Abstract
The theory is proposed for solving problems of adhesion mechanics that is based on the concept of an anisotropic layer that serves as a contact between the adhesive and substrate. All boundary conditions in contact problems and the original equations are satisfied exactly; i.e., the mathematical Cauchy problem is solved. The possibilities of the theory are demonstrated by solving a specific problem of multiple destruction of a fiber in a polymer matrix during stretching of the Kargin—Malinsky model, which simulates the behavior of a reinforced polymer. The solution results explain the unusual experimental results.
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REFERENCES
R. A. Turusov, Adhesive Mechanics (Moscow State University of Civil Engineering, Moscow, 2016) [in Russian].
A. S. Freidin and R. A. Turusov, Properties and Calculation of Adhesive Joints (Khimiya, Moscow, 1990) [in Russian].
A. V. Turazyan and A. L. Rabinovich, “On stress distribution in an elementary model of a unidirectional structure,” Dokl. Akad. Nauk SSSR 191 (6), 1305–1307 (1970).
T. Hayachi, Photoelastsche Untersuchungen der Spannungs-Verteilung in der durch Fasern verstarkten Platte: Nonhomogenity and Plasticity (Hill Book, New York, 1959).
B. W. Rosen, “Strength of uniaxial fibrous composites,” in Mechanics of Composite Materials (Pergamon, New York, 1970).
R. A. Turusov, “Elastic and temperature behavior of a layered structure. I. Part, Experiment and theory,” Mech. Compos. Mater. 50 (6), 1119–1130 (2014).
R. A. Turusov, “Elastic and temperature behavior of a layered structure. Part II. Calcuulation results,” Mech. Compos. Mater. 51 (1), 175–183 (2015).
R. A. Turusov and L. I. Manevich, “Contact layer method in adhesive mechanics,” Polym. Sci., Ser. D 3 (1), 11–19 (2010).
L. I. Manevich and A. V. Pavlenko, “On taking into account the structural heterogeneity of the composite when assessing the adhesive strength,” Prikl. Mekh. Tekh. Fiz., No. 3, 140–145 (1982).
L. I. Manevich and R. A. Turusov, “Asymptotic method in adhesive mechanics,” Polym. Sci., Ser. D 4, 321–330 (2011). https://doi.org/10.1134/S1995421211040101
R. A. Turusov, K. T. Vuba, and A. S. Freidin, “Investigation of the influence of temperature and humidity factors on the strength and deformation properties of glued joints of wood with steel reinforcement,” Tsentr. Nauchno-Issled. Inst. Stroit. Konstr. im. V.A. Kucherenko, No. 24, 86–124 (1972).
R. A. Turusov, A. A. Nikishin, and V. G. Ivanova-Mumzhieva, “Some problems associated with the determination of adhesion strength,” in Proc. Int. Symposium “Polymers-73” (Varna, 1973), pp. 198–203.
R. A. Turusov, A. A. Nikishin, and Yu. A. Gorbatkina, “The boundary layer method in the problems of mechanics of a rigid deformable body,” in Proc. Int. Symposium “Polymers-73” (Varna, 1973), pp. 229–233.
R. A. Turusov, Zh. D. Sakvarelidze, and Yu. M. Malinskii, “Investigation of the mechanism of destruction of reinforced plastics at normal and elevated temperatures,” in Proc. Conf. “Reinforced Plastics–74” (Karlovy Vary, 1974), pp. 97–103.
R. A. Turusov, Zh. D. Sakvarelidze, Yu. M. Malinskii, and K. T. Vuba, “Stretching of composite rods taking into account bending as a model of adhesive joints,” Tsentr. Nauchno-Issled. Inst. Stroit. Konstr. im. V.A. Kucherenko, No. 53, 72–80 (1975).
R. A. Turusov and K. T. Vuba, “The role of an inhomogeneous stress state in assessing the strength of models of adhesive joints,” in Physics of Strength of Composite Materials (Leningrad Institute of Nuclear Physics, Leningrad, 1979), pp. 75–84 [in Russian].
R. A. Turusov and K. T. Vuba, “Stress state and features of assessing the strength of adhesive joints in shear,” Fiz. Khim. Obrab. Mater., No. 5, 87–94 (1979).
R. A. Turusov and K. T. Vuba, “Stress state and peculiarities of assessing the strength of adhesion joints at tearing off,” Fiz. Khim. Obrab. Mater., No. 2, 108–115 (1980).
R. A. Turusov, E. A. Bogachev, and A. B. Elakov, “The role of the intensity of the adhesive interaction and the stiffness of the matrix in the transfer of forces from the whole fiber to the broken one in the fibrous composite and in the realization of the strength of the reinforcing fibers. Part I,” Mekh. Kompoz. Mater. Konstr. 22 (3), 430–451 (2016).
R. A. Turusov, E. A. Bogachev, and A. B. Elakov, “The role of the intensity of the adhesive interaction and the stiffness of the matrix in the transfer of forces from the whole fiber to the broken one in the fibrous composite and in the realization of the strength of the reinforcing fibers. Part II,” Mekh. Kompoz. Mater. Konstr. 22 (4), 536–547 (2016).
Z. Hashin, “Thermoelastic properties of particulate composites with imperfect interface,” J. Mech. Phys. Solids 39 (6), 745–762 (1991).
Z. Hashin, “The spherical inclusion with imperfect interface,” J. Appl. Mech. 58 (2), 444–449 (1991).
Z. Hashin, “Extremum principles for elastic heterogenous media with imperfect interface and their application to bounding of effective elastic moduli,” J. Mech. Phys. Solids 40 (4), 767–781 (1992).
R. Lipton and B. Vernescu, “Variational methods, size effects and extremal microgeometries for elastic composites with imperfect interface,” Math. Mod. Methods Appl. Sci. 05 (08), 1139–1173 (1995).
Y. Benveniste and T. Miloh, “Imperfect soft and stiff interfaces in two-dimensional elasticity,” Mech. Mater. 33 (6), 309–324 (2001).
A. J. Nairn, Liu Yung Ching, and Galiotis Costas, “Analysis of stress transfer from the matrix to the fiber through an imperfect interface: Application to Raman data and the single-fiber fragmentation test,” in Fiber, Matrix and Interface Properties, Ed. by C. Spragg and L. Drzal (ASTM Int., West Conshohocken, PA, 1996), pp. 47–66. https://doi.org/10.1520/STP38225S.
G. I. Gurevich, Deformability of Media and Propagation of Seismic Waves (Nauka, Moscow, 1973) [in Russian].
A. Yu. Sergeyev, R. A. Turusov, N. I. Baurova, and A. M. Kuperman, “Stresses arising during cure of the composite wound on the cylindrical surface of an element of exhaust system,” Mech. Compos. Mater. 51 (3), 1–16 (2015).
V. I. Andreev, R. A. Turusov, and N. Yu. Tsybin, “Application of the contact layer in the solution of the problem of bending the multilayer beam,” Procedia Eng. 153, 59–65 (2016).
N. Yu. Tsybin, R. A. Turusov, and V. I. Andreev, “Comparison of creep in free polymer rod and creep in polymer layer of the layered composite,” Procedia Eng. 153, 51–58 (2016).
V. I. Andreev, R. A. Turusov, and N. Yu. Tsybin, “Determination of stress-strain state of a three-layer beam with application of contact layer method,” Mosk. Gos. Stroit. Univ., No. 4, 17–26 (2016).
A. Yu. Sergeev, R. A. Turusov, and N. I. Baurova, “Strength of the joint of an anisotropic composite and a cylindrical element of the exhaust system of road vehicles,” Mech. Compos. Mater. 52 (1), 1–14 (2016).
A. Yu. Sergeev, R. A. Turusov, and N. I. Baurova, “Determination of the adhesion strength of joints on the example of testing samples by pulling fiber from the matrix,” Compos. Nanostruct. 9 (1), 2–12 (2016).
Yu. A. Gorbatkina and V. G. Ivanova-Mumzhieva, Adhesion of Modified Epoxies to Fibers (Torus, Moscow, 2018).
N. Yu. Tsybin, R. A. Turusov, and V. I. Andreev, “Calculation of two-layer cylinder with application of contact layer model,” IOP Conf. Ser.: Mater. Sci. Eng. 456 (1), 012063 (2018). https://doi.org/10.1088/1757-899X/456/1/012063.
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Turusov, R.A. Adhesion Interaction and Adhesion Mechanics. Theory and Its Application. Polym. Sci. Ser. D 14, 522–531 (2021). https://doi.org/10.1134/S1995421221040250
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DOI: https://doi.org/10.1134/S1995421221040250