PSI - Issue 76

Jürgen Bär et al. / Procedia Structural Integrity 76 (2026) 27–34

29

as shown by the blue dashed line in Fig. 1. The intrinsic crack length a 0,H and the corresponding threshold stress range for crack propagation   th,a,EH are calculated using equations (2) and (3), respectively: 0, = 1 ∙ ( ∆ ℎ, ∙∆ ) 2 (2) ∆ ℎ, , = ∆ ℎ, ∙√ ∙( + 0, ) (3) However, the El Haddad model does not consider the build-up of crack closure effects in the short crack stage. They develop with increasing crack length, which leads to significantly smaller threshold values for short cracks (Tanaka 1988, Maierhofer 2015), meaning that El Haddad's approximation can lead to non-conservative fatigue limits. McEvily and Minakawa (McEvily 1987) proposed an expression to model the influence of crack closure with increasing crack length on the fatigue crack propagation threshold ∆ K th . Chapetti (Chapetti 2017) incorporated this expression (Equation (4)) into a model for the KT diagram (orange dotted line in Fig. 1) and showed that the models of Kitagawa and Takahashi as well as El Haddad are not conservative in the technical relevant region of short cracks. ∆ ℎ, ℎ = ∆ +(∆ ℎ, −∆ )∙[1− (− ∙( − )) ] ∙√ ∙ (4) = 4 1 ∙ ∆ (∆ ℎ, −∆ ) (5) These three models differ significantly in the transition zone. Therefore, experimental validation is essential here. By introducing notches as crack initiation points and determining the fatigue limit of the notched samples, this study aims to experimentally validate these models. The staircase method according to DIN 50100 (DIN e.V. 2022) is normally used to create the KT diagram, in which several sets of samples with different notch depths are used to determine the fatigue limit ∆σ th . However, this requires a large number of samples with identical notches and is therefore time-consuming. As an alternative, this study proposes a new method that aims to determine the threshold stresses for the KT diagram in a faster way using single specimens and potential drop measurements in the vicinity of the notch. 2. Kitagawa-Takahashi diagram of the investigated steels In this work, the Kitagawa-Takahashi diagram of the low-alloyed steel S690QL (DIN e.V. 2023) and a normalized variant of this steel were investigated. Both steels were austenitized at 920°C for 15 min. The steel S690QL, hereinafter referred to as Steel V, was quenched in water and tempered for 30 min at 600°C. The normalized variant, Steel N, was cooled in air after the austenitizing treatment. The mechanical properties of the two steels are given in Table 1.

Table 1. Mechanical Properties of the investigated steels. Yield Strength [MPa] UTS [MPa]

Elongation at break [%]

Youngs Modulus [GPa]

Steel N Steel V

502 816

743 848

21 19

203 208

The KT diagram for the two steels was constructed using the three models introduced above with experimental determined values given in Table 2. The plain fatigue limit  e was determined through the staircase method, the threshold value for long cracks  K th,LC was taken from cyclic R-curve measurements. The geometry factor Y was obtained through Finite Element Analysis and the grain size d in EBSD measurements.