Experimental-Theoretical Method for Assessing the Stiffness and Adhesion of the Coating on a Spherical Substrate

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Abstract

Known methods and approaches are ineffective or not applicable at all in the study of mechanical characteristics and adhesion of coatings of complex structure, initially formed on non-planar surfaces. A device has been developed that includes fragments of spherical substrates with rings for mounting along the contour, a pressure source of the working medium with a pressure gauge, a line with a valve for supplying the working medium, a measuring complex and a line for etching the working medium. In a fragment of a spherical substrate there is a small diameter hole, in the area of which a cover is formed according to a given technology. The working medium is fed through a small hole in the tray. A segment of the coating detached from the substrate forms a dome in the form of an ellipsoid fragment. A numerical model of deformation of a coating fragment in the form of a spherical segment with a complex contour is being developed using well-known software complexes. At each step of loading by the “targeting” method, varying the modulus of elasticity and the Poisson’s ratio, we approach the parameters of the experimental dome and determine the actual mechanical and stiffness properties of the coating under study. We calculate the normal separation forces through the radial forces determined by the current numerical model, and then determine the coupling stresses. The developed experimental-theoretical method is an effective tool for evaluating the mechanical properties and stiffness of coatings of complex structure, as well as the adhesion of the coating to a spherical substrate.

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1. Introduction One of the most developed approaches for protecting surfaces from environmental influences is coating. Surface coatings are widely used in all branches of production and life [1-3]. They provide protection and insulation of the surface of structures operating in various environments and under the influence of various physical fields. Based on the operating conditions, various coatings and adhesives of complex structure are developed, providing the necessary qualities [4-8]. Active work is underway to create functional and intelligent coatings for corrosion protection [9-15]. During the operation of structures, protective coatings fail first of all, which can lead to serious consequences, in particular, to intensive corrosion wear of the bearing elements of the structure. When choosing a coating, adhesive and its application technology, questions arise related to determining their necessary parameters, evaluating their mechanical properties and their service life depending on operating conditions. Methods for evaluating the mechanical properties of coatings. Various approaches are used to study the mechanical characteristics of coatings [6-8]. The indenter method [16], which allows determining the properties of a material in the vicinity of a given point, has become widely used. There are studies based on the molecular approach [17], in which difficulties arise in describing the structure of the coating at the molecular level. However, for coatings of complex structure, the indenter method and the molecular approach are ineffective. There is a large variation in the results of the study by the standard uniaxial tensile testing method of coatings of a complex structure in the shape of a rectangle based Figure 1. Fragment and installationdiagram S o u r c e : made by N.M. Yakupov on the Russian state standard GOST 14236-81. Polymer films. Tensile Test Method; ASTM D 412-41. An effective approach to assessing the mechanical properties of films is the experimental - theoretical ETM method [18], which allows evaluating the integral properties of coatings. ETM is based on the synthesis of experimental data and relations from the theory of thin shells. Figure 1 shows a diagram of the device. The installation allows testing of round-shaped samples in plan. The sample is placed on the device, loaded with a uniform surface pressure p and the form of deformation of the sample is monitored. The dependence “pressure p - deflection H” is obtained from the experiment, and then, using the relations of the theory of shells, the mechanical properties of the coating are determined [18]. Methods for assessing the adhesion of coatings. Various methods have been developed to determine the adhesion strength of the coating to the substrate. There are, for example, USSR copyright certificate No. 183459; RF patents No. 689411, No. 2207544. These developments have some disadvantages, in particular, technological difficulties and do not provide the necessary accuracy. A method is known for estimating the adhesion of an elastic coating to a substrate based on the parameters of the “bubble” [19]. A method has been developed for determining the adhesion of rigid and flexible coatings to the substrate (RF Patent No. 2421707), which allows assessing the adhesive properties taking into account the mechanical characteristics and thickness of the coating (Figure 2). At the same time, the spread of results is reduced. Modern coatings have a complex structure and are formed, as a rule, directly on the surfaces of structures of various shapes, in particular, on cylindrical, spherical and toroidal surfaces [20]. Known methods and approaches are ineffective or completely inapplicable in the study of the mechanical characteristics of coatings of complex structure, initially formed on non-planar surfaces. The purpose of this work is to develop an effective tool for determining the stiffness properties of coatings of complex structure and adhesive on a spherical substrate. Figure 2. Installation diagrams: G1 - for rigid coatings; G2 - for flexible coatings S o u r c e : made by N.M. Yakupov 2. Method for assessing the adhesion of the coating on a spherical substrate The test device consists of a set of fragments of spherical substrates of various diameters, a pressure source of the working medium with a pressure gauge, a line with a valve for supplying the working medium, a measuring complex and a line for etching the working medium. There is a small diameter hole in the substrate, in the area of which a coating is formed according to a given technology. A fragment of the installation diagram is shown in Figure 3. Figure 3. Diagram of the experimental setup (G1); dome parameters: the base of the spherical segment (G2), the base of the ellipsoid fragment in plan (G3), the diametrical section of the spherical segment (G4) S o u r c e : made by N.M. Yakupov The algorithm of the method. During the experiment, the working medium, in particular, air, is smoothly fed into the inner cavity of the spherical substrate - cavity A (Figure 3, G1). When the pressure reaches a certain value, the coating slowly comes off. At the same time, a dome is formed. In the simplest case, a dome is formed in the form of a spherical segment with radius r (axisymmetric variant) with a flat base in the form of a circle with radius a (Figure 3, G2). In a more general case, a dome is formed that is close in shape to an ellipsoid fragment; at the same time, the base of the dome is a spatial curve lying on a spherical surface of radius R and having in plan a shape close to an ellipse with semi-axes a and b (Figure 3, G3). At the first stage, the stiffness property of the coating is investigated. At each step of loading p, the form of deformation of the coating under pressure p is monitored, the dome parameters are measured: a, b and H. Next, numerical models of deformation of a coating fragment in the form of a spherical segment with radius r , in a particular case, or in the form of an ellipsoid fragment having a shape close to an ellipse with semi-axes a and b are developed . In this case, either well-known software systems, for example, ANSYS, or a spline version of the finite element method (CB FEM) are used [21; 22]. At each step of loading p by the “targeting” method, varying the properties of the material, for example, for an elastic coating with the elastic modulus Ej and the Poisson's ratio νj , we approach the dome parameters corresponding to the experimental parameters a, b and H. The mechanical parameters E and ν , at which the maximum approximation of the numerical model to the experimental shape of the dome is observed, characterize the actual mechanical properties of the coating under study. Further, if necessary, it is possible to calculate the stiffness of the coating for stretching B and bending D: = ; = . (1) ( ) ( ) Thus, we determine the actual mechanical properties of the coating under study and determine the stressstrain state of the coating. At the same time, special attention is paid to the determination of tangential forces Т1 and deformation of the coating, in the radial (normal) ε1 and tangential ε2 directions near the contour of the dome. Якупов С.Н., Гумаров Г.Г., Якупов Н.М. Строительная механика инженерных конструкций и сооружений. 2023. Т.19. № 6. С. 577-582 At the second stage, we investigate the adhesive properties of the coating to the spherical surface of the substrate. Based on the radial forces At the second stage, we investigate the adhesive properties of the coating to the spherical surface of the substrate. Based on the radial forces Т1 obtained at the first stage, we determine the normal separation forces Тotr. For a dome in the form of a spherical segment, based on Figure 3, the separation forces are the same along the entire contour and can be determined by the formula: . (2) [( ) ] For the more general case, the contour separation forces vary depending on the parameters a and b. However, if we take into account that the maximum forces of separation of the coating will be in the area of the small semi-axis b, then the separation forces can be determined by the formula: . (3) [( ) ] Further, according to certain normal separation forces Тotr, determine the coupling tension ηotr by the formula: = . (4) ( ) Performing the procedure for calculating the coupling voltage ηotr (рi) according to this algorithm for a number of pressures рi (i = 1 ÷ n), we determine the average values ηotr-sr by the formula: ηotr-sr = ( ηotr (рi) ) / n. (5) 3. Conclusion 1. A coating of a complex structure, initially formed on a fragment of a spherical substrate, is investigated. The working medium was fed through a small hole in the substrate. A segment of the coating torn from the substrate formed a dome in the form of an ellipsoid fragment. 2. A numerical model of deformation of a coating fragment in the form of a spherical segment has been developed using well-known software systems. At each step of loading by the “targeting” method, varying the modulus of elasticity and the Poisson’s ratio, when approaching the parameters of the experimental dome, the actual mechanical and stiffness properties of the coating under study were determined. According to the radial forces determined by the current numerical model, the normal separation forces are calculated and the coupling stresses are determined. The developed experimental-theoretical method is an effective tool for assessing the mechanical properties and rigidity of coatings of complex structure, as well as the adhesion of the coating to a spherical substrate.
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About the authors

Samat N. Yakupov

Federal Research Center «Kazan Scientific Center of Russian Academy of Sciences»

Author for correspondence.
Email: tamas_86@mail.ru
ORCID iD: 0000-0003-0047-3679

PhD in Technical Sciences, senior researcher

Kazan, Russian Federation

Gabdrauf G. Gumarov

Federal Research Center «Kazan Scientific Center of Russian Academy of Sciences»; E.K. Zavoisky Physical-Technical Institute

Email: ifoggg@gmail.com
ORCID iD: 0000-0001-6803-2330

Candidate of Physical and Mathematical Sciences, Head of the Laboratory of Radiation Chemistry and Radiobiology, E.K. Zavoisky Physical-Technical Institute, Kazan Scientific Center, Russian Academy of Sciences; Senior Researcher, Federal Research Center «Kazan Scientific Center of Russian Academy of Sciences», Institute of Mechanics and Engineering

Kazan, Russian Federation

Nukh M. Yakupov

Federal Research Center «Kazan Scientific Center of Russian Academy of Sciences»

Email: yzsrr@mail.ru
ORCID iD: 0000-0001-8248-1589

Dr. Sci. (Eng.), leading researcher

Kazan, Russian Federation

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