PSI - Issue 68

Dragan Pustaić et al. / Procedia Structural Integrity 68 (2025) 16 – 23 Dragan Pustaić, Martina Lovrenić-Jugović / Structural Integrity Procedia 00 (2025) 000–000

18

3

example, numerically , by means of the Finite Element Method, FEM, and program package Abaqus. Afterwards, the corresponding analytical expression is determined by fitting a curve which approximates well that distribution.

Fig. 1. (a) Thin, infinite plate with straight crack of length 2 a loaded with two pairs of concentrated forces which open the crack; (b) fictitious elastic crack which contains the small plastic zones around the crack tips; (c) variable cohesive stresses act on a part of a fictitious elastic crack. In this paper the analytical expression which was suggested by the authors M. Hoffman and T. Seeger (1985), will be used. The same expression was used by the other authors in their papers, too, for example Chen et al. (1992), Pustaić et al. (2018, 2019, MSMF 9 and 2022, MSMF 10), and so on. That expression has shown as a very good and accurate approximation of the real stress distribution

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2. Stress intensity factors from the external loading and from the cohesive stresses The stress intensity factor from the external loading, K ext , at the tip of fictitious elastic crack, was derived in the PhD Thesis, Pustaić (1990), and it amounts

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The expression will be transformed so that the new independent variable , P = r p / [2 b ], is introduced as done in the papers Pustaić et al. (2018, 2019, MSMF 9 and 2022, MSMF 10). Formally, it can be written as P = P ( r p , a ). By inversion of this expression it, r p = r p ( P , a ) is obtained, finally assuming the form r p = (2 Pa ) / (1 – 2 P ). The stress intensity factor from the cohesive stresses, K coh , is determined by means of the Green´s functions method , as it was indicated in the papers Chen et al. (1992), Pustaić et al. (2019 and 2022., Structural Integrity Procedia) and others. It can be written

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Before integrating it is necessary to change the limits of the integration. It can be achieved by a substitution, ξ = 1 + ( a – x ) / r p , Chen et al. (1992). The expression (3) now can be written by means of a new independent variable, ξ

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