15. Simulation of thermomechanical processes in functionally-gradient materials of inhomogeneous structure in the manufacturing and operation of rocket structural elements

15. Simulation of thermomechanical processes in functionally-gradient materials of inhomogeneous structure in the manufacturing and operation of rocket structural elements

Usov A. V., Kunitsyn М. V.

Institute of Mechanical Engineering of Odessa National Polytechnic University, Odessa, Ukraine

Kosm. teh. Raket. vooruž. 2020, (1); 137-148
https://doi.org/10.33136/stma2020.01.137
 
Language: Ukrainian
Annotation:
The strength of real solids depends essentially on the defect of the structure. In real materials, there is always a large number of various micro defects, the development of which under the influence of loading leads to the appearance of cracks and their growth in the form of local or complete destruction. In this paper, based on the method of singular integral equations, we present a unified approach to the solution of thermal elasticity problems for bodies weakened by inhomogeneities. The purpose of the work is to take into account the heterogeneities in the materials of the elements of the rocket structures on their functionally-gradient properties, including strength. The choice of the method of investigation of strength and destruction of structural elements depends on the size of the object under study. Micro-research is related to the heterogeneities that are formed in the surface layer at the stage of preparation, the technology of manufacturing structural elements. Defectiveness allows you to adequately consider the mechanism of destruction of objects as a process of development of cracks. In studying the limit state of real elements, weakened by defects and constructing on this basis the theory of their strength and destruction in addition to the deterministic one must consider the probabilistic - statistical approach. In the case of thermal action on structural elements in which there are uniformly scattered, non-interacting randomly distributed defects of the type of cracks, the laws of joint distribution of the length and angle of orientation of which are known, the limiting value of the heat flux for the balanced state of the crack having the length of the "weakest link" is determined. The influence of heterogeneities of technological origin (from the workpiece to the finished product) that occur in the surface layer in the technology of manufacturing structural elements on its destruction is taken into account by the developed model. The strength of real solids depends essentially on the defect of the structure. In real materials, there are always many various micro defects, the development of which under the influence of loading leads to the appearance of cracks and their growth in the form of local or complete destruction. In this paper, based on the method of singular integral equations, we present a unified approach to the solution of thermal elasticity problems for bodies weakened by inhomogeneities. The purpose of the work is to take into account the heterogeneities in the materials of the elements of the rocket structures on their functionally gradient properties, including strength. The choice of the method of investigation of strength and destruction of structural elements depends on the size of the object under study. Micro-research is related to the heterogeneities that are formed in the surface layer at the stage of preparation, the technology of manufacturing structural elements. Defectiveness allows you to adequately consider the mechanism of destruction of objects as a process of development of cracks. In studying the limit state of real elements, weakened by defects and constructing on this basis the theory of their strength and destruction besides the deterministic one must consider the probabilistic - statistical approach. With thermal action on structural elements in which there are uniformly scattered, non-interacting randomly distributed defects of the cracks, the laws of joint distribution of the length and angle of orientation of which are known, the limiting value of the heat flux for the balanced state of the crack having the length of the "weakest link" is determined. The influence of heterogeneities of technological origin (from the workpiece to the finished product) that occur in the surface layer in the technology of manufacturing structural elements on its destruction is taken into account by the developed model. The solution of the singular integral equation with the Cauchy kernel allows one to determine the intensity of stresses around the vertexes of defects of the cracks, and by comparing it with the criterion of fracture toughness for the material of a structural element, one can determine its state. If this criterion is violated, the weak link defect develops into a trunk crack. Also, a criterion correlation of the condition of the equilibrium defect condition with a length of 2l was got, depending on the magnitude of the contact temperature. When the weld is cooled, it develops "hot cracks" that lead to a lack of welding elements of the structures. The results of the simulation using singular integral equations open the possibility to evaluate the influence of thirdparty fillers on the loss of functional properties of inhomogeneous systems. The exact determination of the order and nature of the singularity near the vertices of the acute-angled imperfection in the inhomogeneous medium, presented in the analytical form, is necessary to plan and record the corresponding criterion relations to determine the functional properties of inhomogeneous systems.
Key words: mathematical model, linear systems, singular integral equations, impulse response, defects, criteria for the destruction of stochastically defective bodies, Riemann problem, thermoelastic state.

Bibliography:

1. Gakhov F. D. Kraievye zadachi. M.: Nauka,1977. 640 s.
2. Gakhov F. D. Uravneniia tipa svertki. M.: Nauka, 1978.296 s.
3. Litvinchuk G. S. Kraievye zadachi i singuliarnye integralnye uravneniia so sdvigom. M.: Nauka, 1977. 448 s.
4. Muskhelishvili N. I. Singuliarnye integralnye uravneniia. M.: Nauka, 1968. 512 s.
5. Panasiuk V. V. Metod singuliarnykh integralnykh uravnenii v dvukhmernykh zadachakh difraktsii. K.: Nauk. dumka, 1984. 344 s.
6. Siegfried PROSSDORF Einige Klassen singularer Gleichungen.Akademie Verlag Berlin, 1974. 494 s. https://doi.org/10.1007/978-3-0348-5827-4
7. Oborskii G. А. Modelirovanie sistem : monografiia. Odessa: Astroprint, 2013. 664 s.
8. Usov A. V. Matematicheskoe modelirovanie protsessov kontrolia pokrytiia elementov konstruktsii na baze SIU. Problemy mashinostroeniia. 2010. Т.13. №1. s. 98−109.
9. Kunitsyn M. V., Tribocorrosion research of NI-Al2O3/TIO2 composite materials obtained by the method of electrochemical deposition. M.V. Kunitsyn, A.V Usov. Zb. nauk. prats, Suchasni tekhnolohii v mashinobuduvanni. Vyp. 12. Kharkiv: NTU KhPI, 2017. s. 61−70.
10. Savruk M. P. Chislennyi analiz v ploskikh zadachakh teorii tershchin. K.: Nauk. dumka, 1989. 248 s.
11. Usov A. V. Vvedenie v metody optimizatsii i teoriiu tekhnicheskikh sistem. Odessa: Astroprint, 2005. 496 s.
12. Popov G. Ya. Kontsentratsiia uprugikh napriazhenii vozle shtampov, razrezov, tonkikh vkliuchenii i podkreplenii. M.: Nauka, 1982. 344 s.
13. Cherepanov G. P. Mekhanika khrupkogo razrusheniia. M.: Nauka., 1974. 640 s.
14. Stashchuk N. G. Zadachi mekhaniki uprugikh tel s treshchinopodobnymi defectami. K.: Nauk. dumka, 1993. 358 s.
15. Ekobori T. Nauchnye osnovy prochnosti i razrusheniia materialov. Per. s yap. K.: Nauk. dumka, 1978. 352 s.
16. Morozov N. F. Matematicheskie voprosy teorii treshchin. M.: Nauka, 1984. 256 s.
17. Popov G. Ya. Izbrannye trudy. Т. 1, 2. Odessa: VMV, 2007. 896 s.
18. Grigirian G. D., Usov A. V., Chaplia М. Yu. Vliianie shlifovochnykh defektov na prochnost detalei nesushchei sistemy. Vsesoiuzn. konf. Nadezhnost i dolgovechnost mashin i priborov. 1984. s.101−106.
19. Rais Dzh. Matematicheskie metody v mekhanike razrusheniia. Razrushenie. V 2 t. М.: Mir, 1975.Т.2. S. 204−335.
20. Karpenko G. V. Fiziko-khimicheskaia mekhanika konstruktsionnykh materialov: V 2-kh t. K. : Nauk. dumka, 1985. Т. 1 228 s.
21. Kormilitsina Е. А., Salkovskii F. М., Usov A. V., Yakimov А. V. Prichiny poiavliniia defektov pri shlifovanii magnitotverdykh splavov. Tekhnologiia elektrotekhnicheskogo proizvodstva. М.: Energiia. № 4. 1982. s.1−5.
22. Usov A. V. Smeshannaia zadacha termouprugosti dlia kusochno-odnorodnykh tel s vkliucheniiami i treshchinami. IV Vsesoiuzn. konf. Smeshannye zadachi mechaniki deformiruemogo tela: Tez. dokl.-Odessa,1990. s.116.
23. Yakimov А. V., Slobodianyk P. T., Usov A. V. Teplofizika mekhanicheskoi obrabotki. K.: Nauk. dumka,1991. S. 270.
24. Vitvitskii P. M., Popina S. Yu. Prochnost i kriterii khrupkogo razrusheniia stokhaticheski defektnykh tel. K.: Nauk. dumka, 1980. 187 s.

Full Text(PDF) || Content 2020 (1)