PSI - Issue 53

Francesco Collini et al. / Procedia Structural Integrity 53 (2024) 74–80

75

2

Author name / Structural Integrity Procedia 00 (2023) 000–000

Atzori Lazzarin Meneghetti diagram U-notched components (2 α =0)

σ g

Defect-free region

Full notch sensitivity

Defect sensitivity

Partial notch sensitivity

Long crack - sharp notch region

K tg σ g

v I

K

∆ σ 0

√

γ 1

2 πx

σ yy , (log scale) σ yy

γ

∆ K th √ πa eff

σ g

1

2 α

∆ σ g , (log scale)

0 . 5

x, (log scale)

ρ

1

2 a

∆ σ 0 K tg

Schematic trend Real trend

σ g

Range of the gross nominal stress

2 tg · a 0

a N = K

Effective crack size , a eff (log scale) a 0

Atzori Lazzarin Meneghetti diagram V-notched components (2 α̸ =0 ,ρ̸ =0)

2 α =0 ◦ 2 α =90 ◦ 2 α =60 ◦ 2 α =135 ◦

∆ σ 0

2 α

∆ K v

th γ 1 eff

√

πa

γ 1

1

∆ σ 0 K tg

γ 1 =0 . 5

∆ σ g , (log scale)

1

a 0 Range of the gross nominal stress a

1 γ tg · a 0

a v 0

v 0

2 tg · a 0 a N = K

a N = K

Effective sharp V-notch size , a eff (log scale)

Fig. 1: Atzori-Lazzarin-Meneghetti (ALM) diagram; a) reference system, schematic linear elastic stress field at the V-notch tip; b) ALM diagram for U-notched components, c) ALM diagram for V-notched components.

the existence of a characteristic crack size below which the fatigue limit is no longer dependent on the crack (and defect) size, and it approaches that of the defect-free material. Concerning the notch sensitivity, Frost et al. (1974), by examining the e ff ect of the notch acuity of U-notches (quantified by the theoretical stress concentration factor K t ) of constant depth under mode I loading, observed that beyond a specific value of K t , the fatigue strength becomes independent on K t and they behave as cracks of the same depth. Despite originating from di ff erent phenomenological behaviors, Atzori and Lazzarin (2001) identified a connec tion between these seemingly di ff erent phenomena. They introduced a diagram describing both the defect and notch sensitivity, o ff ering a unified representation for estimating the fatigue limit of centered notches and cracks under mode I loading with a unified approach independent of the crack size and notch acuity. Subsequently, in Atzori et al. (2003a), the idea was extended to real components weakened by U-notches in mode I loading by introducing the concept of the e ff ective crack size (figure 1 b)) and later, in Atzori et al. (2005), including also open V-notches (figure 1 c)) subjected to mode I loading. In the case of V-notches, di ff erent design curves are obtained for di ff erent V-notch opening angles; however, the equations are formally identical; thus, for a given V-notch opening angle, only one curve can describe both the defect sensitivity and notch sensitivity (1 c), d)). In this paper, the ALM diagram is extended to the case of multiaxial loading. To determine the threshold conditions of components weakened by notches, cracks, or defects depending on the local multiaxial stress state, size, and acuity, the averaged Strain Energy Density model is employed. It is a phenomenological model based on Neuber’s physical idea, according to which the fatigue behavior