Issue 46

A. Baltach et alii, Frattura ed Integrità Strutturale, 46 (2018) 252-265; DOI: 10.3221/IGF-ESIS.46.23 253 and the distribution of the induced compressive residual stresses around the expanded hole [1; 4]. Indeed, several researchers have concluded that the fatigue lifetimes of the cold expanded fastener structures increases by a factor of 3 to 10, and this depends on the amount of the induced compressive residual stresses [2;5;6]. In this context, a number of related parameters can interfere to maximize the expected result of the cold expansion. Primarily, Mention may be made about the type of the oversized tool used for expansion. So, the cold hole expansion is usually conducted using an oversized ball technique [6; 7; 8; 9; 10; 11] or a tapered pin mandrel technique [1; 12; 13; 14; 15; 16]. On this subject, Gopalakrishna and co-authors [8] experimentally studied and compared the cold expansion of holes in Al 2024 using a Split-sleeve with taper pin technique and a split-sleeve with a ball technique. They concluded that, the former technique yielded 200% greater fatigue life improvement than that of the latter. In any case, it is well known that the entrance face of the hole exhibits the lowest circumferential compressive stress. Therefore, this region will possess the least fatigue enhancement [3; 17]. This is confirmed by experimental tests on pristine test coupons which have shown that fatigue cracks in cold expanded holes frequently initiate from this location, see for example [12]. In the same way, several researches substantiate the susceptibility of the dominant effect of the interference degree of the cold expansion process [8; 18; 19; 20]. In this regard, the literature is unanimous on the fact that increasing the degree of expansion increases the lifetime of the holed structure see for example [18; 21]. These latter, among others, confirm the hypothesis that, it is the induced residual stresses which are the important parameter for the fatigue lifetime improvement. Nevertheless, Amrouche and co authors in [6] and recently Yongshou and co authors in [20] concluded that the degree of expansion did not influence the magnitude of compressive residual stresses but it has an influence on the size of the compressive residual stresses zone and the size of the plastic strain zone. To this is added the effect of friction between the mandrel and the hole surface, which was argued to have a local effect on the circumferential compressive residual stresses. Effectively, Yongshou and co authors in [20] have studied, numerically, the effect of the friction coefficient and they had found that the friction coefficient affects the radial residual stress around the maximum value and the circumferential residual stress near the hole edge. In the same context, Yuan [23] have confirmed experimentally and numerically the latter finding. So, according to [12; 15; 16; 22; 23], the residual stress distribution is not uniform throughout the plate thickness having a maximum compressive value around the mid-thickness position and a minimum value at the mandrel entrance face of the hole edge. As a consequence, fatigue cracks usually initiate at a location near the entrance face. In order to compensate for the problem of non-uniformity, several solutions were proposed. The most one is the double expansion, see [7; 16; 24; 25; 26]. A short time exposing to elevated temperature was also proposed by Chakherlou and Aghdam [27]. Early in 2004, Chakherlou and Vogwell proposed a novel method which creates a near- uniform compressive tangential residual stress around a fastener hole using a tapered pin with a mating tapered split sleeve [28; 29]. More then, a geometrical solution for the hole or the mandrel were proposed. For example, Jang and coworkers [30] proposed to apply a chamfer into the hole and Rana, Makabe and Fujiwara [31] used a quasi elliptical shaped pin mandrel to optimize residual stresses around the hole edge. The present work proposes to optimize the residual stress profile resulting by a cold expansion technique. For this purpose, we propose to vary the taper degree of the tapered pin mandrel and analyzing the effect of the expansion tool shape on the resulted residual stresses around the hole edge throughout the plate thickness. Thus, the selected mandrels shapes are the most common used, such as a rigid ball and a conical mandrel (tapered pin). G EOMETRIES AND PROCEDURE he main goal of this work is to analyze the effect of the mandrel shape on the effectiveness of the cold expansion method and then attempt to optimize the cold expansion by searching the appropriate geometry of the mandrel. The plate dimensions are presented in Fig. 1. The 6.32 mm thickness model corresponds to the model studied by Chakherlou and Vogwell [12] to allow comparison and validation of the results. Fig. 1 shows the dimensions of the plates, which contains the hole diameter to receive the cold expansion. Thereafter, the study will be oriented towards the analysis of the residual stresses induced across the face of the hole and its vicinity by two types of mandrel, essentially a tapered pin technique and a ball technique as shown in Fig. 2a and Fig. 2b, respectively. For the tapered pin, different tapers are used to perform the cold expansion. Geometries of the mandrels In this work, two types of Mandrel are considered. On one hand, a rigid ball with a diameter D = 5.23mm (Fig. 3b), and on the other hand, a conical pin with a small diameter "d" equal to the initial hole diameter of the plates d = 5 mm and a large diameter "D" equal to D = 5.23 mm (Fig. 3a). Both mandrels give a same interference degree "i" defined by the relation: T