Issue 47

Yu. G. Matvienko et alii, Frattura ed Integrità Strutturale, 47 (2019) 303-320; DOI: 10.3221/IGF-ESIS.47.23 304 I NTRODUCTION resent innovations in aircraft manufacture are based on advanced technologies. One of them is the cold expansion process that leads to enhance the fatigue life of structures with fastener holes [1]. The cold working introduces a zone of compressive residual stresses around the hole. Fatigue life improvement is mainly related to the circumferential residual stress influence that, firstly, delays the initial crack appearance increasing the damage tolerance life. Secondly, residual stress influence leads to reducing the effective range of stress intensity factor (SIF) decreasing fatigue crack growth rates [2–3]. Thus, it is generally agreed that residual stresses have a significant positive influence on fatigue life of structural components with cold expanded holes. However, the improvement in fatigue performance is difficult to quantify. Various techniques have been proposed in the literature to solve this problem. Theoretical methods of residual stress analysis, based on the study of analytical solutions in closed form, were developed in [4–6]. Numerical approaches were also created by using the finite element method in 2D or 3D formulation [7–12]. Most of these papers include experimental determination of residual stresses by non-destructive and destructive methods to obtain data that are essential for a validation of finite element simulation. Non-destructive experimental techniques are mainly related to X-ray diffraction [2]. Destructive (mechanical) methods of residual stress determination are based on local material removing [13–16]. Several experimental studies have considered the improvement in fatigue performance due to the presence of compressive residual stresses [17–19]. Fatigue predictions assume that the improvement arises because the crack is closed during part of the load cycle and therefore the effective range of stress intensity factor is reduced [8, 20–21]. A set of works is devoted to an accurate analysis of SIF values for cracks located in the vicinity of cold expanded holes [22–24]. These data are essential for more realistic predictions of fatigue crack growth rates through the use of various models that are based on linear fracture mechanics and superposition principal [25–27]. The main problem of such an approach resides in the fact that the superposition principle may be erroneous when partial crack closure on the crack surfaces occurs. Thus, specific methodology has to be adopted to estimate the stress intensity factor as a result of the residual stress field influence. Moreover, the residual stress change due to fatigue loading should be taken into account. One of the most typical approaches to an investigation of fatigue crack growth rates for cracks emanating from cold expanded holes is presented in [28]. The obtained experimental information is used for numerical simulation of residual stresses caused by elastic-plastic deformation of the hole. Experimental and numerical values of circumferential residual stress component averaged through the thickness are well matched. Three-dimensional finite element calculations of the SIF around a circular crack at the edge of a plain hole and a cold-expanded hole have been made. The dependencies of SIF at the mandrel entrance face vs. applied load for different corner crack lengths are obtained. Fatigue crack growth rates have been measured for cracks growing from plain holes and cold expanded holes. Comparison of measured fatigue crack growth rate of corner cracks with finite element predictions for different surface cracks lengths up to crack of 5 mm length is presented. Comparison of the finite element simulation and experimental measurement of “crack growth rate vs. crack length” showed an expected good agreement for the case of a plain hole with stress ratio R = 0.7. For a plain hole with R = 0.1, the finite element simulation over-predicted the crack growth rate. For cold expanded holes, the agreement between simulation and measurement was only reasonable. Crack growth rate predictions are very sensitive to the calculation of stress intensity factor range. Such a calculation relies on a sufficiently accurate model of the material behaviour and a simulation of the cold expansion process, which is difficult to achieve. Powerful approach to quantify the influence of cold-worked process on fatigue by numerical and experimental tests is proposed in [29]. The residual stress intensity factor for a crack emanating from cold-expanded hole is achieved through the use of weight function method [22]. The effective SIF vs. the crack length profiles are obtained for different expansion levels and for a plain hole. The crack propagation is evaluated with good approximation by finite-element method using a model in which compressive residual stress acts to reduce the crack opening SIF. The crack length curves as a function of the number of cycles for different maximum external loads ( R = 0.1) are constructed. Experimental investigations of crack growth process are of importance to create reliable methods inherent in fatigue life evaluation of cold-expanded holes. A remarkable example of such a study of very high methodological and technical level is presented in [30]. Non-contact full-field strain measurements by combined using digital image correlation (DIC) and thermoelastic stress analysis (TSA) were used to compare the strains during crack growth around plain and cold-expanded holes. These two systems provide the measurements of simultaneous mandrel entry (DIC) and exit (TSA) surface strains surrounding a crack initiating from a cold-expanded hole. Crack opening displacements, evaluated from the strain data obtained from DIC, are substantially reduced by the residual compressive stresses from cold expansion, while the overall fatigue data show the life improvement achieved at various applied stress levels. The most important outcome consists of P