PSI - Issue 66

Slobodanka Boljanović et al. / Procedia Structural Integrity 66 (2024) 535– 542 S. Boljanovi ć and A. Carpinteri/ Structural Integrity Procedia 00 (2025) 000–000

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Table 2. Evaluated fatigue life for a pipe (Fig.1b) and corresponding applied maximum stresses ( R = 0.1). Experiments are discussed by Aln et al. (1997), and relevant calculations are the present research results ( N cal ).

a 0 (mm)

b 0 (mm)

S max (MPa)

exp.. (cycles)

N cal. (cycles)

R

N

3.0 2.0 3.0

6.0 4.0

325.9 325.9

0.1 0.1 0.1

21187 52910 15,367

19750 45410 13,910

17.4

257.15

Fig. 4. Fatigue degradation analysis: a vs. N and b vs. N ((a) a = 3 mm and (b) a = 2 mm), experiments discussed by Ahn et al. (1997) and calculated curves are the present research results.

4.3. The effects of stress ratio and the pipe thickness through the fatigue analysis Finally, the failure strength of a pipe with a semi-elliptical flaw (Fig.1b) is analyzed in order to explore the stress ratio impact under fatigue loading. Initial part-through flaw whose sizes are equal a 0 = 1.5 mm, b 0 = 2.75 mm in depth and surface crack growth direction is located in a pipe ( t = 6.5 mm, R 0 = 20.7 mm), made of carbon steel (E = 205 GPa, C A = C B = 3.2 10 -13, m A = m B = 3.72). External loading is characterized by maximum stress equal to S max = 350 MPa with three different stress ratio values: R = 0.1, 0.2 or 0.3, respectively. Fatigue-induced degradation is evaluated here using Eq.11 together with Eq.1 to 9, as has been discussed in previous sections. Relevant numbers of loading cycles generated, as functions of crack length in depth and surface direction for three values of stress ratio, are shown in Fig.5a and b, respectively. Failure-relevant outcomes indicate that, if the stress ratio R increases from 0.1 to 0.3, the residual life increases by 59.6% for the examined pipe with semi-elliptical flaw. Furthermore, the safety-critical analysis in terms of the residual life is performed here taking into account the thickness effect. The three different damaged pipes (Fig.1b) with thickness and diameter equal to t = 6 mm, 7.8 mm 10.14 mm and R 0 = 19.11 mm, respectively, are subjected to bending ( S max = 340 MPa, R = 0.1). The semi-elliptical flaw is characterized by length sizes equal to a 0 = 1.5 mm, b 0 = 3.5 mm in depth and surface crack growth direction, respectively. Since the pipe is made of carbon steel, the same material parameters are used as those previously adopted in this section.