Session: 12-07-04: Mechanics of Soft Materials
Paper Number: 99794
99794 - Direct Determination of the Stress Components During Hertzian Contact on a Soft Solid Using Photoelastic Tomography
The contact between a rigid sphere and a soft substrate is investigated using 3D, integrated photoelasticity. In the experiment, a 44 x 44 x 47 mm3 cuboid from 5% wt. gelatin is placed inside a circular polariscope. A styrene sphere of 15 mm diameter, that can be considered rigid, is pressed against the cuboid with forces varying from 10 to 300 N. The retardation and principal stress orientation of the light rays that emerge from the cuboid can be simultaneously measured using a polarization camera (Photron, CRYSTA PI-5WP). This phase retardation has been accumulated incrementally, during the passage of the rays from the axisymmetric stress field (Hertzian contact). In general, this problem is ill-posed; however, assuming that the structure of the stress field is known from Hertz’ theory, the phase retardation and principal stress orientation can be analytically calculated and compared to the experimental ones. To accomplish this, the cuboid is virtually dissected into a series of thin slices perpendicular to the direction of travel of the light rays (optically equivalent model). Then, the contribution of each slice and principal orientations on the integrated retardation is computed using Mueller calculus, i.e., the Mueller matrix and Stokes parameters. It is found that at relatively small forces, where the contact radius between the sphere and substrate is much smaller than the sphere diameter, the agreement is very good, indicating that Hertz’s theory is valid. However, at larger forces, where the contact radius approaches to the sphere radius, i.e., the sphere starts to sink inside the cuboid, this agreement begins to deteriorate. This is reasonable as the Hertzian contact theory assumptions cease to hold. To explore the effects of finite deformations in the results, which is analytically intractable, a finite element model of the contact problem is also described. For computational efficiency, this replaces the cuboid domain with am axisymmetric one, having a fine mesh of linear, reduced integration elements. A similar finding as before is reported here, as well, i.e., that at the smaller forces the agreement between numerics, theory and experiment is very good, but that it deteriorates as the force increases. Finally, it has been discovered that at the axis of symmetry of the problem and at the location of the maximum equivalent stress, all three principal stresses can be determined from the photoelastic experiment. Hence the conditions that lead to the onset of yielding and/or failure can be determined experimentally.
Presenting Author: Yannis Korkolis The Ohio State University
Presenting Author Biography: Yannis P. Korkolis graduated from the National Technical University of Athens (NTUA) with a five-year diploma in Mechanical Engineering. Following a two-year employment in industry and the military, he returned to NTUA to obtain a Master’s degree in Computational Mechanics. Subsequently, he pursued a PhD in Engineering Mechanics at the University of Texas at Austin, working on the formability and hydroforming of anisotropic aluminum tubes. In August 2009, he was appointed Assistant Professor at the Department of Mechanical Engineering at the University of New Hampshire, where he taught courses in Design, Manufacturing, and Mechanics. In January 2019 he moved to The Ohio State University. His research aims at interfacing mechanics of materials, constitutive modeling, failure and actual manufacturing processes. He has worked on constitutive modeling of advanced aluminum alloys, formability and failure prediction, microforming, modeling of machining operations, sheet metal forming, and tube hydroforming.
Authors:
Benjamin Mitchell University of New HampshireYuto Yokoyama Tokyo University of Agriculture and Technology
Ali Nassiri The Ohio State University
Yoshiyuki Tagawa Tokyo University of Agriculture and Technology
Brad Kinsey University of New Hampshire
Yannis Korkolis The Ohio State University
Direct Determination of the Stress Components During Hertzian Contact on a Soft Solid Using Photoelastic Tomography
Paper Type
Technical Presentation