Research and simulation of plastic zone around the Griffith’s crack
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Keywords:
Griffith’s crack, plastic zone, stress concentration, elastoplastic deformation, finite volume method, OpenFOAMAbstract
In this paper, by using the structural strength criterion of Neuber – Novozhilov, a formula of the critical load for plane blunt and sharp cracks is obtained. According to the obtained formula modeling of sharp crack as a thin ellipse with a ratio of small and major semi axes one to ten is carried out. With application of a software package OpenFOAM, based on the finite volume methods, by creating a solver for small elastoplastic deformation, we found the shape and size of plastic zone around the blunt and sharp cracks. A size of plastic zone based on calculation results satisfactorily agrees with the experimental data in researches of Hahn and Rosenfield, and shape – with data of Tuba. The results allow evaluating the impact of the microstructure to ductile material and on the behavior of structures made from such materials.References
1. Sedov L.I. Continuum Mechanics // M.: Nauka, 1984. – Vol. 2. – 560 p. (Rus.)
2. Kornev V.M. Hierarchy strength criteria of structured brittle environments // Applied Mechanics and Technical Physics. – 2000. – Vol. 41, No 2. – P. 177–187. (Rus.)
3. Mikhailov S.E. A functional approach to non-local strength conditions and fracture criteria. 1. Body and point fracture // Engineering Fracture Mechanics. – 1995. – Vol.52, No 4. – P.731-743.
4. Mikhailov S.E. A functional approach to non-local strength conditions and fracture criteria. 2. Discrete fracture // Engineering Fracture Mechanics. – 1995. – Vol.52, No 4. – P.745-754.
5. Petrov Y.V. Smirnov V.I. On the strength of materials with small defects // Solid Mechanics. – 2006. – Vol.4. – P.165-178. (Rus.)
6. http://www.openfoam.org/
7. Broek D. Elementary engineering fracture mechanics // Martinus Nijhoff Publishers, The Hague. – 1982. – 469 p.
8. Tuba I.S. A method of elastic-plastic plane stress and strain analysis // J. Strain Analysis. – 1966. –Vol.1. – P.115-122.
9. Hahn G.T., Rosenfield A.R. Plastic flow in the locale on notches and cracks in Fe–3Si steel under conditions approaching plane strain // Rept. to Ship structure Committee, 1968.
2. Kornev V.M. Hierarchy strength criteria of structured brittle environments // Applied Mechanics and Technical Physics. – 2000. – Vol. 41, No 2. – P. 177–187. (Rus.)
3. Mikhailov S.E. A functional approach to non-local strength conditions and fracture criteria. 1. Body and point fracture // Engineering Fracture Mechanics. – 1995. – Vol.52, No 4. – P.731-743.
4. Mikhailov S.E. A functional approach to non-local strength conditions and fracture criteria. 2. Discrete fracture // Engineering Fracture Mechanics. – 1995. – Vol.52, No 4. – P.745-754.
5. Petrov Y.V. Smirnov V.I. On the strength of materials with small defects // Solid Mechanics. – 2006. – Vol.4. – P.165-178. (Rus.)
6. http://www.openfoam.org/
7. Broek D. Elementary engineering fracture mechanics // Martinus Nijhoff Publishers, The Hague. – 1982. – 469 p.
8. Tuba I.S. A method of elastic-plastic plane stress and strain analysis // J. Strain Analysis. – 1966. –Vol.1. – P.115-122.
9. Hahn G.T., Rosenfield A.R. Plastic flow in the locale on notches and cracks in Fe–3Si steel under conditions approaching plane strain // Rept. to Ship structure Committee, 1968.
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Bibossinov, A. Z., Iskakbayev, A. I., & Bekbauov, B. E. (2015). Research and simulation of plastic zone around the Griffith’s crack. International Journal of Mathematics and Physics, 6(2), 23–26. Retrieved from https://ijmph.kaznu.kz/index.php/kaznu/article/view/144
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Informatics and Mathematical Modeling
