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Modeling of Elastoplastic Stress States in Crack Tip Regions

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Abstract

Although fracture mechanics offers a way to assess the probability of fracture in materials with critically stressed notches, its criteria can hardly account for complex configurations of structures (e.g., welded ones), residual stresses, and inhomogeneity of material properties. Besides, the use of strength criteria accounting for local plasticity requires special tests. Therefore, strength criteria based on physical deformation and fracture models are developed. Here, for analyzing the strength of a cracked material based on a generalized brittle fracture criterion, we propose a mathematical model of the elastoplastic stress state of its prefracture zone ahead of the crack tip. The model proceeds from several assumptions on plastic strains under simplified loading conditions, and its coefficients as well as characteristic load dependences of stresses and strains are found from extensive finite element data on materials with edge and surface cracks. From comparison with numerical data it follows that the proposed method of estimation gives an error of about 10%. The model provides an analytical description of the first principal stress in prefracture zones under loading, and its use in the brittle fracture criterion opens the way to assess to the strength of a wide range of structures.

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REFERENCES

  1. Matvieenko, Yu.G., Models and Criteria of Fracture Mechanics, Moscow: Fizmatlit, 2006.

  2. Zhu, X.K. and Joyce, J.A., Review of Fracture Toughness (G, K, J, CTOD, CTOA) Testing and Standardization, Eng. Fract. Mech., 2012, vol. 85, pp. 1–46.

    Article  Google Scholar 

  3. Barsom, J.M. and Rolf, S.T., Fracture and Fatigue Control in Structures. Application of Fracture Mechanics, Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1987.

  4. Matvienko, Yu.G., Trends of Nonlinear Fracture Mechanics in Mechanical Engineering Problems, Izhevsk: Institute of Computer Sciences, 2015.

  5. Sibilev, A.V. and Mishin, V.M., Criterion of Cold Brittleness of Steel Specimens Based on the Criterion of Local Fracture, Fundam. Issled. Tekh. Nauki, 2013, no. 4, pp. 843–847.

    Google Scholar 

  6. Sokolov, S. and Grachev, A., Local Criterion for Strength of Elements of Steelwork, Mech. Eng. Res. Education, 2018, vol. 12, no. 5, pp. 448–453.

    Google Scholar 

  7. Sokolov, S.A., Grachev, A.A., and Vasilev, I.A., Strength Analysis of a Structural Element with a Crack under Negative Climatic Temperatures, Vestn. Mashinostr., 2019, no. 11, pp. 42–46.

    Google Scholar 

  8. Vasil’ev, I.A. and Sokolov, S.A., Elastoplastic State of Stress of a Plate with a Crack, Russ. Metallurgy (Metally), 2020, no. 3, pp. 1065–1069.

    Article  ADS  Google Scholar 

  9. Kim, Y.J., Son, B., and Kim, Y.J., Elastic-Plastic Finite Element Analysis for Double-Edge Cracked Tension (DE(T)) Plates, Eng. Fract. Mech., 2004, vol. 71, pp. 945–966.

    Article  Google Scholar 

  10. Tarafder, M. and Tarafder, S., Modelling of Crack-Tip Blunting Using Finite Element Method. Report NML-GAP0088-03-2006, Jamshedpur: National Metallurgical Laboratory, 2006.

  11. Zhang, J., He, X.D., Suo, B., and Du, S.Y., Elastic-Plastic Finite Element Analysis of the Effect of Compressive Loading on Crack Tip Parameters and Its Impact on Fatigue Crack Propagation Rate, Eng. Fract. Mech., 2008, vol. 75, pp. 5217–5228.

    Article  Google Scholar 

  12. Ji, X. and Zhu, F., Finite Element Simulation of Elastoplastic Field Near Crack Tips and Results for a Central Cracked Plate of LE-Lhp Material under Tension, Acta Mech. Sinica, 2019, vol. 35(4), pp. 828–838. https://doi.org/10.1007/s10409-019-00846-1

    Article  ADS  MathSciNet  Google Scholar 

  13. Stepanova, L.V. and Adylina, E.M., Stress-Strain State in the Vicinity of a Crack Tip under Mixed Loading, J. Appl. Mech. Tech. Phys., 2014, vol. 55, pp. 885–895.

    Article  ADS  MathSciNet  Google Scholar 

  14. Beliakova, T.A. and Kulagin, V.A., The Eigenspectrum Approach and T-Stress at the Mixed-Mode Crack Tip for a Stress-State-Dependent Material, in Proc. Mater. Sci.: 20th Eur. Conf. Fracture (ECF20), 2014, vol. 3, pp. 147–152.

    Article  Google Scholar 

  15. Hajdu, S., The Investigation of the Stress State Near the Crack Tip of Central Cracks Through Numerical Analysis, Proc. Eng., 2014, vol. 69, pp. 477–485.

    Article  Google Scholar 

  16. Jovanović, D.B., Stress State and Deformation (Strain) Energy Distribution Ahead Crack Tip in a Plate Subjected to Tension, Facta Univ. Mech. Automat. Control Robotics, 2002, vol. 3, no. 12, pp. 443–455.

    Google Scholar 

  17. Kotousov, H.Z., Fanciulli, A., and Berto, F., On the Evaluation of Stress Intensity Factor from Displacement Field Affected by 3D Corner Singularity, Int. J. Solids Struct., 2013, vol. 78–79, pp. 131–137.

    Google Scholar 

  18. Kumar, B. and Chitsiriphanit, S., Significance of K-Dominance Zone Size and Nonsingular Stress Field in Brittle Fracture, Eng. Fract. Mech., 2011, vol. 78, no. 9, pp. 2042–2051.

    Article  Google Scholar 

  19. Shawn, A. and Nagaraj, K., Effects of the Strain-Hardening Exponent on Two-Parameter Characterizations of Surface-Cracks under Large-Scale Yielding, Int. J. Plasticity, 2011, vol. 27, pp. 920–939.

    Article  Google Scholar 

  20. Seitl, S., Knesl, Z., Vesely, V., and Routil, L., A Refined Description of the Crack Tip Stress Field in Wedge-Splitting Specimens-A Two-Parameter Fracture Mechanics Approach, Appl. Comput. Mech., 2009, no. 3, pp. 375–390.

    Google Scholar 

  21. Steuwer, A., Rahman, M., Shterenlikht, A., Fitzpatrick, M.E., Edwards, L., and Withers, P.J., The Evolution of Crack-Tip Stresses during a Fatigue Overload Event, Acta Mater., 2010, vol. 58, pp. 4039–4052.

    Article  ADS  Google Scholar 

  22. Kopelman, L.A., Fundamentals of Strength Theory of Welded Structures, St. Petersburg: Lan, 2010.

  23. Linkov, A.M., Plastic Deformation of a Washer Soldered onto a Plate, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 1971, no. 1, pp. 80–85.

  24. Neiber, G., Stress Concentration, Moscow: Gostekhizdat, 1947.

  25. Kachanov, L.M, Fundamentals of the Theory of Plasticity, Moscow: Nauka, 1969.

  26. Sokolov, S.A. and Tulin, E.A., Method of Calculating the Stress Intensity Coefficient for Crack in the Field of Stress Concentrator, Izv. TulGU, 2020, no. 5, pp. 328–335.

    Google Scholar 

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Authors and Affiliations

  1. Peter the Great Saint Petersburg Polytechnic University, 195251, St. Petersburg, Russia

    S. A. Sokolov & D. E. Tulin

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  1. S. A. Sokolov
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  2. D. E. Tulin
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Correspondence to S. A. Sokolov.

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Translated from in Fizicheskaya Mezomekhanika, 2021, Vol. 24, No. 2, pp. 34–40.

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Sokolov, S.A., Tulin, D.E. Modeling of Elastoplastic Stress States in Crack Tip Regions. Phys Mesomech 24, 237–242 (2021). https://doi.org/10.1134/S1029959921030024

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  • DOI: https://doi.org/10.1134/S1029959921030024

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