PSI - Issue 75

Andrew Halfpenny et al. / Procedia Structural Integrity 75 (2025) 219–233 Author name / Structural Integrity Procedia (2025)

220

2

1. Introduction Fatigue is a progressive damaging phenomenon in a material caused by variable loads, causing a component to fail even if the resulting stresses it experiences are well below the static strength of the material. Fatigue failure represents the main failure mechanism in components subject to cyclic loading and typically involves two main stages: • Crack initiation: one or more cracks nucleate in the material. • Crack propagation: after initiation, the cracks propagate until failure of the component, provided they are subject to sufficiently high cyclic stress. The duration of these two stages depends on several factors such as material properties, structural design, and application. It is also worth highlighting that there are instances where a crack, after entering a low-stress region, stops propagating before failure of the component. In such cases, the crack does not compromise the component's durability and structural integrity and may be considered acceptable in-service (damage tolerance approach). Historically, crack initiation and propagation have been analysed using different physical models. While crack initiation is typically studied using strain-life (EN) models, crack propagation is generally studied using principles of fracture mechanics. Fracture mechanics, born from the early works of Griffith (1921) and Irwin (1958), is based on the assumption that a crack already exists in a component and that, if subject to a favourable stress and strain state at its tip, it progressively propagates until complete failure of the component or to unacceptable deformation in the crack region. The crack propagation takes place through damage mechanisms at an atomic scale in the so-called process zone ahead of the crack tip. In the second half of the 20 th century, a significant research effort was dedicated to understanding and characterising crack propagation under cyclic loading, including the definition of the threshold, propagation, and fast fracture regions both experimentally and computationally, as well as taking into consideration mean stress effects and crack retardation. This produced a multitude of crack growth laws and crack retardation models that, unfortunately, scattered across numerous scientific publications. This paper aims to be a collection of the most relevant fatigue crack growth laws and crack retardation models, allowing engineers to efficiently review these laws and models and make informed decisions. 2. Crack Growth Laws An effective way of describing how a crack propagates in a given material is by plotting how the crack growth rate, , changes with the stress intensity range, ∆ . This type of plot is well-known as crack growth curve and, as shown in Fig. 1a, it is characterised by three distinct regions: • Region I describes the slow crack growth rate for small cracks close to a threshold value of stress intensity range, ∆ ℎ , below which it is assumed that a crack will not propagate. In this region, the microstructure has a significant effect. • Region II describes the propagation behaviour of a crack for most of its life. In this region, the crack growth curve follows a power-law behaviour and is controlled by Linear Elastic Fracture Mechanics (LEFM) with little influence of microstructure. • Region III describes the fast fracture behaviour before final failure. In this region, the influence of microstructure becomes significant again, together with the thickness of the component.