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

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Fig. 2. Dependence of the non-dimensional crack loading, F / (σ 0 ·a) , on the variable, P , i.e. on the plastic zone magnitude r p , around the crack tip, for the different values of strain hardening exponent, n .

Fig. 3. Dependence of the Hypergeometric function 2 F 1 ( α; β; γ; z ), on the variable, P , for the different values of strain hardening exponent, n .

The family of curves, according to the Fig. 4, was computed and constructed, on the base of the expression (8). That family gives the dependence of the loading, F /( σ 0 ∙ a ), on the variable, P , and the distance, c , of the force for n = 2.

Fig. 4. Dependence of non-dimensional crack loading, F / (σ0·a) , on the position of the force, F, on the crack surface, c / a, and on the variable, P , for n = 2. 4. Cubic equation for explicit computing of the plastic zone magnitude depending on the external loading of the crack In order to determine the plastic zone magnitude around the crack tip, r p , depending on the external crack loading, F , explicitly , the start line is the equation following from the stress non-singularity condition within the tip of the fictitious elastic crack, K ext + K coh = 0. That equation equals

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