The paper is devoted to the stress-strain analysis near the crack tip in a power-law material under mixed-mode loading. In the paper by the use of the eigenfunction expansion method the stress-strain state near the crack tip under plane stress conditions is found.  The type of the mixed-mode loading is specified by the mixity parameter which is varying from 0 to 1. The value of the mixity parameter corresponding to Mode II crack loading is equal to 0, whereas the value corresponding to Mode I crack loading is equal to 1.  It is shown that the eigenfunction expansion method results in the nonlinear eigenvalue problem. The numerical solution of the nonlinear eigenvalue problem for all the values of the mixity parameter and for all practically important values of the strain hardening (or creep) exponent is obtained. It is found that the mixed-mode loading of the cracked plate gives rise to a change of the stress singularity in the vicinity of the crack tip. The mixed-mode loading of the cracked plate results in the new asymptotics of the stress-strain fields which is different from the classical Hutchinson-Rice-Rosengren stress field. The approximate solution of the nonlinear eigenvalue problem is either obtained by the perturbation theory technique (small parameter method). In the framework of the small parameter method the small parameter presenting the difference between the eigenvalue of the nonlinear problem and the unperturbed linear problem is introduced. The analysis carried out shows clearly that the stress singularity in the vicinity of the crack tip is changing under mixed-mode deformation in the case of plane stress conditions. The angular distributions of the stress and strain components (eigenvalue functions) in the full range of values of the mixity parameter are given.

Keywords: stress-strain state near the crack tip, mixed-mode loading, mixity parameter, nonlinear eigenvalue problem, perturbation technique.

Larisa V. Stepanova – Doctor of Physical and Mathematical Sciences, Associate Professor, e-mail: stepanovalv@samsu.ru.

Ekaterina M. Yakovleva – Postgraduate student, e-mail: adulinaem@samsu.ru

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Dangerous conditions with respect to pipelines are often caused by sharp defects which occur in pipe walls. Non-through surface cracks attract particular interest. Generally such cracks have a compound front form, in other words, they are multiparameter. Modern methods of nondestructive inspection do not give complete information on the front shape with adequate accuracy. In global practice defects are approximated with the semielliptical cracks to simplify calculation methods. In this case the defect is considered as a two-parameter one, and it is only defined by the maximum depth and length.

This paper examines a steel pipe, which has been weakened by the semielliptical non-through surface crack. The crack has a longitudinal orientation and is common to the external pipe area. The pipe is exposed to internal pressure. Fracture mechanics problem is resolved with the ANSYS CAE-system. Stress intensity factor distribution for the crack front points is under analysis. These values were obtained by using invariant J-integral. J-integral values were calculated using the integration over a region technique. The obtained results are compared with the data published by other authors. These data resulted from the analysis of pipes and cylindrical pressure vessels weakened by non-through cracks. The results of numerical modelling correlate accurately with the existing solutions. The accuracy of the fracture mechanics problem solution can be significantly increased by using regular mesh with multiple finite elements along the crack front. The investigation of fracture mechanics parameters identified the presence of the edge effect, common to the area where the crack front goes to the pipe surface. Edge effect refers to the local maximum values which are much higher than the crack front end points. These values should be used while investigating the crack propagation under variable loadings, that is when pulsations take place in loaded condition.

Keywords: pipe, non-through surface crack, fracture mechanics, stress intensity factor, finite element method, ANSYS.

Sergey V. Glushkov  – Teaching Assistant, e-mail:proch@ssau.ru

 Yurii V. Skvortsov – CSc. in Technical Sciences, Assistant Professor, e-mail: proch@ssau.ru

 Sergey N. Perov  – Doctor of Technical Sciences, Assistant Professor, e-mail: perov@imi-samara.ru

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This article presents the results of the experimental studies under repeated sign-variable loadings of steel tubular specimens under stretching-compression and torsion. The experiments were carried out using an automated testing machine for complex loading SN-EVM named after A.A. Ilyushin in the vector space of deformations (rigid loading). The experimental data allowed to evaluate the Bauschinger effect and the magnitude of secondary yield limits at various allowances for residual deformation. The article provides the influence of the allowance for residual deformation on the radius and position of the center of the spherical yield surface in the stress space, used in plastic flow theories. With an increase of the allowance for residual deformation, both the parameter that characterizes the Bauschinger effect and the radius of the yield surface increase, while the displacement of its center decreases. When the length of the arc of plastic deformation increases, the parameter that characterizes the Bauschinger effect decreases and tends to a stationary value. It is established that the radius of the spherical yield surface makes a temporary decrease and then increases as the length of the arc of plastic deformation grows. Some mathematical models of the plastic flow theory relate this decrease in the radius of the yield surface not to a change in the material's internal structure at the mesolevel and the orientation of microstresses, but to the elastic softening of an initially isotropic body, considering this strain rate to be negative, by mistake. For the realized types of the experimental paths of the repeated loading-unloading with breaks by 180 degrees, the verification of the postulate of isotropy by A.A. Ilyushin shows that it is carried out quite well, when it comes to its scalar and vector properties.

Keywords: plasticity, elasticity, sign-variable loading, Bauschinger effect, yield surface, deformation processes, postulate of isotropy

Vladimir G. Zubchaninov – Doctor of Technical Sciences, Professor, e-mail: vgz@rambler.ru

 Andrey A. Alekseev – CSc in Technical Sciences, Assistant Professor, e-mail: alexeew@bk.ru

 Vadim I. Gultyaev – Doctor of Technical Sciences, Assistant Professor, e-mail: vig0@mail.ru

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uprugoplasticheskom deformirovanii metallov [Experimental study
of Baushinger effect and yield surface at elastoplastic deformation of metals]. PNRPU Mechanics Bulletin, 2013, No. 1, pp. 94-105.

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12. Golenkov V.A., Malinin V.G., Malinina N.A. Strukturno-analiticheskaia mezomekhanika i ee prilozheniia [Structural-analytical mesomechanics and its applications]. Moscow: Mashinostroenie, 2009, 634 p.

The processes occurring in the metallic samples under the impact of electrical current of high density are considered.  The processes occurring in the vicinity of microdefects in the form of flat cracks under the action of electric current are studied. The dynamic problem is solved numerically for a representative element of the material with a crack.  The problem is solved in two stages using finite elements method. At the first stage, we have studied the thermal electrodynamic problem in order to obtain the temperature distribution and the regions of phase transformations in the material. Regions of the phase transformations (melting and evaporation of the material) are cross-calculated without the explicit allocation of the phase boundaries.At the second stage, we have solved a coupled unsteady thermomechanical problem of deformation of the heated elastoplastic sample taking account of the initial temperature field distribution in the material obtained at the first stage at different moments of time. Additionally, quasistatic thermomechanical problem was solved in order to obtain the displacement field (residual strain) after temperature equalization in the material.

The influence of the size and orientation of microcracks on the localization of the electromagnetic field in the region of the defect is examined. The calculations on the base of the proposed model show that the current density at the tips of the microcracks may by an order exceed the current density applied to the sample. Numerical modelling has shown, that large gradients of electromagnetic field and current arise in the vicinity of the microdefects, which leads to intensive heating, melting and evaporation of the metal in the tips of the microcracks. The melted material flows into the microcrack under the action of thermal stresses.  At the same time its evaporation takes place. The shores of the microcracks converge. All these processes lead to a "healing" of defects.

Keywords: electroplasticity, direct numerical modelling, defective material, electromagnetic field and temperature localization, melting, evaporating

Konstantin V. Kukudzhanov – CSc in Physical and Mathematical Sciences, Senior Research, e-mail: kconstantin@mail.ru

 Alexander L. Levitin – Junior Research, e-mail: alex_lev@ipmnet.ru

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This paper suggests a variant of dimensionless parameters for a wide range of shell structures. Dimensionless parameters have been used for shallow shells of rectangular planform for a long time. There is no universal form of dimensionless relations for shells of a general type, since the Lamé parameters are different for each type of shells, as far as their values and dimensions are concerned. Therefore, the work shows the dimensionless relations for strains, stresses, forces, moments and the functional of total potential energy of deformation. These relations consider geometrical nonlinearity, transverse shears, material orthotropy, as well as the introduction of ribs according to the structural anisotropy method with their shear and torsional rigidity taken into account. The authors show a further approach to solving strength and stability problems with respect to different types of shells in dimensionless parameters. Some methods intended to solve nonlinear strength problems are not quite correct, when dimensional parameters are used (for example, the methods based on the best parameter continuation method). In dimensionless parameters, all calculation are beyond doubt, as far as their correctness is concerned. The article also provides the calculations of some shell structures in dimensionless and dimensional parameters and shows their consistency. The introduction of dimensionless parameters in the course of calculation of such structures allows to obtain more comprehensive information on the stress and strain state of shells and detect strain features for a whole range of such shells. Also, this approach is suitable for optimizing the choice of structural parameters. The authors analyze some differences in critical loads that were obtained in the dimensionless and dimensional solutions of the problem.

Keywords: shells, dimensionless parameters, mathematical model, stiffened shells, Lamé parameters, orthotropy, rotational shells, stability, dimensionless load, dimensionless functional

Vladimir V. Karpov – Doctor of Technical Sciences, Professor, e-mail: vvkarpov@lan.spbgasu.ru

 Alexey A. Semenov – CSc. in Technical Sciences, Head of Department of Information Technologies, e-mail: sw.semenov@gmail.com

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3D simulation considers the process of non-standard deformation of the liquid sodium-cooled fast reactors in case of  an emergency shutdown of main circulation pumps in the primary circuit aggravated with the emergency protection system failure (beyond design basis accident of ULOF type). Coolant circulation loss causes melting of the reactor core and generates increased pressure in the power density area filled with sodium evaporations. Progressing expansion of the power density area in the coolant increases the reactor vessel stress level and may cause its destruction. Under such circumstances, ensuring the radiation safety of the Nuclear Power Plant personnel and the surrounding environment requires localization of the accident consequences within the reactor pressure vessel, which is impossible in case of its seal failure.

The current Langrangian formula analyses the coolant and reactor structure motions.
The equation of motion is derived from the virtual power balance. Elastic-plastic deformation of structure materials is fitted to the plastic flow theory correlation to the isotropic hardening. In case of liquid coolant, the relation of the hydrostatic pressure and density is fitted to the quasi-acoustic type equation of state. The contact of the coolant with the reactor structural elements is simulated in the nonponetrating conditions. The solution is based on the moment scheme of the finite element method and explicit finite-difference scheme of time integration of a "cross" type implemented on the "Dinamika-3" computer system. The 8-node finite elements with poly-linear functions of the form are used to discretize the defining equations system for spatial variables.

The change in the stressed-strained state of the fast reactor vessel in the conditions of the beyond design basis accident of ULOF type. The authors analyse the possibility of localizing the consequences of the beyond design basis accident within the reactor pressure vessel.

Keywords: reactor, beyond design basis accident, hydrodynamic pressure, finite elements method, strength

Valentin G. Bazhenov – Doctor of Physical and Mathematical Sciences, Professor, Senior Researcher, e-mail: bazhenov@mech.unn.ru

 Maxim N. Zhestkov – Postgraduate student, e-mail: mnzhestkov@yandex.ru

 Alexander I. Kibec – Doctor of Physical and Mathematical Sciences, Professor, Senior Researcher, e-mail: kibec@mech.unn.ru

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The article is devoted to the experimental investigation of the defects’ influence on the residual strength of composites structure, as well as the possibility of using local repair operations.

The objects of the research are structurally similar elements of acoustical sandwich panels (ASP) after a local repair of defects, such as a through breakdown. The specimens were produced by the serial technology from a fiberglass prepreg.

The research was carried out using a universal electromechanical system Instron 5982 and servo-hydraulic system Instron 8801. For the analysis of the stress-strain state of the deformable elements, the authors used the non-contact three-dimensional digital optical system Vic-3D, the mathematical apparatus which is based on the method of digital image correlation (DIC). To control the internal geometry of the specimen and assess possible defects, the inspection infrared thermal imaging system FLIR SC7000 was used. The techniques of a joint use of testing and measuring systems under static and cyclic tests were offered.

For comparison, the repaired sandwich panel specimens were tested under tension and tension under a preliminary cyclic loading with the registration of the deformation fields and thermal images. Their deformation and fracture mechanisms are analyzed, and their loading diagrams are obtained. The experimental data were obtained from the Vic3d system study of the evolution inhomogeneous fields of axial and transverse deformation on the surface of repaired sandwich panels under static loading and cyclic tests. By using the infrared thermal imaging system of the internal structure, the processes of the defects development and the temperature distribution on the surface of the test specimen were detected.

Keywords: experimental mechanics, composite materials, techniques of tests, digital image correlation, infrared thermographic system, estimation of bearing capacity, sandwich panels, local repair of fibrous composites, fatigue tests, tension tests

Dmitry S. Lobanov – Junior Scientific Associate, e-mail: cem.lobanov@gmail.com

Valery E. Wildemann – Doctor of Physical and Mathematical Sciences, Professor, e-mail: wildemann@pstu.ru

Elena M. Spaskova – Postgraduate Student, Junior Scientific Associate, e-mail: cem.spaskova@mail.ru

Aleksandr I. Chikhachev – Postgraduate Student, Engineer, e-mail: stfw@mail.ru

Advanced ceramics are widely used in responsible structures that work at conditions of high temperature changes, strong electrical fields and impact loads. Sintered ceramics are usually porous which affects their strength and elastic properties. In the first part of this work the results of experimental and numerical strength investigations of hot-pressed alumina ceramic are presented. The disk-shaped specimens with different porosity (4-23 %) were subjected to Piston-on-Ring bending test up to failure. Ultimate tensile strength is varied in the range of 180…490 MPa. Finite element method was used for stress state analysis of ceramic disk during bending test.  Elastic properties of porous ceramic for numerical simulations were determined by using the known approximation of dependences “property – porosity” and some experimental data. In the second part of this work three-dimensional numerical micromodel was created in ANSYS. This model is a cube with set pores up to 160 of spherical forms. The diameter of sphere is given by Weibull distribution with mean value m = 0.139 μm and standard deviation s = 0.075 μm (defined by SEM analysis of fracture surfaces). Scale parameter λ = 0.164 μm and shape parameter k = 1.919 of the Weibull distribution was determined by the least squares method. The authors generated three to six models with a random distribution of pores for each average porosity; and analyzed stress state under axial tension for each case. The maximum normal stress, stress concentration factor, elastic modulus and Poisson's ratios are dependent on the average porosity. The values of the tensile strength were defined for different porosity according to the Rankine criterion (maximum normal stress criterion). These values are in a good agreement with the experimental results before porosity of 15 %.

Keywords: advanced ceramics, porosity, strength, elastic module, Poisson ratio, finite element analysis

Anastasia V. Ignatova – Engineer, e-mail: ignatovaav@susu.ac.ru

 Oleg A. Kudryavtsev – Ph. D. student, e-mail: kudriavtcevoa@susu.ac.ru

 Sergei B. Sapozhnikov – Doctor of Technical Sciences, Professor, e-mail: ssb@susu.ac.ru

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This article suggests a method intended to form differently directed test forces while conducting mechanical tests of laboratory material samples with the use of a standard single-drive testing machine. The method in question allows to generate a mentioned system of forces affecting a sample by using the sample's inclined edges and their contact reactions when it interacts with a prismatic support that has corresponding bevels. The article considers a diagram that is intended to support and load a prismatic sample and carries out the test force formation in question. It also gives reasons for choosing angles of the sample's inclined edges on the basis of design modeling of deformation of its model with the use of a numerical finite element method apparatus and resolution of a contact problem of a deformable solid body. The authors give recommendations on how to practically use optimal inclination angles of supporting surfaces in order to create a biaxial stretching diagram. The article provides the results of a design analysis of prismatic samples' strain-stress state depending on its main geometrical parameters. It also describes the approbation of the samples in question while determining strength parameters of tempered spring steel 50HFA being under biaxial stretching. The results obtained from destructing the samples are analyzed on the basis of the Pisarenko-Lebedev limit state equation. The parameters in question are determined on the basis of numerical analysis of the tested sample sets' strain-stress state at the time of their destruction. The conducted analysis considered a contact interaction of the sample with supporting elements and possible appearance of plastic deformations in the sample material. The authors give their experimental evaluation of a reduced limit value of the first main stress in the seat of destruction of the 50HFA steel samples under biaxial stretching as compared to the uniaxial one.

Keywords: laboratory sample, differently directed forces, single-drive machine, contact reaction, finite element method, strength parameters, biaxial stretching, structural strength, modeling, strength criterion, stress-strain state

Evgeniy V. Zenkov – CSc in Technical Sciences, Senior Lecturer, e-mail: jovanny1@yandex.ru

 Lev B. Tsvik  – Doctor of Technical Sciences, Professor, e-mail: tsvik_l@mail.ru

1. Vilimok Ia.A., Nazarov K.A, Evdokimov A.K. Napriazhennoe sostoianie i prochnost' ploskikh obraztsov pri odnoosnom i dvukhosnom rastiazhenii [Intense condition and strength of flat specimens under uniaxial and biaxial tension] // Izvestiia TulGU. Tekhnicheskie nauki. 2013, No. 11, pp. 388-393.

2. Pisarenko G.S., Iakovlev A.P., Matveev V.V. Spravochnik po soprotivleniiu materialov – Kiev. [Handbook of resistance of materials]: Izd-vo Del'ta, 2008, 816 p.

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4. Kogaev V.P., Makhutov N.A., Gusenkov A.P. Raschety detalei mashin i konstruktsii na prochnost' i dolgovechnost' [The calculations of machine parts and structures for strength and durability]. M.: Mashinostroenie, 1985, 224 p.

5. Tsvik L.B. Zen'kov E.V. Opredelenie prochnostnykh kharak­teristik materialov eksperimental'nykh prizmaticheskikh obraztsov pri dvukhosnom rastiazhenii [Determining the strength characteristics of materials prismatic samples with experimental bia­xial stretching] // Vestnik mashinostroeniia, 2015, No. 1, pp. 42-46.

6. Esiev T.S., Basiev K.D., Steklov O.I. Obrazets dlia ispytaniia metalla pri dvukhosnom napriazhennom sostoianii [The test piece of metal under biaxial stress state] // Patent RF № 2073842. – Opubl. 20.02.1997, Biulleten' izobretenii RF, 1997, No. 7.

7. Vansovich K.A., Iadrov V.I. Ustalostnye ispytaniia stal'nykh krestoobraznykh obraztsov s treshchinoi pri dvukhosnom nagruzhenii [Fatigue testing of steel cruciform specimens with a crack under biaxial loading] // Omskii nauchnyi vestnik 2012, No. 3, pp. 117-122.

8. Vansovich K.A., Iadrov V.I. Eksperimental'noe izuchenie skorosti rosta poverkhnostnykh treshchin v aliuminievom splave AK6 i v stali 20 pri dvukhosnom nagruzhenii [Experimental study of the rate of growth of surface cracks in the aluminum alloy and steel AK6 20 under biaxial loading] // Izvestiia Samarskogo nauch­nogo tsentra Rossiiskoi akademii nauk, 2013, No. 4, pp. 436-438.

9. O vliianii kharaktera napriazhennogo sostoianiia na plastichnost' i razrushenie konstruktsionnykh stalei [On the influence of the nature of the stress state on the ductility and fracture of structural steel] / Iu.A Gagarin [i dr.] // Problemy prochnosti, 1978, No. 6, pp. 70-75.

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kl. G 01 N3/28. – Opubl. 07.02.93g. Biull. No. 5. 

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12. Zen'kov E.V., Tsvik L.B., Zapol'skii D.V. Prizmaticheskii obrazets dlia otsenki prochnosti materiala [Prismatic sample to estimate the strength of the material] // Patent RF № 2516599. – Opubl. 27.03.2014, Biulleten' izobretenii RF., 2014, No. 9.

13. Targ S.M. Kratkii kurs teoreticheskoi mekhaniki [A short course of theoretical mechanics.]. M.: Visshaya shkola, 1986, 416 p.

14. Galin L.A. Kontaktnye zadachi teorii uprugosti i viazkouprugosti. [Contact problems of the theory of elasticity and viscoelasticity] – M.: Nauka, 1980, 304 p.

15. Zenkov E.V., Andreev A.A. Metodika eksperimentalnogo issledovania polei deformaciy na osnove ispolzovania cifrovoi opticheskoi sistemi [Methods of experimental study of deformation fields through the use of digital optical system]. Problemi transporta Vostochnoi Sibiri: sbornik nauchnih trudov IV Vserossiskoi nauchno-prakticheskoi konferencii IrGUPS [Problems of transport of Eastern Siberia: Proceedings of the IV All-Russian scientific-practical conference IrGUPS]. Irkutsk, 2013, Ch. 1, pp. 95-99.

16. Zen'kov E.V., Tsvik L.B. Raschetno-eksperi­mental'naia otsenka napriazhenno-deformirovannogo sostoianiia laboratornogo obraztsa s galtel'nym [Calculation-experimental evaluation of the stress-strain state of the laboratory sample to fillet] // Vestnik IrGTU. Irkutsk, 2013, No. 9, pp. 70-78.

17. Sutton M.A., J.-J.Orteu, H.Schreier. Image Correla­tion for Shape, Motion and Deformation Measurements // Uni­versity of South Carolina, Columbia, SC, USA, 2009. – 364 p.

18. Malinin N.N. Prikladnaia teoriia plastichnosti i polzuchesti [Applied theory of plasticity and creep.]. M.: Mashinostroenie, 1975, 398 p

This work is devoted to investigation of the heat source evolution during quasistatic tensile testing of titanium alloy ОТ4-0 specimens using a contact heat flux sensor and infrared thermography. The purpose of the study is to evaluate the possibility of using two different measurement (contact and non-contact) methods to monitor the state of material by changing the heat source value registered on the specimen surface during deformation. The obvious advantages of infrared thermography are non-contact temperature measurements of the material surface under various conditions and heat source field calculations. However this method has a number of limitations associated with the reflectivity of the tested material, noisy signal caused by external factors, heat transfer conditions between the specimen and environment, and accuracy of heat source calculations. These problems do not allow using infrared thermography under operating conditions in order to evaluate the energy state of materials and structures. The paper attempts to verify the heat source value arising during the elastic-plastic deformation of the material using infrared thermography data. For this purpose, a Seebeck effect heat flux sensor has been developed by the authors. Contact sensor and infrared thermography data give time dependence of the heat flux value arising during the elastic-plastic deformation of the material. The satisfactory agreement of the results shows that contact and non-contact measurements can be used either in combination (to verify the heat source value, its distribution over the material surface and heat exchange conditions for specimen and environment) or separately (as an express method to evaluate material conditions at different stages of loading).

Keywords: infrared thermography, contact heat flux sensor, quasistatic tension, energy dissipation, elastic-plastic deformation

Anastasia Yu. Iziumova – Junior Researcher, e-mail: fedorova@icmm.ru

 Aleksei N. Vshivkov – Ph. D. student, e-mail: vshikov.a@icmm.ru

 Aleksandr E. Prokhorov – Ph. D. student, e-mail: prokhorov.a@icmm.ru

 Oleg A. Plekhov – Doctor of Physical and Mathematical Sciences, e-mail: poa@icmm.ru

 Balasubramaniam Venkatraman – Doctor of Sciences in Computer Applications, e-mail: bvenkat@igcar.gov.in

1. Vshivkov A.N., Prokhorov A.E., Uvarov S.V., Plekhov О.А. Osobennosti mekhanicheskogo povedeniia armko-zheleza pri ispytanii v rezhime gigatsiklovoi ustalosti [Peculiarities of mechanical behavior of armco-iron under fatigue in gigacyclic regime]. PNRPU Mechanics Bulletin, 2014, No. 4, pp. 18-32.
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3. Terekhina A.I., Fedorova A.Yu., Bannikov M.V., Plekhov O.A. Razrabotka metoda otsenki predela vynoslivosti materiala po dannym infrakrasnoi termografii [A development of a method for estimation of the endurance limit of the material using infrared
   thermography data] // PNRPU Mechanics Bulletin, 2012, No. 4, pp. 115-127.
4. Sony Punnosen, Amretendu Mukhopadhyay, Rajdeep Sarkar, Zafir Alam, Dipak Das, Vikas Kumar. Determination
   of critical strain for rapid crack growth during tensile deformation in aluminide coated near-α titanium alloy using infrared thermography. Materials Science & Engineering, 2013,
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5. Huilong Dong, Boyu Zheng, Feifan Chen. Infrared sequence transformation technique for in situ measurement of thermal diffusivity and monitoring of thermal diffusion. Infrared Physics & Technology, 2015, Vol. 73, pp. 130-140. doi: 10.1016/j.infrared.2015.09.021
6. Vavilov V.P. Noise-limited thermal/infrared nondestructive testing. NDT & E International, 2014, Vol. 61, pp. 16-23.
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7. Zhang H.X., Wu G.H., Yan Z.F., Guo S.F., Chen P.D., Wang W.X. An experimental analysis of fatigue behavior of AZ31B magnesium alloy welded joint based on infrared thermography. Materials and Design, 2014, Vol. 55, pp. 785-791. doi: 10.1016/j.matdes.2013.10.036
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9. Williams P., Liakat M., Khonsari M.M., Kabir O.M.
   A thermographic method for remaining fatigue life prediction of welded joints. Mater Des, 2013, Vol. 51, pp. 916-23. doi: 10.1016/j.infrared.2015.06.003
10. Adil Benaarbiaa, André Chrysochoos, Gilles Robert. Kinetics of stored and dissipated energies associated with cyclic loadings of dry polyamide 6.6 specimens. Polymer Testing, 2014, Vol. 34, pp. 155-167. doi: 10.1016/j.polymertesting.2014.01.009
11. Srinivasan Nagarajan, Raghu Narayanaswamy, Venkatraman Balasubramaniam. Study on the kinetics of thermomechanical response accompanying plastic instability in mild steel. Mechanics of Materials, 2015, Vol. 80, pp. 27-36. doi: 10.1016/j.mechmat.2014.09.004
12. Oliferuk W., Maj M., Zembrzycki K. Determination of the Energy Storage Rate Distribution in the Area of Strain Localization Using Infrared and Visible Imaging.
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The paper describes the methodology of fractal dimension definition for deformation curves on the basis of the minimal covering method. The methodology allows to obtain the integral quantitative estimation of fracture of structural composite materials under compression and define the location of the fracture path parametric point. We compared the offered method to the algorithms for definition of the Hurst exponent and fractal dimension by the square covering method. The work shows the advantage of the methodology based on definition of the fractal dimension using the minimal covering method.

To perform the mechanical testing of dispersal reinforced fine-grained concrete compositions, we used the WilleGeotechnik® hardware and software system additionally equipped with a climatic chamber allowing for temperature (from –40 to +100 °С) and humidity (from 10 to 96 %) adjustment during the loading. The change of stress and deformations of the samples during the loading was registered spaced at 0.01 sec.

We used the following materials as the main components of disperse reinforced fine-grained concrete: CEM I 42.5B concrete, gravel sand, condensed and densified microsilicasuspension MKU-85, polycarboxylate superplasticizing agent Melflux 1641 F. Dispersed reinforcement of concrete was ensured by a separate adding of three types of fiber, i.e. the polypropylene multifilament fiber, polyacrylonitrile synthetic fiber FibARM Fiber WВ and astralene modified basalt microfiber Astroflex-MBM.

We defined the values of indices of fractality and fractal dimension of stress incrementation and deformations of deformation curves for fine-grained concrete using the minimal covering method. On the basis of the fractal analysis of dynamic series, we defined the location and vicinity of the point of transition from the quiescent condition to the apparent trend for the concrete sample. We revealed the change of location of the parametric point and fractal dimension values depending on the type of fiber. It was discovered that the incorporation of 1 % of the polypropylene multifilament fiber or 5 % of the astralene modified basalt microfiber Astroflex-MBM resulted in the substantial increase of the first critical level, up to 54 and 47 % accordingly, both in the stress incrementation and deformation analyses compared to 19 and 28 % for the compositions containing 1.5 % of the polyacrylonitrile synthetic fiber.

The proposed methodology of the fractal analysis of deformation curves on the basis of the minimal covering method allows to obtain valuable information about the fracturing process of different composite materials.

Keywords: deformation curves, composite construction materials, dispersed reinforcement, fine-grained concrete, the minimal covering method, the Hurst method, fractality index, fractal dimension, fracture path parametric points

Vladimir P. Selyaev – Academician of the RAACS, Doctor of Technical Sciences, Professor, e-mail: ntorm80@mail.ru

 Tatyana A. Nizina – Doctor of Technical Sciences, Professor, e-mail: nizinata@yandex.ru

 Artemy S. Balykov – Ph. D. student, e-mail: artbalrun@yandex.ru

 Dmitriy R. Nizin – Ph. D. student, e-mail: nizindi@yandex.ru

 Alexey V. Balbalin – Ph. D. student, e-mail: 06.89@mail.ru

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This paper considers the subcritical elastic-plastic deformation of a three-layer composite and the layer separation accompanied by the fracture of an adhesive layer. The problem is reduced to the system of two variational equilibrium conditions with respect to the bonded layers' velocity fields by means of averaging a stress component in the adhesive layer across its thickness. When we solve an elastic-plastic problem in terms of subcritical deformation, the d-area is distinguished where the fracture criterion is reached. The distribution of load (node forces) that affects a body from the d-area is determined by resolving a pre-critical deformation problem with the known motion law of the d-area boundary. As the next step, we consider changes in the body’s stress-strain state (SSS) during the fracture of the d-area. We solve the elastic-plastic problem under simple unloading of the body’s d-surface and remaining an external load that corresponds to the beginning of the fracture process. During the d-unloading, the formation of new plastic areas, partial unloading and reaching the fracture criterion are possible. As a result, the body’s SSS at the moment when local unloading begins differs from its state when the d-unloading ends. This constitutes a principal distinction from the common procedure of “killing the elements” when the element rigidity (after reaching the fracture criterion) is supposed to be close to null. Herewith the body state outside a removed element is considered to be unchangeable; and the generation of unloading and additional loading zones (after the element is excluded) is not considered. In case of linear elasticity, the solution of the problem with a removed area under fixed external load coincides with the d-unloading solution by virtue of the solution uniqueness and the superposition principle. However, the solution of the elastic-plastic problem for the body with the removed area under simple loading will not coincide with the d-unloading solution. The paper presents the solutions of composite delamination problems that illustrate the simple d-unloading method both in linear elastic and in elastic-plastic formulations.

Keywords: composite, Neuber-Novozhilov approach, characteristic size, fracture, simple process, elastic-plastic deformation, variational equation, finite element method

Vadim V. Glagolev – Doctor of Physical and Mathematical Sciences, Professor, e-mail: vadim@tsu.tula.ru

 Alexey A. Markin – Doctor of Physical and Mathematical Sciences, Professor, e-mail: markin-nikram@yandex.ru

 Artem A. Fursaev – Ph. D. student, e-mail: artemkajs@mail.ru

Metal hydrides are among the optimum solutions for hydrogen storage in terms of effectiveness and safety. Magnesium and its alloys can reversibly absorb hydrogen in large amounts, so according to the DOE's requirements and making those materials attractive for applications. At first, determining a fast hydrogen saturation of Mg-based alloys consisted in grinding the materials up to micrometric grain size. A significant increase of the specific surface of the treated powders by plastic strain processing leads to delivering very reactive samples. Also, huge improvement of H-sorption characteristics of bulk Mg-alloys was shown to be efficient under Equal Channel Angular Pressing (ECAP) treatments. During ECAP treatments, the achievement of a fine grained microstructure in bulk samples is accompanied by the formation of a clear texture. 

The main achievements expected from the application of ECAP treatments to Mg-rich alloys are the formation of ultra-fine microstructures with high angle boundaries, which drastically changes the characteristics of the alloy; volume homogenization of the microstructure for the best final stability of the hydrogenation properties of the refined material. Since, in most cases, a two or even more ECAP passes should be applied to deliver highly reacting materials, the operating temperature must be adjusted in terms of ductile to fragile characteristics in order to avoid irreversible cracking of the bulk sample.

After the application of the ECAP process, the resulting strain was characterized using different methods, such as mechanical engineering, numerical simulations and experimental methods. The present article reports on the sample strain process by using the grid evaluation method.

Keywords: equal-channel angular pressing, magnesium alloys, grid method, the strain analysis, temperature

Nataliya E. Skryabina – Doctor of Physical and Mathematical Sciences, Professor, e-mail: natskryabina@mail.ru

 Valery N. Aptukov – Doctor of Technical Sciences, Professor, e-mail: aptukov@psu.ru

 Petr V. Romanov – Ph. D. student, e-mail: petr_rom@yahoo.com

 D. Fruchart – Research, e-mail: daniel.fruchart@neel.cnrs.fr

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7. Estrin Y., Yi S.B., Brokmeier H.-G., Zuberova Z., Yoon S.C., Kim H.S., Hellmig R.J. Microstructure, texture and mechanical properties of the magnesium alloy AZ31 pro­cessed by ECAP // Int. J. Mater. Res. 2008. Vol. 99. P. 50-55.

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9. Skryabina N.E., Aptukov V.N., Romanov P.V., Fruchart D.  Impact of equal-channel angular pressing on mechanical behavior and microstructure of magnesium alloy // Bulletin of the Perm National Research University. Mechanics. 2014.  № 3. P. 113-128.

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In the last 15-20 years, mathematical models have become the most important “tool” for development and creation of technology of thermomechanical processing of metals and alloys due to the occurrence of new class models based on physical theories which replace macrophenomenological models based on macro experiments. Among the founders of crystal plasticity are G. Taylor, G.  Bishop, R. Hill, T.G.  Lin and others. Many others researchers from the Soviet Union and Russia made a significant contribution to the development of this scientific direction, they are R.Z. Valiev, Ya.D. Vishnyakov, S.D. Volkov, O.A. Kaibyshev, V.A.  Likhachev, V.E. Panin, V.V. Rybin, T.D.  Shermergor and others. A physically based approach requires a deep understanding of the internal mechanisms and processes that accompany thermomechanical effects caused by inelastic deformation at different scale levels. One of the most important processes for the microstructure formation (and thus for mechanical properties) of finished products obtained by thermomechanical processing methods is the process of recrystallization. In this regard, this article provides an overview of the existing theories of recrystallization, special emphasis is given to nucleation of recrystallized grains. Basic physical mechanisms of nucleation of recrystallized grains are the mechanism based on the classical theory of fluctuations suggested by E.J. Beck and D. Turnbull;  the mechanism of nucleation and growth of polycrystal subgrains formed as a result of polygonization (R.W. Cahn, P.A. Beck, A. Cottrell, W. G. Burgers); P.A. Beck’s and P.R. Sperry’s mechanism of grain boundary migration that initially exists in the polycrystal; 4) the mechanism of nucleation and growth of new grains as a result of coalescence of polygonized subgrains (H. Hu, J.C.M.  Li, H.  Fujita). Implementation of one of these mechanisms of new grains formation depends on the current state of the defective structure resulting from the history of thermomechanical deformation. The analysis of the existing models describing the inelastic deformation under high temperatures shows the need for consideration and inclusion of high-temperature processes, which accompany plastic deformation, in the models describing physical mechanisms.

Keywords: thermo-mechanical processing of metals, recrystallization, polygonization, recovery, physical mechanisms of inelastic deformation

Nikita S. Kondratev – CSc in Physical and Mathematical Sciences, Junior Researcher, e-mail: kondratevns@gmail.com

 Peter V. Trusov – Doctor of Physical and Mathematical Sciences, Professor, e-mail: tpv@matmod.pstu.ac.ru

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In order to construct a theory that adequately describes the effects of cyclic loadings, it is initially necessary to analyze the experimental plastic loop of a hysteresis of stainless steel SS304; and three types of backstresses responsible for the displacement of the center of the surface of loading are specified on this steel. For each type of backstresses, we have formulated evolution equations on basis of the equations of the theory of plastic flow under combined hardening. We have allocated the material functions which close the theory, and formulated the basic experiment and method of the material functions identification.

Evaluating the work of different types of backstresses on the field of plastic deformations under cyclic loadings with various magnitudes of the deformation up to the experimental values of the number of cycles before failure, it has been obtained that the work of backstresses of the second type is a universal characteristic of the material. This result made it possible to formulate the kinetic equation of damage accumulation, based on which we have considered the processes of nonlinear damage accumulation. To determine the material functions, responsible for the destruction, we have formulated the basic experiment and identification method.  The authors have given material functions for stainless steel SS304.

We have investigated the processes of elastic-plastic deformation of stainless steel SS304 with non-stationary hard cyclic loading under block changes of amplitude and mean deformation of the cycle. Also the processes of soft non-stationary and non-symmetric cyclic loading (ratcheting) under block changes of amplitude and mean stress cycle have been examined. The results of calculations are compared with the experimental results. The results of calculations are compared with the experimental results.

Computational research of nonlinear processes of damage accumulation and low cycle fatigue of stainless steel SS304 are conducted under symmetric hard cyclic loading both at the constant amplitude of strain and block change of the amplitude of strain. The calculation results show that the scope of deformation reduction leads to increase of the nonlinearity of damage accumulation, while the increase of the deformation scale results in the fact that the accumulation of damages tends to be linear. There is a significant deviation from the rule of linear summation of damages under a satisfactory conformity of calculation results with the experiments.

In order to construct a theory that adequately describes the effects of cyclic loadings, it is initially necessary to analyze the experimental plastic loop of a hysteresis of stainless steel SS304; and three types of backstresses responsible for the displacement of the center of the surface of loading are specified on this steel. For each type of backstresses, we have formulated evolution equations on basis of the equations of the theory of plastic flow under combined hardening. We have allocated the material functions which close the theory, and formulated the basic experiment and method of the material functions identification.

Evaluating the work of different types of backstresses on the field of plastic deformations under cyclic loadings with various magnitudes of the deformation up to the experimental values of the number of cycles before failure, it has been obtained that the work of backstresses of the second type is a universal characteristic of the material. This result made it possible to formulate the kinetic equation of damage accumulation, based on which we have considered the processes of nonlinear damage accumulation. To determine the material functions, responsible for the destruction, we have formulated the basic experiment and identification method.  The authors have given material functions for stainless steel SS304.

We have investigated the processes of elastic-plastic deformation of stainless steel SS304 with non-stationary hard cyclic loading under block changes of amplitude and mean deformation of the cycle. Also the processes of soft non-stationary and non-symmetric cyclic loading (ratcheting) under block changes of amplitude and mean stress cycle have been examined. The results of calculations are compared with the experimental results. The results of calculations are compared with the experimental results.

Computational research of nonlinear processes of damage accumulation and low cycle fatigue of stainless steel SS304 are conducted under symmetric hard cyclic loading both at the constant amplitude of strain and block change of the amplitude of strain. The calculation results show that the scope of deformation reduction leads to increase of the nonlinearity of damage accumulation, while the increase of the deformation scale results in the fact that the accumulation of damages tends to be linear. There is a significant deviation from the rule of linear summation of damages under a satisfactory conformity of calculation results with the experiments.

The paper presents such new results as:

- specifying three types of backstresses responsible for kinematic hardening analyzing the  experimental loops of plastic hysteresis;

- establishing the work universality of the second type backstresses under low-cycle and high-cycle fatigue on basis of experimental results analysis;

- constructing the theory of plastic flow under combined hardening and kinetic equations of damage accumulation on the basis of the evolution equations for three types of backstresses;

- identifying the material parameters and verifying the proposed theory.

Keywords: plastic deformation, backstresses, damage accumulation, cyclic loading, low-cycle integrity, nonlinear damage summation

Valentin S. Bondar – Doctor of Physical and Mathematical Sciences, Professor, e-mail: bondar@mami.ru

 Vladimir V. Danshin  – CSc in Physical and Mathematical Sciences, Associate Professor, e-mail: tm@mami.ru

 Dmitry A. Makarov – CSc in Physical and Mathematical Sciences, Associate Professor, e-mail: makarovda@yandex.ru

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