Finite element analysis of elastic-plastic state of crack at the interface between infinite plane and circular inclusion

Authors

  • V. J. Adlucky Oles Honchar National University of Dnipro https://orcid.org/0000-0002-4787-9409
  • A. Yu. Hodes Oles Honchar National University of Dnipro
  • V. V. Loboda Oles Honchar National University of Dnipro

DOI:

https://doi.org/10.17721/1812-5409.2019/1.3

Abstract

The problem on determining of elastic-plastic stress-strain state of infinite plane with a circular inclusion made from another material and an arc crack at the interface under action of arbitrary mechanical loadings applied at infinity is considered using the FEM approach. The problem is resolved within the framework of contact model for which the possibility of appearance of contact macrozones between crack faces is assumed. The isotropic hardening of materials with bilinear approximation of stress-strain curves is considered. The infinite plane is modeled by square domain whose size is of an order of magnitude greater than inclusion diameter. Contact interaction of crack faces is simulated using gap elements. To obtain the energy release rate the J-integrals are calculated along several closed contours around the crack tips. The comparison of obtained results with available analytical solutions for linear elasticity shows that insignificant differences take place during transformation from pure elastic to elastic-plastic stress-strain state.

Key words: arc crack, elastic-plastic state, finite element method, contact problem.

Pages of the article in the issue: 20-23

Language of the article: Ukrainian

References

TOYA, M.A. (1974) A crack along the interface of a circular inclusion embedded in an infinite solid. J. Mech. and Phys. Solids. 22(5). p. 325-348.

COTTRELL, B., RICE, J.R. (1980) Slightly curved or kinked cracks. Int. J. of Fracture. p. 155-169.

HODES, A.YU., LOBODA, V.V. (2015) A contact problem for an arc interfacial crack. Bulletin of Dnepropetrovsk University: Mechanics. 19 (2). p. 3-17.

KACHANOV, L.M. Foundations of theory of plasticity (1969). M.: Nauka.

ZIENKIEWICZ, O.C., TAYLOR, R.L. (2005) The Finite Element Method for Solid and Structural Mechanics. Elsevier.

KERSTAIN, I.M., KLYUSHNIKOV, V.D., LOMAKIN, E.V., SHESTERIKOV, S.A. (1989) Foundations of experimental fracture mechanics. M.: Publishing house of Moscow University.

No 1 (2019)

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How to Cite

Adlucky, V. J., Hodes, A. Y., & Loboda, V. V. (2019). Finite element analysis of elastic-plastic state of crack at the interface between infinite plane and circular inclusion. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (1), 20–23. https://doi.org/10.17721/1812-5409.2019/1.3

Issue

No. 1 (2019)

Section

Differential equations, mathematical physics and mechanics

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