Figure 4 - uploaded by Yuto Yokoyama
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(a) Measured retardation field after unloading force í µí°¹ = 196.2 mN and (b) mean retardation Δ in the measurement area after unloading. í µí± is the radius of sphere.
Source publication
Integrated photoelasticity is investigated for a soft material subjected to a three-dimensional stress state with large deformation. Our measurement target is designed based on the three-dimensional Hertzian contact problem, i.e., a solid sphere is pressed against a gelatin gel (Young’s modulus is about 4.2 kPa) with varying applied forces from zer...
Context in source publication
Context 1
... verify the elasticity of the gelatin, the mean retardation after unloading is measured (Fig. 4). To avoid viscoelastic effects, measurements are taken 1 minute after unloading and repeated after 2 minutes. For í µí°¹ < 200 mN, the retardation goes back to less than 6 nm (4.4% of the maximum measurable value) after unloading. Retardation after unloading varies in the region below 6 nm and does not increase with the loading force. ...
Citations
Hertzian contact of a rigid sphere and a highly deformable soft solid is investigated using integrated photoelasticity. The experiments are performed by pressing a styrene sphere of 15 mm diameter against a 44 × 44 × 47 mm³ cuboid made of 5% wt. gelatin, inside a circular polariscope, and with a range of forces. The emerging light rays are processed by considering that the retardation of each ray carries the cumulative effect of traversing the contact-induced axisymmetric stress field. Then, assuming Hertz's theory is valid, the retardation is analytically calculated for each ray and compared to the experimental one. Furthermore, a finite element model of the process introduces the effect of finite displacements and strains. Beyond the qualitative comparison of the retardation fields, the experimental, theoretical, and numerical results are quantitatively compared in terms of the maximum equivalent stress, surface displacement, and contact radius dimensions. A favorable agreement is found at lower force levels, where the assumptions of Hertz theory hold, whereas deviations are observed at higher force levels. A major discovery of this work is that, at the maximum equivalent stress location, all three components of principal stress can be determined experimentally and show satisfactory agreement with theoretical and numerical ones in our measurement range. This provides valuable insight into Hertzian contact problems since the maximum equivalent stress controls the initiation of plastic deformation or failure. The measured displacement and contact radii also reasonably agree with the theoretical and numerical ones. Finally, the limitations that arise due to the linearization of this problem are explored.
