Poisson ratio effects and critical values in spherical and cylindrical hertzian contacts

1. ABSTRACT This work determines the location of the greatest elastic di stress in spherical and cylindrical Hertzian contacts based upon the distortion energy and the maximum shear stress theories. The ratios between the maximum pressure, the von Mises stress, and the maximum shear stress ar e determined and fitted by empirical formulations for a wide range of the Poisson ratio, which represents materia l compressibility. Some similarities exist between cylindrical and spherical contacts, where for many metallic m aterials the maximum von Mises or shear stresses emerge beneath the surface. However, in cylindrical contact i f ny of the materials is excessively compressible then the maximum von Mises stress appears at the surface. The cor responding Poisson ratios are found. The critical forces that cause yielding onset, and the corresponding interferenc es a d radius or half-width contact are derived along with the maximum stored strain energy. It is shown that the distressing stresses decrease as Poisson’s ratio increases (i.e., as the material approaches incompressibility) . The results obtained herein are then used to calibrate FEA meshes intended for cases that do not have closed-form solutions.