Theoretical Estimation of the Strength of Thin-film Coatings
The theoretical strength of a perfect crystal lattice, which corresponds to the simultaneous breaking of intermolecular bonds, is very high – only ten times less than the Young’s modulus. Strength of real solids is several orders of magnitude smaller. This is linked with the existence of lattice defects. In the work of the various types of defects are considered only crack. Although really brittle materials is very small. Question of cracks in brittle solids is of great practical importance because many plastic materials (metals) are destroyed “brittle” manner. Problem of brittle fracture paid much attention. Trying to explain the discrepancy between the actual and theoretical values of strength in the presence of cracks was made by Griffith in his theory of brittle fracture of amorphous materials. He suggested that the real materials have a large number of small cracks, which can act as stress concentrators, increasing their value to the theoretical strength. The process reduces the gap while increasing the length of cracks until complete separation of the sample into two parts. In this paper we propose a simplified model of the phenomenon of destruction of elastic material, which allows to establish a connection between the theoretical tensile strength and the actual breaking stress. The model is based on the idea that each representative elementary particle continuum elastic medium incorporates the micro-crack. So that the material, as in Griffith’s theory, there is a whole network of micro-cracks. Fracturing process occurs due to the merger with the apparent micro-cracks (assuming no cracks) voltage equal to the actual tensile strength, and tensile material reaching peaks between neighboring cracks voltage theoretical tensile strength. Evaluation carried out calculations of the magnitude of micro-cracks and damage some materials. Installed in the connection between the theoretical tensile strength and the real destructive voltage calculation results correspond to known concepts and reference data.
KeywordsElementary representative area Theoretical tensile strength Actual breaking stress Size of micro-cracks damage
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The work was performed within the framework of the basic part of the State task for 2017 - 2019, project code 1.5265.2017 / BCh.
- Aptukov VN (2007) Model’ uprugo-povrezhdennoi ortotropnoi sredy [model of the elastic damaged orthotropic environment]. Vestnik Permskogo universiteta Seriia: Matematika Mekhanika Informatika 7(12):84–90Google Scholar
- Astaf’ev VI, Radaev YN, Stepanova LV (2001) Nelineinaia mekhanika razrusheniia [Nonlinear Mechanics of Damage]. Izdatel’stvo “Samarskii universitet”Google Scholar
- Busov VL (2007) Rasseianie ul’trazvukovykh voln na mikrotreshchinakh v fragmentirovannykh polikristallakh [ultrasonic wave scattering by microcracks in the fragmented polycrystals]. Akustichnii vestnik Acoustic Bulletin 10(3):19–24Google Scholar
- Frolenkova LY, Shorkin VS (2013) Metod vychisleniia poverkhnostnoi energii i energii adgezii uprugikh tel [method of calculating the surface and adhesion energies of elastic bodies]. Vestnik Permskogo natsional’nogo issledovatel’skogo politekhnicheskogo universiteta Mekhanika PNRPU Mechanics Bulletin 1:235–259Google Scholar
- Hild F, Forquin P, Denoual C, Brajer X (2005) Probabilistic-deterministic transition involved in a fragmentation process of brittle materials: Application to high performance concrete. Latin American Journal of Solids and Structures 2(1):41–56Google Scholar
- Kachanov LM (1974) Osnovy mekhaniki razrusheniia [Fundamentals of Mechanics of Damage]. Moskva: NaukaGoogle Scholar
- Nowacki W (1975) Teoriia uprugosti [Elasticity Theory]. Mir, Moskva Panin VE, Egorushkin VE (2009) Physical mesomechanics and nonequilibrium thermodynamics as a methodological basis for nanomaterials science. Physical Mesomechanics 12(5):204–220Google Scholar
- Petch NJ (1968) Metallographic aspects of fracture. In: Liebowitz H (ed) Fracture: An Advanced Treatise, Academic Press, New York, vol 1: Microscopic and Macroscopic Fundamentals, pp 376–420Google Scholar
- Rabotnov Y (1970) O razrushenii tverdykh tel [On the Damage of Solid Bodies]. Sudostroenie, Leningrad Rybin VV (1986) Bol’shie plasticheskie deformatsii i razrushenie materialov [Large Plastic Deformations and Damage of Materials]. Moskva: MetallurgiiaGoogle Scholar
- Sarafanov GF, Pereverzentsev VN (2010) Zarozhdenie mikrotreshchin v fragmentirovannoi strukture [nucleation of microcracks in the fragmented structure]. Vestnik Nizhegorodskogo universiteta im N I Lobachevskogo 5(2):90–94Google Scholar
- Sedov LI (1972) A Course in Continuum Mechanics, vol 1-4.Wolters-Noordhoff Publ., Groningen Vitkovsky IV, Konev AN, Shorkin VS, Yakushina SI (2007) Theoretical estimation of discontinuity flaw of adhesive contacts between multilayer elements of the liquid metal blanket in a fusion reactor. Technical Physics The Russian Journal of Applied Physics 52(6):705–710Google Scholar
- Volynskii AL, Iarysheva LM, Moiseeva SV, Bazhenov SM, Bakeev NF (2006) Novyi podkhod kotsenke mekhanicheskikh svoistv tverdykh tel ekstremal’no malykh i bol’shikh razmerov [new approach to an assessment of mechanical properties of solid bodies of extremely small and big sizes]. Rossiiskii khimicheskii zhurnal Zhurnal Rossiiskogo khimicheskogo obshchestva im D I Mendeleeva Russian Journal of General Chemistry 50(5):126–133Google Scholar
- Zhurkov SN, Kuksenko VS, Petrov VA, Savel’ev VN, Sulgonov U (1977) O prognozirovanii razrusheniia gornykh porod [about forecasting of destruction of rocks]. Izvestiia AN SSSR Fizika Zemli Izvestiya - Academy of Sciences of the USSR Physics of the Solid Earth 6:11–18Google Scholar