Determining the exponent of the unloading curve when flattening a sphere

Abstract

To study the flattening of the sphere, it is proposed to use the kinetic indentation diagram by the plane. Given the known values of the reduced elastic modulus, applied force, maximum and residual deformation, it is possible to determine the contact area. It is indicated that in this regard, the exponent of the unloading curve of a pre-loaded sphere with a flat rigid surface plays an important role. The analysis of methods for determining the unloading curves of unloading for the finite element models, taking into account strain hardening, is carried out. It is shown that dependences of the unloading curves during flattening on the relative indentation in the form and the range of values differ from the similar ones during indentations of the sphere. The dependence between the exponents of the unloading curves for the force and for the area is determined. The range of correct use of the results of the finite element analysis of a hemisphere for rough surfaces is indicated. The exponent of the unloading curve after flattening the spherical segment from the half-space property is determined.