engleski

Cohesive Model Application in the Assessment of Plastic Zone Magnitude for One Particular Case of Crack Loading

The answer of the thin, infinite, central cracked plate, subjected to in-plane loading, is investigated. The plate is made from the ductile metallic material. The two pairs of the concentrate, compressible forces, F, act on the crack surface in the direction perpendicular to it, i.e. in the direction parallel to the axis, y, which is, also, the axis of symmetry. The other edges of the plate, at infinity, are free of loading. The forces, F, open the crack and they are monotonously increased. As, it is well known, if the response of the plate material on the external loading is pure elastic, the stress singularity at the crack tip will be appeared. But, in the case of elastic-plastic response of a plate material there will be no stress singularity at the crack tip, i.e. the normal stress, will assume the ultimate value. The occurrences within the cohesive zones around the crack tips are rather complex and we will try to contribute in the mathematical description of those phenomena. The certain parameters of EPFM, such as, the stress intensity coefficient and the magnitude of cohesive zone, are investigated. An isotropic and non-linear strain hardening of a plate material is assumed. Non-linear strain hardening at uniaxial state of stress is described by the Ramberg-Osgood´s equation. The investigations were carried out for the several different values of the strain hardening exponent n which is changed among the discrete values n = 2, 3, 4, 5, 7, 10, 15, 25, 50 and 1000. One well- known cohesive model (Dugdale´s model) was applied in the crack tip plasticity investigating. Also, it was assumed that the cohesive stresses within the plastic zone are changed according to non- linear law. The stress intensity coefficient from the cohesive stresses is calculated by integrating, using the Green functions method. In the frame of applied cohesive model, the all mathematical expressions were derived fully exact, analytically. Also, the new algorithm was established which enables direct calculation the plastic zone magnitude depended on the magnitude of external loads. The all obtained results are presented in the form of the diagrams. The contemporary mathematical tools, like the software package Wolfram Mathematica, were used. The solutions for the stress intensity coefficient and the magnitude of plastic zone are presented through the special, Gamma and the Hypergeometric functions. References [1] Pustaić, D. and Lovrenić-Jugović, M., Procedia Structural Integrity, vol. 23, 2019, 27- 32. [2] Pustaić, D. and Lovrenić-Jugović, M., Proc. of the 9th Int. Congress of Croatian Society of Mechanics, ISSN 2623-6133, Marović, P., Krstulović- Opara, L. and Galić, M., eds., Split, Croatia, 2018. [3] Wolfram Mathematica 7.0, Champaign II, 2017, http://www.wolfram.com/products/mathematica/. [4] Guo, W., Engineering Fracture Mechanics, vol. 51 (1), 1995, 51-71. [5] Neimitz, A., Engineering Fracture Mechanics, vol. 71 (11), 2004, 1585-1600. [6] Pustaić, D. and Lovrenić, M., Proc. of the 5th Int. Congress of Croatian Society of Mechanics, Matejiček, F. et al., eds. Trogir, Croatia, 2006. [7] Pustaić, D. and Štok, B., Proc. of the 12th European Conference on Fracture, Brown, M. W., de los Rios, E. R. and Miller, K. J., Sheffield, 1998, 889-894.

EPFM, cohesive stress, isotropic and non-linear strain hardening material, Ramberg-Osgood´s equation, strain hardening exponent, stress intensity coefficient, plastic zone magnitude around crack tip, analytical methods, Green functions method, Wolfram Mathematica.

Rad je međunarodno recenziran (peer review) i bit će objavljen u međunarodnom časopisu Structural Integrity Proceedia, (Izdavač: Elsevier), početkom 2023. godine.