Skip to main content
Log in

Comparative Creep Analysis of Spherical Shell Made up of Different Materials

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

A comparative approach and mathematical modelling is done for the purpose of solving creep problem in the spherical shell made up of different materials subjected to uniform internal pressure. The technique of generalization of strain measures and Seth’s transition theory is used to deal with the nonlinear effects arising from creep. The method is independent of various adhoc assumptions like creep law, yield criterion, axial strain rate, infinitesimally small deformation etc. Results are compared for different type of materials and depicted graphically.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. J. Donea and S. Giuliani, “Creep analysis of transversely isotropic bodies subjected to time-dependent loading,” Nuclear Eng. Des. 24 (3), 410–419 (1973). https://doi.org/10.1016/0029-5493(73)90010-1

    Article  Google Scholar 

  2. S. Hulsarkar, “Transition theory of creep of shells under uniform pressure,” ZAMM 46 (7), 431–437 (1966). https://doi.org/10.1002/zamm.19660460704

    Article  ADS  Google Scholar 

  3. S. Hulsarkar, “Elastic plastic transitions in transversely isotropic shells under uniform pressure,” Indian J. Pure Appl. Math. 12 (4), 552–557 (1981).

    MATH  Google Scholar 

  4. G. A. Thurston, “A numerical solution of non-linear equations for axisymmetric bending of shallow spherical shells,” J. Appl. Mech. 28 (4), 557–562 (1961). https://doi.org/10.1115/1.3641782

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. S. K. Gupta and R. L. Dharmani, “Creep transition in thick-walled cylinder under internal pressure,” ZAMM 59 (10), 517–521 (1979). https://doi.org/10.1002/zamm.19790591004

    Article  MATH  ADS  Google Scholar 

  6. S. K. Gupta, S. Sharma and S. Pathak, “Creep transition in a thin rotating disc of variable density,” Def. Sci. J. 50 (2), 1–7 (2000). https://doi.org/10.14429/dsj.50.3397

    Article  MATH  Google Scholar 

  7. S. K. Gupta and P. Thakur, “Creep transition in a thin rotating disc with rigid inclusion,” Def. Sci. J. 57 (2), 185–195 (2007). https://doi.org/10.14429/dsj.57.1745

    Article  Google Scholar 

  8. V. N. Chekhov and S. V. Zakora, “Stress concentration in a transversely isotropic spherical shell with two circular rigid inclusions,” Int. Appl. Mech. 47 (4), 111–118 (2011). https://doi.org/10.1007/s10778-011-0470-1

    Article  MathSciNet  MATH  Google Scholar 

  9. P. Thakur, “Creep transition stresses of a thick isotropic spherical shell by finitesimal deformation under steady – state of temperature,” Therm. Sci. 15 (2), 157–165 (2011). https://doi.org/10.2298/TSCI101004083P

    Article  Google Scholar 

  10. P. Thakur, S. B. Singh, and J. Kaur, “Thermal creep stresses and strain rates in a circular disc with shaft having variable density,” Eng. Comput. 33, 698–712 (2016). https://doi.org/10.1108/EC-05-2015-0110

    Article  Google Scholar 

  11. P. Thakur, N. Gupta, and S. B. Singh, “Creep strain rates analysis in cylinder under temperature gradient materials by using Seth’s theory,” Eng. Comput. 34, 1020–1030 (2017). https://doi.org/10.1108/EC-05-2016-0159

    Article  Google Scholar 

  12. P. Thakur, G. Verma, D. S. Pathania, and S. B. Singh, “Thermal creep stress and strain analysis in Non-homogeneous Spherical shell,” J. Theor. Appl. Mech. 55 (4), 1155–1165 (2017). https://doi.org/10.15632/jtam-pl.55.4.1155

    Article  Google Scholar 

  13. P. Thakur, M. Sethi, K. Gupta and R. K. Bhardwaj, “Thermal stress analysis in a hemispherical shell made up of transversely isotropic materials under pressure and thermo-mechanical loads,” ZAMM 101, e202100208 (2021). https://doi.org/10.1002/zamm.202100208

  14. P. Thakur and M. Sethi, “Elasto-plastic deformation in an orthotropic spherical shell subjected to temperature gradient,” Math. Mech. Solids 25 (1), 26–34 (2020). https://doi.org/10.1177/1081286519857128

    Article  MathSciNet  MATH  Google Scholar 

  15. G. Verma, P. Thakur, and P. Rana, “Elastic-plastic analysis of transversely isotropic spherical shell under internal pressure,” in Proceedings of the 3rd International Conference on Recent Advances in Mathematical Sciences and its Applications 2019, Ed. by B.P. Chamola and P. Kumari (AIP, 2019), 020031. https://doi.org/10.1063/1.5086653

  16. B. R. Seth, “Transition theory of elastic- plastic deformation, creep and relaxation,” Nature 195, 896–897 (1962). https://doi.org/10.1038/195896a0

    Article  ADS  Google Scholar 

  17. B. R. Seth, “Measure concept in Mechanics,” Int. J. Non-Lin. Mech. 1 (1), 35–40 (1966). https://doi.org/10.1016/0020-7462(66)90016-3

    Article  Google Scholar 

  18. I. S. Sokolnikoff, Mathematical Theory of Elasticity (Mc-Graw Hill Book Company, Inc., New York, 1946).

    Google Scholar 

  19. P. Thakur, M. Sethi, N. Kumar, et al., “Analytical solution of hyperbolic deformable disk having variable density,” Mech. Solids 56 (6), 1039–1046 (2021). https://doi.org/10.3103/S0025654421060194

    Article  ADS  Google Scholar 

  20. K. Gupta, P. Thakur, and R. K. Bhardwaj, “Elasto-plastic stress analysis in a tube made of isotropic material and subjected to pressure and mechanical load,” Mech. Solids 57 (3), 617–628 (2022). https://doi.org/10.3103/S002565442203013X

    Article  ADS  Google Scholar 

  21. S. Gupta and G. Verma, “Creep transition of spherical shell under internal pressure,” ISJ Theor. Appl. Sci. 24 (4), 201–207 (2015). https://doi.org/10.15863/TAS.2015.04.24.35

    Article  Google Scholar 

  22. D. S. Pathania and G. Verma, “Temperature and pressure dependent creep stress analysis of spherical shell,” Int. J. Appl. Mech. Eng. 24 (1), 105–115 (2019). https://doi.org/10.2478/ijame-2019-0007

    Article  Google Scholar 

  23. G. Verma and P. Rana, “Creep transition in the rotating spherical shell under the effect density variable by Seth’ transition theory,” in Proceedings of the International Conference on Mathematical Sciences and its Applications 2016, Ed. by B.P. Chamola and P. Kumari (AIP, America, 2017), pp. 0200201–20. https://doi.org/10.1063/1.4973270

  24. G. Verma and P. Thakur, “Creep stresses in a Spherical shell under steady state temperature,” in Proceedings of the 2nd International Conference on Recent Advances in Mathematical Sciences and its Applications 2017, Ed. by B.P. Chamola and P. Kumari (AIP, 2017), 0200331-9.

  25. F. K.G. Odquist, Mathematical Theory of Creep and Creep Rupture (Clarendon Press, Oxford, 1974).

    Google Scholar 

Download references

ACKNOWLEDGMENTS

The authors are grateful to the referee for his critical comments, which led to a significant improvement of the paper.

Funding

This research received no specific grant from any funding agency.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to G. Verma or P. Thakur.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Verma, G., Thakur, P. Comparative Creep Analysis of Spherical Shell Made up of Different Materials. Mech. Solids 57, 1214–1221 (2022). https://doi.org/10.3103/S0025654422050120

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654422050120

Keywords:

Navigation