Analysis of Kinetics and Directions of Elastoplastic Deformation and Fracture


Safety and survivability of equipment are regulated by the strength characteristics of its individual units and elements with possible initial or operational defects such as surface differently oriented semielliptical cracks. Numerical methods of calculation allow obtaining more information about the stress-strain state (SSS) of these elements using the specified calculation algorithms of the corresponding fracture models. A change in the SSS form near the crack contour during the transition from deeper points to surface points depends on the constraint of deformations along their front, i.e., on the 3D character of the SSS. The shape change of defects such as differently oriented surface semielliptical low-cycle cracks is diagnosed on the basis of the experimental results and numerical solutions. The finite element modeling data are implemented on the basis of macros of the ANSYS software package. In this paper, we study the development pattern of elastoplastic fracture under low-cycle loading. The proposed methodology is confirmed by the parametric equations of the shape change kinetics of the considered cracks using a fractographic surface analysis of their development. The surface morphological parameters of the developed defects are analyzed on the basis of the results of testing samples with semielliptical cracks under low-cycle loading. The results of measurements of the intensity fields of elastoplastic deformations at the crack tip and the geometric characteristics of the fracture surface development are presented. An analysis of the dynamics of the local stress-strain state near the contour of differently oriented defects in parts and structural units of equipment shows good agreement between the experimental parameters of the geometry of developing cracks and the parameters obtained by numerical methods. The presented parametric equations clarify the characteristics of nonlinear destruction mechanics that allow evaluating and predicting the survivability and safety performance of critical equipment. The deformation criteria of nonlinear destruction mechanics show the dependence of the fracture development on the 3D character of the stress-strain state that indicates the direction of the geometric development of the fracture surface shape.

This is a preview of subscription content, access via your institution.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.


  1. 1

    Makhutov, N.A., Diformatsionnye kriterii razrusheniya i raschet konstruktsii na prochnost’ (Deformation Fracture Criteria and Strength Calculations of Structural Elements), Moscow: Mashinostroenie, 1981.

  2. 2

    Makhutov, N.A., Konstruktsionnaya prochnost’, resurs i tekhnogennaya bezopasnost’ (Structural Strength, Lifespan, and Industrial Safety), in 2 parts, Novosibirsk: Nauka, 2005.

  3. 3

    Makhutov, N.A. and Makarenko, I.V., Technique of research of kinetics of semi-elliptical superficial inclined cracks at low-cycle loading, Zavod. Lab., 1984, vol. 50, no. 2, pp. 63–66.

    Google Scholar 

  4. 4

    Makhutov, N.A., Frolov, K.V., Stekol’nikov, V.V., Makarenko, I.V., et al., Prochnost’ i resurs vodo-vodyanykh energeticheskikh reaktorov (Durability and Operational Resource of Water-Water Power Reactors), Moscow: Nauka, 1988.

  5. 5

    Makhutov, N.A., Makarenko, I.V., and Makarenko, L.V., Residual stress in inhomogeneous austenitic steels subjected to elastoplastic strain, Zavod. Lab., Diagn. Mater., 1999, vol. 65, no. 4, pp. 249–252.

    Google Scholar 

  6. 6

    Makhutov, N.A., Makarenko, I.V., and Makarenko, L.V., Effect of the anisotropy of physicomechanical properties on the kinetics of cracks in austenitic steels, Strength Mater., 2004, vol. 36, no. 1, pp. 80–84.

    CAS  Article  Google Scholar 

  7. 7

    Makhutov, N.A., Makarenko, I.V., and Makarenko, L.V., A study of fracture kinetics in welded components of nuclear power plant equipment in the presence of surface semi-elliptical variously oriented cracks, Strength Mater., 2010, vol. 42, no. 1, pp. 25–31.

    Article  Google Scholar 

  8. 8

    Makhutov, N.A., Makarenko, I.V., and Makarenko, L.V., Studies on the fracture mechanism and kinetics of randomly oriented surface semielliptic cracks at the multiaxial stress-strain state with deformation criteria of nonlinear fracture mechanics, Strength Mater., 2013, vol. 45, no. 4, pp. 454–458.

    Article  Google Scholar 

  9. 9

    Makhutov, N.A., Makarenko, I.V., and Makarenko, L.V., Calculation and experimental analysis of the stress-strain state for inclined semi-elliptical surface cracks, Inorg. Mater., 2017, vol. 53, no. 15, pp. 1502–1505.

    CAS  Article  Google Scholar 

  10. 10

    ANSYS Mechanical APDL Structural Analysis Guide, Canonsburg, PA: ANSYS, 2010.

  11. 11

    Makhutov, N.A., Makarenko, I.V., and Makarenko, L.V., Particularities a micro-mechanism of cycle elastic-plastic fracture and damage, Proc. Int. Conf. “In-Service Damage of Materials, Its Diagnostics and Prediction,” Ukraine, September 21–24, 2009, Ternopol, 2009, pp. 96–102.

  12. 12

    Predan, J., Močilnik, V., and Gubeljak, N., Stress intensity factors for circumferential semi-elliptical surface cracks in a hollow cylinder subjected to pure torsion, Eng. Fract. Mech., 2013, vol. 105, pp. 152–168.

    Article  Google Scholar 

  13. 13

    Tada, H., Paris, C.P., and Irwin, G.R., The Stress Analysis of Cracks Handbook, New York: Am. Soc. Mech. Eng., 2000, 3rd ed.

    Book  Google Scholar 

  14. 14

    Oh, C.-Y., Kim, Y.-J., Oh, Y.-J., Kim, J.-S., Song, T.-K., and Kim, Y.-B., Evaluation of stress intensity factors due to welding residual stresses for circumferential cracked pipes, Int. J. Pressure Vessels Piping, 2013, vols. 105–106, pp. 36–48.

    Article  Google Scholar 

  15. 15

    Zareei, A. and Nabavi, S.M., Calculation of stress intensity factors for circumferential semielliptical cracks with high aspect ratio in pipes, Int. J. Pressure Vessels Piping, 2016, vol. 146, pp. 32–38.

    Article  Google Scholar 

Download references


This work was supported by the Russian Foundation for Basic Research, project no. 18-08-00572-a.

Author information



Corresponding author

Correspondence to I. V. Makarenko.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by A. Ivanov

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Makhutov, N.A., Makarenko, I.V. & Makarenko, L.V. Analysis of Kinetics and Directions of Elastoplastic Deformation and Fracture. Inorg Mater 56, 1506–1510 (2020).

Download citation


  • surface inclined semielliptical cracks
  • elastoplastic deformations and stresses
  • low-cycle fracture
  • 3D character of the stress-strain state