APPROACHES TO DETERMINING THE PLASTIC ZONE NEAR THE CRACK TIP IN FATIGUE LIFE CALCULATIONS

Abstract

This paper reviews the primary approaches to assessing the plastic zone formed in the vicinity of a fatigue crack tip, and analyses how this is considered in fatigue life calculations for aircraft structures. This topic is relevant because most airframe components experience high-cycle, variable-amplitude loading, and the presence of cracks or stress concentrators can  induce local plastic deformation even at relatively low nominal stress levels. Within the framework of linear elastic fracture mechanics (LEFM), stresses exhibit a singularity at the crack tip; that is, they increase infinitely as the crack tip is approached. In real structural materials, however, such an increase is limited by reaching the yield strength, resulting in the formation of a plastic zone. The size and shape of this zone affect the validity of applying LEFM parameters. The paper analyzes the stress state near the crack tip, the role of the stress intensity factor (SIF), and the conditions for the onset of plastic deformation according to the Mises and Tresca criteria. It also considers the differences between plane stress and plane strain states. Particular focus is given to the classical analytical models of Irwin, Leonov–Panasyuk–Dugdale and their modifications. The analysis includes experimental and numerical methods for refining the plastic zone, such as microhardness measurements, metallographic etching, digital image correlation (DIC), and the finite element method (FEM). The influence of the plastic zone on fatigue crack growth is considered, including the distinction between monotonic and cyclic plastic zones, plasticity-induced crack closure, and the effects of overload, underload, and load interaction in a loading spectrum. Approaches that account for the effects of local plastic deformation both at the crack tip and in the crack wake are critically evaluated, including the Wheeler, Willenborg, Generalized Willenborg, Modified Generalized Willenborg, Hsu, FASTRAN and strip-yield models. The inclusion of the plastic zone in regulatory and reference documents is also discussed. It is demonstrated that the Irwin plastic zone correction method is the most widely used approach in engineering practice for accounting for the plastic zone. It is also established that plastic zone assessment is an important component of analysing the fatigue life and residual strength of aircraft structures. This makes it possible to determine the limits of LEFM applicability, justify the selection of appropriate calculation model, account for the influence of load history and improve the reliability of durability prediction for cracked structural elements.