The paper examines the effect of a chemical reaction of first order on the convective stability of fluid that occupies semi-infinite space limited by liquid-gas surface. The reagent is considered to go through the surface into the liquid, where it reacts resulting the product. It is assumed that the product of the reaction is a surface-active substance and has been adsorbed at the interface according to the law of Langmuir. The problem on linear stability of the base state characterized by the processes of reaction-diffusion with respect to monotonous perturbations of solutal capillary nature has been solved analytically. The neutral curves for Marangoni instability have been obtained.

Keywords: convective stability, reaction-diffusion, adsorption-desorption, solutal Marangoni instability.

Aitova Elizaveta V. (Perm, Russian Federation) – student of the Faculty of Physics, Perm State Humanitarian Pedagogical University (24, Sibirskaya st., 614990, Perm, Russian Federation, e-mail: andreychatenko@gmail.com).

Bratsun Dmitry A. (Perm, Russian Federation) – Doctor of Physical and Mathematical Sciences, Head of the Department of Theoretical Physics, 

1. Eckert K., Acker M., Shi Y. Chemical pattern formation driven by a neutralization reaction. Part I: Mechanism and basic features. Phys. of Fluids. 2004, vol. 16, pp. 385-399.

2. Bratsun D.A., De Wit A. On Marangoni convective patterns driven by an exothermic chemical reaction in two-layer systems. Phys. of Fluids. 2004, vol. 16, no. 4, pp. 1082-1096.

3. Shi Y., Eckert K. Orientation-dependent Hydrodynamic Instabilities from Chemo-Marangoni Cells to Large Scale Interfacial Deformations. Chinese J. of Chem. Eng. 2007, vol. 15, no. 5, pp. 748-753.

4. Shi Y., Eckert K. Acceleration of reaction fronts by hydrodynamic instabilities in immiscible systems. Chem. Eng. Sci. 2006, vol. 61, no. 17, pp. 5523-5533.

5. Rongy L., Trevelyan P.M.J., De Wit A. Dynamics of A+B→C reaction fronts in the presence of buoyancy-driven convection. Phys. Rev. Lett. 2008, vol. 101, no. 8, pp. 084503-084507.

6. Bratsun D.A., De Wit A. Ob upravlenii khemokonvektivnymi strukturami v ploskom reaktore [Control of chemoconvective structures in a slab reactor]. Techn. Phys. 2008, vol. 53, pp. 146-153.

7. Bratsun D.A., De Wit A. Buoyancy-driven pattern formation in reactive immiscible two-layer systems. Chem. Eng. Sci. 2011, vol. 66, no. 22, pp. 5723-5734.

8. Bratsun D.A. Khemokonvectivnoe strukturoobrazovanie v reagiruyushchikh zhidkostyakh [Chemoconvective pattern formation in reactive fluids]. LAM Lambert Academic Publ., 2012. 145 p.

9. Riolfo L.A., Carballido-Landeira J., Bounds C.O., Pojman J.A., Kalliadasis S., De Wit A. Experimental reaction-driven liquid film fingering instability. Chem. Phys. Lett. 2012, vol. 534, pp. 13-18.

10. Pearson J.R.A. On convection cells induced by surface tension. J. Fluid Mech. 1958, vol. 4, pp. 489-500.

11. Ruckenstein E., Berbente C. The occurrence of interfacial turbulence in the case of diffusion accompanied by chemical reaction. Chem. Eng. Sci. 1964, vol. 19, pp. 329-347.

The paper is devoted to the experimental investigation of the mechanical behavior of the Armco iron during gigacycle fatigue tests. The samples were tested on an ultrasonic testing machine USF-2000 with loading frequency 20 kHz. The Wöhler law was obtained for investigated material in the range from 1∙10⁶ to 1∙10¹⁰ cycles. To study the characteristics of the cracks nucleation two new systems for monitoring the physical properties of a sample were developed The techniques were based on the measurements of electric current and magnetic field. It was shown that the significant change of the physical processes accompanying the evolution of structural defects in the material was observed on the final stages of the experiment. The obtained data allowed us to estimate the characteristic time of the sub-surface fatigue cracks evolution that cannot be monitored by the standard non-destructive methods.

Keywords: gigacyclic fatigue, armco-iron, crack length monitoring.

Vshivkov Aleksey Nikolaevich (Perm, Russian Federation) – student of Perm State National Research University (15, Bukireva st., 614990, Perm, Russian Federation, e-mail: aleksey.1992@mail.ru).

Prokhorov Alexander Evgenievich (Perm, Russian Federation) – student of Perm State National Research University (15, Bukireva st., 614990, Perm, Russian Federation, email: alexproher@gmail.com).

Uvarov Sergey Vitalievich (Perm, Russian Federation) – Ph.D. In Technical Sciences, Senior Researcher Institute of Continuous Media Mechanics Ural Branch of Russian Akademy of Sciences (1, Akademic Korolev st., 614013, Perm, Russian Federation, e-mail: usv@icmm.ru).

Plekhov Oleg Anatolievich (Perm, Russian Federation) – Doctor of Physical and Mathematical Sciences, Deputy director Institute of Continuous Media Mechanics Ural Branch of Russian Akademy of Sciences (1, Akademic Korolev st., 614013, Perm, Russian Federation, e-mail: poa@icmm.ru).

1. Zhu X., Shyam A., Jones J.W., Mayer H., Lasecki J.V., Allison J.E. Effects of microstructure and temperature on fatigue behavior of E319-T7 cast aluminum alloy in very long life cycles. Int. J. Fatigue, 2006, vol. 28, pp. 1566-1571, available at: http://www.sciencedirect.com/science/article/ pii/S0142112306000946.

2. Bathias C., Paris P. Gigacycle Fatigue in Mechanical Practice. Taylor & Francis, 2004. 328 p.

3. Botvina L. Gigaciklovaya ystalost – novaya problema fiziki i mehaniki razrysheniya [Gigacycle fatigue – new problem of physics and mechanical damage]. Zavodskaya laboratoriya. Diagnostika materialov, 2004, vol. 70, no. 4, pp. 41-51.

4. Shaniavski A.A., Skvortsov G.V. Fatigue limit – Material property as an opened or closed system? Practical view on the aircraft components failures in GCF area. Fatigue & Fracture of Engineering Materials & Structures, 1999, vol. 22, no. 7, pp. 609-619.

5. Plekhov O., Palin-Luc T., Naimark O., Uvarov S., Saintier N. Fatigue crack initiation and growth in a 35CrMo4 steel investigated by infrared thermography. Fatigue and fracture of engineering materials and structures, 2005, vol. 28, iss. 1, pp. 169-178.

6. Sakai T. Review and prospects for current studies on very high cyclic fatigue of metallic materials for machine structural use. Journal of solid mechanics and materials engineering, 2009, vol. 3, no. 3, pp. 425-439.

7. Wang Q.Y., Berard J.Y., Rathery S., Bathias C. Technical note High-cycle fatigue crack initiation and propagation behaviour of high-strength sprin steel wires, Fatigue &Fracture of Engineering Materials & Structures, 1999, vol. 22, pp. 673-677, available at: http://onlinelibrary. wiley.com/doi/10.1046/j.1460-2695.1999.t01-1-00184.x/abstract.

8. Naimark O., Plekhov O., Betekhtin V., Kadomcev A., Narikova М. Kinetika nakopleniya defektov I dyalnost krivoi Vellera pri gigaciklovoi ysta­losti metallov [The kinetics accumulation of defects and duality Weller’s curve by gigacycle fatigue of metals]. TPJ, 2014, vol. 84, no. 3, pp. 89-94.

9. Plekhov O., Saintier N., Palin-Luc T., Uvarov S., Naimark O. Theoretical analysis, infrared and structural investigation of energy dissipation in metals under quasi-static and cyclic loading. Material Science and Engineering, 2007, vol. 462, no. 1, pp. 367-370.

10. Plekhov O.A., Naimark O., Saintier N. Experimental study of energy accumulation and dissipation in iron in an elastic-plastic transition. Technical Physics. The Russian Journal of Applied Physics, 2007, vol. 52, no. 9, pp. 1236-1238.

11. Naimark O.B., Davydova M., Plekhov O.A., Uvarov S.V. Nonlinear and structural aspects of transitions from damage to fracture in composites and structures. Computers & Structures, 2000, vol. 76, no. 1, pp. 67-75.

12. Wang C., Wagner D., Wang Q.Y., Bathias C. Gigacycle fatigue initiation mechanism in Armco iron. International Journal of Fatigue, 2012, vol. 45, pp. 91–97.

13. Bathias С., Paris P.C. Gigacycle Fatigue in Mechanical Practice. New York: CRC Press, 2004. 328 p.

Goldobin Denis Sergeevich (Perm, Russian Federation) – PhD in Physical and Mathematical Sciences; Senior Researcher "Dynamics of Geological Systems" of the Institute of Continuous Media Mechanics, Ural Branch of Russian Akademy of Sciences (1, Academic Korolev st., 614013, Perm, Russian Federation, e-mail: goldobin@icmm.ru); Senior Lecturer at the Department of Theoretical Physics of Perm State National Research University (15, Bukireva st., 614990, Perm, Russian Federation).

Krauzin Pavel Vasilyevich (Perm, Russian Federation) – Doctoral Student, Institute of Continuous Media Mechanics Ural Branch of Russian Akademy of Sciences (1, Academic Korolev st., 614013, Perm, Russian Fede­ration, e-mail: krauzin@gmail.com).

1. Goldobin D.S., Brilliantov N.V. Diffusive counter dispersion of mass in bubbly media. Phys. Rev. E., 2011, vol. 84, p. 056328.

2. Goldobin D.S., Krauzin P.V. Vlijanie godovoj volny temperatury na diffuzionnyj transport atmosfernogo azota v zatoplennyh pochvah [Influence of annual temperature wave on diffusive transport of atmospheric nitrogen in wetlands]. Vestnik Permskogo Universiteta. Physika, 2012, iss. 4 (22), pp. 44-47.

3. Lyubimov D.V., Shklyaev S., Lyubimova T.P., Zikanov O. Instability of a drop moving in a Brinkman porous medium. Phys. Fluids, 2009, vol. 7, pp. 337-344.

4. Donaldson J.H. [et al.] Development and Testing of a Kinetic Model for Oxygen Transport in Porous Media in the Presence of Trapped Gas. Ground Water, 1997, vol. 35, p. 270.

5. Donaldson J.H., Istok J.D., O’Reilly K.T. Dissolved Gas Transport in the Presence of a Trapped Gas Phase: Experimental Evaluation of a Two-Dimensional Kinetic Model. Ground Water, 1998, vol. 36, p. 133.

6. Barenblatt G.I., Yentov V.M., Ryzhik V.M. Theory of Fluid Flows Through Natural Rocks. Springer, 2010. 412 p.

7. Bird R.B., Stewart W.E., Lightfoot E.N. Transport phenomena. 2^nd ed. N.Y.: Wiley, 2007. 897 p.

On-site measurements of water salinity (which can be directly evaluated from the electrical conductivity) in deepsea sediments is technically the primary source of indirect information on the capacity of the marine deposits of methane hydrates. We show the relation between the salinity (chlorinity) profile and the hydrate volume in pores to be significantly affected by non-Fickian contributions to the diffusion flux – the thermal diffusion and the gravitational segregation – which have been previously ignored in the literature on the subject and the analysis of surveys data. We provide amended relations and utilize them for an analysis of field measurements for a real hydrate deposit.

Keywords: non-Fickian diffusion, hydrate deposits, brine salinity.

Goldobin Denis Sergeevich (Perm, Russian Federation) – Ph.D. in Physical and Mathematical Sciences, Senior Researcher «Dynamics of Geological Systems» of the Institute of Continuous Media Mechanics, Ural Branch of Russian Akademy of Sciences (1, Academic Korolev st., 614013, Perm, Russian Federation, e-mail: goldobin@icmm.ru), Senior Lecturer at the Department of Theoretical Physics of Perm State National Research University (15, Bukireva st., 614990, Perm, Russian Federation).

Pimenova Anastasiya Vladimirovna (Perm, Russian Federation) – Ph.D. student in the Institute of Continuous Media Mechanics, Ural Branch of Russian Akademy of Sciences (1, Academic Korolev st., 614013, Perm, Russian Federation, e-mail: spkv@list.ru).

1. Maslin M. [et al.] Gas hydrates: past and future geohazard? Phil. Trans. Roy. Soc. A., 2010, vol. 368, pp. 2369-2393.

2. Maclennan J., Jones S.M. Regional uplift, gas hydrate dissociation and the origins of the Paleocene-Eocene Thermal Maximu. Earth and Planetary Science Letters, 2006, vol. 245, pp. 65-80.

3. Dunkley Jones T. [et al.] A Palaeogene perspective on climate sensitivity and methane hydrate instability. Phil. Trans. Roy. Soc. A, 2010, vol. 368, pp. 2395-2415.

4. Kennett J.P. [et al.] Methane Hydrates in Quaternary Climate Change: The Clathrate Gun Hypothesis. AGU, Washington D.C., 2003.

5. Nisbet E.G. The end of the ice age. Canadian Journal of Earth Sciences, 1990, vol. 27, pp. 148-157.

6. Paull C.K., Ussler W., Dillon W.P. Is the extent of glaciation limited by marine gas hydrates? Geophys. Res. Lett., 1991, vol. 18, pp. 432-434.

7. Kvenvolden K.A. Potential effects of gas hydrate on human welfare. PNAS, 1999, vol. 96, pp. 3420-3426.

8. McIver R.D. Role of naturally occuring gas hydrates in sediment transport. American Association of Petroleum Geologist Bulletin, 1982, vol. 66, pp. 789-792.

9. Henriet J.-P., Mienert J. Gas Hydrates: Relavance to world margin stability and climate change. Special Publication of the Geological Society of London, 1998, vol. 137.

10. Bugge T., Befring S., Belderson R.H. A giant three-stage submarine slide off Norway. Geo-Marine Letters, 1987, vol. 7, pp. 191-198.

11. Kayen R.E., Lee H.J. Pleistocene slope instability of gas hydrate-laden sediment on the Beaufort sea margi. Marine Geotechnology, 1991, vol. 10, pp. 125-141.

12. Goldobin D.S., Brilliantov N.V. Diffusive counter dispersion of mass in bubbly media. Phys. Rev. E, 2011, vol. 84, 056328. ISSN 1539-3755 (print), 1550-2376 (online).

13. Goldobin, D.S. [et al.] Non-Fickian Diffusion and the Accumulation of Methane Bubbles in Deep-Water Sediments. E-print arXiv:1011.6345.

14. Goldobin D.S. Scaling of transport coefficients of porous media under compaction. Europhys. Lett., 2011, vol. 95, 64004. ISSN 0295-5075 (print), 1286-4854 (online).

15. Davie M.K., Buffett B.A. A numerical model for the formation of gas hydrate below the seafloor. J. Geophys. Res., 2001, vol. 106, pp. 497-514.

16. Davie M.K., Buffett B.A. A steady state model for marine hydrate formation: Constraints on methane supply from pore water sulfate profiles. J. Geophys. Res., 2003, vol. 108, p. 2495.

17. Davie M.K., Buffett B.A. Sources of methane for marine gas hydrate: inferences from a comparison of observations and numerical models. Earth and Planetary Science Letters, 2003, vol. 206, pp. 51-63.

18. Archer D. Methane hydrate stability and anthropogenic climate change. Biogeosciences, 2007, vol. 4, pp. 521-544.

19. Garg S.K. [et al.] A mathematical model for the formation and dissociation of methane hydrates in the marine environment. J. Geophys. Res., 2008, vol. 113, B01201.

20. Haacke R.R., Westbrook G.K., Riley M.S., Controls on the formation and stability of gas hydrate-related bottom-simulating reflectors (BSRs): A case study from the west Svalbard continental slope. J. Geophys. Res., 2008, vol. 113, B05104.

21. Paull C.K., Matsumoto R., Wallace P.J., Dillon W.P. (Eds.) Proceedings of the Ocean Drilling Program. Scientific Results, Ocean Drilling Program, College Station, TX, 2000, vol. 164.

22. Ecker C., Dvorkin J., Nur A. Estimating the amount of hydrate and free gas from surface seismic. SEG Technical Program Expanded Abstracts, 1998, vol. 17, pp. 566-569.

23. Circone S., Kirby S.H., Stern L.A. Direct Measurement of Methane Hydrate Composition along the Hydrate Equilibrium Boundary. J. Phys. Chem. B, 2005, vol. 109, pp. 9468-9475.

24. Bird R.B., Stewart W.E., Lightfoot E.N. Transport Phenomena 2nd ed. Wiley, 2007.

25. Butt F.A., Elverhoi A., Solheim A., Forsberg C.F. Deciphering Late Lenozoic development of the western Svalbard margin from ODP 986 results. Marine Geology, 2000, vol. 169, pp. 373-390.

26. Caldwell D.R. Thermal and Fickian diffusion of sodium chloride in a solution of oceanic concentration. Deep Sea Research and Oceanographic Abstracts, 1973, vol. 20, pp. 1029-1039.

27. Caldwell D.R. Measurements of negative thermal diffusion coefficients observing onset of thermohaline convection. J. Phys. Chem., 1973, vol. 77, pp. 2004.

28. Lee M.W., Paul C.K., Matsumoto R., Wallace P.J., Dillon W.P. Gas hydrates amount estimated from acoustic logs at the Blake Ridge, Sites 994, 995, and 997. (Eds.) Proceedings of the Ocean Drilling Program. Scientific Results. College Station, TX, 2000, vol. 164.

Within decomposition of hoop and radial components of displacement vector to the trigonometrical and generalized power series new exact analytical solutions have been obtained to problems on equilibrium state of combined thick-walled heavy transversally-isotropic spheres which are fixed on the exterior or interior surfaces and are subject to the action of uniform internal or external lateral pressure. In particular obtained analytical solutions can be used for the analysis of the influence of geometry of concrete monolithic supports for spherical mine workings, the properties of reinforced concrete and the sedimentary rock mass surrounding minings on the distribution of stresses and displacements. In the construction of mine workings reinforcement is one of the main production processes otherwise there is no way for their exploitation. Monolithic concrete supports aimed at maintaining labor safety and safety of mineral raw materials and equipment kept inside are usually made of reinforced concrete, i.e. anisotropic material, the weight of which has to be greatly considered.

Keywords: thick-walled combined transversally-isotropic sphere, elastic equilibrium state, gravity forces, exact analytical solution, reinforced concrete monolithic supports for spherical mine workings, sedimentary rock mass surrounding mine, mechanisms of initial stage of damage evolution

Zaitsev Alexey Vyacheslavovich (Perm, Russian Federation) – Ph.D. in Physical and Mathematical Sciences, Associate Professor of the Department for Mechanics of Composite Materials and Constructions, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, Russian Fede­ration, e-mail: zav@pstu.ru).

Sokolkin Yuriy Viktorovich (Perm, Russian Federation) – Doctor of Physical and Mathematical Sciences, Professor, Head of the Department for Mechanics of Composite Materials and Constructions, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, Russian Fede­ration, e-mail: sokolkin@pstu.ru).

Fukalov Anton Alexandrovich (Perm, Russian Federation) – Doctoral Student of the Department for Mechanics of Composite Materials and Constructions, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, Russian Federation, e-mail: mr_aa@mail.ru).

1. Zaitsev A.V., Fukalov A.A. Uprugoe ravnovesie tyazheloy trans­versalno-izotropnoy tolstostennoy sfery s zhestko zakreplennoy vnutrenney poverkhnostiu [Elastic equilibrium state of thick-walled heavy transversally-isotropic spheres fixed on the interior surface]. Vestnik Samarskogo gosudarstvennogo tehnicheskogo uni­ver­siteta. Seriya Fiziko-matematicheskie nauki, 2010, no. 5(21), pp. 85-95.

2. Fukalov A.A., Kutergin A.V. Tochnye analiticheskie resheniya za­dach o ravnovesii uprugikh anizotropnykh tyazhelykh tel s centralnoy i osevoy simmetriey i ikh prilozheniya [Exact analytical solutions to problems of the equilibrium state of elastic anisotropic heavy central and axial-symmetric bodies and their applications]. Vestnik Nizhegorodskogo universiteta imeni N.I. Lobachevskogo, 2011, no. 4 (4), pp. 1831-1833.

3. Zaitsev A.V., Kislitsyn A.V., Kutergin A.V. Fukalov A.A. Ras­pre­delenie napryazheniy v poperechnykh secheniyakh konteinerov iz steklo­plas­tika i polimerbetona, ispolzuemykh dlya dlitelnogo khraneniya vysoko­agres­sivnykh sred [Stress distribution in the cross-sections of containers made of fiberglass and polymer concrete , used for long-term storage of highly aggressive media]. Izvestiya Samarskogo nauchnogo tsentra Rossiyskoy akademii nauk, 2012, vol. 14, no. 4(5), pp. 1230-1234.

4. Zaitsev A.V., Kutergin A.V. Uprugoe ravnovesie tyazhelogo gori­zontalnogo tolstostennogo ortotropnogo tsilindra, nakhodyaschegosya pod deistviem neravnomerno raspredelennogo bokovogo davleniya [Elastic equilibrium state of heavy horizontal thick-walled orthotropic cylinder under the action of non-uniformly distributed lateral pressure]. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika, 2010, no. 4. pp. 36-45.

5. Zaitsev A.V., Kislitsyn A.V. Ob odnom reshenii zadachi Lame dlya sostavnogo protyazhennogo elementa konstrukcii, sostoyaschego iz posa­zhennykh s natyagom tolstostennogo transversalno-izotropnogo vneshnego tsilindra na soosniy izotropniy vnutrenniy [On A solution of Lame problem for a combined long structural element, consisting of thick-walled transversely isotropic external cylinder spanned by the on-axis isotropic internal one]. Vestnik Samarskogo gosudarstvennogo tehnicheskogo universiteta. Seriya Fiziko-matematicheskie nauki, 2007, no. 1(14), pp. 164-167

6. Kozhevnikova L.L., Kuznetsov G.B., Matveenko V.P., Shardakov I.N. Analiticheskoe issledovanie uprugogo ravnovesiya poloy sfery, zhestko zakreplennoy po vneshnemu konturu [Analytical study of the elastic equilibrium of a hollow sphere, rigidly fixed on the outer edges]. Problemy prochnosti, 1974, no. 9, pp. 20-23.

7. Kuznetsov G.B. Uprugost, vyazkouprugost i dlitelnaya prochnost tsilindricheskikh i sfericheskikh tel [Elastic, viscoelastic and long-term strength of cylindrical and spherical bodies]. Moscow: Nauka, 1979. 112 p.

8. Vil'deman V.E., Sokolkin Yu.V., Tashkinov A.A. Mekhanika neuprugogo deformirovaniya i razrusheniya kompozitsionnykh materialov [Mechanics of inelastic deformation and failure of composite materials]. Moscow: Nauka, 1997. 288 p.

9. Pobedrya B.E. Mekhanika kompozitsionnykh materialov [Mechanics of composite materials]. Moscowskiy gosudarstvenniy universitet, 1984. 336 p.

The article is dedicated to the mesolevel model of elastoviscoplastic deformation of hexagonal close-packed crystal (HCP). This model of mesolevel is the main part of the developed two-level model of polycrystal. The features of elastoviscoplastic deformation of HCP-monocrystal carried out by the motion of edge dislocations and twinning are analyzed. The use of the elastoviscoplastic model allows avoiding the problem that occurs in other models, for example, the problem of determination non-uniqueness shear rates. Due to the dislocation nature of twinning, it can be treated as a slip. The necessity of application the asymmetric measure the stress strain state on mesolvel is justified; the asymmetric measure of deformation rate does not depend on the reference system. The relations of the crystalline model using the proposed measure of the stress strain are given. The variants of hardening laws accepted in this work are physically substantiated. The proposed variant of the hardening law for twinning is able to get the results which conform with the experimental data: twining in HCP crystal is carried out quickly then-suspended, because twins of the twinning system prevent spreading of twins in other systems. The usage of the elastoviscoplastic model for the description of inelastic deformation materials with the HCP-lattice with α-titanium as an example is considered. The algorithm of definition the stress strain state is developed; the model is used for the study of simple load cases. The description and analyses of the obtained results of numerical calculation with hardening is stated. The influence of load cases on the nature of the deformation (hardening, volume fraction of twins, etc.) is investigated.

Keywords: HCP-crystals, dislocation slip, twinning, asymmetric measures of stress-strain state, hardening laws.

Matsyuk Kristina Valeryevna (Perm, Russian Federation) – Doctoral Student of Department of Mathematical Modeling of Systems and Processes, Perm National Research Polytechnic University (614990, 29, Komsomolsky av., Perm, Russian Federation, e-mail: Krissss91@mail.ru).

Trusov Peter Valentinovich (Perm, Russian Federation) – Doctor of Physical and Mathematical Sciences, Professor, Head of Department of Mathematical Modeling of Systems and Processes, Perm National Research Polytechnic University (614990, 29, Komsomolsky av., Perm, Russian Federation, e-mail: tpv@matmod.pstu.ac.ru).

1. Trusov P.V., Shvejkin A.I. Mnogourovnevye fizicheskie modeli mono- i polikristallov. Prjamye modeli [Multilevel physical models of single and polycrystals. Direct models]. Physical Mesomechaniks, 2011, vol. 14, no. 5, pp. 5-30.

2. Trusov P.V., Shvejkin A.I. Mnogourovnevye fizicheskie modeli mono- i polikristallov. Statisticheskie modeli [Multilevel physical models of single- and polycrystals. Statistical models]. Physical Mesomechaniks, 2011, vol. 14, no. 4, pp. 17-28.

3. Trusov P.V., Volegov P.S., Janc A.Ju. Nesimmetrichnaya fizi­ches­kaya teoriya plastichno-sti dlya opisaniya evolyutsii mikrostruktury polikristallov [Asymmetrical physical plasticity theory to describe the evolution of the microstructure of polycrystalline]. Physical Mesomechaniks, 2011, vol. 14, no. 1, pp. 19-31.

4. Trusov P.V., Nechaeva E.S., Shvejkin A.I. Primeneniye nesimmetrichnykh mer naprya-zhennogo i deformirovannogo sostoyaniya pri postroyenii mnogourovnevykh konstitu-tivnykh modeley materialov [Non-symmetric stress-strain measures using when construct multilevel constitutive material models]. Physical Mesomechaniks, 2013, vol. 16, no. 2, pp. 15–31.

5. Rybin V.V. Bol'shiye plasticheskiye deformatsii i razrusheniye metallov [Large plastic deformation and fracture of metals]. Moscow: Metallurgiya, 1986. P. 224.

6. Trusov P.V., Shvejkin A.I., Nechaeva E.S., Volegov P.S. Mnogourovnevyye modeli ne-uprugogo deformirovaniya materialov i ikh primeneniye dlya opisaniya evolyutsii vnut-renney struktury [Multilevel model of inelastic deformation of materials and their application for description of internal structure evolution]. Physical Mesomechaniks, 2012, vol. 15, no. 1, pp. 33-56.

7. Trusov P.V., Ashihmin V.N., Shvejkin A.I. Dvuhurovnevaja model' uprugoplasticheskogo deformirovanija polikristallicheskih materia-lov [Two-level model of elastic-plastic deformation of polycrystalline materials]. Mekhanika kompozitsionnykh materialov i konstruktsiy, 2009, vol. 15, no. 3, pp. 327-344.

8. Golovin S.A. Fizicheskiye osnovy plasticheskoy deformatsii: ucheb. posobiye [Physical basis of plastic deformation: studies. allowance]. Tulskiy gosudarstvenniy universitet, 2003. P. 147.

9. Wu X., Kalidindi S.R., Necker C., Salem A.A. Modeling anisotropic stress-strain response and crystallographic texture evolution on
α-titanium during large plastic deformation using Taylor-type models: influence of initial texture and purity. Metallurgical and materials transactions, 2008, vol. 39A, pp. 3046-3054.

10. Hirt D., Lote I. Theory of Dislocations [Teorija dislokacij]. Moscow: Atomizdat, 1972. P. 600.

11. Trusov P.V., Shvejkin A.I. Teoria plastichnosti [Crystal plasticity]. Permskiy natsionalniy issledovatelskiy polytekhniskiy universitet, 2011. P. 419.

12. Pozdeev A.A., Trusov P.V., Niashin Y.I. Bol'shiye uprugoplasticheskiye deformatsii: teoriya, algoritmy, prilozheniya [Large elastoplastic deformation: theory, algorithms, and applications]. Moscow: Nauka, 1986. P. 232.

13. Volegov P.S., Shulepov A.V. Uprugiye konstanty monokristalla v nesimmetrichnoy fizicheskoy teorii plastichnosti [The elastic constants of a single crystal in the asymmetric the physical theory of plasticity]. Vestnik Permskogo gosudarstvennogo politekhnicheskogo universiteta. Mekhanika, 2010, no. 1, pp. 19-34.

14. Trusov P.V., Ashihmin V.N., Shvejkin A.I. Analiz deformirovaniya GTSK-metallov s ispol'zovaniyem fizicheskoy teorii plastichnosti [Analysis of deformation of fcc metals using the physical theory of plasticity]. Fizicheskaya mezomekhanika, 2010, vol. 13, no. 3, pp. 21-30.

15. Kondrat'yev N.S., Trusov P.V. Uprugovyazkoplasticheskaya model' dlya opisaniya defor-mirovaniya OTSK-monokristallov, uchityvayushchaya dvoynikovaniye [Elastoviscoplastic model to describe the deformation of bcc crystals, taking into account the twinning]. Vychislitel'naya mekhanika sploshnykh sred, 2011, vol. 4, no. 4, pp. 20-33.

16. Trusov P.V., Volegov P.S., Shvejkin A.I. Konstitutivnaya uprugovyazkoplasticheskaya model' GTSK-polikristallov: teoriya, algoritmy prilozheniya [Elastoviscoplastic constitutive model fcc-polycrystals: theory, algorithms, applications]. Saarbrucken: LAP LAMBERT Academic Publishing GmbH & Co. KG, 2011. P. 147.

17. Janz A.YU., Volegov P.S. Uprugovyazkoplasticheskaya model' deformatsionnogo uprochneniya polikristallicheskogo agregata: uchet zernogranichnogo uprochneniya [Elastoviscoplastic model hardening polycrystalline aggregate: consideration of grain boundary hardening]. Sbornik nauchnykh trudov: «Molo­dezh­naya nauka Prikamya».Vyp. 11. Permskiy gosudarstvenniy tekhnicheskiy universitet, 2010, pp. 393-398.

18. Asaro R.J., Needleman A. Texture development and strain hardening in rate dependent polycrystals. Acta Metall, 1985, vol. 33, no. 6, pp. 923-953.

19. Inal K., Neale K.W. High performance computational modelling of microstructural phenomena in polycrystalline metals. Mechanics & Construction, 2006, vol. 140, no. 5, pp. 583-593.

The magnetoactive elastomer features a novel type of magnetocontrollable materials exhibiting reversible changes in their properties under the influence of the magnetic field, for which they are classified as Smart materials.

One of the properties possessed by the material is the ability to exhibit the dependence of its viscoelasticity on the applied magnetic field, the phenomenon known as the magnetorheological effect. At the same time scrupulous studies have also resulted in the discovery of an extensive set of fascinating features including the magnetodeformational, magnetostrictional, shape memory (pseudoplasticity), magnetoresistive, and magnetopiezoresistive effects. Such parameters as dielectric permeability and magnetic susceptibility also change under the influence of the field. These properties are defined by dipole interaction among the magnetized particles of the magnetic filler and also by the processes of reversible displacement (structuring) and rotation of the anisotropic particles inside the polymer matrix.

The areas of application of such materials may include the creation and development of functional controllable active and passive damping devices, magnetic field, acceleration, pressure, and deformation sensors, and cell technologies in biological research.

Keywords: magnetorheological, magnetoactive elastomer, magnetic gel, ferroelastic material, magnetodeformational effect, magnetostrictional effect, shape memory effect, magnetoresistive effect, dielectric permittivity.

Stepanov Gennadiy Vladimirovich (Moscow, Russian Federation) – M.Sc. State Scientific Research Institute of Chemistry and Technology of Organoelement Compounds (38, Shosse Enthuziastov, 105118, Moscow, Russian Federation, e-mail: gstepanov@mail.ru).

Kramarenko Elena Yulyevna (Moscow, Russian Federation) – Doctor of Physical and Mathematical Sciences, Professor, Department of Physics, Lomonosov Moscow State University (dom 1, str. 2, Leninskie Gory, 119991, Moscow, Russian Federation, e-mail: kram@polly.phys.msu.ru).

Perov Nikolai Sergeevich (Moscow, Russian Federation) – Doctor of Physical and Mathematical Sciences, Professor, Department of Physics, Lomonosov Moscow State University (1/b.2, d. 1, str. 2, Leninskie Gory, 119991, Moscow, Russian Federation, e-mail: perov@magn.ru).

Semisalova Anna Sergeevna (Moscow, Russian Federation) – Ph.D. in Physics and Mathematics, Physicist, Department of Magnetism, Fakulty of Physics, Lomonosov Moscow State University (1/b.2, d. 1, str. 2, Leninskie Gory, 119991, Moscow, Russian Federation, e-mail: semisalova@magn.ru).

Borin Dmitriy Yurievich (Drezden, Germany) – Ph.D. in Technical Sciences, Technische Universität Dresden, Chair of Magnetofluiddynamics (01062, Dresden, Germany, e-mail: dmitry.borin@tu-dresden.de).

Bogdanov Vladimir Viktorovich (Moscow, Russian Federation) – Ph.D. in Technical Sciences, Associate Professor, Department of Strength of Materials, Moscow State University of Mechanical Engineering (38, ul. Bolshaya Semenovskaya st., 107023, Moscow, Russian Federation, e-mail: bogdanov@mami.ru).

Semerenko Denis Alekseyevich (Moscow, Russian Federation) – Ph.D. in Physical and Mathematical Sciences, Moscow State Technical University after N.E. Bauman (5, 1^st Baumanskaya st., 105005, Bldg.1, Moscow, Russian Federation, e-mail: infavorem@mail.ru).

Bakhtiiarov Anton Velitovich (Moscow, Russian Federation) – M.Sc. State Scientific Research Institute of Chemistry and Technology of Organoelement Compounds (38, Shosse Enthuziastov, 105118, Moscow, Russian Federation, e-mail: abakhtia@gmail.com).

Sviridova Liliya Vadimovna (Moscow, Russian Federation) – M.Sc. State Scientific Research Institute of Chemistry and Technology of Organoelement Compounds (38, Shosse Enthuziastov, 105118, Moscow, Russian Federation, e-mail: mumilina@yandex.ru).

Storozhenko Pavel Arkadievich (Moscow, Russian Federation) – Prof. State Scientific Research Institute of Chemistry and Technology of Organoelement Compounds (38, Shosse Entuziastov, 105118, Moscow, Russian Federation, e-mail: gstepanov@mail.ru).

1. Method for allowing rapid evaluation of chassis elastomeric devices in motor vehicles. Patent US No. 5974856, 1999.

2. Variable stiffness bushing using magnetorheological elastomers. Patent EP No. 0784163, 1997.

3. Method and apparatus for measuring displacement and force. Patent US No. 5814999, 1999.

4. Magnetorheological nanocomposite elastomer for releasable attachment applications. Patent US No. 7430788, 2009.

5. Jolly M.R., Carlson J.D., Munoz B.C., Bullions T.A. The magnetoviscoelastic response of elastomer composites consisting of ferrous particles embedded in a polymer matrix. J. Intelligent Mat. Syst. Struct., 1999, no. 67, pp. 613-622.

6. Ginder J.M., Clark S.M., Schlotter W.F. and Nichols M.E. Magnetostrictive Phenomena in Magnetorheological Elastomers. International Journal of Modern Physics, 2002, no. 16, pp. 2412-2418.

7. Bellan C., Bossiss G. Field Dependence of Viscoelastic Properties of MR Elastomers. International Journal of Modern Physics, 2002, no. 16, pp. 2447-2453.

8. Demchuk S.A., Kuz’min V.A. Viscoelastic Properties of Magnetorheological Elastomers in the Regime of Dynamic Deformation. Journal of Engineering Physics and Thermophysics, 2002, vol. 75, no 2.

9. Zhou G.Y. Shear properties of a magnetorheological elastomer. Smart Mater. Struct., 2003, no. 12, pp. 139-146.

10. Zhou G.Y., Zhang P.Q. Investigation of the dynamic mechanical behavior of the double-barreled configuration in a magnetorheological fluid damper. Smart Mater. Struct., 2002, no 11, pp. 230-238.

11. Zhou G.Y., Jiang Z.Y. Deformation in magnetorheological elastomer and elastomer-ferromagnet composite driven by a magnetic field. Smart Mater. Struct., 2004, no. 13, pp. 309-316.

12. Zhou G.Y., Li J.R. Dynamic behavior of a magnetorheological elastomer under uniaxial deformation: I. Experiment. Smart Mater. Struct., 2003, no. 12, pp. 859-872.

13. Zhou G.Y., Wang Q. A linear time-variant system for signal modulation by use of magnetorheological elastomer-suspended beams. Smart Mater. Struct., 2005, no. 14, pp. 1154-1162.

14. Zhou G.Y., Wang Q. Magnetorheological elastomer-based smart sandwich beams with nonconductive skins. Smart Mater. Struct., 2005, no. 14, pp. 1001-1009.

15. Zhou G.Y., Wang Q. Design of a smart piezoelectric actuator based on a magnetorheological elastomer. Smart Mater. Struct., 2005, no. 14, pp. 504-510.

16. Zhou G.Y Complex shear modulus of a magnetorheological elastomer. Smart Mater. Struct., 2004, no. 13, pp. 1203-1210.

17. Zhou G.Y., Wang Q. Study on the adjustable rigidity of magnetorheological-elastomer-based sandwich beams. Smart Mater. Struct., 2006, no. 15, pp. 59-74.

18. Guan X., Dong X., Ou J. Magnetostrictive effect of magnetorheological elastomer. Journal of Magnetism and Magnetic Materials, 2008, no. 320, pp. 158-163.

19. Filipcsei G., Zrinyi M. Preparation and Responsive Prospects of Magnetically Soft Poly (N-isopropilacrylamide) Gels. Macromolecules, 2000, no. 33, pp. 1716-1719.

20. Zrinyi M., Feher J., Filipcsei G. Novel Gel Actuator Containing TiO2 Particles Operated under Static Electric field. Macromolecules, 2000, no. 33, pp. 5751-5753.

21. Szabo D., Szeghy G., Zrinyi M. Shape Transition of Magnetic Field Sensitive Polymer Gels. Macromolecules, 1998, no. 31, pp. 6541-6548.

22. Gila´nyi T., Varga I., Me´szaros R., Filipcsei G. and Zrı´nyi M. Interaction of Monodisperse Poly(N-isopropylacrylamide) Microgel Particles with Sodium Dodecyl Sulfate in Aqueous Solution. Langmuir, 2001, no. 17, pp. 4764-4769.

23. Raikher Yu.L., Stolbov O.V. Magnetodeformational effect in ferrogel objects. J. Magn. Magn. Mater., 2005, vol 289, pp. 62-65

24. Raikher Yu.L., Stolbov O.V. Magnetodeformational effect in ferrogel samples. J. Magn. Magn. Mater., 2003, vol. 258, pp. 477-479.

25. Raikher Yu.L., Rusakov V.V. Viscoelastic ferrogel: Dynamic magnetic susceptibilities. Brazilian J. Phys., 2001, vol. 31, no. 3, pp. 366-379.

26. Nikitin L.V., Mironova L.S., Stepanov G.V., Samus A.N. The Influence of a Magnetic Field on the Elastic and Viscous Properties of Magnetoelastics. Polymer Science, Ser. A., 2001, vol. 43, no. 4, pp. 443-450.

27. Nikitin L.V., Stepanov G.V., Mironova L.S. and Samus A.N. Properties of magnetoelastics synthesized in external magnetic. Journal of Magnetism and Magnetic Materials, 2003, vol. 258-259, pp. 468-470.

28. Nikitin L.V., Mironova L.S., Kornev K.G., Stepanov G.V. The magnetic, elastic, structural and magnetodeformational properties of magnetoelastics. Polymer science, Ser. A., 2004, vol. 46, no. 3, pp. 301-309.

29. Nikitin L.V., Stepanov G.V., Mironova L.S., Gorbunov A.I. Magnetodeformational effect and effect of shape memory in magnetoelastics. Journal of magnetism and magnetic materials, 2004, no. 272-276, pp. 2072-2073.

30. Raikher Yu.L., Stolbov O.V., Stepanov G.V. Shape instability of a magnetic elastomer membrane. J. Phys. D: Applied Physics (Fast Track Communications), 2008, vol. 41(15): 152002 (4 pages).

31. Raikher Yu.L., Stolbov O.V. Numerical modeling of large field-induced strains in ferroelastic bodies: Continuum approach. J. Phys.: Condensed Matter, 2008, vol. 20(20): 204126 (5 pages).

32. Stepanov G.V., Borin D.Yu., Raikher Yu.L., Melenev P.V., Perov N.S. Motion of ferroparticles inside the polymeric matrix in magnetoactive elastomers. J. Phys.: Condensed Matter, 2008, vol. 20(20): 204121 (5 pages).

33. Farshad M., Benine A.Magnetoactive elastomer composites. Polymer Testing, 2004, no. 23, pp. 347-353.

34. Farshad M., Le Roux M. Compression properties of magnetostrictive polymer composite gels. Polymer Testing, 2005, no. 24, pp. 163-168.

35. Abramchuk S., Kramarenko E., Stepanov G., Nikitin L.V., Filipcsei G., Khokhlov A.R., Zrinyi M. Novel highly elastic magnetic materials for dampers and seals I: Preparation and characterization of the elastic materials. Polymers for Advanced Technologies, 2007, vol. 18, no. 11, pp. 883-890.

36. Stepanov G.V., Abramchuk S.S., Grishin D.A., Nikitin L.V., Kramarenko E.Yu., Khokhlov A.R. Effect of a Homogeneous Magnetic Field on the Viscoelastic Behavior of Magnetic Elastomers. Polymer, 2007, vol. 48, pp. 488-495.

37. Chertovich A.V., Stepanov G.V., Kramarenko E.Y., Khokhlov A.R. New Composite Elastomers with Giant Magnetic Response. Macromolecular Materials and Engineering, 2010, vol. 295, no. 4, pp. 336-341.

38. Balabin I., Bogdanov V., Borin D., Adam F., Stepanov G. Magnitorheological elastomer with memory share effect as a component of the energy absorbing’s cover for the bumper of a vehicle. Automobil Industry, 2010, no. 10.

39. Balabin I., Bogdanov V., Jovanis S. Stossstanger von Kfz als effektive Träger des Schutztraumafunktion von Verkehrsteilnehmer. Journal of Assosiation Automotive Engineering, 2010, no. 5, pp. 31-35.

40. Balabin I., Bogdanov V., Borin D., Stepanov G., Semerenko D. Einsatz des MR-elastomers in Energieabsorbtionsaufbau der Fahrzeugstossstange. Zeitschrift der Assoziation der Automotive Ingenieure, 2010, no. 6, (in russian).

41. Bogdanov V., Borin D., Bokov R. Investigation and Optimization the strengths and rigids Parameters of MRE, used in the Construktions of safety Bumpers of Vehicles. Collection N. Novgorod N.I. Lobatschewski State University, 2011, no. 4.

42. Balabin I., Bogdanov V. Safety of Vehicles: Dualism of modern intellectual Systems demand the 

The solution of a uniform problem on simi-infinite crack parallel to free in plane strain conditions is obtained and studied. Following [1–4] by using Laplace transform the problem is reduced to matrix Riemann problem. The asymptotic expressions for stress field near the crack tip (stress intensity factor, SIF) as well as the asymptotic expressions the crack surface displacements far apart from the crack tip were obtained. The obtained expressions for SIFs coincides with the expressions [1–4]. It is shown that the leading terms of the displacements correspond to displacement of a beam (plate) loaded by the total force and moment far from the point of its conjugation with the elastic half-plane, at which the boundary conditions are of the type of elastic clamping, i.e. the angle of rotation and two components of displacement at the clamped point are proportional to the acting total force (two components) and bending moment. The relation is expressed by means of 3x3 matrix of coefficients of the effective elastic clamping. The expressions for the coefficients of proportionality related to the bending moment and longitudinal force are obtained in the form of integrals. Some components of the matrix were obtained also by comparison of two expressions for the elastic energy release: calculated from SIFs and calculated by the work of forces while the equivalent beam deflecting. The obtained results were compared with the available numerical data. The obtained solution may be useful for solving problems related to deformation of beam and console structures as well as problems of delamination and buckling of coatings.

Keywords: delamination, interface crack, matrix factorization, elastic clamping.

Ustinov Konstantin Borisovich (Moscow, Russian Federation) – Ph.D. in Physical and Mathematical Sciences, Associate Professor, Senior Researcher of laboratory of Geomechaanics of A.Yu Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences (101-1, Vernadskiy av., 119526, Moscow, Russian Federation, e-mail: ustinov@ipmnet.ru).

1. Zlatin A.N., Khrapkov A.A. Polubeskonechnaya treshina, parallelnaya granitse uprugoi poluploskosti [Semi-infinite crack, parallel to boundary of elastic half-space]. Doklady AN SSSR, 1986, vol. 31, pp. 1009-1010.

2. Zlatin A.N., Khrapkov, A.A. Uprugaya poluploskost, oslablennaya treshinoi, parallelnoi ee granitse [Elastic half-plane, weakened by a crack, parallel to its boundary]. Issledovania po uprugosti i plastichnosti, 1990, vol. 16. Problems of modern fracture mechanics, pp. 68-75.

3. Zlatin A.N., Khrapkov A.A. Vektornaya zadacha Rimana c nenu­le­vym indeksom pokazatelya matritsy-koeffitsienta [Vector Riemann problem with non-zero index of the exponent of the matrix coefficient]. Izvestiya Vsesoyuznogo nauchno-issledovatelskogo instituta imeni B.E. Vedeneeva, 1985, vol. 181, pp. 12-16.

4. Khrapkov A.A. Wiener-Hopf method in mixed elasticity theory problems. S.-P., 2001, 144 p.

5. Noble B., Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations. Pergamon Press, Inc., New York, 1959. 246 p.

6. Entov V.M., Salganik R.L. K modeli khrupkogo razrusheniya Prandtlya [On the model of brittle fracture by Prandtl]. Mechanics of solids. Izvestiya Rossiyskoy akademii nauk MTT. 1968, no. 6, pp. 87-99.

7. Salganik R.L. Tonkii sloi, ispytyvayushii skachek kharakteristik, v beskonechnom uprugom tele [Thin layer suffering a discontinuity in characteristics in an infinite elastic body]. Mechanics of solids. Izvestiya Rossiyskoy akademii nauk MTT. 1977, no. 2, pp. 154-163.

8. Doetsch G. Anleitung zum Praktischen Gebrauch der Laplace Transformation und der Z-Transformation. Oldenburg Verlag, München, 1989. 256 p.

9. Yu H.-H., Hutchinson J.W. Influence of substrate compliance on buckling delamination of thin films. Int. J. Fract., 2002, vol. 113, pp. 39-55.

10. Ustinov K.B., Dyskin A.V., Germanovich L.N. Asymptotic analysis of extensive crack growth parallel to free boundary. 3^rd Intern. Conf. Localized Damage. Southamption: Comput.mech. Publ., 1994, pp. 623-630.

11. Dyskin A.V., Germanovich L.N., Ustinov K.B. Asymptotic analysis of crack interaction with free boundary. Inern. J. Solids Structures, 2000, vol. 37, no. 6, pp. 857-886.

12. Ustinov K.B. Ob utochnenii granichnykh usloviy dlya balochnoi modeli kantilevera atomno-silovogo mikroskopa i ikh vliyanii na interpretatsiyu izmereniy [On refinement of boundary conditions for the beam model of cantilever of Atomic-Force microscope and its influence on interpretation of the results of measurements]. Mechanics of solids. Izvestiya Rossiyskoy akademii nauk MTT, 2008, no. 3, pp. 182-188.

13. Cotterell B., Chen Z. Buckling and cracking of thin film on compliant substrates under compression. Int. J. Fracture, 2000, vol. 104, no. 2, pp. 169-179

14. Ustinov K.B. On shear delamination of a thin layer from a half-plane [O sdvigovom otsloenii tonkogo sloya ot poluploskosti]. Preprint IPMech RAS No. 1047, 2013. 30 p.

15. Ustinov K.B. Esche raz k zadache o poluploskosti, oslablennoi polubeskonechnoi treshinoi, parallelnoi granitse [Once more to the problem on a half-plane, weakened by a semi-infinite crack, parallel to its boundary]. Preprint IPMech RAS No. 1046, 2013. 31 p.

16. Ustinov K.B. Ob otsloenii sloya ot poluploskosti dlya nekotorogo klassa razlichnyh uprugih svoistv [On delamination of a layer from a half-plane for some class of different elastic properties]. Preprint IPMech RAS, No. 1048, 2013, 50 p.

The article is devoted to the research of carbon composites fracture kinetics based on the acoustic emission characteristics. Tensile and compression tests were conducted on the samples produced from carbon reinforced polymer on different stages of technological conversion. During experiments the monitoring of acoustic emission was carried out in a continuous mode with an acoustic emission measurement system Vallen AMSY- 6 as well as its synchronization with the electromechanical system Instron 5882 and advanced non-contacting video extensometer (AVE) Instron. The filtration of registered acoustic emission signals was carried to high and low-frequency noise reduction. The peak amplitude and the energy parameters are selected as main parameters of the acoustic emission signals. The damage parameter is introduced to analyze fracture kinetics. This parameter characterizes the degree of defect accumulation in the material. As a result, main acoustic emission’s parameters versus displacement diagrams and damage accumulation curves are constructed. The correlation signals between fracture kinetics are brought out. The main stages of the carbon reinforced polymer fracture are distinguished based on a parametric acoustic emission analysis. Difference in the recorded signals, depending on the types of test and manufacturing material is observed.

Keywords: experimental mechanics, tensile test, compression test, carbon reinforced polymer, acoustic emission, damage mechanisms.

Shilova Alisa Igorevna (Perm, Russian Federation) – Undergraduate Student of Department of Mechanics of Composite Materials and Constructions, Engineer of the Center of Experimental Mechanics, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, Russian Federation, e-mail: cem.shilova@gmail.com).

Vildeman Valery Ervinovich (Perm, Russian Federation) – Doctor of Physical and Mathematical Sciences, Director of the Center of Experimental Mechanics, Professor of Mechanics of Composite Materials and Structures, Professor, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, Russian Federation, e-mail: wildemann@pstu.ru).

Lobanov Dmitry Sergeevich (Perm, Russian Federation) – Doctoral Student, Junior Scientific Associate of the Center of Experimental Mechanics, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, Russian Federation, e-mail: cem.lobanov@gmail.com).

Lyamin Yuriy Borisovich (Perm, Russian Federation) – Head of department, Ural Research Institute of Composite Materials (57, Novozvyaginskaya av., 614014, Perm, Russian Federation, e-mail: uniikm@yandex.ru).

1. Nerazrushaushchiy kontrol’: spravoshchnik [Nondestructive testing: handbook]. Ed. V.V. Klyuev. Vol. 17: Part 1: Ivanov V.I., Vlasov I.E. Metod akusticheskoiy emissii [Acoustic emission method]. Moscow: Mashinostrojeniye, 2006. 340 p.

2. Kollakot R. Diagnostika razrusheniy [Diagnostic of damage]. Moscow: Mir, 1989. 512 p.

3. Panin S.V., Burkov M.V., Byakov A.V., Lyubutin P.S., Khizhnyak S.A. Staging of a localized deformation during tension of specimens of a carbon-carbon composite material with holes of different diameters according to acoustic-emission, surface-deformation mapping, and strain-gauging data. Russian journal of nondestructive testing, 2012, vol. 48, no. 10, pp. 598-608.

4. Kim Y.-B., Choi N.-S. Characteristics of thermo-acoustic emission from composite laminates during thermal load cycles. KSME international journal, 2003, no. 17, pp. 391-399.

5. Pollock A. Acoustic Emission Inspection. Metals Handbook. Ninth Edition ASM International, 1989, no. 17, pp. 278-294.

6. Satalla N., Alber M., Kahraman S. Analyses of acoustic emission response of a fault breccias in uniaxial deformation. Bulletin of engineering geology and the environment, 2010, no. 69, pp. 455-463.

7. Taghizadeh J., Najafabadi M.A. Classification of Acoustic Emission Signals Collected During Tensile Tests on Unidirectional Ultra High Molecular Weight Polypropylene Fiber Reinforced Epoxy Composites Using Principal Component Analysis. Russian journal of nondestructive testing, 2011, no. 47, pp. 491-500.

8. Woo S.-C., Kim J.-T., Kim J.-Y., Kim T.-W. Correlation of fracture processes and damage mechanisms of armor structural materials under high strain rates with acoustic emission characteristics. International journal of impact engineering, 2013, no. 63, pp. 29-42.

9. Eksperimentalnyie issledovaniya svojstv materialov pri slozhnykh termomekhanicheskikh vozdejstviyakh [Experimental investigation of the materials properties under complex thermomechanical influences]. Ed. V.E. Vildeman. Moscow: Fizmatlit, 2012. 204 p.

10. Babushkin A.V., Lobanov D.S., Kozlova A.V., Morev I.D. Research of the effectiveness of mechanical testing methods with analysis of features of destructions and temperature effects. Frattura ed Integrita Strutturale, 2013, vol. 24, pp. 89-95.

11. Vildeman V.E., Babushkin A.V., Nikulin S.M., Tretyakov M.V., Lobanov D.S., Struk N.V. Eksperimentalnyie issledovaniya deformatsionnyih i prochnostnyih svoystv nanomodifitsirovannyih steklotekstolitov [Experimental investigatiom of of the deformation and strength properties of nano-modified fiberglass]. Zavodskaya laboratoriya. Diagnostika materialov, 2012, vol. 78, no. 7, pp. 57-61.

12. Rizzo P., Lanza di Scalea F. Acoustic emission monitoring of carbon-fiber-reinforced-polymer bringe stay cables in large-scale testing. Experimental mechanics, 2001, vol. 43, no. 3, pp. 282-290.

Were worked out the basic steps in conducting an experiment on electrodynamic test system Instron ElectroPuls E10000. Were conducted uniaxial dynamic trials tensile / compression at various temperature and dynamic trials biaxial tensile / compression and torsion simultaneously. Been ascertained the effect of temperature on the dynamic mechanical properties (phase angle between the axial stress and strain, the dynamic modulus in tension / compression) for different values of the strain amplitude loading and were built depending. Was held comparative analysis of the values of the dynamic mechanical properties (phase angle between the axial stress and strain, the dynamic modulus in tension / compression, the phase angle between the shear stress and strain, the dynamic modulus in torsion) under uniaxial and biaxial (bimodal) loadings with identical parameters deformation.

Keywords: strain amplitude, biharmonic (two-frequency) loading, dynamic mechanical properties (analysis), dynamic modulus of elasticity, angle of lag between stress and deformation, loss angle, low-modulus viscoelastic composites, polymeric materials, tensile, compression, torsion, shear deformation, dynamic cyclic loading, bimodal (biaxial) loading, uniaxial loading, temperature, frequency, amplitude of the angle of twist, mode, the phase angle between the modes.

Yankin Andrey Sergeevich (Perm, Russian Federation) – junior researcher at the Center of Experimental Mechanics Perm National Research Polytechnic University (29, Komsomolsky av., 614000, Perm, Russian Fede­ration, e-mail: yas.cem@yandex.ru).

Bulbovich Roman Vasilevich (Perm, Russian Federation) – Doctor of Technical Sciences, Dean of the Faculty of Aerospace, Professor of Aerospace Technology and Power Plants Perm National Research Polytechnic University (29, Komsomolsky av., 614000, Perm, Russian Federation,
e-mail: dekan_akf@pstu.ru).

Slovikov Stanislav Vasilevich (Perm, Russian Federation) – Ph.D. in Technical Sciences, a senior researcher at the Center of Experimental Mechanics Perm National Research Polytechnic University (29, Komsomolsky av., 614000, Perm, Russian Federation, e-mail: sws@au.ru).

Vildeman Valeriy Ervinovich (Perm, Russian Federation) – Doctor of Physics and Mathematics Sciences, Professor, Director of the Center of Experimental Mechanics, Professor of Mechanics of Composite Materials and Structures, Professor, Perm National Research Polytechnic University (29, Komsomolsky av., 614000, Perm, Russian Federation, e-mail: wildemann@pstu.ru).

1. Moskvitin V.V. Soprotivlenie vyazkouprugikh materialov (primenitelno k zaryadam raketnikh dvigateley na tverdom toplive) [The resistance of visco-elastic materials (in relation to the charges of solid propellant rocket engine)]. Moscow: Nauka, 1972. 328 p.

2. Slovikov S.V., Bulbovich R. V. Experimentalnoe issledovanie dinamicheskikh mekhanicheskikh svoistv vyazkouprugikh materialov [Experimental study of the dynamic mechanical properties of visco-elastic materials]. Vestnik Permskogo gosudarstvennogo tekhnicheskogo universiteta. Mekhanika, 2010, no. 2, pp. 104-112.

3. Slovikov S.V. Metodika issledovaniya zavisimosti mekhanicheskikh svoistv poliuretanovykh izdeliy ot temperatury [Technique to study the mechanical properties of polyurethane-based products on the temperature]. Vestnik Permskogo natsionalnogo issledovatelskogo poli­tekhni­cheskogo universiteta. Mekhanika, 2012, no. 2, pp. 177-189.

4. Slovikov S.V. Sovershenstvovanie eksperimentalnogo metoda issledovanija dissipativnykh i prochnostnykh svojstv poliuretana [Improvement of the experimental method of research and the strength of the dissipative polyurethane]. Vestnik Permskogo nacionalnogo issledovatelskogo politehnicheskogo universiteta. Mehanika, 2013, no. 2, pp. 145-153.

5. Shadrin V.V., Komar L.A., Bashin G.P., Yarushin A.V. Vliyanie temperatury i soderzhaniya napolnitelya na dinamicheskie moduli nanokompozita s polietilenovoy matritsey [Effect of temperature and filler content on the dynamic moduli of the nanocomposite with a polyethylene matrix]. Vestnik Permskogo universiteta. Matematika. Mekhanika. Informatika, 2011, no. 4, pp. 64-68.

6. Marco Aurilia, Filomena Piscitelli, Luigi Sorrentino, Marino Lavorgna, Salvatore Iannace. Detailed analysis of dynamic mechanical properties of TPU nanocomposite: The role of the interfaces. European Polymer Journal, 2011, vol. 47, iss. 5, pp. 925-936.

7. Yanqia Wang, Richard A. Palmer, Jon R. Schoonover, Steven R. Aubuchon. Dynamic mechanical analysis and dynamic infrared linear dichroism study of the frequency-dependent viscoelastic behavior of a poly (ester urethane). Vibrational Spectroscopy, 2006, vol. 42, iss. 1, pp. 74-77.

8. José Daniel D. Melo, Donald W. Radford. Time and temperature dependence of the viscoelastic properties of CFRP by dynamic mechanical analysis. Composite Structures, 2005, vol. 70, iss. 2, pp. 240-253.

9. Goertzen W.K., Kessler M.R. Dynamic mechanical analysis of carbon/epoxy composites for structural pipeline repair. Composites Part B: Engineering, 2007, vol. 38, iss. 1, pp. 1-9.

10. Vildeman V.E., Tretyakov M.P., Tretyakova T.V., Bulbovich R.V. Slovikov S.V., Babushkin A.V., Ilyanich A.V., Lobanov D.S., Ipatova A.V. Eksperimentalnyye issledovaniya svoystv materialov pri slozhnykh termomekhanicheskikh vozdeystviyakh [Experimental studies of the properties of materials under complex thermomechanical impacts]. Ed. by V.E. Vil­de­man Moscow: Glavnaya redaktsiya fiziko-mate­ma­tiches­koy literatury, 2012. 204 p.

11. Adamov A.A., Matveyenko V.P., Trufanov N.A., Shardakov I.N. Metody prikladnoy vyazkouprugosti [Methods applied viscoelasticity]. Yekaterinburg, Uralskoje otdelenije Rossiyskoy akademii nauk, 2003. 411 p.

12. Yankin A.S., Slovikov S.V., Bulbovich R.V. Opredilenie dina­mi­cheskikh mekhanicheskikh svoystv nizkomodulnikh vyazkouprugikh kompozitov pri bigarmonicheskom zakone nagruzheniya [Determination of the dynamic mechanical properties of low-modulus viscoelastic composites at the biharmonic law of loading]. Mekhanika kompozitsionnykh materialov i konstruktsiy, 2013, no. 1, pp. 141-151.

13. Yankin A.S., Slovikov S.V., Bulbovich R.V. Determination of the dynamic mechanical properties of low-modulus viscoelastic composites at the biharmonic law of loading. Composites: Mechanics, Computations, Applications, 2013, vol. 4, iss. 2, pp. 139-150.