PSI - Issue 76

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

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Nomenclature a

notch depth

intrinsic crack length in the El Haddad model

a 0,H

half of the notch surface length

c d k Y

microstructural length in the Chapetti model

parameter in the Chapetti model

boundary correction factor Δ K th,LC threshold for long crack propagation  K dR

microstructural threshold value in the Chapetti model

plain fatigue limit

  e   th

fatigue limit in presence of defects

1. Introduction The fatigue limit of materials is a decisive parameter for the design and reliability of components, especially when defects such as cracks or notches are present. Such defects have a significant influence on the fatigue limit and often serve as the initiation point for crack formation. For reliable life predictions, robust models are required that consider the material's resistance to crack formation and propagation. The Kitagawa-Takahashi (KT) diagram (Kitagawa 1976) plays an important role in evaluating the fatigue limit of materials with small notches, defects or cracks.

El Haddad Chapetti

Stress Range Δ σ

Transition Region

PlainFatigue Limit Δ σ e

Crack Arrest

a 0,H

Defect Size‘ a ‘

Fig. 1. Schematic KT diagram with the models by El Haddad and Chapetti.

The KT diagram graphically represents the relationship between the defect size a and the fatigue limit in presence of defects ( ∆σ th ) of a material (Fig. 1). It combines the plain fatigue limit ∆ σ e and the propagation of fatigue cracks into a diagram whose right boundary is formed by the long crack propagation threshold Δ K th,LC : ∆ ℎ, = ∆ ℎ, ∙√ ∙ (1) Although this basic design (black line in Fig. 1) provides a simple and intuitive tool, it oversimplifies the behavior in the transition zone between short and long cracks. El Haddad's model (El Haddad 1979) introduces a fictitious intrinsic crack length a 0,H , which forms a smooth transition from the plain fatigue limit to the threshold of long cracks,