PSI - Issue 40

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Procedia Structural Integrity 40 (2022) 264–274

15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures Analytical, experimental, and numerical methods for the analysis of strength and service life of rocket engines 15th International Conference on Mechanics, Resource and Diagnostics of Materials and Stru tures Analytical, experimental, and numerical methods for the analysis of strength and service life of rocket engines

N.A. Makhutov, M.M. Gadenin, D.O. Reznikov*, O.N. Yudina Mechanical Engineering Research Institute, 4 Maly Kharitonievsky lane, Moscow, 101990, Russia N.A. Makhutov, M.M. Gadenin, D.O. Reznikov*, O.N. Yudina Mechanical Engineering Research Institute, 4 Maly Kharitonievsky lane, Moscow, 101990, Russia

© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resources and Diagnostics of Materials and Structures. Abstract The paper presents the analysis of strength, service life, and structural integrity of rocket space engines that is based on the combined application of traditional and new experimental, analytical, and numerical methods of calculation, testing, and diagnostics of the state and integrity of their load-bearing components at all stages of the engine life cycle. A computerized data bank on the parameters of the design equations, based on the results of special experiments in laboratory, bench, and field conditions was created. Mathematical and physical modeling was used to conduct refined strength analysis for the most critical components of the rocket engine. The finite element analysis of stress-strain response of the engine critical components to loading regimes was performed. Safety factors for strength, plasticity, and service life of load bearing components were established. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. Keywords: Liquid-fuel rocket engine, strength; life-time, tests; modeling, databank; knowledge base 1. Introduction The creation of engines for modern rocket space systems is one of the critical areas of comprehensive basic and applied research carried out in Russia and other countries that develop space systems and technologies (Frolov, Abstract The paper presents the analysis of strength, service life, and structural integrity of rocket space engines that is based on the combined application of trad tional and new exp rim ntal, analy ic , and numerical methods of calculation, te ting, and diagnostics of the state and integrity of their load-b aring componen s t all stages of the engine life cy le. A comput r zed data bank n the paramet rs of th design equati ns, b sed on the r sults of special experiments in laboratory, bench, and field co ditions was created. Mathematical and physical mo eli g was used t conduct r fined strength analysis for the most crit cal mponents of th rocket engine. The finite element analysis of tress-strain respo se of the engine critical co ponents to l ading regimes was performed. Saf ty factors for strength, plasticity, and service life of load b aring components were established. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review u der re ponsibility of scientific committe of the15th International C nference on Mechanics, Resource and Diagnostics of Materials and S ructur s. Keywords: Liquid-fuel rocket engine, strength; life-time, tests; modeling, databank; knowledge base 1. Introduction The creation of engines for modern rocket space systems is one of the critical areas of comprehensive basic and applied search carried out in Russia and other coun ries that develop space systems and technologi s (Frolov,

* Corresponding author. Tel.:+7 495 623 5835; fax:+7 495 623 58 35. E-mail address: mibsts@mail.ru * Corresponding author. Tel.:+7 495 623 5835; fax:+7 495 623 58 35. E-mail address: mibsts@mail.ru

2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. 2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review u der responsibility of t scientific committe of the15th Int rnational C ference o Mechanics, Resource and Diagnostics of Materials and Structures.

2452-3216 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resources and Diagnostics

of Materials and Structures. 10.1016/j.prostr.2022.04.036

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1998; Makhutov, 2008; Dawn Carmichael D., 2019). The rocket engines considered in this paper belong to the category of critically and strategically important objects of the manmade environment. The analysis of their strength, service life, and integrity is based on the combined application of traditional and new experimental, analytical and numerical methods of calculation, testing, and diagnostics of the state and integrity of their load-bearing components at all stages of their life cycle (Frolov, 1998; Makhutov, 2008; Makhutov, 2017; Rouhollah Pour, H., 2018). These technologies include: - design technologies that are based on analytical and numerical solutions of boundary value problems related to the assessment of stress-strain states and criterion assessments of strength and service life; - manufacturing technologies for the main and auxiliary components of critical technical systems with the development of mathematical and physical models of structural materials, as well as mechanical, thermal, laser, electronic, powder, superfine, and nano-processing procedures; - technologies for laboratory, bench, and field tests of critical components and prototypes of analyzed units using experimental multiparameter technical diagnostics of operating procedures and the condition of load-bearing components; - operation control technologies that take into account hazardous normal and emergency situations with the use of new methods and systems for technical diagnostics of accumulated damages, reaching limiting states and emergency protection.

Nomenclature a H

hydrogen diffusion into the metal and its concentration

accumulated damage modulus of elasticity amplitudes of strains

d E e a e C e n е y

fracture strain maximun strain nominal strain

e max

yield strain of the material

e

strain rate;

0 e K t M b M t

strain rate during standard tests theoretical stress concentration factor

bending moment torsion moment

strain hardening exponent numbers of loading cycles numbers of revolutions safety factors for strains number of launches safety factor for stresses transverse forces centrifugal forces operational reliability service life service life

m N

n

n e N l N n N s n σ Q

q P p r e r σ

pressure strain ratio stress ratio temperature

t

melting temperature

m T

speed

v

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operating torsion time amplitudes of stresses maximum stress

τ

σ а

σ max

nominal stress fracture stress

σ n σ c

yield stress at at temperature t yield stress at room temperature t 0 ultimate strength at at temperature t ultimate strength at room temperature t 0

t y 

0 y 

t u 

0 u 

flows of liquids, (oxygen, hydrogen) and gas combustion products

Ф

t 

increase in material temperature relative narrowing at fracture

ψ с

the ductility of steels in an atmosphere of gaseous hydrogen

ψ cH

Fig. 1. The framework for solving the main problems of the life cycle in the development and operation of a rocket engine.

In terms of the uniqueness of the design, complexity, and importance of the step-by-step solution of the problems of strength, service life, and safety at all stages of the life cycle of rocket and space systems (Fig. 1), a special place was and is still occupied by the problems of design and operation of liquid-propellant rocket engines (LRE) of various types that are distinguished by their power capacity, purpose, and types of fuel and oxidizer employed (Makhutov, 2011; Makhutov, 2013; Makhutov, 2019; Wei Wang, 2019).

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For many decades the Mechanical Engineering Research Institute of the Russian Academy of Sciences has been collaborating with leading institutes and specialists from design bureaus of the rocket and space industry in solving these problems. The results of the basic research and applied developments performed in this area are presented in

Makhutov (2011), Makhutov (2013), Makhutov (2019). 2. Analytical studies and standard strength analysis

The creation of liquid-propellant rocket engines (LPE) that use oxygen and hydrogen in the liquid state at cryogenic temperatures as fuel and oxidizer components was a problem of particular scientific novelty and practical importance (Fig. 2). At the first stages of the creation of liquid-propellant rocket engines, the main importance was the validation of strength of their units under extreme influences (pressure p , temperature t , speed v , numbers of revolutions n , numbers of loading cycles N , and operating time τ). In analytical studies of stress -strain states the equations of the theory of bars, plates, shells in linear (elastic) and nonlinear (elastoplastic) formulations were used.     , ( , , , , )( , , ) b t е F p t v n Q M M    . (1) In this case inertial, weight, aerohydrodynamic impacts on the analyzed load-bearing components were reduced to the axial and transverse forces Q, torsion Mt and bending Mb moments that were taken into account in the calculations.

Fig. 2. Oxygen-hydrogen liquid rocket engine RD-120.

Strength analysis carried out for these components is based on nominal and maximum stresses σ n , σ max and strains e n , e max at critical points of dangerous cross- sections, as well as on the fracture stresses σ c and strains е c .

 

  

, n n   c c e e

(2)

      , n 





        max , , n e e





,   n

, ( , n

,

e e

 

 

max

max

max

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where n σ and n e are the stress and strain safety factors, respectively (1 ≤ n σ ≤ n e ). The values fracture stresses σ c and strains e c are in a complex functional dependence on the operational factors:     c c , , , , Ф е F N t    , (3) where Ф are flows of liquids, (oxygen, hydrogen) and gas combustion products. The scientifically rigorous implementation of analytical expressions (1) – (3) implies the development of: - knowledge bases about fundamental laws of propagation of hazardous processes in liquid-propellant rocket engines; - computerized data banks on the systematized parameters of the design dependencies, based on the results of special experiments in laboratories, bench, and field conditions. The creation of the rocket and space industry in the 50s-70s of the twentieth century in the USSR and the USA showed that the operational reliability P of carrier rockets could not be provided only by normative calculations. The increase in reliability was also caused by the increase in the number of launches N l , during which various damages and failures were detected and gradually eliminated, and also various scenarios of failures, accidents, and catastrophes were analyzed.

Fig. 3. The relationship between the probability of safe operation and the number of launches of carrier rockets: 1- Saturn; 2- Shuttle; 3- Blocks; 4- Centaurus; 5- Titanium -3; 6 - Arian; 7 - Delta; 8- Zenith; 9- Atlas; 10 – Proton. As the methods of designing and testing carrier rockets of the first, second and third generations improved, an increase in reliability was achieved at lower N l . (Fig. 3). 3. Experimental studies of the states of stresses The development of rocket and space technology and computer technologies made it possible to comprehensively apply not only analytical solutions of strength and service life problems according to expressions (1) - (3), but also to move to a scientifically valid approach to new verification calculations using mathematical and physical modeling (Makhutov, 2008; Makhutov, 2011; Makhutov, 2013; Makhutov, 2017; Makhutov, 2018) for the most critical components of a liquid-propellant engine - first of all, rotors and blades of turbopump units (Fig. 4).

6

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a

c

b

Fig. 4. Turbopump unit of a liquid-propellant engine (a), its rotor (b), and an impeller of a hydrogen pump TPU with its model for the study of the stress-strain response. Two main experimental methods for physical modeling were developed in Mechanical Engineering Research Institute in cooperation with JSC KBKhA: - testing of models of the impeller of the hydrogen pump of the turbopump unit (TPU) made of optically active materials under centrifugal loading in the air at room temperature; - tests of full-scale impellers at the bench under operational loading (50,000 rpm) in a cryogenic liquid medium. These tests made it possible to obtain initial information about the stress-strain response of the unit according to expression (2). Dangerous critical zones and points were identified when the stress and strain distribution fields were analyzed (Fig. 5). The mathematical modeling in solutions of boundary-value problems was carried out using the theory of stress and strain concentration     max max , , ( , , ) t n n e F K e m    , (4) where K t is the theoretical stress concentration factor, determined experimentally; m is the strain hardening exponent in the power-law approximation of the real stress-strain curve of the material. a b

Fig. 5. Model of the pump impeller and the diagram of sections for determining the stress-strain response (a) and the distribution of the photoelasticity bands in the model (b).

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The value of the exponent m is established according to the experimental stress-strain curve of laboratory specimens under the corresponding conditions (temperatures, strain rates). ( / ) m y y e e    , (5) where е y is the yield strain of the material.

Fig. 6. Stresses in the turbine blade (x10 MPa).

4. Numerical analysis of stress states Numerical solutions of nonlinear boundary value problems in the form of expressions (1), (2), (4), (5) were developed as the methods and the computational capabilities of computer systems were improved. These methods include: - the method of successive approximations using elastic solutions with a variable secant modulus of elasticity for different strains; In the final version, the FEM turned out to be the most effective. The stress distribution patterns (Fig. 6) for the turbine blades of a turbopump unit subjected to centrifugal forces ( q ) and temperature changes ( t ) were obtained by FEM. 5. Implementation of integrated methods A fundamentally new issue in the formulation and implementation of analytical and numerical solutions according to expressions (1) – (5) for TPU rotors was the need to account for thermal effects (Makhutov, 2018; Gadenin, 2018) caused by internal heat release and an increase in material temperature t  due to cyclic plastic strains max e :   max max ; , e t t t t t F e a      , (6) - variational-difference method; - method of integral equations; - finite element method (FEM).

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where a t is the experimentally determined factor of transformation of deformation energy into thermal energy. According to data obtained in special experiments   max , , , t a F e q N   (7) With elastoplastic strains e max at the level of 0.5-1.5% and a loading frequency of up to 50-100 Hz, the temperature rise reached 100-10,000 0 C. This, in turn, increased strains e max and caused an additional rise in temperatures. A new limit state that consists of metal ignition became possible in the oxygen-enriched environment at the operating temperatures that lie in the range t e =600÷800 0 С. It was also important to take into account the effect of hydrogen on the ultimate characteristics of the mechanical properties of materials σ c , e c in expression (3) (Makhutov, 2006; Makhutov, 2008; Makhutov, 2011). In this case, the effect of hydrogen diffusion into the metal and its concentration a H in the studied direction is described by a complex functional dependence:     max ; , , , c H H е F a a F e t N    . (8) The third factor to be taken into account in the analysis of strength and service life was the combination of different frequency modes of cyclic loading when high-frequency low-amplitude cycles from vibrations and pulsations of pressure and temperatures are superimposed on low-frequency high-amplitude cycles of thermomechanical loading. Ensuring strength and service life during testing and operation of liquid-propellant engines should be based on an integrated system of design equations (1) – (8). It can only be achieved through combined application of analytical and numerical methods, organization of the fundamentally new experiments and incorporation of the obtained information into an integrated smart data bank system and a knowledge base that would allow ensuring the operability of units of rocket and space systems in extreme operating conditions (Frolov, 1998; Makhutov, 2008; Makhutov, 2011; Makhutov, 2013; Makhutov, 2017; Makhutov, 2018; Gadenin, 2018; Aliyev, 2018, Deepak Sharma, 2019). The information on the operational loading of the turbines is the initial data for solving this problem (Fig.7).

Fig. 7. Changes in time of operational impacts (pressure p , temperature t , and the number of revolutions of the turbine n ).

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For low cryogenic temperatures achieved during cooling (for liquid hydrogen t min = – 253 °С and oxygen t min = – 183 °С) and high operating temp eratures when the engines are switched on ( t = +620 ÷ 800 °С) at pressures р max up to 32÷ 90 MPa and number revolutions n max up to 50,000 rpm, there are both high ranges Δ t max , Δ р max , Δ n max , and low Δ t , Δ р , Δ n at low frequencies. Low-frequency processes are superimposed on high-frequency ones that are induced by oscillations and pulsations. For the indicated operating temperatures t and structural materials used in the liquid-propellant engine, the basic mechanical properties (yield strength σ y , ultimate st rength σ u ) are determined by the expressions                 0 0 , 1 1 exp , , T T y u y u t u t y       (9) o + t ) and room temperature t 0 = 20°С, respectively; β у and β u are material characteristics depending on σ y 0 and σ u 0 (at 500 ≤ σ у0 ≤ 900 MPa the value of β у decreases from 70 to 40). For cases with self-heating and possible ignition of a metal in an oxygen atmosphere, the term For cases with self-heating and possible ignition of a metal in an oxygen atmosphere, the term (1/ T m -1/ T 0 )- (1/ T m -1/ T )) is used in       0 where σ y t , σ u t , σ y 0 and σ u 0 yield stress and ultimate strength at a given temperature t ( T = 273

equation (9) instead of the term (1/ T m -1/ T 0 ), where T m is the melting temperature. Real loading processes developing in time τ cause strain e at different strain rates the characteristics σ у and σ u are changed with the change of the temperature t :         y u m ,m y u t ue t ye , e e , 0 0 0          ,

 e de d   ; at the same time

(10)

-3 s -1 ; m

where 0 e is the strain rate during standard tests, 0 e = (1 ÷ 5) ∙ 10

y and m u are characteristics of the material's

sensitivity to the dynamic loading. For yield stress at 500 ≤ σ y ≤ 900 MPa, the value of m y decreases 0.045 ≤ m y ≤ 0.010.

The amplitudes of stresses σ а and strains e a , stress ratios r σ and strain ratios r e are estimated according to Fig. 7 and expression (1) for cycles with pressure ranges Δ р and temperature ranges Δ t , maximum and minimum values p max , p min , t max , t min :

  

  









  

  

  

  

  a a ,e 

max

min

max , e e

min

,

(11)



2

2

    r ,r 

  , e e

  max min

max  

.

e

min



Cyclic service life (durability) N at given values { σ а , e a } and { r σ , r e } are determined according to the modified Coffin-Manson-Langer equation for pseudoelastic stresses (Makhutov, 2008; Makhutov, 2011; Makhutov, 2013):

m

t u

   

p     



1

E

,

(12)

e E    a a

, 1 75

e



n

1 1

1 1

r r

r r

 

 

t к

1





  N 4

  N 4

m

m

e e

 





p

e

where E is the modulus of elasticity, ψ с is the relative narrowing at fracture of the laboratory specimen; m p and m e are the characteristics of the material (for σ a ≤ σ u ≤ 1000 MPa, the value of m p increases from 0.5 to 0.6, and the value of m e decreases from 0.12 to 0.08). Plasticity decreases with decreasing temperature t and increasing strain rate e  . When the high-frequency loading is superimposed on the low-frequency one (according to Fig. 7) the service life N n decreases (Makhutov, 2008; Makhutov, 2011; Gadenin, 2018):

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10

 

  



n an a к

 

(13)

 n n N N f f

where f n and

* an  are the frequency and amplitude of high-frequency loading stresses,

f , * a  , N - frequency, stress amplitude, and durability of the main low-frequency loading; κ n is the material characteristic. With the increase in the strength of the material (500 ≤σ u ≤1000 MPa), the value of κ n increases (0.9≤κ n <1.6). It is important for a liquid-propellant rocket engine that in an atmosphere of gaseous hydrogen the ductility of steels ψ cH in expression (12) decreases (Makhutov, 2011; Makhutov, 2013):

1   , 

(14)

h

m

1   

 

K p

cH c  

к 



H

H

H H

where K H is a characteristic of material sensitivity to hydrogen embrittlement, that depends on temperature (4≤ K H ≤ 6); p H is the pressure in a hydrogen environment; m H ≈0.15; h H ≈0.07 ÷ 0.08. For liquid-propellant rocket engines with increasing service life τ (from 70 to 5,000 s), it is necessary to take into account (Makhutov, 2008; Makhutov, 2011; Makhutov, 2017) the effect of time τ on the main mechanical properties ( σ у , σ u , ψ c ):                   m к y u к y u , , , , 0  . (15) where m τ is a material characteristic that increases exponentially with the increasing temperature t   T m m exp u u t u       0 . (16)

-3 to 6∙10 -3 , and the m

The value of β u τ increases with an increase in σ u from 5∙10

τ u value can be taken constant and

equal to 1∙10 -3 . The accumulated damage d in the i -mode of the cyclic loading (at amplitudes of stresses * with the number of cycles N i ) is estimated using the equation (12) and summated:

ai  and strains e ai and

(17)

 



 / i

d

N N

i

In the case of single-use rocket engines, the service life N s ≤ 25; for multiple use engines the total number of cycles can be increased up to N s ≤ 250. Performing calculations for the entire system of equations (1) - (16) makes it possible to establish safety factors for strength, plasticity, and service life characteristics, taking into account temperatures t , strain rate e , hydrogen pressure H , time τ :   maxs H u t ,e, p , n       ,   max , , , c H s e t e p n e    ,   s n H N N N ,N ,N ,N n   , (18) where σ max s , e max s , and N s are the maximum stresses, strains, and durability during operation. During the creation and operation of liquid-propellant rocket engines, these safety factors were gradually reduced and were established (Makhutov, 2008; Makhutov, 2011, Makhutov, 2017; Makhutov 2018) not lower than: n σ >1.1÷1.2; n e >1.5÷2.0; n N >2.5 ÷ 3. Further development of the outlined approach to the comprehensive analysis of performance and limit states of liquid-propellant rocket engines can be carried out only with the use of new complex technologies and systems with

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the application of generalized analytical approaches to ensure safe functioning of complex technical systems from the standpoint of not only strength and service life, but also integrity based on the risk concept (Frolov, 1998; Makhutov, 2008; Makhutov, 2011, Makhutov, 2017; Aliyev, 2018; Makhutov, 2018). Acknowledgements The work was financially supported by the Russian Foundation for Basic Research (Project 20-58-00019 Bel_a) References Aliyev, A.G., Shahverdiyeva, R.O., 2018. Perspective Directions of Development of Innovative Structures based on Modern Technologies / International Journal of Engineering and Manufacturing 8, 4, 1-12. Dawn Carmichael D., Archibald, J., 2019. A Data Analysis of the Academic use of Social Media. International Journal of Information Technology and Computer Science 11, 5, 1-10. Deepak Sharma, Bijendra Kumar, Satish Chand, 2019. A Trend Analysis of Machine Learning Research with Topic Models and Mann-Kendall Test. International Journal of Intelligent Systems and Applications 11, 2, 70-82. Gadenin, M.M., 2018.Study on Damaging and Fatigue Life of Constructions under Single- and Two-Frequency Loading Modes Based on Deformational and Energy Approaches. Inorganic Materials 54,15, 1543-1550. Frolov, K.V., Makhutov, N.A., Gadenin, M.M., 1998. Safety of Russia. Legal, social, economic, scientific and engineering aspects. Management of service life for high risks objects. Functioning and development of complex economic, technical, power, transportation, and communication systems and service lines. Part 2. Maintenance of safe functioning of complex technical systems at different stages of their life cycle. MGF Znanie publ. Moscow, pp.416 (in Russian). Makhutov, N.A., 2008. Strength and Safety: Basic and Applied Research. Nauka publ. Novosibirsk, pp.528 (in Russian). Makhutov, N.A., 2017. Safety and Risks: System Researches and Developments. Nauka publ. Novosibirsk, pp. 724 (in Russian). Makhutov, N.A, Gadenin, M.M., 2011. Engineering Diagnostics of Remaining Service Life and Safety. Spektr Publishing House. Moscow, pp. 187 (in Russian) Makhutov, N.A., Rachuk, V.S., Gadenin, M.M., at al, 2011. Strength and service life of liquid-fuel rocket engines. Nauka publ. Moscow, pp.525 (The series “Research of stresses and strength of rocket engines”) (in Russian) Makhutov, N.A., Rachuk. V.S., Gadenin, M.M., at al., 2013. Stress-strain states of liquid-fuel rocket engines. Nauka publ. Moscow, pp. 646 (The series “Research of stresses and strength of rocket engines”) (in Russian) Makhutov, N.A., Gadenin, M.M., 2019. Laws of accumulation of low-cycle fatigue damages taking into account operational parameters of the loading history. Herald of the Perm National Research Polytechnic University. Space Technics 56, 1, 45-57. Makhutov, N.A., Aksenov, S.P., Gadenin, M.M., et al, 2018. Research of local stress-strain and limit states of high-speed rotor structures. Pumps. Turbines. Systems 3, 28, 5-19. Makhutov, N.A., Gadenin, M.M., Alymov, V.T., at al, 2006. Estimation of strength and service life of structural materials at the impact of gaseous hydrogen of high pressure. Industrial laboratory. Diagnostics of materials 72, 5, 35-41 Makhutov, N.A., Gadenin, M.M., 2018. Development of basic and applied research in the field of machine sciences with use of strength, lifetime, survivability, and safety criteria. Industrial laboratory. Diagnostics of materials 84,10, 41-52. Rouhollah Pour, H., Asgari Marnani, J., Tabatabei, A.A., 2018. A Novel Method for Crack Detection in Steel Cantilever Beam Using Wavelet Analysis by Combination Mode Shapes. International Journal of Image, Graphics and Signal Processing 10, 4, 1-12. Wei Wang, Gang Zhang, Jun-De Han, Wei Ma, 2019. Computational Method Investigation of Solid Ducted Rocket. International Journal of Engineering and Manufacturing 9, 1, 1-10.

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© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resources and Diagnostics of Materials and Structures. Abstract A study of the mechanical behavior of elastomeric nanocomposites with a styrene-butadiene rubber matrix and filler in the form of single- wall nanotubes TUBALL ™ (made by OCSiAl) has been carried out. Materials filled by N -330 grade Carbon Black as a nanofiller was used for comparison. Studies have shown that the introduction of a small amount of nanotubes (7 phr) into styrene-butadiene rubber significantly affects the viscoelastic properties of the material, the softening effect and the growth of residual strain. In addition, the material becomes substantially anisotropic during the milling process. The rigidity of the material in one direction is many times higher than the rigidity in the perpendicular direction © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. Keywords: Filled rubbers; nanofillers; mechanical properties; nanotubes. 1. Introduction Research on filled elastomers has been going on for many years [1]. Despite this, there are still many unanswered questions in this area. In particular, many questions arise around the interaction of filler particles and polymer matrix [2]. The fact is that different filler particles change the mechanical properties of the matrix in different ways. Without careful research it is not clear what physical and chemical processes are behind this. Often, researchers limit themselves by mechanical testing without going into the physical mechanisms that determine the behavior of 15th International Conference on Mechanics, Resource and Diagnostics of Materials and Stru tures Anisotropic properties of styrene-butadiene rubber filled with single-wall nanotubes A.L. Svistkov, V.V. Shadrin, A.Yu. Beliaev* Institute of Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences, Perm, Russian Federation Abstract A study of the mechanical behavior of elastomeric nanocomposites with a styrene-butadiene rubber matrix and filler in the form of ingle- wall nanotubes TUBALL ™ (m de by OCSiAl) has been carried out. Materi ls filled y N -330 gr de Carbo Black as a na ofiller was used for comparison. Stu ies have shown that the introduc ion of ma l amount of nanotubes (7 phr) into styre e-butadiene rubber significantly affects the iscoelastic prop rt es f the material, the softening effect and the growth of residual str in. In addition, the m terial becomes substantially anisot opic during the mi ling pr c ss. Th rigidity of the ma erial in one direct on is many times high than the rigidity in he perpendicular i ection © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of scientific committe of the15th International Conference on Mechanics, Resource and Diagnostics of Materials and S ructur s. Keywords: Filled rubbers; n ofillers; mechanical properties; nanotubes. 1. Introduction Research on filled elastomers has been going on for many years [1]. Despite this, there are still many unanswered questions in this area. In particul r, many questions arise around the interac ion of filler particles and polym r matrix [2]. The fact is that different filler particles change the mechanical properties the matrix in different ways. Wi hout careful research it s not clear wha physic l and chemic l processes are behind this. Often, researchers limit themselves by mechan cal testing wit out going into the physical m chanisms that e ermine the b havior of 15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures Anisotropic properties of styrene-butadiene rubber filled with single-wall nanotubes A.L. Svistkov, V.V. Shadrin, A.Yu. Beliaev* Institute of Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences, Perm, Russian Federation

*A.Yu. Beliaev. Tel.: +7-342-237-8315. E-mail address: belyaev@icmm.ru *A.Yu. Beliaev. Tel.: +7-342-237-8315. E-mail address: belyaev@icmm.ru

2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. 2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review u der responsibility of t scientific committe of the15th Int rnational C ference o Mechanics, Resource and Diagnostics of Materials and Structures.

2452-3216 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resources and Diagnostics

of Materials and Structures. 10.1016/j.prostr.2022.04.054

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the material. This approach is justified from the point of view of applied science and the introduction of materials into real production. The discovery that the addition of carbon black to rubber gum significantly changes the mechanical properties of the material gave impetus to the study of elastomeric composites. Over the years many studies have been carried out on various fillers, ranging from classic carbon black to various fillers of mineral origin [3-6]. With the discovery of various nanocarbons (graphene, fullerenes, carbon nanotubes, etc.), the question about their usage as fillers for polymer composites was posed. Special attention should be paid to the usage of nanotubes [7-11]. Due to the fact that one linear particle size of such filler significantly exceeds the other two, this can significantly change the mechanical behavior of the material in comparison with granular fillers. One of the interesting properties of composites with carbon nanotubes is anisotropy [12-16]. In this case, the induced anisotropy is a consequence of the milling. A significant problem, that complicates the usage of nanotubes as filler in industry, is the complexity and high cost of manufacturing. Therefore it is of interest to study TUBALL ™ nanotubes, the production of which has already been launched on an industrial scale by OCSiAl, as filler for elastomeric materials. These are single-walled nanotubes (SWCNT) with a length of about 5 µm [17]. This work is devoted to the study of elastomeric nanocomposites with styrene-butadiene (SBR) matrix, where SWCNT TUBALL ™ are used as filler. 2. Materials and methods The objects of research are elastomeric composites based on SBR-1705 HI- AR. Purification of TUBALL ™ nanotubes from impurities of amorphous carbon and metal-catalysts was carried out at Federal State Unitary Enterprise S.V. Lebedev Institute of synthetic rubber by the method of self-propagating high-temperature synthesis [18]. Filler, used for comparison, was Carbon Black N-330. The most interesting effects from the usage of nanotubes are significant increase of the rigidity of the material when a relatively small amount of nanotubes is introduced into the elastomer and the material acquires anisotropic properties. The passage of the material through the rollers, in a process of milling, affects the preferred orientation of nanotubes. As a result material anisotropy appears. In accordance with this fact samples were cut in two directions for each material. This is the direction of the last passage of the material through the rollers and the Figure 1 shows the loading curves of a sample made of an elastomeric nanocomposite based on SBR and filling with 7 mph SWCNT. The sample was stretched to an elongation factor λ = 1.5. Then the delay for 30 minutes was carried out. After that a complete unloading of the sample with a 30 minutes delay and further deformation to rupture was carried out. Experiments have shown that sample, cut in the rolling direction, is approximately 2 times more rigid than in the perpendicular direction. Residual strains after unloading are about 17-18%, which is a lot in order to use this nanocomposite as a construction material. The strong softening effect of the material indicates damage appearing during the first deformation. This effect is probably connected with movements of the nanotubes relative to each other, which lead to the appearance of ruptures in the elastomeric binder. Further step was an attempt to reduce the damage of the nanocomposite upon deformation. Carbon black filler, which was additionally introduced into the material, was widely used in the twentieth century to improve the mechanical behavior of elastomers. Adding of carbon black filler leads not only to increasing of the material rigidity but also to increasing of fracture stresses and deformations. It was suggested to check the hypothesis that combination of two fillers will allow achieving a better effect of reinforcing of the material and reduce the growth of damage during deformation. direction perpendicular to it. 3. Results and discussion

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Fig. 1. Test results of an elastomeric nanocomposite based on 7 mph SWCNT filling. The solid line the sample is cut along the direction of rolling, the dotted line – across.

a

b

Fig. 2. Test results of an elastomeric nanocomposite based on BSK with fillings: a - 50 mph of carbon black; b - 7 mph of SWCNT and 43 mph of carbon black at the maximum elongation ratio λ = 1.5. The solid line corresponds to the sample cut along the rolling direction, the dotted line – across.

. The results of testing are shown in Fig. 2. For comparison the result is shown for an elastomer filled with 50 mph carbon black only (Fig. 2, a). This is a common isotropic nanocomposite. Replacing part of the carbon black with SWCNT leads to significant material properties changing. Figure 2b shows the experimental results for a material containing 43 mph of carbon black and 7 mph of SWCNT. The material has become anisotropic and its rigidity (especially in the direction of the preferred orientation of nanotubes) has increased. The effect of significant softening and growth of permanent deformations still occurs in the material with SWCNT. Residual strains after

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unloading of SBR filled with carbon black are about 10% while in the material with the addition of SWCNT they are about 30% in the direction of rolling and 15% in the perpendicular direction. Value of λ at break for the composite with carbon black is about 6.2. For the composite with the addition of SWCNT the λ va lue at break is about 4.5 in the rolling direction and 2.5 in the transverse direction respectively. Taking into account that composite operate under conditions with lower deformations in real constructions, it made sense to see how the test results would change with a decrease of the maximum elongation ratio in the considered deformation cycle. Fig. 3 shows the loading curves of materials at maximum elongation rate λ = 1.3.

a

b

Fig. 3. Test results of an elastomeric nanocomposite based on BSK with fillings: a - 50 mph of carbon black; b - 7 mph of SWCNT and 43 mph of carbon black at the maximum elongation ratio λ = 1.3. The solid line corresponds to the sample cut along the rolling direction, the dotted line – across.

Test results showed that at lower deformations of the nanocomposite there is a significant decrease in the residual strains of the considered material. In the nanocomposite filled with carbon black residual strains decreased from 8% to 3%. In the material with carbon black and nanotubes the decrease is from 18% to 10% in the sample cut along the axis of the rolling direction and from 10% to 5% in the sample cut in the perpendicular direction. It can be expected that with delay increasing up to several hours the residual strains will be even less. 4. Conclusion Studies of the mechanical behavior of elastomeric composites based on SBR-1705 HI-AR with the addition of TUBALL ™ nanotubes have shown that even a small filling of SWCNT leads to a noticeable change in the mechanical characteristics of the material. Anisotropic properties, determined by the direction of the last passage of the material between the rollers, are formed during the milling process. This can be valuable in the manufacture of products with the desired anisotropy of individual parts of the construction. The addition of TUBALL ™ SWCNT to the SBR leads to a pronounced manifestation of the effect of material softening during the first deformation (Mullins effect) and an increase in residual strains. However, in the case when material is operated in the area of deformations not exceeding 30%, the effect of accumulation of residual strains can be acceptable for many applications.

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