Photoelastic and finite element analysis of different size spheres in contact

The photoelastic stress-freezing technique is applied to observe the stress distribution inside two spheres of different sizes compressed together elastically. After the stress is frozen in, thin slices of the material containing the symmetry axis are prepared for observation through a polariscope. The stress distribution is compared with both the finite element numerical analysis and the Hertz analytical theory which is limited to small deformations. Among the three, the agreement between the experimental results and the finite element analysis is the best. The deviation from the Hertz theory is less in the larger sphere contacting a smaller one than in the smaller sphere contacting a larger one.