PSI - Issue 74

Dragan Pustaić et al. / Procedia Structural Integrity 74 (2025) 70 – 76 Dragan Pustaić / St ructural Integrity Procedia 00 (20 2 5) 000 – 000

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be greater when compared to t = p 0 / σ 0 , for the equal value of, r p . Much more concentrated force, F , ( F = p 0 ∙ a , c = (1/2) a ), from the uniformly distributed, continuous loading, p 0 , acting over the crack surface, will be necessary for the small plastic zone magnitude around the crack tip. 4. Algorithm for an explicit determining the dependence of the plastic zone magnitude on the external crack loading An algorithm will be described which will enable us, to compute, explicitly, the plastic zone magnitude, r p , in dependence on the external crack loading, p 0 , by means of the diagram from the Fig. 2, t = p 0 / σ 0 = f ( P , n ). That dependence, in non-dimensional form, hence as, r p / a = f 1 ( p 0 / σ 0 ), will be presented diagrammatically on the Fig. 5. The algorithm will be described for one curve, n = 2. The diagram is computed and constructed with software Wolfram Mathematica, by filling in the Table 2. Firstly, the discrete values, p 0 / σ 0 , are selected in range from 0.00 to 3.719, (first row in the table). The corresponding value of the continuous loading, p 0 , [MPa], is calculated and placed in the second row. By means of the function “Get Coordinates” in program package Wolfram Mathematica, the corresponding variable P is red off from the Fig. 2 and the obtained values, P , are written in the third row of the table. Finally, with so red off values, P , the plastic zone magnitude, r p , ( r p = [2 Pa / (1 – 2 P )], a = 10 mm, σ 0 = 310 MPa), is calculated and written in the fourth row of the table. At the end, the diagram is constructed as on the Fig. 5, in non dimensional form. Table 2. Algorithm for the explicit determining the dependence of the plastic zone magnitude on the external crack loading, for n = 2. p 0 / σ 0 , - 0 0.5 1 1.5 2 2.5 3 3.5 3.719 p 0 , MPa 0 155 310 465 620 775 930 1085 1152.89 P , - 0 0.04749 0.1140 0.1669 0.2079 0.2428 0.2701 0.2923 0.3000 r p , mm 0 1.0495 2.9534 5.0105 7.1174 9.4401 11.7486 14.0732 15.000

Fig. 5. Dependence of the plastic zone magnitude, r p , around the crack tip on monotonously increased external crack loading, p 0 , in a non-dimensional form, for different values of the strain-hardening exponent, n .

5. Conclusion The results of investigations of the dependence of plastic zone magnitude, r p , around the crack tip, on monotonously increased, continuous loading, p 0 , which acts over the crack surface, according to Fig. 1.a, were presented in this paper.