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Nanoscience and Technology: An International Journal
ESCI SJR: 0.228 SNIP: 0.484 CiteScore™: 0.37

ISSN Imprimir: 2572-4258
ISSN En Línea: 2572-4266

Nanoscience and Technology: An International Journal

Formerly Known as Nanomechanics Science and Technology: An International Journal

DOI: 10.1615/NanomechanicsSciTechnolIntJ.v6.i2.30
pages 117-133

A MODEL OF CONTACT OF ELASTIC BODIES WITH ACCOUNT FOR THEIR ADHESION

N. A. Dolgov
G. S. Pisarenko Institute of Strength Problems, National Academy of Sciences of Ukraine, 2 Timiryazevskaya Str, Kiev, 01014, Ukraine
S. N. Romashin
I.S. Turgenev Orel State University, 95 Komsomolskaya Str., Orel, 302026, Russian Federation
L. Yu. Frolenkova
I.S. Turgenev Orel State University, 95 Komsomolskaya Str., Orel, 302026, Russian Federation
V. S. Shorkin
Federal State Higher Education Institution Orel I. S. Turgenev State University, 29 Naugorskoe Highway, Orel, Russian Federation

SINOPSIS

A model of contact interaction of elastic bodies, taking into account their adhesion, is presented. The adhesive forces are normally described using the notions of long-range surface-distributed forces. The Lennard-Jones potential, suggesting the presence of the finite distance between the surfaces of interacting bodies, is used. Its parameters are determined in terms of the surface energy, parameters of the Lennard-Jones interatomic potential, and the geometry of contacting bodies. The depth of location of real physical sources of nonlocal forces is commensurate with the width of the surface zone of their action. Therefore, it cannot be ignored when compared with the width of the near-surface field of adhesive forces. It means that nonlocal adhesive forces cannot be considered as surface forces. The presence of the equilibrium distance different from zero in the case of contact interaction of elastic bodies does not agree with the hypothesis of continuity. In this work, the adhesive forces are volume-distributed. They are nonlocal, potential, and acting between the pairs and triads of infinitely small elementary particles of interacting bodies. The potentials of pairwise particle interaction are proportional to the product of the volumes of interacting particles. The proportionality factors (hereinafter called the potentials) are monotonously decreasing functions of distances between the particles, irrespective of their position in relation to the body boundary. The triple interaction potential is proportional to the product of pairwise potentials. Functions, approximating the potentials, contain three parameters. The first two parameters are equal to the maximum of their values observed for zero distance between the particles. The third parameter defines the rate of decrease of the potential with the growing distance between the particles. All parameters for homogeneous, isotropic, linearly elastic materials are determined based on classical experiments of tension and compression, shear, and the characteristic of nonlinearity of an acoustic branch of the dispersion law. It is assumed that interaction of particles of different materials in a solid solution and in two bodies from these materials can be the same. Therefore, in order to determine the interaction potential parameters for particles of different materials, use is made of the data of experiments on determination of nonlinear concentration dependences of Young's modulus and the shear modulus of the solid solutions. Continuous material is considered to be deformable, if the distance at least between two material particles of it changes. Relative displacement of particles is expanded into a series in terms of the exterior pow¬ers of the radius vector of one relative to the other. The series retains the required number of terms. The expansion coefficients, i.e., displacement gradients of different orders, represent characteristics of the deformed state. It is assumed that elastic deformation energy depends on them. The interaction potentials for particles of the same material are also expanded into series in terms of the exterior power of the radius vector of their relative position. The enumerated actions make it possible to build a system of equilibrium equations, boundary-value conditions and conditions of conjugation of stress and displacement fields of interacting bodies based on the kinematic variational principle. The adhesion energy and force are calculated depending on the distance between semi-infinite bodies, based on the literature data on mechanical properties of the elastic state of aluminum, copper, and their solid solution. The result is compared with similar results obtained by the solid-state physics methods. The correspondence found is satisfactory


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