PSI - Issue 79

D. Marhabi et al. / Procedia Structural Integrity 79 (2026) 34–52

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Figure 2: Over-Energy for various stresses of 30NCD16 Steel

The threshold stress σ * of any curve (Fig. 2) are designed respectively in table 1 by the threshold stress σ * min initiating small crack and the threshold stress σ * max propagate the crack. The stresses σ * min are lower than endurance limit σ -1

Specimen 1

Specimen 2 Specimen 3

Specimen 4

 Rb  m 517 280 494 245 435 205 405 172  m  Rb  m  Rb  m  Rb

Bending stress (MPa)

threshold stress σ * min threshold stress σ * max

167,25 753,95

178,39 730,09

180,08 684,99

165,89 665,69

Table 1: Threshold stress in aerea of cylindrical specimen

In experimental specimens of square cross-section with spheroidal graphite cast iron [3], the authors loaded in fully reversed four point plane bending under constant stress. They have noted that micro-cracks existed after only 50,000 cycles on the specimen loaded at the endurance limit 268 MPa and at 230 MPa. But with the specimen loaded at 180 MPa, the micro-cracks which appeared between 150,000 and 300,000 cycles were always very small. Hence, considerations of minimum threshold stress analysis may help the damage-tolerant design 6. SMALL CRACK ASSOCIATED TO THRESHOLD STRESS For fatigue small cracks and their corresponding crack length a, there are different methods in engineering [5]. The total fatigue life is divided into three parts as shown in figure 3.

Fracture

a 1

a 2

Fatigue Crack Nucleation

Macrocrack growth

Small Crack growth

LEFM and long crack h

Non propagation fatigue cracks

Total Fatigue life

Figure 3: Classification of total Fatigue life

In fig. 3, a 1 is defined as the lower limit of the smallest crack. a 2 is defined as the upper limit of small cracks, when a > a 2 , the linear elastic fracture mechanics can be used to predict crack, otherwise small crack theory must be used.