Approximate method for local elastic-plastic problems solving

Aeronautical and Space-Rocket Engineering

Strength and thermal conditions of flying vehicles


Аuthors

Svirskii Y. A.*, Bautin A. A.**, Luk’yanchuk A. A., Basov V. N.

Central Aerohydrodynamic Institute named after N.E. Zhukovsky, TsAGI, 1, Zhukovsky str., Zhukovsky, Moscow Region, 140180, Russia

*e-mail: yury.svirsky@tsagi.ru
**e-mail: andrey.bautin@tsagi.ru

Abstract

In the last twenty years, durability computing techniques with account for local elastic-plastic strain-stress state have achieved a status of the Industry Standard while producing aviation, automotive, cargo and earth moving equipment all over the world. Although the fundamental concepts of this approach are quite simple, the large-scale automation and this technique application for strength calculation of both large dynamically loaded structures and machines driving gears led, in one hand, to the new possibilities emergence for engineers, but, on the other hand, they created extra challenges for the designers of the durability evaluation software. Presently, there is a possibility of dynamic models application for aviation structure loading computing, finite element models, allowing compute local strains by the applied loads, and techniques for more accurate plasticity computing for damageability estimation.

The article considers one of the methods for solving the elastic-plastic problem at cycle-by-cycle calculation, which can be applied for the durability evaluation with account for non-linear effects of interaction of loads of various values, especially after rare loads of high values. The need for analytical methods for elastic-plastic stresses computation developing and improving is caused by high labor intensity and low computing speed through numerical methods, such as finite element method.

The article proposes a new approximate formula for determining elastic plastic stresses and strains at the point of failure. The proposed approach is based on the solution of the elastic-plastic problem by the finite element method for the static case, as well as the method developed by the authors for fitting the static and cyclic stress-strain curves based on standard constants and the Masing principle. The suggested formula for determining the dependencies of local stresses and strains on nominal stresses for typical concentrators provides the necessary dependencies, close in accuracy to the results determined by the finite element method. This formula application will allow developing effective methods for durability computing based on local elastic-plastic stresses and strains under multi-cycle loading, being typical for aircraft structures.

The article presents comparisons of local stresses dependencies at the most stressed points on nominal stresses, obtained with the proposed formula and the finite element method for typical stress concentrators of the aircraft structure such as strips with free hole, fillet, and stringer runout.

Keywords:

durability computing technique by local tensions, durability of elements with typical concentrators, finite element model of bolted joint, cyclic deformation curve

References

  1. Martin J.F., Topper T.H., Sinclair G.M. Computer based simulation of cyclic stress–strain behavior with Applications to Fatigue. Materials Research and Standards, 1971, vol. 11, no. 2, pp. 23–29.

  2. Wetzel R.M. Smooth Specimen Simulation of Fatigue Behaviour of Notches. Journal of Materials JMLSA, 1968, vol. 3, no. 3, pp. 646-657.

  3. Jhansale H.R., Topper T.H. Cyclic deformation and fatigue behavior of axial and flexural members – a method of simulation and correlation. 1st International Conference on Structure Mechanics in Reactor Technology (Berlin, September 1972). Part L, pp. 433–455.

  4. Conle A., Topper T.H. Sensitivity of fatigue life predictions to approximations in the representation of metal cyclic deformation response in a computer-based fatigue analysis model. 2nd International Conference on Structure Mechanics in Reactor Technology (Berlin, September 1973), pp. 10-14.

  5. Conle A., Nowack H. Verification of a Neuber-based Notch Analysis by the Companion–specimen Method. Experimental Mechanics, 1977, vol. 17, no. 2, pp. 57-63. DOI: 10.1007/BF02326427

  6. Crews J.H., Hardrath H.F. A Study of Cyclic Plastic Stresses at a Notch Root. Experimental Mechanics, 1966, vol. 6, pp. 313-320. DOI: 10.1007/BF02327511

  7. Conle F.A., Chu C.-C. Fatigue analysis and the local stress–strain approach in complex vehicular structures. International Journal of Fatigue, 1997, vol. 19, no. 93, pp. 317–323. DOI: 10.1016/S0142-1123(97)00045-5

  8. Lee Y., Taylor D. Strain-Based Fatigue Analysis and Design. Fatigue Testing and Analysis. Theory and Practice. Chapter 5. Elsevier Inc., USA, 2005, pp.181-236. DOI: 10.1016/B978-0-7506-7719-6.X5000-3

  9. Neuber H. Theory of Stress Concentration for Shear-Strained Prismatical Bodies with Arbitrary Nonlinear Stress-Strain Law. Journal of Applied Mechanics, 1961, vol. 28, no. 4, pp. 544-550. DOI: 10.1115/1.3641780

  10. Raschety i ispytaniya na prochnost’. Metody skhematizatsii sluchainykh protsessov nagruzheniya elementov mashin i konstruktsii i statisticheskogo predstavleniya rezul’tatov. GOST 25.101-83 (Strength calculation and testing. Representation of random of machine elements and structures and statistical evaluation of results. State Standard 25.101-83), Moscow, Standarty, 1983, 25 p.

  11. Standard Practice for Cycle Counting for Fatigue Loading (Reapproved 1997). ASTM E1049-85. ASTM International, United States, 1997, 10 p.

  12. Molsky K., Glinka G. A Method of Elastic-plastic Stress and Strain Calculation at a Notch Root. Material Science and Engineering, 1981, vol. 50, no. 1, pp. 93-100. DOI: 10.1016/0025-5416(81)90089-6

  13. Ramberg W., Osgood W.R. Description of stress-strain curves by three parameters. National Advisory Committee for Aeronautics (NACA) TN-902, 1943, Washington, DC, United States, 29 p.

  14. Patwardhan P.S., Nalavde R.A., Kujawski D. An Estimation of Ramberg-Osgood Constants for Materials with and without Luder’s Strain Using Yield and Ultimate Strengths. Procedia Structural Integrity, 2019, vol. 17, pp. 750-757. DOI: 10.1016/j.prostr.2019.08.100

  15. Volkov E.A. Chislennye metody (Numerical methods), Saint Petersburg, Lan’, 2008, 248 p.

  16. Masing G. Eigenspannungen und Verfestigung beim Messing. The Second International Congress of Applied Mechanics (Zurich, 1926).

  17. Masing G. Zur Heyn'schen Theorie der Verfestigung der Metalle durch verborgen elastish Spannungen. Wissenschaftliche Veröffentlichungen aus dem Siemens-konzern, III Band, Erstes Heft, 1923.

  18. Raschetnye znacheniya kharakteristik aviatsionnykh metallicheskikh konstruktsionnykh materialov (The calculated values of the characteristics of aircraft metallic structural materials), Moscow, OAK, 2011, 304 p.

  19. Peterson R.E. Stress Concentration Factors: Charts and Relations Useful in Making Strength Calculations for Machine Parts and Structural Elements. Chapman & Hall, 1954, 155 p.

  20. Pankov A.V. Uchenye zapiski TsAGI, 1990, vol. XXI, no. 3, pp. 95-102.

  21. Pankov A.V., Stebenev V.N. Uchenye zapiski TsAGI, 1990, vol. XXI, no. 4, pp. 74-80.

  22. Pankov A.V. Uchenye zapiski TsAGI, 1994, vol. XXV, no. 3-4, pp. 126-133.

  23. Pankov A.V. Uchenye zapiski TsAGI. 1995, vol. XXVI, no. 1-2, pp. 166-174.

  24. Dunaev V.V., Gromov V.F., Makarov A.F., Eryomin M.V. Assembly tie change kinetics for bolted joint items with radial interference. Aerospace MAI Journal, 2011, vol. 18, no. 4, pp. 27-37.

  25. Gromov V.F., Dunaev V.V., Eryomin M.V., Makarov A.F. Improvement of aviation structure quality and life in mechanical joint. Aerospace MAI Journal, 2010, vol. 17, no. 1, pp. 18-24.

mai.ru — informational site of MAI

Copyright © 1994-2020 by MAI