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.
Highlights
Determination of contact characteristics at the joint of rough surfaces is a difficult problem, both from the point of view of describing rough surfaces, and from the point of view of the mechanics of contact of individual asperities
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
Let us carry out similar research of the exponent of the unloading curve for the finite element models (FEM) [15], in which the equations are used for the force and contact area: ( ) A∗ = ω∗ 1 + exp 1 − ω∗ α −1, (24)
Summary
Determination of contact characteristics at the joint of rough surfaces is a difficult problem, both from the point of view of describing rough surfaces, and from the point of view of the mechanics of contact of individual asperities. In [16], an engineering method is given for calculating the contact characteristics during flattening of a sphere by modernizing the Drozd-Matlin model [10, 17] In this case, the results of modeling were used to determine the residual deformation during flattening of the sphere. Given the known values of the reduced modulus of elasticity, applied force, maximum and permanent deformation, it is possible to determine the contact area. In this regard, an important role is played by the exponent of the unloading curve of a pre-loaded sphere by a flat rigid surface, the refinement of the values of which is the purpose of this work
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