On the calculation of unsteady thermal stresses in elastoplastic solids
DOI:
https://doi.org/10.7242/1999-6691/2017.10.3.20Keywords:
elasticity, plasticity, thermal stresses, shrink fit, assembly with interferenceAbstract
The features of estimated prediction of thermal stress evolution are considered in terms of the one-dimensional boundary problem of the theory of thermal stresses, in which a shrink fit assembly of cylindrical parts is simulated on the assumption of piecewise linear plasticity conditions. The problem solution is principally based on the classical maximum shear stress criterion (Tresca-Saint Venant yield criterion), whereas the maximum reduced shear stress criterion (Ishlinsky-Ivlev yield criterion) is used only for comparison of calculation results. It is shown that the use of piecewise linear potentials makes it possible to integrate an equilibrium equation in both reversible deformation area and various irreversible deformation areas. Dependences thus obtained are used in a time-step calculation algorithm. Calculations have shown that, as the temperature changes, stresses in the materials of the assembly can change plastic flow pattern. It means that the correspondence of plastic flow to a certain facet of loading surface passes into the correspondence to an edge and then to other facet. These circumstances cause irreversible deformation areas to be divided into parts in which the plastic flow obeys different sets of simultaneous equations, which take into account the assignment of the stress states to different facets and edges of the loading surface. The designed algorithm makes it possible to trace the moments of appearance and disappearance of such plastic flow areas, as well as their propagation in the deformed material. The calculations demonstrate the possibility of occurrence of a repeated plastic flow during unloading in a certain area of the assembly after return of the process to reversible deformation conditions on cooling. It has been established that taking into account the change of plastic flows caused by the use of piecewise linear plastic potentials has an essential impact on the distribution of current and residual stresses and on the final tightness of the assembly.
Downloads
References
Berniker E.I. Posadka s natagom v masinostroenii. - Leningrad: Masinostroenie, 1966. - 168 s.
2. Parkus G. Neustanovivsiesa temperaturnye naprazenia. - M.: Fizmatlit, 1963. - 252 s.
3. Boli B., Uejner Dz. Teoria temperaturnyh naprazenij. - M.: Mir, 1964. - 512 s.
4. Gohfel’d D.A. Nesusaa sposobnost’ konstrukcij v usloviah teplosmen. - M.: Masinostroenie, 1970. - 260 s.
5. Dopuski i posadki: Spravocnik. V 2-h castah / V.D. Magkov, M.A. Palej, A.B. Romanov, V.A. Braginskij. - L.: Masinostroenie, 1982. - C. 1. - 543 s.
6. Bland D.R. Elastoplastic thick-walled tubes of work-hardening material subject to internal and external pressures and to temperature gradients // J. Mech. Phys. Solids. - 1956. - Vol. 4, no. 4. - P. 209-229. DOI
7. Islinskij A.U., Ivlev D.D. Matematiceskaa teoria plasticnosti. - M.: Fizmatlit, 2001. - 704 s.
8. Perzyna P., Sawczuk A. Problems of thermoplasticity // Nucl. Eng. Des. - 1973. - Vol. 24, no. 1. - P. 1-55. DOI
9. Ohno N., Wang J.D. Transformation of a nonlinear kinematic hardening rule to a multisurface form under isothermal and nonisothermal conditions // Int. J. Plasticity. - 1991. - Vol. 7, no. 8. - P. 879-891. DOI
10. Orҫan Y., Gamer U. Elastic-plastic deformation of a centrally heated cylinder // Acta Mechanica. - 1991. - Vol. 90, no. 1. - P. 61-80. DOI
11. Chaboche J.L. Thermodynamically based viscoplastic constitutive equation: theory versus experiment // ASME Winter Annual Meeting. - USA, GA: Atlanta, 1991. - P. 1-20.
12. Lippmann H. The effect of a temperature cycle on the stress distribution in a shrink fit // Int. J. Plasticity. - 1992. - Vol. 8, no. 5. - P. 567-582. DOI
13. Gamer U. A concise treatment of the shrink fit with elastic-plastic hub // Int. J. Solids Struct. - 1992. - Vol. 29, no. 20. - P. 2463-2469. DOI
14. Mack W. Thermal assembly of an elastic-plastic hub and a solid shaft // Arch. Appl. Mech. - 1993. - Vol. 63, no. 1. - P. 42-50. DOI
15. Knazeva A.G. Teplofiziceskie osnovy sovremennyh vysokotemperaturnyh tehnologij. - Tomsk: Izd-vo TPU, 2009. - 357 s.
16. Bondar’ V.S., Dansin V.V., Kondratenko A.A. Variant teorii termoplasticnosti // Vestnik PNIPU. Mehanika. - 2015. - No 2. - S. 21-35. DOI
17. Kovtanuk L.V. Modelirovanie bol’sih uprugoplasticeskih deformacij v neizotermiceskom slucae // Dal’nevostocnyj matematiceskij zurnal. - 2004. - T. 5, No 1. - S. 110-120.
18. Rogovoj A.A. Opredelausie sootnosenia dla konecnyh uprugo-neuprugih deformacij // PMTF. - 2005. - T. 46, No 5. - S. 138-149. DOI
19. Burenin A.A., Kovtanuk L.V. Bol’sie neobratimye deformacii i uprugoe posledejstvie. - Vladivostok: Dal’nauka, 2013. - 312 s.
20. Aleksandrov S.E., Cikanova N.N. Uprugoplasticeskoe naprazenno-deformirovannoe sostoanie v plastine s zapressovannym vkluceniem pod dejstviem temperaturnogo pola // MTT. - 2000. - No 4. - S. 149-158
21. Alexandrov S., Alexandrova N. Thermal effects on the development of plastic zones in thin axisummetric plates // J. Strain Anal. Eng. - 2001. - Vol. 36, no. 2. - P. 169-175. DOI
22. Sevcenko U.N., Steblanko P.A. Vycislitel’nye metody v stacionarnyh i nestacionarnyh zadacah teorii termoplasticnosti // Problemi obcisluval’noi mehaniki i micnosti konstrukcij. - 2012. - No 18. - S. 211-226.
23. Sevcenko U.N., Steblanko P.A., Petrov A.D. Cislennye metody v nestacionarnyh zadacah teorii termoplasticnosti // Problemi obcisluval’noi mehaniki i micnosti konstrukcij. - 2014. - No 22. - S. 251-264.
24. Gorskov S.A., Dac E.P., Muraskin E.V. Rascet ploskogo pola temperaturnyh naprazenij v usloviah plasticeskogo tecenia i razgruzki // Vestnik CGPU im. I.A. Akovleva. Seria: Mehanika predel’nogo sostoania. - 2014. - No 3(21). - S. 169-175.
25. Burenin A.A., Kovtanuk L. V., Pancenko G.L. Neizotermiceskoe dvizenie uprugovazkoplasticeskoj sredy v trube v usloviah izmenausegosa perepada davlenia // DAN. - 2015. - T. 464, No 3. - S. 284-287. DOI
26. Aleksandrov S.E., Lomakin E.V., Dzeng J.-R. Resenie termouprugoplasticeskoj zadaci dla tonkogo diska iz plasticeski szimaemogo materiala, podverzennogo termiceskomu nagruzeniu // DAN. - 2012. - T. 443, No 3. - S. 310-312. DOI
27. Aleksandrov S.E., Lamina E.A., Novozilova O.V. Vlianie zavisimosti predela tekucesti ot temperatury na naprazennoe sostoanie v tonkom polom diske // Problemy masinostroenia i nadeznosti masin. - 2013. - No 3. - S. 43-48. DOI
28. Burenin A.A., Dac E.P., Muraskin E.V. Formirovanie pola ostatocnyh naprazenij v usloviah lokal’nogo teplovogo vozdejstvia // MTT. - 2014. - No 2. - S. 124-131. DOI
29. Pozdeev A.A., Nasin U.I., Trusov P.V. Ostatocnye naprazenia: teoria i prilozenia. - M.: Nauka, 1982. - 112 s.
30. Bengeri M., Mack W. The influence of the temperature dependence of the yield stress on the stress distribution in a thermally assembled elastic-plastic shrink fit // Acta Mechanica. - 1994. - Vol. 103, no. 1. - P. 243-257. DOI
31. Kovacs A. Residual stresses in thermally loaded shrink fits // Periodica Polytechnica. Ser. Mech. Eng. - 1996. - Vol. 40, no. 2. - P. 103-112.
32. Dac E.P., Tkaceva A.V., Sport R.V. Sborka konstrukcii <> sposobom goracej posadki // Vestnik CGPU im. I.A. Akovleva. Seria: Mehanika predel’nogo sostoania. - 2014. - No 4(22). - S. 225-235.
33. Burenin A.A., Dac E.P., Tkaceva A.V. K modelirovaniu tehnologii goracej posadki // SibZIM. - 2014. - T. 17, No 3. - S. 40-47. DOI
34. Bykovcev G.I., Ivlev D.D. Teoria plasticnosti. - Vladivostok: Dal’nauka, 1998. - 528 s.
35. Loginov U.N. Med’ i deformiruemye mednye splavy: Uceb. posobie. - Ekaterinburg: UGTU-UPI, 2006. - 136 s.
36. Marocnik stalej i splavov / Pod obs. red. A.S. Zubcenko. - M.: Masinostroenie, 2003. - 784 s.
Downloads
Published
Issue
Section
License
Copyright (c) 2017 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.