
performing a non-linear contact analysis, the design of the substrate was optimised so as
to give a linear response, high stiffness, deflection in the measurable range, and
negligible cross-talk between neighbouring grains. Fabrication and inspection techniques
were developed to enable samples to be manufactured to this design.
The deformation of the gold interface layer is measured using interferometry. The
interferometer utilised a frequency tunable laser which acts both as the light source and
the phase shifting device. The optical arrangement is based on the Fizeau set-up. This
has removed several problems such as multiple reflections and sensitivity to vibration
that occurred when using a Mach-Zehnder configuration. A fifteen-frame phase shifting
algorithm, was developed based on a Hanning window, which allows the phase
difference map to be obtained. This is then unwrapped in order to obtain the indentation
profile. The deflection profile is then converted to a single indentation depth value by
fitting a Lorentzian curve to the measured data.
Calibration of the substrate is carried out by loading at 9 different locations
simultaneously. Spatial and temporal variations of the calibration constants are found to
be of order 10-15%. Results are presents showing contact force distributions under both
piles of sand and under face-centred cubic arrangements of stainless steel balls.
Reasonable agreement was obtained in the latter case with both the expected mean force
and the probability density function predicted by the so-called 'q' model. The experimental techniques are able to measure small displacements down to a
few nanometers. To the best of my knowledge these experiments are the first to employ
the interferometer method in attempting to measure the contact force distribution at the
base of a granular bed.|
|Description: ||A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.|
|Appears in Collections:||PhD Theses (Mechanical, Electrical and Manufacturing Engineering)|
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